Semi-active MR technology for enhancing vehicle stability and ...

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Semi-active MR technology for enhancing vehicle stability and ride comfort Semi-active MR technology for enhancing vehicle stability and ride comfort

Shuaishuai Sun University of Wollongong

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Recommended Citation Recommended Citation Sun, Shuaishuai, Semi-active MR technology for enhancing vehicle stability and ride comfort, Doctor of Philosophy thesis, School of Mechanical, Materials and Mechatronic Engineering, University of Wollongong, 2016. https://ro.uow.edu.au/theses/4805

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Department of Mechanical, Materials & Mechatronic

Semi-active MR technology for enhancing vehicle stability and ride

comfort

Shuaishuai Sun

This thesis is presented as part of the requirement for the

Award of the Degree of Doctor of Philosophy

of the Engineering

University of Wollongong

August 2016

ii

DECLARATION

I, Shuaishuai Sun, declare that this thesis, submitted in fulfilment of the requirements

for the award of Doctor of Philosophy, of the School of Mechanical, Materials and

Mechatronics Engineering, University of Wollongong, is wholly my own work

unless otherwise referenced or acknowledged. The document has not been submitted

for qualifications at any other academic institution.

Shuaishuai Sun

August, 2016

iii

ABSTRACT

With the popularisation and rapid development of railway transportation, how to

maintain train stability and reduce unwanted vibration to make the ride more

comfortable has become an emerging research topic. This is why this project has

included magnetorheological (MR) technology into railway vehicles to improve their

performance.

Critical speed is an index and a key technology that directly indicates train stability,

which is why the critical speeds of trains are calculated and analysed based on the

dynamic equations of railway vehicles. These analyses revealed that secondary

lateral damping and primary longitudinal stiffness are the most sensitive suspension

parameters influencing critical speeds. In an attempt to improve dynamic

performance, the secondary lateral dampers were replaced with conventional

magnetorheological fluid (MRF) dampers; with the simulation and experimental

results indicating that the semi-active suspension installed with MR dampers raised

the critical speed and achieved a higher level of stability. The primary longitudinal

stiffness is meant to be stiff when a train is running straight to maintain the stability

and then soft when the train is turning, for better trafficability. To solve this

dilemma, an innovative magnetorheological elastomer (MRE) based primary

longitudinal rubber joint with variable stiffness characteristics has been developed.

The simulation shows that controlling the MRE joint when a train runs on straight

and curved track can satisfy these apparently conflicting requirements and realise

good trafficability on curved track and high stability on straight track.

The second major task of this thesis is to control vibrations so that a higher level of

ride comfort can be achieved. To this end, an advanced MR damper with high

adjustability of damping and stiffness has been designed and fabricated. The results

field, amplitude, and frequency tests using an MTS machine verified its variable

stiffness and damping capability. A new model that can predict the performance of

the damper very well was then developed. The effect that this variable stiffness and

damping damper has on trains was investigated numerically and the results verified

that it definitely improved the ride comfort. Other attempts to improve ride comfort

resulted in the development of two advanced seat suspensions, with one targeting

lateral vibration control and the other for vertical vibration control. To control seat

suspension for lateral vibration, four MRE isolators were fabricated, and then the

iv

property of the isolator(s) was tested and the performance of the seat suspension was

evaluated. The results indicated a much more comfortable ride than the passive seat

suspension due to the MRE isolator based seat suspension. Moreover, with regards to

other types of seat suspension to control vertical vibration, an innovative rotary MR

damper was used to build the seat suspension. The rotary MR damper based

suspension uses less MRF; it has low sealing requirements, and it avoids settlement.

An evaluation of the capability of the rotary MR damper based seat suspension to

reduce vibration by simulation and experimental methods further verified its

effectiveness controlling vibration.

v

ACKNOWLEDGEMENTS

First and foremost, I would like to express my wholehearted appreciation to my

supervisor, Prof. Weihua Li, who guides me during all my time at the University of

Wollongong. At the beginning of my PhD study, it is Prof. Weihua Li who leads me

onto the right track on my research by offering valuable suggestions and guidelines.

During our weekly meeting, Prof. Weihua Li, as an expert in MR area possessing

tremendous knowledge, always provides me valuable recommendations and

suggestions to advance my research progress. He also always tries his best to satisfy

all my needs to conduct my research and always fully support my right movements

on research. In addition, he is not only a research supervisor but more importantly a

life guider. He always teaches me how to be a wise person and the importance of

being respectful. His hardworking attitude always inspires me to achieve more

outcomes. It is the unselfish help, inspirational guidance, encouragement and patient

from Prof. Weihua Li that lead me where I am today and I highly appreciate him for

everything.

I also would like to thank my co-supervisors, Dr. Huaxia Deng, Prof. Haiping Du

and Prof. Gursel Alici who give me very helpful discussion during my PhD study. In

addition, I would like to extend my deep sense of gratitude to all my family, my

lovely parents, brothers and sister, and my wife, Jian Yang. Your encouragement and

emotional support helped me pass through many tough stages during my research.

I also want to extend my gratitude to all my good friends and colleagues, Donghong

Ning, Xin Tang, Dan Yuan, Xinxin Shao, Wenfei Li, Zhiwei Xing, Tanju Yildirim,

Jun Zhang, Sheng Yan, Gangrong Peng, for your stay with me and happiness you

shared with me. Finally, I would like to thank all of you who helped me to grow up

to the person I am now.

vi

TABLE OF CONTENTS

DECLARATION ......................................................................................................... ii

ABSTRACT ................................................................................................................ iii

ACKNOWLEDGEMENTS ......................................................................................... v

TABLE OF CONTENTS ............................................................................................ vi

LIST OF FIGURES ..................................................................................................... x

LIST OF TABLES .................................................................................................... xiv

1 Introduction ............................................................................................................... 1

1.1 Research Background and Motivation ......................................................... 1

1.2 Research objectives ...................................................................................... 2

1.3 Outline .......................................................................................................... 3

2 Literature review ....................................................................................................... 5

2.1 Adaptive suspension for railway vehicles .......................................................... 5

2.1.1 Semi-active damper for railway vehicles ................................................. 5

2.1.2 Adaptive wheelset positioning technology for railway vehicles.............. 6

2.2 MR materials and their applications ............................................................ 7

2.2.1 MRF materials and their applications ...................................................... 7

2.2.2 MRE materials and their applications ...................................................... 9

2.3 Variable stiffness and damping for vibration control ................................ 12

2.4 Semi-active MR seat suspension ................................................................ 15

2.5 Conclusions ................................................................................................ 17

3 Analysis of vibration and stability of railway vehicles and its improvement with

MR damper ................................................................................................................ 18

3.1 Introduction ................................................................................................ 18

3.2 Mathematical model and calculation of train’s critical speeds .................. 19

3.2.1 Analytical model of train ....................................................................... 19

3.2.2 Calculation of the critical speed of a train ............................................. 22

3.2.3 Theoretical analysis of the effect of an MR damper on train critical

speed 25

3.3 The effect of train speed on the damping ratio of each train DOF ............ 26

3.4 The influence of suspension parameters on critical speeds of each train

DOF 29

3.5 The sensitivity analysis of the critical speed of a train .............................. 34

vii

3.6 The simulation of a train with an MR damper ........................................... 38

3.6.1 Modelling of a train ................................................................................ 39

3.6.2 Modelling of MR damper....................................................................... 40

3.6.3 The control strategy................................................................................ 42

3.6.4 Assembly of semi-active train and simulation ....................................... 42

3.6.5 Simulation and results ............................................................................ 43

3.7 The experimental research on the effect of the MR damper on the stability

of a train ................................................................................................................. 45

3.7.1 Experimental facilities ........................................................................... 45

3.7.2 Setup of experiment system ................................................................... 46

3.7.3 Results of experiment ............................................................................. 47

3.8 Conclusion ................................................................................................. 48

4 Investigation of the MRE rubber joint for train ...................................................... 49

4.1 Introduction ................................................................................................ 49

4.2 The design and working mechanism of the MRE joint.............................. 50

4.3 Prototype .................................................................................................... 52

4.3.1 Fabrication and characterise of MRE ..................................................... 52

4.3.2 Assembly of MRE joint ......................................................................... 53

4.4 Dynamic testing of the MRE rubber joint .................................................. 55

4.4.1 Testing .................................................................................................... 55

4.4.2 Testing results and discussion ................................................................ 55

4.5 Simulation evaluation of the MRE joint on a train .................................... 58

4.5.1 Test the trafficability of the train on a curve track ................................. 58

4.5.2 The stability evaluation of the train with MRE rubber joint .................. 63

4.6 Conclusion ................................................................................................. 63

5 Compact variable stiffness and damping damper for vehicle suspension system .. 64

5.1 Introduction ................................................................................................ 64

5.2 Variable stiffness and damping damper ..................................................... 64

5.2.1 Design and working principle of the advanced MR damper.................. 64

5.2.2 Prototype of the advanced MR damper .................................................. 66

5.2.3 Test and result discussion....................................................................... 67

5.2.4 Modelling and parameter identification ................................................. 73

5.3 Simulation of railway vehicle with variable stiffness and damping damper

80

viii

5.3.1 Control strategy ...................................................................................... 81

5.3.2 Simulation results and discussions ......................................................... 83

5.4 Conclusion ................................................................................................. 84

6 Horizontal Vibration Reduction of a Seat Suspension Using MRE Isolators ......... 86

6.1 Introduction ................................................................................................ 86

6.2 Structure and working principle of the MRE isolator ................................ 86

6.3 Prototype and testing of the MRE isolator ................................................. 88

6.3.1 Fabrication of the MRE isolator ............................................................. 88

6.3.2 Experimental testing............................................................................... 88

6.3.3 Frequency shift property evaluation ...................................................... 91

6.4 Vibration suppression evaluation of seat suspension mounted with four

MRE isolators ........................................................................................................ 92

6.4.1 Structure of the seat suspension mounted with MRE isolators .............. 92

6.4.2 Experimental testing system .................................................................. 93

6.4.3 Control algorithm ................................................................................... 94

6.4.4 Experimental results ............................................................................... 94

6.5 Conclusions ................................................................................................ 97

7 A seat suspension with a rotary MR damper for vertical vibration control ............ 99

7.1 Introduction ................................................................................................ 99

7.2 The structure and design of the seat suspension ........................................ 99

7.2.1 The structure of the innovative seat suspension with rotary MR damper

99

7.2.2 The design of the rotary MR damper based seat suspension ............... 100

7.3 The property test of the seat suspension and results discussion .............. 103

7.3.1 Testing method ..................................................................................... 103

7.3.2 Test results ........................................................................................... 103

7.4 Numerical effectiveness evaluation of the rotary MR seat suspension.... 107

7.4.1 The dynamic model of the seat suspension .......................................... 107

7.4.2 Control algorithm ................................................................................. 109

7.4.3 The numerical simulation results ......................................................... 109

7.5 Experimental effectiveness evaluation of the rotary MR seat suspension111

7.5.1 Test system ........................................................................................... 111

7.5.2 Test results ........................................................................................... 112

7.6 Conclusion ............................................................................................... 115

ix

8 Conclusions and future work ................................................................................ 117

8.1 Improving the stability of railway vehicles .............................................. 117

8.1.1 Analysing the mechanism of the vibration and stability of railway

vehicles ............................................................................................................. 117

8.1.2 Application of the MR damper for railway vehicles ............................ 117

8.1.3 Investigation of the MRE rubber joint for train ................................... 118

8.2 Reduced vibration and improved ride comfort of railway vehicles ......... 118

8.2.1 Compact variable stiffness and damping damper for railway vehicles 118

8.2.2 Advanced seat suspensions with MR technology ................................ 119

8.3 Recommendation for future work ............................................................ 120

8.3.1 Optimisation of the design of variable stiffness and damping dampers

120

8.3.2 Optimise the stiffness variation range of the MRE rubber joint .......... 121

8.3.3 Experimental investigation of a train mounted with variable stiffness and

damping damper or an MRE rubber joint ........................................................ 121

References ................................................................................................................ 122

PUBLICATIONS DURING MY PHD STUDY ..................................................... 134

x

LIST OF FIGURES

Figure 2.1 State variation of MRF (© 2005 Lord Corporation) .................................. 8

Figure 2.2 Schematic of magnetic particle dispersion [57]........................................ 10

Figure 2.3The transmissibility of one DOF with different suspension systems [82]. 12

Figure 2.4The schematic structure of the MrEPI [90] ............................................... 15

Figure 2.5 Variable stiffness and damping mechanism [92]...................................... 15

Figure 2.6 Experimental setup for vibration control [105] ........................................ 16

Figure 3.1 Analytical model of a train ....................................................................... 20

Figure 3.2 Damping ratios of the front truck wheelsets ............................................. 26

Figure 3.3 Damping ratios of the rear truck wheelsets .............................................. 27

Figure 3.4 Damping ratios of truck frames ................................................................ 28

Figure 3.5 Damping ratios of car body response modes ............................................ 28

Figure 3.6 Critical speed versus primary lateral damping ......................................... 30

Figure 3.7 Critical speed versus secondary lateral damping ...................................... 31

Figure 3.8 Critical speed versus primary lateral stiffness .......................................... 32

Figure 3.9 Critical speed versus secondary lateral stiffness ...................................... 33

Figure 3.10 Train critical speed versus various bogie damping................................. 36

Figure 3.11 Train critical speed versus various bogie stiffness ................................. 36

Figure 3.12 Sensitivity of train critical speed versus various bogie damping ........... 37

Figure 3.13 Sensitivity of train critical speed versus various bogie stiffness ............ 37

Figure 3.14 The average sensitivity of train critical speed with respect to different

bogie stiffness and damping parameters ............................................................ 38

Figure 3.15 Dynamic model of a train ....................................................................... 39

Figure 3.16 Dynamic model of suspension of train .................................................. 39

Figure 3.17 MR damper model .................................................................................. 40

Figure 3.18 Force-displacement (a) and force-velocity (b) relationship of MR damper

............................................................................................................................ 41

Figure 3.19 Composition of semi-active train model................................................. 42

Figure 3.20 The displacement of wheelset vs the speed of the train with a passive-off

damper ................................................................................................................ 43

Figure 3.21The displacement of wheelset vs the speed of the train with a passive-on

damper ................................................................................................................ 44

xi

Figure 3.22 The displacement of the wheelset vs the speed of a train with an semi-

acitve MR damper .............................................................................................. 44

Figure 3.23 Railway vehicle ...................................................................................... 46

Figure 3.24 Installation of MR dampers .................................................................... 47

Figure 3.25 RMS of lateral acceleration of the bogie ................................................ 48

Figure 4.1 The structure of the MRE rubber joint ..................................................... 50

Figure 4.2 The working mechanism of the MRE rubber joint: (a) Train runs on curve

line with soft longitudinal stiffness (b) Train runs on straight line with hard

longitudinal stiffness .......................................................................................... 52

Figure 4.3 The storage modulus and loss modulus of MRE under different magnetic

flux densities: (a) Storage modulus; (b) Loss modulus ...................................... 54

Figure 4.4 The prototype of the MRE rubber joint .................................................... 54

Figure 4.5 Test of the MRE rubber joint .................................................................... 55

Figure 4.6 The response of the MRE rubber joint to different magnetic field........... 56

Figure 4.7 The stiffness variation under different currents ........................................ 56

Figure 4.8 The response of the MRE rubber joint to different amplitudes ................ 57

Figure 4.9 The response of the MRE rubber joint to different frequencies ............... 58

Figure 4.10 The angle of the attack ............................................................................ 58

Figure 4.11 The angle of attack on curve track with 600m radius ............................. 59

Figure 4.12 The lateral displacement of the wheelset on curve track with 600m radius

............................................................................................................................ 60

Figure 4.13 The lateral force of the wheelset on curve track with 600m radius ........ 61

Figure 4.14 The angle of attack on curve track with 3000m radius .......................... 61

Figure 4.15 The lateral displacement of the wheelset on curve track with 3000m

radius .................................................................................................................. 62

Figure 4.16 The lateral force of the wheelset on curve track with 3000m radius ...... 62

Figure 5.1 Design and photograph of the advanced MR damper .............................. 65

Figure 5.2 Scheme of Connection Mode ................................................................... 65

Figure 5.3 Force displacement relationship under I1=0A .......................................... 69

Figure 5.4 Effective stiffness as a function of the current applied to the external

damper ................................................................................................................ 70

Figure 5.5 Variable damping performance under various currents ........................... 72

Figure 5.6 Equivalent damping and energy consumption as a function of the applied

current to the internal damper ............................................................................ 73

xii

Figure 5.7 Force-displacement loops under different frequency ............................... 73

Figure 5.8 Phenomenological model for the advanced MR damper .......................... 74

Figure 5.9 The flow chart of parameter identification using IP-GA .......................... 76

Figure 5.10 Comparison between the simulated response and the measured response:

(a) Variable damping property (b) Variable stiffness property .......................... 78


(a) Variable damping property (b) Variable stiffness property .......................... 79

Figure 5.12 Control system of variable stiffness and damping suspension ............... 81

Figure 5.13 Car body response in time domain ......................................................... 82

Figure 5.14 Car body response in frequency domain ................................................ 84

Figure 5.15 Acceleration RMS of car body ............................................................... 84

Figure 6.1 Structure of the MRE isolator ................................................................... 88

Figure 6.2 The experiment setup for testing the dynamic performance of MRE

isolator ................................................................................................................ 89

Figure 6.3 Relationship between force and displacement under different currents ... 90

Figure 6.4 Relationship between equivalent stiffness and current ............................. 90

Figure 6.5 Relationship between force and displacement with different amplitudes 91

Figure 6.6 Transmissibility of the MRE isolator under different currents ................. 92

Figure 6.7 Structure of the MRE seat suspension ...................................................... 93

Figure 6.8 Experiment setup for seat vibration testing: (a) Schematic diagram (b)

Experimental setup ............................................................................................. 93

Figure 6.9 The equivalent SDOF system ................................................................... 94

Figure 6.10 Acceleration and displacement responses of seat suspension under

different sinusoidal excitations: (a) 5Hz. (b) 7Hz. (c) 10Hz ............................ 96

Figure 6.11 Responses of seat under sweep frequency sinusoidal excitation ............ 97

Figure 7.1 The structure of the innovative seat suspension: (a) working mechanism

(b) photograph of the suspension system ......................................................... 100

Figure 7.2 The structure of the rotary MR damper .................................................. 101

Figure 7.3 The test results of the seat suspension :(a) different currents (b) different

amplitudes (c) different frequencies................................................................. 105

Figure 7.4 The comparison between the experimental peak force and calculated peak

force.................................................................................................................. 106

Figure 7.5 The mathematic model of seat suspension ............................................. 108

Figure 7.6 The fitting result of the mathematic model............................................. 108

xiii

Figure 7.7 The simulation response of seat under harmonic excitation ................... 110

Figure 7.8 The simulation response of seat under random excitation...................... 111

Figure 7.9 The effectiveness evaluation system for the seat vibration control: (a)

Sketch (b) Experiment...................................................................................... 112

Figure 7.10 The test results of the MR seat suspension under harmonic excitation: (a)

1.3Hz (b) 1.75Hz .............................................................................................. 113

Figure 7.11 The transmissibility of the MR seat suspension under different

frequencies ....................................................................................................... 114

Figure 7.12 The performance of MR seat suspension under random excitation ..... 115

xiv

LIST OF TABLES

Table 3.1 Nomenclature of train dynamic model symbol .......................................... 23

Table 3.2 The value of the key initial parameter ....................................................... 24

Table 3.3 Motions of the 15-degree-of-freedom train model ................................... 24

Table 3.4 Nomenclature of critical speeds of each DOF ........................................... 30

Table 4.1 value of the main size................................................................................. 50

Table 5.1 The parameters of the two springs ............................................................. 67

Table 5.2 The identified parameters........................................................................... 77

Table 6.1 The reduction percentage under different frequencies ............................... 97

Table 7.1The size of the rotary MR damper ............................................................ 102

Table 7.2 The parameters for the MRF-132DG ....................................................... 102

Table 7.3The identified model parameters............................................................... 108

Table 7.4 The rules of the Fuzzy controller ............................................................. 109

Table 7.5 The acceleration RMS values .................................................................. 115

1

1 INTRODUCTION

1.1 Research Background and Motivation

Trains are an efficient solution to the high demand for transportation in a society in a

globalised economy. Compared to other forms of transportation, trains have

advantages of high speed travel, they are safe [1-3], environmentally friendlier, and

deliver cheaper unit delivery costs. However, these advantages can be offset by

challenges such as induced vibration and noise that inevitably lead to a series of

problems such as instability and unsatisfactory ride comfort; these are the most

serious issues that need to be addressed [3, 4] because train stability is closely related

to the comfort and even safety of passengers; in fact, high stability can also protect

the train and the rail from damage caused by mutual friction and collisions. Stability

is normally characterised by critical speed, such that the higher the critical speed the

more stable the train is. This is why the critical speed of a railway vehicle is intrinsic

and independent of the type of excitation type; it is a fixed scalar once the suspension

system of a train has been configured and assembled, and therefore an adjustable

semi-active suspension system rather than passive suspension is potentially a far

better choice for achieving a high critical speed [5]. The theoretical results show that

the secondary lateral damper and the primary longitudinal stiffness are the

parameters most closely related to the critical speed, so finding advanced technology

to make a secondary lateral damper and a longitudinal rubber joint controllable to

improve the critical speed becomes an urgent task.

In terms of a secondary lateral damper, apart from passive control, semi-active

control has the potential to improve the critical speed because it requires less energy

and can adjust the system parameters in real time [6, 7]. Many researchers have done

excellent work on the semi-active control of railway vehicles [8-10], and the

application of MR technology to railway vehicles has been reported by several

groups [11, 12]. However, the above research mainly focused on improving ride

comfort, whereas research into using MR dampers to improve the critical speed is

rare. In order to help fill this gap, this research investigated the application of a

traditional MR damper to improve critical speed both theoretically and

experimentally.

As well as the secondary lateral damper, the primary longitudinal rubber joint is

another important component that affects the critical speed. To date, passive rubber

2

joints are widely used in railway vehicle, and while having harder longitudinal

stiffness guarantees stability in a straight track, it leads to bad trafficability as a train

begins to turn. A perfect primary longitudinal joint is supposed to overcome this

conflict, i.e. it should be stiff when the train is running straight and then soft as it is

turning. To solve this problem, this research proposed an innovative MRE based

rubber joint whose stiffness is controllable. With this characteristic, the new MRE

joint can provide hard stiffness to ensure stability when a railway vehicle runs on

straight track and offer soft stiffness to realise good trafficability on a curved track.

To control the ride comfort, many semi-active devices have been developed in recent

years and then used to reduce vibration of railway vehicles. However, variable

stiffness and damping suspension systems with better vibration control than

suspension systems with only variable damping has not been investigated in existing

literature, and furthermore, a practical variable stiffness and damping device suitable

for railway vehicles has not yet been reported. To compensate for this deficiency,

this thesis developed a compact variable stiffness and damping MR damper which is

suitable for trains, and whose contribution to ride comfort has also been investigated.

Using the train suspension system to mitigate vibration from its source is a good

idea, but it cannot be denied that preventing vibration from being transmitted to the

drivers or passengers using an advanced seat suspension is a much more efficient

way to improve ride comfort. Since trains experience vibration vertically and

laterally, this thesis investigated two different seat suspensions. One is an MRE

based seat suspension for controlling lateral vibration and the other is rotary MR

damper based seat suspension for controlling vertical vibration.

1.2 Research objectives

The overall aim of the research is to develop controllable devices to improve the

overall dynamic performance of trains, including improving the stability, reducing

vibration, enhancing ride comfort, and improving trafficability on curved track.

The specific objectives of this research are as follows:

(1). Analysing the stability mechanism of railway vehicles based on a 15 degrees of

freedom dynamic model, and determine the parameters that affect its stability.

(2). Analyse how affectively traditional MR dampers and MRE based stiffness

variable rubber joints improve the stability and trafficability of railway vehicles.

3

(3). Develop a compact variable stiffness and damping MR damper for railway

vehicles and build a mathematic model to predict the dynamic performance of a

variable stiffness and damping MR damper.

(4). Develop advanced seat suspensions to reduce the lateral and vertical vibrations

in railway vehicles.

1.3 Outline

This thesis starts with an introduction of the research background and motivation,

objectives, and outline.

Chapter 2 presents a literature review on existing adaptive technology for railway

vehicles, including semi-active dampers and wheelset positioning technology, MR

materials and their applications, variable stiffness and damping devices, and seat

suspension technologies.

Chapter 3 describes building a 15 DOFs model of railway vehicles to analyse their

stability. The influence that each suspension parameter has on a train’s vibration and

critical speed was analysed theoretically and indicated that the secondary lateral

damper and primary longitudinal stiffness are the two important parameters that

affect stability. The secondary lateral damper was subsequently replaced by a MR

damper and its contribution to improving stability was investigated theoretically and

experimentally.

In Chapter 4 the effect that primary longitudinal stiffness has on the critical speed of

railway vehicles was further investigated and verified, and an innovative MRE based

rubber joint was prototyped and tested. Including MRE in the rubber joint design

improves the variable stiffness; an advantage that satisfied the requirements for hard

and soft stiffness. The simulation result indicated that the innovative MRE joint can

provide hard stiffness to stabilise a train running at high speed in a straight line and

also offer soft stiffness to realise good trafficability when it passes thought a curved

line.

Chapter 5 focuses on improving the vibration and ride comfort of railway vehicles.

To achieve this, an innovative MRF based damper which synergises the attributes of

variable stiffness and variable damping via a compact assembly of two MRF

damping units and springs was developed, and its ability to improve the dynamic

performance was theoretically verified.

4

Chapter 6 and Chapter 7 presents two innovative MR technology based semi-active

seat suspensions to further improve the ride comfort. Four MRE isolators are

prototyped and assembled for a seat suspension to control lateral vibration and a

rotary damper is mounted on a seat suspension to control vertical vibration. An

evaluation of this vibration control indicates that the MR technology based seat

suspension performed better than passive seat suspensions.

Chapter 8 concludes the main findings of this thesis and discusses future research

work.

5

2 LITERATURE REVIEW

2.1 Adaptive suspension for railway vehicles

2.1.1 Semi-active damper for railway vehicles

Active and semi-active control is two typical methods used to improve system

performances. Whereas active control is better at reducing vibration, the

disadvantages of possible instability, complex control algorithms, and large power

consumption limit its common use. More interest has recently been given to semi-

active control because it requires less power, the hardware is cheaper, and it performs

well. In fact a great deal of research work on semi-active control of railway vehicles

has already been done. For example, O’Neill and Wale [13] have done some pioneer

work on the application of semi-active suspensions to improve the ride quality of

trains. In their study, solenoid valves and semi-active dampers were developed to

control vibration, while Tang developed a semi-active damper with a butterfly valve

and mounted it on a quarter vehicle which was then tested in their laboratory [14].

Stribersky et al. [15] designed another hydraulic damper whose orifice was

controlled by a fast-acting throttle valve. The hydraulic damper improves ride quality

by up to 15% according to the measured RMS of the accelerations. Some semi-active

suspension systems for railway vehicle have been commercialised by Kayaba (KYB)

Corporation in Japan, or by KONI Railway in the Netherlands. However, the

composition of the oil cylinders and mechanical valves reduces the reliability and

response time of variable orifice dampers, which also increases their maintenance

costs.

Another semi-active control method can be realised by placing smart fluids into the

damper. Electrorheological (ER) fluids and MR fluids are two typical controllable

fluids which can change from a free flowing viscous fluid into a semi-solid. Their

composition without extra moving parts makes them simple and reliable. ER fluids

are excited by high voltage, which limits its use in many areas because of safety

concerns, whereas MR fluids only need a low voltage source to excite a magnetic

field, which means a semi-active suspension with MR fluids is better suited for

trains. As a semi-active control device, an MR damper uses the unique characteristics

of MR fluids to provide simple, quiet, rapid-response interfaces between electronic

controls and mechanical systems, which makes it an ideal option for trains.

6

2.1.2 Adaptive wheelset positioning technology for railway vehicles

It is becoming more important for rail vehicles to operate at high speed in order to

improve transportation efficiency, but so too is improving the steering capability

when they run on curved track in order to achieve low maintenance costs for both

vehicles and tracks [16]. Consequently, compatibility between the dynamic stability

which allows trains to operate at high speed and good curved track trafficability

while maintaining low maintenance is an urgent requirement for modern railway

vehicles.

The stability of trains running at high speed requires stiff wheelset positioning that

will resist the hunting motion of wheelsets and soft wheelset positioning stiffness to

achieve good curving performance. This leads to an incompatibility between stability

design and curving performance when designing the wheelset positioning stiffness of

conventional passive trucks. In order to overcome this conflict, the GontiTech

Company developed a radial hydraulically controlled wheelset positioning system

which mainly contains the guide column for the truck frame, positioning rubber, and

hydraulic oil. This ingenious design uses the different excitation frequency induced

by the distinct running speed of the train on straight track and curve track. This

positioning system can offer soft longitudinal stiffness under lower excitation

frequency when the train runs on a curved line at lower speed and provide hard

longitudinal stiffness under high excitation frequency when the train operates on a

straight line at higher speeds. With this method the proposed wheelset positioning

system overcomes the conflict between high speed stability and curved line

performance to a certain extent, but there is still room for improvement.

Another way to overcome this conflict is to introduce active control to the truck

design. Some existing research has reported on an investigation into active control to

realise good steering and high speed stability [17-20]. Unfortunately, active control

will lead to problems such as high power consumption, large expense on hardware,

and even instability due to improper control.

Semi-active control however, is a compromise between active and passive control

with the advantages of fail-safe characteristics, lower power consumption, and

cheaper hardware; and it is a better way to solve this conflict. Suda et al. proposed an

asymmetric truck to achieve both good curving performance and stability. In [21-24],

the primary longitudinal stiffness of the leading and trailing wheelsets is asymmetric,

7

which means the longitudinal stiffness of the leading wheelset is softer than the

trailing wheelset. Soft longitudinal stiffness can decrease the lateral force and the

angle of attack of the leading wheelsets which improves curved track trafficability,

while the hard longitudinal stiffness of the trailing wheelset can keep the train stable

at high speed. This longitudinal stiffness of the wheelsets can be reversed when a

train’s running direction changes. The simulation result and experimental result

verified that the proposed asymmetric suspension solved the conflict between high

speed stability and curving track performance. This kind of truck has been assembled

on a Series 383 EMU train and is now in daily use. However, according to the

evaluation this asymmetric system still decreases the critical speed compared to a

conventional symmetric system. Since MRE is an important member of the MR

material family, it can vary its stiffness rapidly, which makes it an ideal material to

develop an adaptive wheelset positioning technology, but since this has rarely been

investigated this research will help to fill the gap.

2.2 MR materials and their applications

MR materials, as typical smart controllable materials whose properties can be

controlled by an external magnetic field, consist mainly of Magnetorheological

fluids, elastomers, gel and foams[25]. MRF is in a fluid state and its shear stress is

very sensitive to a magnetic field, which means it can be used to develop variable

damping dampers. On the other hand MRE is an elastomeric material whose stiffness

can be controlled by a magnetic field. MR foam means MRF is constrained in a

capillary action in an absorbent matrix such as a sponge, open-celled foam, felt or

fabric. MR gel is relative younger than the other three and it is in gel state between

solid and fluid. Since MRF and MRE are the two MR materials used most

frequently, their property and applications will be further introduced in the following

two sections.

2.2.1 MRF materials and their applications

MRF materials

Dating back to 1948, Jacob Rabinow discovered MRF at the US National Bureau of

Standards, which are a class of smart fluids whose yield stress is controllable. MRFs

consist of magnetic particles at micron size, e.g., iron or cobalt particles, and carrier

fluid e.g., silicone oil or hydraulic oil [26, 27]. The magnetic particles in MRF can

8

freely move in their carrier fluid when no magnetic field is applied, as shown in

Figure 2.1(a), but they lose their free mobility and form a chain-like structure along

the direction in which a magnetic field is applied. This means the magnetic field

enables the magnetic particles to become polarised and then attract one another, as

shown in Figure 2.1(b). The variability of the structural arrangement of these

ferromagnetic particles gives MRF the ability to change its viscosity and yield stress.

From the perspective of traditional materials, MRF is outstanding because its soft

morphology and controllable rheology by an external magnetic field means it can

achieve a rheological transition and exhibit viscoelastic properties within a few

milliseconds.

(a) Without magnetic field applied (b) Magnetic field applied

Figure 2.1 State variation of MRF (© 2005 Lord Corporation)

MR damper and its application to railway vehicles

To date, various semi-active devices using MRFs have been developed, of which MR

dampers that offer variable damping and reliable operations at a modest cost have

been extensively used in vehicle suspension systems, landing gear systems, ship

vibration reduction systems, civil structures, and so on [28-35].

The application of MR dampers on trains has been reported by a few groups; for

example, Liao and Wang [36] studied the application of an MR damper to control the

vertical vibration of trains, while Wang and Liao [37, 38] further verified that an MR

damper improved a train’s ride comfort by replacing four secondary lateral dampers

with MR dampers. A model of a full scale railway vehicle with 17 degrees of

freedom was integrated with an MR damper and its controller was built. A dynamic

model of the train was then used to design a linear quadratic Gaussian control law for

the MR damper. Random and periodical track irregularities based on real testing data

were incorporated into the dynamic model to evaluate the semi-active suspension

9

system, and the results showed that the semi-active suspension system can provide

better ride comfort than the passive on or passive off modes.

Some MR dampers for railway vehicle have been designed and prototyped, for

instance, Guo and Gong developed a twin-tube and bypass MR damper for railway

vehicles [39], and Lau and Liao [40] designed an MR damper for secondary lateral

damper of railway vehicles. Many control algorithms for MR dampers have also

been developed; Zong et al. [10] investigated a robust control algorithm for an MR

damper to suppress lateral vibration, and then verified its effectiveness using the

simulation method. Ma and Yang investigated a self-adapted fuzzy control and

adaptive fuzzy control for the secondary lateral semi-active damper of the railway

vehicle, respectively [41, 42]. Wang and Liao designed an LQG control algorithm for

the secondary vertical MR damper and proved its effectiveness by numerical

simulation [37]. Ha et al. developed a fuzzy sky to ground hook control algorithm for

a secondary lateral MR damper [43]. Some experimental evaluations of using an MR

damper to reduce vibrations in a railway vehicle were carried out by testing scaled or

full scaled railway vehicles mounted with MR dampers. Shin et al developed and

tested a 1/5 scaled MR damper used to replace a secondary lateral damper in a

railway vehicle [44, 45]. This scaled MR damper was then mounted onto a 1/5 scaled

railway vehicle and then tested on a scaled test rig. The skyhook control algorithm

and H∞ control algorithm were designed to control the MR damper at work, and the

test results verified that the MR damper definitely reduced vibration in a railway

vehicle. Lee et al. designed and developed an MR damper which was then mounted

onto a full scale railway vehicle [46], controlled it with the skyhook control

algorithm and tested it on a roller rig. The results indicated that the MR damper

improved the ride comfort level by approximately 1dB. The research mentioned

above focused mainly improving the ride comfort with MR technology, but the

contribution an MR damper makes to train stability has rarely been investigated. This

thesis therefore carries out an experimental and numerical study to investigate the

effect that an MR damper has on the critical speed of trains.

2.2.2 MRE materials and their applications

MRE materials

10

MRE is a stiffness variable smart material that generally consists of micro-sized

magnetic particles dispersed in a non-magnetic matrix[47]. In a magnetic field the

ferromagnetic particles inside MRE have an MR effect which increases its stiffness

and damping, but it immediately returns to soft state when the magnetic field is

removed. Compared to MRFs, MREs have the advantage of high stability and no

sealing issues [48].

There are two main types of typical MREs, depending on the curing method used:

anisotropic MR elastomers and isotropic MR elastomers. Take silicon rubber based

MRE fabrication as an example. In the first step, iron particles are placed into a

container and then silicon oil is poured in; this is then mixed with silicone rubber

until all the materials are mixed thoroughly. The mixture is then placed into a

vacuum case to remove any air bubbles [49-51], and then removed and poured into a

mould. After 24 hours of curing at room temperature, this isotropic MRE can be

fabricated [52]. The iron particles inside MRE will be randomly dispersed, as shown

in Figure 2.2(a). In terms of anisotropic MRE [53], curing should be completed in the

presence of a strong magnetic field [54-56] because this enables the ferromagnetic

particles to form chained structures, as shown in Figure 2.2(b)

(a) Without a magnetic field (b) With a magnetic field

Figure 2.2 Schematic of magnetic particle dispersion [57]

Many studies [57, 58] have reported the dynamic property test of MRE specimens, of

which the main conclusions are: (1) an increase in the volume percentage of

ferromagnetic particles in MRE improves the modulus variation range; (2) The

increase in the shear modulus of MRE varies when magnetic flux density with

different strengths is applied, and it will saturate at stronger magnetic flux densities;

(3) There is a sharp reduction in the MR effect at high strains. The main reason for

11

the strain dependency of MRE is an onset of magnetic yielding by the chain

structure.

Applications of MRE

Since MRE can vary its stiffness quickly and is controllable, it is an ideal smart

material with which to develop an adaptive tuneable vibration absorber and isolator

[59-65]. MRE mainly works in two modes, the shear working mode and the squeeze

working mode.

The use of shear working mode MRE to develop an absorber has already been

investigated by a number of researchers. Ginder and his co-workers did pioneering

work on the development of an adaptive tuneable vibration absorber based on MRE

[66]. Following his work, Deng et al. applied another wire coil to the MRE absorber

to further broaden its effective bandwidth [67]. In order to further improve the

vibration absorption of an MRE absorber, Gong’s group extended their research by

using an active force to develop an active-adaptive vibration absorber to overcome

the damping of MRE [68, 69]. As well as the MRE absorbers working in shear mode,

as reviewed before, research work exploring the MRE absorbers working in squeeze

mode has also been carried out. Popp et al. analysed the MR effect of MRE based

absorbers under shear and squeeze modes by experimental studies and simulations

[48]. Sun et al. investigated the difference of the frequency shift range between MRE

absorbers working in shear and squeeze modes and reached the same conclusion.

Furthermore, they developed a new compact MRE absorber that works in the

squeeze mode [70, 71] to widen the frequency range and extend the scope of its

application, and then experimentally verified how effectively it attenuated vibrations.

Lerner and Cunefare developed three different kinds of MRE absorbers working in

shear, squeeze, and longitudinal mode [72]. Their experimental test showed that

MRE absorbers working in shear mode and longitudinal mode varied their natural

frequency by 183% and 473%, respectively, while the squeezed MRE absorber

changed by 507%, which is the maximum natural frequency variation of the three

working modes.

As well as the absorber, the existing literatures have developed a series of MRE

based adaptive base isolators [73, 74]. Hwang et al. [75] conducted a conceptual

study on using MRE to a base isolation system for building structures. Usman et al.

[76] numerically evaluated the dynamic performance of a smart isolation system

12

using MRE and validated the capability of isolating unwanted vibration by attaching

an MRE isolator to a structure with five DOFs. The results showed that the MRE

isolation system outperformed a conventional system by reducing the response of a

structure under various seismic excitations. Behrooz et al. [77, 78] presented the

performance of a MRE based variable stiffness and damping isolator (VSDI) used in

a scaled building system. Li et al. further developed a large scale and highly

adjustable laminated MRE isolator for protecting buildings from earthquakes [79,

80]. In [81], Li et al. presented a successful development and experimental

evaluation of a smart base isolation utilising MRE. In order to realise negative

changing stiffness, Yang et al. developed a stiffness softening MRE base isolator by

adopting two permanent magnets that can energise the MRE continuously without

consuming power, while the solenoids produce an electromagnetic field that is

opposed to the permanent magnetic field, so the lateral stiffness of the MRE isolator

can be lower. This new stiffness softening base isolator can operate in a passive hard

mode under normal operating conditions without requiring any power and keep the

building stable, and it only needs to be activated to a soft or semi-active mode when

certain earthquake events trigger the system.

2.3 Variable stiffness and damping for vibration control

Figure 2.3The transmissibility of one DOF with different suspension systems [82]

Stiffness and damping are the fundamental and important mechanical features that

13

must be controlled in many technical systems in order to achieve the desired dynamic

behaviour and address any undesired vibration. The reduction of vibration has been

inevitably connected to the concepts of variable damping or variable stiffness,

wherein ‘variable’ means controllability, real-time, and reversibility. The dynamic

performance of a single DOF system with variable stiffness and damping

characteristics can be obtained, as Figure 2.3 shows. Here, variations in damping will

induce changes in the resonance magnitude by adjusting the dissipated vibration

energy (compare lines A, B, C or lines D, E, F), and the variable stiffness will change

the transmissibility of vibration by changing the natural frequencies of the controlled

system (compare line A and D or B and E or C and F). The figure shows that variable

damping can suppress vibration better than a constant damping system. Specifically,

variable damping can achieve lower transmissibility, shown as the green line G. In

fact the figure indicates that another important conclusion can be drawn, the

transmissibility of the variable stiffness and damping system can be lowered further,

which is shown as the red line H. Many studies have been carried out based on this

foundation or with the concept of dual controllability of stiffness and damping [83-

86]. Liao et al. embedded a voice coil motor into an MRE isolator to realise variable

stiffness and damping characteristics [54]. Zhang et al. [87, 88] developed a variable

stiffness and damping MR damper that contains an air spring, separate films, an MR

valve and accumulator. The dynamic response obtained experimentally showed that

the stiffness and damping can be adjusted over a relatively large range. Following

this research, Sun et al. investigated an innovative suspension system for railway

vehicles that include an MRF based variable stiffness air spring and an MR damper.

This research theoretically verified that the variable stiffness and damping

suspension suppresses vibration better than suspensions with only variable damping

or variable stiffness [89]. Zhu et al. proposed a variable stiffness and damping

isolator by connecting the pneumatic spring and the MR damper compactly, as

shown in Figure 2.4 [90]. In this compact design, the MR damper varies the damping

of the isolator while the pneumatic spring gives the isolator the variable stiffness

capability. Moreover, the pneumatic spring makes switching between passive and

active vibration control modes realistic, and also provides more flexibility and

versatility in applications. Raja et al. developed another variable stiffness and

damping device: an MR fluid damper–liquid spring suspension system for heavy off-

14

road vehicles. This new device can change its damping and stiffness and its

maximum force can reach 10000N [91], but its stiffness and damping cannot change

separately and its stroke is limited. Greiner-Petter et al. recently reported a unique

structure that uses MRF to realise variable stiffness and damping characteristics [92].

As Figure 2.5 shows, this semi-active MRF mechanism offers variable stiffness and

damping by utilising two MR valves and two springs. The experimental results prove

that the damping of this system is continuously variable but its effective stiffness can

only be varied between three different values instead of consecutively. In order to

verify the effectiveness of a variable stiffness and damping suspension, Liu et al.

proposed a structure with two voigt elements (each one consisting of a constant

spring and a controllable damper) in series to control variable stiffness and damping

[93]. In their design, damping and stiffness cannot be controlled independently

because the two MR dampers are installed in series, so Liu and his group then

proposed a new structure which can vary its stiffness and damping independent of

each other [82]. This new structure also has two MR dampers. A vibration testing

experiment was carried out to evaluate how well it isolated vibration, and showed

that the variable stiffness and damping suspension performed best at isolating

vibrations. Spelta et al. developed a novel algorithm to control the variable stiffness

and damping suspension to further improve the ride comfort of vehicles [94]. The

simulation demonstrated that a variable stiffness and damping suspension controlled

by their control algorithm improved vibration isolation better than suspensions with

only variable damping. Xu et al.’s simulation also verified their usefulness in

enhancing vehicle stability by replacing a passive front suspension system with a

variable stiffness and damping structure in the vehicle [95, 96]. This better

performance by the variable stiffness and damping system has been verified by the

simulation and experimental methods, but devices capable of varying both their

stiffness and damping for practical applications have rarely been developed. Based

on this motivation, this thesis has developed an advanced MR damper with variable

stiffness and damping capabilities, and it is presented in chapter 5.

15

Figure 2.4The schematic structure of the MrEPI [90]

Figure 2.5 Variable stiffness and damping mechanism [92]

1. voice coil, 2. air bearing, 3. flexure hinge, 4.spherical joint, 5. force sensor,

6. laser interferometer mirror, 7. fixed stop, 8. laser interferometer

2.4 Semi-active MR seat suspension

Advancing seat suspension is another possibly way to further improve passenger’s

ride comfort. Semi-active suspension systems with adaptive damping or tuneable

stiffness items are cheaper, stable, and possess good vibration reduction

performance, and as such have drawn a great deal of attention [97-104]. An MR

damper, as an effective device to improve the ride comfort of a seat, has been

investigated by many researchers. As Figure 2.6 shows, Choi et al. [105] used MR

16

dampers to attenuate the vertical vibration of a seat. A seat testing platform with a

hydraulic shaker was embedded into a full car dynamic model. The hardware was

and realised in a loop simulation and the MR damper based seat suspension was

evaluated under a skyhook algorithm control. The results indicated that the seat

mounted with an MR damper outperformed the passive seat.

Figure 2.6 Experimental setup for vibration control [105]

Another important function of seat suspension is to protect the driver in the event of

a crash, especially with military equipment. Wereley’s group mounted an MR

damper onto the seat suspension of an aircraft [106-108] to improve the

crashworthiness of the seat and protect the soldiers. Bai and Wereley also extended

their work on applying MR seat suspension to mitigate the effects of ground vehicle

crashes [109]. Most of these above mentioned seat suspensions work with a linear

MR damper, however semi-active seat suspension that utilizes a rotary MR damper

has rarely been investigated. Compared to conventional seat suspensions with a

linear MR damper which needs a large amount of MRF to fill the reserve of the

linear MR damper, suspension based on a rotary damper utilises a smaller amount of

MRF because the reserve of the rotary MR damper is much smaller than a linear one;

this advantage significantly reduces the cost of this type of seat suspension. Another

advantage over linear dampers is there is no need to seal a rotary MR damper

because the working mechanism of a linear MR damper relies on the difference in

pressure between two sides of the piston, which means the pressure on one side is

quite high and this needs good sealing. With a rotary MR damper, the working

mechanism is different and the MRF pressure is quite low so it is easy to solve the

sealing problem. Considering these two advantages, this thesis designed and

investigated seat suspension based on a rotary MR damper; this is expounded in

chapter 7.Some research using MRE for seat suspension has been reported. For

17

example, Du and Li proposed an innovative MRE isolator for seat suspension that

incorporated the driver model and developed a sub-optimal H∞ controller to improve

its vibration attenuation [110, 111]. Existing MRE based seat suspension mainly

focuses on controlling vertical vibration, whereas seat suspension targeting lateral

vibration control has rarely been studied. Lateral vibration exists in many control

targets, especially trains, and therefore should be well controlled, so to fill in this

research gap, this thesis proposed an innovative MRE based seat suspension to

control lateral vibration, and presented it in Chapter 6.

2.5 Conclusions

This chapter reviewed the adaptive technology currently available for improving the

dynamic performance of trains, including semi-active damper technology and

adaptive wheelset positioning technology. The MR materials and their applications

have been also introduced in this section.

This review has clearly detailed existing gaps in the application of MR technology

onto railway vehicles. Since the use of MR suspension to improve train stability has

rarely been investigated, a compact variable stiffness and damping structure suitable

for railway vehicles has not yet been found, advanced seat suspension for vibration

control rarely reported, the wheelset positioning technology should be further

improved to realise good trafficability on curved line and high speed stability. Based

on these motivations, the current research into enhancing vehicle stability and ride

comfort with semi-active MR technology is presented in the following chapters.

18

3 ANALYSIS OF VIBRATION AND STABILITY OF RAILWAY VEHICLES

AND ITS IMPROVEMENT WITH MR DAMPER

3.1 Introduction

Generally, two main reasons induce the high-speed train vibration: the resonance and

instability of the vehicle/structure system. Resonance refers to the phenomenon that

the external disturbance of the vehicle is equal or close to the natural frequency of

the whole system. For solving this resonance issue, a well-designed passive damper

is commonly used. However, the parameters of passive damper are fixed, which

means that once the system is designed, the damper cannot be adjusted. Additionally,

a fixed passive damper may become ineffective due to other phenomena such as

instability of the vehicle which is speed dependent. When the train speed reaches a

critical value, the amplitude of the train vibration grows exponentially with time and

theoretically reaches infinity in a linear system. For the reason that this instability of

the vehicle/structure system is intrinsic and independent of the excitation type, a

conventional passive damper is unadequate to maintain the system stability. It is

therefore crucial to study the mechanism of this train instability and find a

controllable damper that can address the issues.

In this chapter, the problems of stability and vibration of the railway vehicle were

systematically analysed. Specifically, a 15 DOF dynamic model of a train was

developed. Based on this dynamic model and equations, the damping ratio of each

DOF of 15 was calculated. When the damping ratio reduces and crosses the zero line,

the train becomes unstable and reaches its critical speed. Thus, the critical speed of

each DOF with respect to the suspension stiffness and damping was worked out. The

sensitivity of a train’s critical speed with respect to the suspension parameters were

analysed as well. The result reveals that the secondary lateral damper impacts the

train’s critical speed most as well as the primary longitudinal stiffness. As a result,

the secondary lateral damper which is the most influential damper was replaced with

a controllable MR damper to improve the train stability. In order to investigate the

effect of MR dampers on train’s critical speed, a train installed with MR dampers

was simulated by a combined simulation of ADAMS and MATLAB. Then the MR

dampers installed in a train are tested in a roller rig test platform to explore the effect

of MRF damping on train stability.

19

3.2 Mathematical model and calculation of train’s critical speeds

Many other typical train mathematical models have been presented in existing

literatures [112]. Wang [37] established a 17-DOF train model to study the effect of

the semi-active suspension on train’s stability. Liu [113] proposed four different train

dynamic models with 17-DOF, 19-DOF, 31-DOF, and 35-DOF, respectively, in his

PhD thesis. Considering all of the DOFs for characterizing train dynamics is not

really necessary, it just makes the calculation process more complicated. For this

reason, many researchers put forward a train component dynamic model with less

DOF. For example, Scheffel proposes an 8-DOF train wheelset model [114]. The

main disadvantage of these component models is that they cannot reflect the dynamic

performance of the whole train. Considering the both accuracy and modelling

complex, a 15-DOF train dynamic model is adopted in this section. The damping

ratio of each DOF, as well as the train critical speed, is worked out based on the train

dynamic equations.

3.2.1 Analytical model of train

As shown in Figure 3.1, the dynamic model established in this paper is a typical train

containing the front truck frame and the rear truck frame. The structure of the train

model is the same as the commercialised train tested in section 3.7. Each truck frame

built in this paper contains the primary suspension and the secondary suspension.

Primary suspension connects wheelset and bogie frame. Secondary suspension is the

connecting component of bogie frame and car body. The nomenclature used in

developing the 15 DOF passenger vehicle model are defined in Table 3.1 and the key

parameter values are given in Table 3.2. These values are from the commercialised

train tested in section 3.7. The details of the 15 DOFs are illustrated in Table 3.3. The

dynamic equations of motion for the wheelsets, truck frames, and car body are as

follows:

20

Figure 3.1 Analytical model of a train

Car body dynamics

The following equations are the car body dynamics characterized by the lateral (𝑦c),

yaw (𝜓c), and roll (𝜃c) motions.

c c sy c sy t2 sy t1 sy t1 sy t2 sy c sy 4 c 4 sy c2 2 2 2 m y C y C y K y C y K y K y C h h K (3.1)

2

cz c sy t1 sy t2 sy b sy c sy b t1 sy b t2 sy b t1 sy b t2(2 2 ) I K K K l K C l y C l y K l y K l y

2

sy b c2 C l (3.2)

2 2 2 2

cx c sz 4 sy 4 c sz 3 sy 4 c sy 4 t1 sy 4 t2 4 sy t1(4 2 ) (4 2 ) I C b C h K b K h C h y C h y h K y

sy 4 c 4 sy t2 4 sy c2 2 C h y h K y h K y (3.3)

Truck dynamics

The governing equations of the truck dynamics of trains can be characterized by the

lateral (𝑦t𝑖) and yaw (𝜓t𝑖) motions, in which the subscript i=1, 2 (1 is the leading

truck and 2 is the trailing truck). The equations for the leading truck are as follows:

t t1 pd py sy t1 py 1 py 2 sy c sy c py sy t1 sy b c(2 2 ) (2 ) m y K K K y C y C y C y K y C C y K l

pd py 1 pd py 2 sy 4 c sy b c 4 sy c sy b c( ) ( ) K K y K K y C h C l h K K l (3.4)

21

2

tz t1 py 1 py 2 py t1 sy c px 1 pd py sy t12 2 8 (4 8 8 ) I C y C y C K K b K K K

2 2

pd py 1 pd py 2 1 px 1 1 px 2(2 2 ) (2 2 ) 2 2 K K y K K y b K b K (3.5)

The equations for the trailing truck are as follows:

t t2 pd py sy t2 py 3 py 4 sy c sy c py sy t2(2 2 ) (2 ) m y K K K y C y C y C y K y C C y

pd py 3 pd py 4 sy 4 c sy b c 4 sy c sy b c( ) ( ) K K y K K y C h C l h K K l (3.6)

2

tz t2 py 3 py 4 py t2 sy c px 1 pd py sy t22 2 8 (4 8 8 ) I C y C y C K K b K K K

2 2

pd py 3 pd py 4 1 px 3 1 px 4(2 2 ) (2 2 ) 4 K K y K K y b K b K (3.7)

Wheelset dynamics

The train includes four pairs of wheelsets. Two of them are installed in the leading

truck while the other two are installed in the trailing truck. The lateral motions (yωi,

i=1-4) and yaw ( ψωi , i=1-4) motions are used to characterize the wheelsets

dynamics. The governing equations for the lateral motions (yωi, i=1-4) are given by:

1 1 py 22 1 c 22 pd py 1 py t1 py t1 pd py t1[ (2 ) / ] ( 2 ) 2 (2 2 ) m y C f v y K f K K y C y C K K

pd py t1( ) K K y (3.8)

2 2 py 22 2 py t1 py t1 c 22 pd py 2 pd py t1[ (2 ) / ] 2 ( 2 ) (2 2 ) m y C f v y C y C K f K K y K K

pd py t1( ) K K y (3.9)

3 3 py 22 3 pd py t2 c 22 pd py 3 py t2 py t2[ (2 ) / ] ( ) ( 2 ) 2 m y C f v y K K y K f K K y C y C

pd py t2(2 2 ) K K (3.10)

4 4 py 22 4 pd py t2 py t2 py t2 c 22 pd py 4[ (2 ) / ] ( ) 2 ( 2 ) m y C f v y K K y C y C K f K K y

pd py t2(2 2 ) K K (3.11)

The governing equations for the yaw motions (ψωi, i=1-4) are given by:

2 2 2

z 1 1 px 1 1 px t1 11 o 1 11 o 12 2 [(2 ) / ] [(2 ) / ] I b K b K f l v f a r y (3.12)

2 2 2


2 2 2


2 2 2


22

3.2.2 Calculation of the critical speed of a train

Based on the above equations, the governing equation can be written as

[ ]{ } [ ]{ } [ ]{ } { } M q C q K q 0 (3.16)

where

T

c c c 1 1 2 2 3 3 4 4 t1 t1 t2 t2{ } [ ] y y y y y y yq

is the generalized coordinates vector.

Defining the state vector as:

{𝑦} = {𝑞�̇�} (3.17)

Then the above governing equation can be written as:

{ } [ ]{ }y yA (3.18)

where

[A] = [[A1] [A2][A3] [0]

] (3.19)

which is known as the dynamic matrix. Where

1

1[ ] [[ ] [ ]]A M C

1

2[ ] [[ ] [ ]]A M K

3[ ] [ ]A I

23

Table 3.1 Nomenclature of train dynamic model symbol

Symbol Definition

mω Mass of wheelset

Iωx Roll moment of inertia of wheelset

Iωy Pitch moment of inertia of wheelset

Iωz Yaw moment of inertia of wheelset

r0 Centred wheel rolling radius

mt Mass of truck

Itx Roll moment of inertia of truck

Ity Pitch moment of inertia of truck

Itz Yaw moment of inertia of truck

mc Mass of car body

Icx Roll moment of inertia of car body

Icy Pitch moment of inertia of car body

Icz Yaw moment of inertia of car body

kpx Primary longitudinal stiffness

kpy Primary lateral stiffness

kpz Primary vertical stiffness

cpy Primary lateral damping

cpz Primary vertical damping

ksy Secondary lateral stiffness

ksz Secondary vertical stiffness

csy Secondary lateral damping

csz Secondary vertical damping

hts Vertical distance from truck frame centre

of gravity to secondary suspension

hcs Vertical distance from car body centre of

gravity to secondary suspension

htp Vertical distance from truck frame centre

of gravity to primary suspension

hwp Vertical distance from primary suspension

to truck frame centre of gravity

l Half of truck centre pin spacing

b Half of wheelbase

a Half of wheelset contact distance

dp Half of primary spring lateral distance

ds Half of secondary suspension spacing

v The travelling speed of the vehicle train

f11 Lateral creep coefficient

f22 Spin creep coefficient

lc Total length of car body

lb Half distance of two truck centre

h4 Vertical distance from car body centre of

gravity to secondary springs

kc Contact stiffness

δ Effective wheel conicity

24

Table 3.2 The value of the key initial parameter

Parameter Value Parameter Value

mw 2080 kg Icy 1500800 kg•m2

Iwx 749 kg•m2 Icz 1200500 kg•m

2

Iwy 125 kg•m2 kpx 780000 N/m

Iwz 1026 kg•m2 kpy 960000 N/m

r0 0.43m kpz 1046000 N/m

mt 2560 kg cpy 17000 N•s/m

Itx 2084 kg•m2 cpz 15000 N•s/m

Ity 1405 kg•m2 ksy 178400 N/m

Itz 2496 kg•m2 ksz 193000 N/m

mc 32500 kg csy 56400 n•s/m

Icx 90500 kg•m2 csz 37000 n•s/m

dp 1m lc 21m

ro 0.43 h4 0.25

Table 3.3 Motions of the 15-degree-of-freedom train model

Component Motion

Lateral Roll Yaw

Front truck leading wheelset yω1 -- ψω1

Front truck trailing wheelset yω2 -- ψω2

Rear truck leading wheelset yω3 -- ψω3

Rear truck trailing wheelset yω4 -- ψω4

Front truck frame yt1 -- ψt1

Rear truck frame yt2 -- ψt2

Carboy yc θc ψc

The mass matrix [M], damping matrix [C], and stiffness matrix [K] can be obtained.

Then the eigenvalue of the dynamic matrix, λ, is calculated using MATLAB.

2 1,2 j j j ji ( 1, 1 ) i j n (3.20)

where n denotes the number of degree-of-freedom

αj and βj are the real and imaginary part of the eigenvalue of system

dynamic matrix, respectively.

25

The damping ratio can be expressed as follows:

2 2/ j j j j (3.21)

Following the above equations, the damping ratios of the 15 DOFs can be worked

out. As the train speed is included in the train dynamic matrix, any variation in the

speed of the train induces a change in the damping ratio. Thus, as the train speed

increases, the damping ratios may reduce and cross the zero line. The train speed at

the point where the damping ratio crosses the zero line is the critical speed.

Consequentially, the critical speeds of each DOF can be worked out.

3.2.3 Theoretical analysis of the effect of an MR damper on train critical speed

The motion of the vehicle with MR dampers is given by:

[ ]{ ( )} [ ( )]{ ( )} [ ( )]{ ( )} [ ( , , )] [ ] x t v x t v x t A x xM C K F 0 (3.22)

where {x(t)} is the general displacement column, [M], [C], and [K] are the mass,

damping, and stiffness matrices, respectively. They are speed dependent and can be

derived by multi-body dynamics analysis. F(A, x, �̈�) is the introduced force by MR

damper which is related to current and displacement.

If the vehicle system has a passive damper, the eigenvalue equation is derived as:

2

p[ ] [[ ( )] [ ]] [ ( )] [ ] v vM C C K 0 (3.23)

where [Cp] is the damping of the passive damper. From Eq. (2.22), the eigenvalue of

the vehicle/structure system is speed dependent. At certain speeds, the real part of the

eigenvalue may become positive, which induces the vehicle/structure instability. This

speed is called the critical speed. When the train becomes unstable, the amplitude of

the motion grows exponentially in time and theoretically achieves infinity in a linear

system. The intrinsic instability of the vehicle/structure system is independent of the

type of excitation. Therefore, once the whole system has been designed, a passive

damper cannot improve the stability property in the system because the eigenvalue is

determined when the parameters of the system are fixed. Similarly, if the vehicle

system has an MR damper, the eigenvalue equation becomes:

2

MR MR[ ] [[ ( )] [ ]] [[ ( )] [ ]] [ ] v vM C C K K 0 (3.24)

where [CMR] and [KMR] are the variable damping and variable stiffness induced by

MR dampers, respectively, and these two parameters definitely have impacts on the

critical speed. With a properly designed MR damper and a suitable control algorithm,

26

the critical speed is able to be further improved and the vibration of railway vehicles

close to the critical speed can be well controlled by an MR damper.

3.3 The effect of train speed on the damping ratio of each train DOF

The dynamic matrix of a train model contains the train’s speed in addition to the

suspension parameters. Thus, as the velocity of a train increases, the damping ratio of

the train varies. The damping ratio of each DOF determines this DOF’s critical

speed. In order to investigate the different influence of each DOF on critical speeds,

the damping ratios of the train’s 15 DOFs with different train speeds are calculated.

The damping ratio of the front truck wheelsets, rear truck wheelsets, truck frames,

and car body with respect to train speed are shown from Figure 3.2 to Figure 3.5

respectively.

Figure 3.2 Damping ratios of the front truck wheelsets

The influence of train speed on the damping ratios of the front truck wheelsets is

presented in Figure 3.2. The figure shows that the damping ratios of the lateral and

yaw motions of the trailing wheelsets of the front truck performs similarly under

different train speeds. Specifically, their damping ratios increase slightly until

reaches the peak at 0.47 and 0.48, respectively, then decrease continually but do not

cross the zero line. The figure also indicates that the damping ratio of the lateral and

yaw motion of the leading wheelsets is not sensitive to the train speed because an

40 60 80 100 120 140 1600.32

0.34

0.36

0.38

0.4

0.42

0.44

0.46

0.48

0.5

Train Speed(m/s)

Dam

pin

g R

atio

Front truck leading w heelset lateral+yaw

Front truck leading wheelset lateral

Front truck leading wheelset y aw

Front truck trailing wheelset lateral

Front truck trailing wheelset y aw

27

increase in train speed from 40m/s to 160m/s only decreases the damping ratio of the

leading wheelset by 3%.

Figure 3.3 Damping ratios of the rear truck wheelsets

Figure 3.3 shows the influence of train speed on the damping ratios of the rear truck

wheelsets. The figure indicates that the damping ratio of the leading wheelset of rear

truck reduces significantly and crosses the zero line at 133m /s, which is the critical

speed of the rear truck leading wheelset. The damping ratio of the trailing wheelset

of rear truck is basically unchanged at first but decreases sharply when train’s speed

is over 100m/s, and then crosses the zero line at 110m /s which is the critical speed

of the leading wheelset of rear truck.

40 60 80 100 120 140 160-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Train Speed(m/s)

Da

mp

ing

Ra

to

Rear truck leading w heelse lateral+yaw

Rear truck leading wheelset lateral

Rear truck leading wheelset y aw

Rear truck trailing wheelset lateral

Rear truck trailing wheelset y aw

28

Figure 3.4 Damping ratios of truck frames

The effect of speed variations on the damping ratios of truck frames is illustrated in

Figure 3.4. The damping ratio of the front truck frame is inversely proportional to the

train speed and does not cross the zero line. The damping ratio of the rear truck

frame declines until the train speed reaches 100m /s, then the damping ratio increases

dramatically and levels off at 0.5.

Figure 3.5 Damping ratios of car body response modes

40 60 80 100 120 140 1600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Train Speed(m/s)

Dam

pin

g R

atio

Front truck frame lateral+yaw

Front truck f rame lateral

Front truck f rame y aw

Rear truck f rame lateral

Rear truck f rame y aw

40 60 80 100 120 140 1600.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Train Speed(m/s)

Dam

pin

g R

atio

Carbody lateral

Carbody y aw

Carbody roll

29

As shown in Figure 3.5, the damping ratio of the car body is basically not influenced

by the train speed. The damping ratio always remains above the zero line means the

car body is stable even though the train reaches a high level of speed. Based on the

above figures, the damping ratios of each DOF respect to different train speed vary

from each other. From the damping ratio analysis, the rear truck wheelset and rear

truck frame are more unstable than other components of the train.

3.4 The influence of suspension parameters on critical speeds of each train

DOF

When the damping ratio reduces and crosses the zero line, the train reaches its

critical speed. The change of suspension parameters induces a variation of the

crossing point which determines each DOF’s critical speed. Therefore, the critical

speed of a train is directly related to the suspension parameters and it is crucial to

study the effect of suspension parameters on the critical speeds of each train DOF.

As the train speed increases, some certain train DOFs become unstable, which means

that those unstable DOFs have achieved their critical speed. Once any one of the 15

DOFs reaches its critical speed, the whole train is regarded as to have reached its

critical speed. Thus the critical speed of the whole train is determined by the smallest

one of the 15 critical speeds. Critical speeds which exceed 200m/s are out of

discussion in this paper because the current operating speed is much lower than

200m/s. The following figures show the effect of the train suspension parameters on

the critical speeds of several train DOFs. For the sake of simplicity in describing the

following figures, C with different subscripts represents the critical speeds of

different train DOFs. Specifically, C with two subscript letters represents the critical

speeds of the truck frame. The first letter, ‘f ’or ‘r’, is used to represent the front and

rear truck frames, respectively. The secondary letter, ‘l’ or ‘y’, represents the lateral

motion and the yaw motion. C with three subscript letters represents the critical

speeds of the wheelsets. The first letter, ‘f’ or ‘r’, is used to identify the front truck

frame and the rear truck frame, respectively. The secondary letter (‘t’ or ‘l’) is used

to identify the trailing and leading wheelsets. The third letter (‘l’ or ‘y’) identifies the

lateral and yaw motions. The different meanings of each symbol are also shown in

Table 3.4.

30

As plotted in Figure 3.6, the effect of the primary lateral damping on the critical

speeds of each train DOF is demonstrated. The increase in primary lateral damping

continually improves the Cfl and Cfy but reduces Crtl and Crty slightly. Crll and Crly had

the same trend of declining first and bottoming out at 120m/s then showing an

upward trend.

Table 3.4 Nomenclature of critical speeds of each DOF

Symbol Definition

Cfl Critical speed of front truck frame lateral

motion

Cfy Critical speed of front truck frame yaw

motion

Crl Critical speed of rear truck frame lateral

motion

Cry Critical speed of rear truck frame yaw

motion

Crll Critical speed of rear truck leading

wheelset lateral motion

Crly Critical speed of rear truck leading

wheelset yaw motion

Crtl Critical speed of rear truck trailing

wheelset lateral motion

Crty Critical speed of rear truck trailing

wheelset yaw motion

Cfty Critical speed of front truck trailing

wheelset yaw motion

Figure 3.6 Critical speed versus primary lateral damping

104

105

106

107

80

100

120

140

160

180

Primary lateral damping(Ns/m)

Critical speed (

m/s

)

Front truck frame lateral+ yaw







200

31

The effect of the primary lateral damping on the critical speed of the whole train is

the same as it is on Crtl. This is because the value of Crtl is the minimum at each point

and thus it indicates the critical speed of the whole train. In other words, the whole

train’s critical speed is dominated by the lateral motion of the trailing wheelset of the

rear truck when the primary lateral damping is changed. Based on the curve, this

increase in the primary lateral damping reduces the critical speed by 8.3%.

Figure 3.7 Critical speed versus secondary lateral damping

Figure 3.7 shows the effect of the secondary lateral damping on the critical speeds of

each train DOF. As the secondary lateral damping increases, Crl and Cry show a basic

upward trend, whereas Cfty, Cfy, and Crll reduce constantly. Cfl, Crly, Crtl, and Crty

share the same trend of declining before 8×104Ns /m then increasing after that point

as the secondary lateral damping keeps increasing. Based on the figure, with the

variation of the secondary lateral damping, the whole train critical speed is restricted

by the lateral and yaw motions of the rear truck frame before 5×104N s /m. Then the

yaw motion of the rear truck trailing wheelset and yaw motion of the front truck

frame dominate the whole train’s critical speed in turn. The critical speed of the

103

104

105

20

40

60

80

100

120

140

160

180

Secondary lateral damping(N*s/m)

Critical speed (

m/s

)

Front truck trailing wheelset yaw

Front truck frame lateral

Front truck frame yaw


Rear truck leading wheelset yaw


Rear truck trailing wheelset yaw

Rear truck frame lateral

Rear truck frame yaw

railway vehicle

200

32

whole railway vehicle climbs to 130m/s and finally levels off as the secondary lateral

damping increases.

Figure 3.8 Critical speed versus primary lateral stiffness

Figure 3.8 indicates the effect of the primary lateral stiffness on the critical speeds of

each train DOF. The variation of the primary lateral stiffness from 1000N/m to

1×107N/m increases Crtl, Crll, Crty, and Crly by 43%, 43%, 50%, and 49%,

respectively, whereas Crl and Cry show a downward trend, Cfl and Cfy reduce before

7×105N/m and then rise to 200m/s after that.

As shown in Figure 3.8 the whole train critical speed is limited by the lateral motion

of the trailing wheelset of the rear truck and the rear truck frame when the primary

lateral stiffness is changed. The critical speed of the train increases to 110m/s before

it shows a downward trend as the primary lateral stiffness increases.

103

104

105

106

107

20

40

60

80

100

120

140

160

180

Primary lateral stiffness(N/m)

Critical speed (

m/s

)

Front truck frame lateral+ yaw







Rear truck f rame lateral

Rear truck f rame y aw

railway v ehicle

33

Figure 3.9 Critical speed versus secondary lateral stiffness

As shown in Figure 3.9, Crly and Cfy decrease at first and then show an upward trend,

but Cry and Crl remain basically the same. The increase in the secondary lateral

stiffness reduces Crll and Crl but enhances Crtl and Crty.

Based on the analysis of the figure, the lateral and yaw motions of the rear truck

frame confine the whole train’s critical speed. This figure also shows that the critical

speed of a train is inversely proportional to its secondary lateral stiffness. This

increase in the secondary lateral stiffness from 1000N/m to 1×107N/m reduces the

critical speed by 4%.

The above four figures provide the effect of a suspension parameter on the critical

speeds of each train DOF, which offers a guideline to the design of the suspension

system. The change trends of the critical speed with respect to different suspension

parameters vary from each other. These four figures also show that the critical speed

of the whole train is dominated by the critical speeds of the rear truck frame and the

wheelsets of rear truck. Thus, the conclusion that the critical speeds of the rear truck

frame and the wheelsets of rear truck restrict the whole train critical speed can be

drawn. As a result, more attention should be paid to the rear truck frame and the

wheelsets of rear truck when we intend to improve the train critical speed.

103

104

105

106

107

50

100

150

200

Secondary lateral stiffness(N/m)

Critical speed (

m/s

)

Rear truck trailing wheelset lateral + yaw

Front truck frame lateral

Front truck frame yaw


Rear truck leading wheelset yaw


Rear truck trailing wheelset yaw

Rear truck frame lateral

Rear truck frame yaw

railway vehicle

34

3.5 The sensitivity analysis of the critical speed of a train

The effect of suspension parameters on the critical speeds of each train DOF was

plotted in the former section where the influence of various suspension parameters on

the whole train critical speed was discussed. In this section, the sensitivity of the

whole train critical speed with respect to the suspension parameters is calculated to

investigate which parameter impacts the train critical speed most.

The sensitivity analysis, focusing on the relationship between the parameters and the

system response, has been adopted in many research areas [115, 116]. Based on the

sensitivity analysis, the designer can carry out a systematic trade-off analysis [115].

Jang and Han devised a way to conduct dynamic sensitivity analysis for studying

state sensitive information with respect to changes in the design variables [117]. Park

applied sensitivity analysis into the pantograph dynamic analysis for a rail vehicle

[118]. Similarly, the sensitivity analysis for the effect of bogie stiffness and damping

on the critical speeds will make a big contribution to enhance train critical speed. It

can predict which stiffness and damper will affect the critical speed more and which

range of the bogie parameter will have a severe impact on the critical speed. In

summary, the results of the sensitivity analysis can guide the design of bogie

parameters. The sensitivity analysis of bogie stiffness and damping on the critical

speeds, however, is very rare in the existing research to the best of the author’s

knowledge. Based on this motivation, the sensitivity of the train critical speed with

respect to the suspension parameters is calculated in this section. The calculation

method of the sensitivity of the 𝑖th suspension parameter 𝑥𝑖 is given as,

w

w

/

i

i

C xS

C x (3.25)

where S is the sensitivity of the critical speed, 𝛥𝐶w is the variation of train critical

speed induced by the change of suspension parameters, 𝐶w is the changed critical

speed, 𝛥𝑥𝑖 is the variation of the ith suspension parameter, and 𝑥𝑖 is the changed ith

suspension parameter.

The relationship between the critical speed and the lateral and vertical damping is

shown in Figure 3.10. It is seen from this figure that the train critical speed is

insensitive to the variation of the primary and secondary vertical damping.

This increase in the primary lateral damping results in a reduction of the train critical

speed. Compared to the above three curves, the critical speed is more sensitive to the

35

secondary lateral damping. As the secondary lateral damping increases, the train

critical speed jumps to 136m/s and then declines gently to 112m/s.

Figure 3.11 presents the calculated results of the train critical speed with respect to

the lateral and longitudinal stiffness. As shown in Figure 3.11, the train critical speed

is less sensitive to the primary and secondary lateral stiffness compared to the

primary longitudinal stiffness. Similarly, the train speed is not sensitive to any

variation of the primary longitudinal stiffness from 1000N/m to 2×105N/m, but when

the primary longitudinal increases from 2×105N/m to 2×10

6N/m, the train critical

speed is improved by 300%.

Figure 3.12 indicates the sensitivity of the critical speed with respect to the vertical

and lateral damping. It is observed that the train critical speed is affected by the

secondary lateral damping (Csy), secondary vertical damping (Csz), primary lateral

damping (Cpy), and primary vertical damping (Cpz), but Csz, Cpy, and Cpz are not as

sensitive as Csy. The figure also shows that the sensitivity ascends and peaks at 0.45,

which is around 8×105Nm/s, and then it shows a downward trend and reduces to 0,

around 5×107

Nm/s, as the Csy increases.

Figure 3.13 shows the sensitivity of the critical speed with respect to the secondary

lateral stiffness (Ksy), the primary lateral stiffness (Kpy), and the primary longitudinal

stiffness (Kpx). But the sensitivity of critical speeds corresponding to Ksy and Kpy

remains at a lower level compared with that corresponding to Kpx. This is explained

that as Kpx increases, the sensitivity remains unchanged at first, and then jumps to

1.05 around 1×106N/m and descends to 0 when the stiffness increases to 1×10

7N/m.

The average sensitivity of different bogie stiffness and damping parameters is

illustrated in Figure 3.14 where Kpx and Csy are the two parameters that affect the

train critical speed most. Here the influence of Ksy, Kpy, and Cpy on train critical

speed is reduced in turn and Cpz and Csz have almost no effect on the critical speed.

36

Figure 3.10 Train critical speed versus various bogie damping

Figure 3.11 Train critical speed versus various bogie stiffness

103

104

105

106

107

50

60

70

80

90

100

110

120

130

140

damping(N*m/s)

Critical speed(m

/s)

critical speed v ersus primary lateral damping

critical speed v ersus primary v ertical damping

critical speed v ersus secondary lateral damping

critical speed v ersus secondary v ertical damping

103

104

105

106

107

20

40

60

80

100

120

140

160

180

200

Stiffness(N/m)

Critical speed(m

/s)

critical speed v ersus primary lateral stif f ness

critical speed v ersus secondary lateral stif f ness

critical speed v ersus primary longitudinal stif f ness

37

Figure 3.12 Sensitivity of train critical speed versus various bogie damping

Figure 3.13 Sensitivity of train critical speed versus various bogie stiffness

103

104

105

106

107

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

damping(N*m/s)

Sensitiv

ity

critical speed versus primary lateral damping

critical speed versus primary vertical damping

critical speed versus secondary lateral damping

critical speed versus secondary vertical damping

103

104

105

106

107

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Stiffness(N/m)

Sensitiv

ity

critical speed v ersus primary lateral stif f ness

critical speed v ersus secondary lateral stif f ness

critical speed v ersus primary longitudinal stif f ness

38

Figure 3.14 The average sensitivity of train critical speed with respect to different

bogie stiffness and damping parameters

It can be seen from the above figures that the secondary lateral damping and the

primary longitudinal stiffness are the two most sensitive parameters impacting the

critical speed compared to the other bogie parameters of the train. Thus, more

attention should be paid to these two parameters when we aim to increase the train

critical speed. It can also be concluded that the most sensitive range of the secondary

lateral damping is from 1×104

Ns/m to 5×105 Ns/m while the most sensitive range of

the primary longitudinal stiffness is from 1×105 N/m to 3×10

6N/m.

3.6 The simulation of a train with an MR damper

Based on the above analysis, the secondary lateral damping influences train’s critical

speed most, and as a result, the secondary damper is replaced by an MR damper in

this simulation as an attempt to increase the critical speed. In this paragraph, a train

model imbedded with four MR dampers is established by ADMAS software and the

control strategy is built in MATLAB/SIMULINK. In this way, the simulation of a

train with MR dampers can be realized and a random irregular track is applied to

investigate how the MR dampers contribute to improving the train critical speed.

0.00

0.05

0.10

0.15

0.20

KpxKsyKpyCszCsyCpz

Sen

sitiv

ity

Cpy

39

3.6.1 Modelling of a train

In order to establish the dynamic model of the train, software called ADAMS/RAIL

is used in this research because it contains detailed models of the suspension

components such as the wheelset, bogie frame, train body, and so on.

The model established in this paper is a two-axle railway vehicle containing a front

truck and a rear truck frame, as shown in Figure 3.15. The truck frames, as shown in

Figure 3.16, built in this paper contain the primary suspension and the secondary

suspension. The primary suspension consists of four primary vertical dampers and

four primary vertical springs while the secondary suspension consists of two

secondary vertical dampers, two secondary vertical springs, and two secondary

lateral dampers.

Figure 3.15 Dynamic model of a train

Figure 3.16 Dynamic model of suspension of train

40

3.6.2 Modelling of MR damper

Different kinds of models have been used to describe the behaviour of MR dampers,

such as the Bingham model, the Bouc-Wen model, the viscoelastic-plastic model,

and so on. The dynamic phenomenological model adopted in this paper to describe

the dynamic performance of the MR damper is based on the model built by Yang

[119]. This model is based on the Bouce-Wen model, including the MR fluid stiction

phenomenon and the shear thinning effects illustrated in Figure 3.17. The damper

force 𝐹𝑂 is determined by following equations:

1

o o o o o| || | | | n nz x z z x z A x (3.26)

o o o o o o o o o( ) oF f z k x c x x m x (3.27)

2 o( | |)

o o 1( )

pa x

c x a e (3.28)

The damping force is determined by Eq. (3.27), and the functional parameter αo is

governed by the input current. ko, fo, and 𝑐𝑜(�̇�𝑜) are the accumulator, friction force,

and post-yield plastic damping coefficient, respectively. mo is adopted to emulate the

MR fluid stiction and inertia effect, and Eq. (3.26) represents the Bouce-Wen model.

The evolutionary variable z is determined by γ, βo, Ao, and n. The force-displacement

and force-velocity relationship of the MR damper used in this simulation is shown in

Figure 3.18.

Figure 3.17 MR damper model

41

a

b

Figure 3.18 Force-displacement (a) and force-velocity (b) relationship of MR damper

42

3.6.3 The control strategy

The main purpose of the controller is to determine the desired damping force in order

to enhance the train critical speed. The control strategy adopted in this article is

skyhook-groundhook hybrid control. Details of the skyhook-goundhook control

strategy are as follows:

F𝑠𝑘𝑦 = {−α𝑐max(�̇�2 − �̇�1) �̇�2(�̇�2 − �̇�1) ≥ 0

−α𝑐min(�̇�2 − �̇�1) �̇�2(�̇�2 − �̇�1) < 0 (3.29)

F𝑔𝑛𝑑 = {−(1 − α)𝑐max(�̇�2 − �̇�1) �̇�1(�̇�2 − �̇�1) ≥ 0

−(1 − α)𝑐min(�̇�2 − �̇�1) �̇�1(�̇�2 − �̇�1) < 0 (3.30)

F = F𝑠𝑘𝑦 + F𝑔𝑛𝑑 (3.31)

where F𝑠𝑘𝑦 is the force generated by the skyhook control strategy. F𝑔𝑛𝑑 ithe force

generated by the groundhook strategy. α is the scalar denoting the force proportion

generated by skyhook control. The 𝑐max and 𝑐min are the maximum and minimum

damping coefficients that the damper can provide. �̇�1 𝑎𝑛𝑑 �̇�2 are the absolute lateral

velocities of the bogie frame and the car body, respectively. The parameter α is set to

be 0.2.

3.6.4 Assembly of semi-active train and simulation

The dynamic model of the train is established in ADAMS, while the MR damper

model and control strategy are built in MATLAB. The composition of the semi-

active train model is shown in Figure 3.19.

Figure 3.19 Composition of semi-active train model

43

3.6.5 Simulation and results

The combination of ADAMS and Matlab is adopted in this simulation where the

train with the MR damper will be simulated on a random irregular track. Three

different suspension systems are simulated in this section. They are semi-active,

passive-on, and passive-off. The definitions of the three suspension systems are as

follows: semi-active: suspension system with controlled MR dampers mounted on

the secondary suspension system; passive-on: suspension system with uncontrolled

MR dampers (constant applied current 1 A by providing relatively high damping)

mounted on the secondary suspension system; passive-off: suspension system with

uncontrolled MR dampers (constant applied current 0 A by providing relatively low

damping) mounted on the secondary suspension system. The simulation results of the

train installed with passive-on damper, passive-off damper, and semi-active damper

are shown in Figure 3.20, Figure 3.21, and Figure 3.22 respectively.

Lateral displacement of the wheelset was measured to characterize the train critical

speed. According to the Yongqiang liu’s work [120], the displacement of the

wheelset will remain at a low level before the train reaches its critical speed and

jump to a high level after the train reaches the critical speed. The gap between the

rail and the flange of the wheelset usually is approximate 6mm. If the lateral

displacement of the wheelset exceeds 6mm, the flange of the wheelset keeps hitting

the rail, which indicates the train is not unstable.

Figure 3.20 The displacement of wheelset vs the speed of the train with a passive-off

damper

44

Figure 3.21The displacement of wheelset vs the speed of the train with a passive-on

damper

Figure 3.22 The displacement of the wheelset vs the speed of a train with an semi-

acitve MR damper

Figure 3.20 shows the displacement of the wheelset of a train with a passive-off

secondary lateral damper. The figure indicates that the displacement remains at a low

level before the train speed reaches 76.4 m/s and then it suddenly jumps to a high

level, more than 6mm, denoting that 76.4 m/h is the critical speed of the train. Figure

3.21 demonstrates that the critical speed of the train mounted with passive-on MR

damper is 88.6 m/h. Similarly, Figure 3.22 indicates that the critical speed of train

with a semi-active MR damper is 91.1 m/s. From Figure 3.20 and Figure 3.21, it can

45

be found out that the increase of the damping coefficient of secondary dampers leads

to the increase of train critical speed. Also, the three Figures demonstrate that the

critical speed of the train with a controllable MR damper is higher than the train with

passive-on or passive-off damper.

In this section a train with an MR damper is established by ADMAS and MATLAB.

The Bouce-Wen model is adopted to model the MR damper and the skyhook-

groundhook hybrid control strategy is used to control the damping force. The

simulation result illustrates that the MR damper improves the train critical speed.

3.7 The experimental research on the effect of the MR damper on the stability

of a train

The simulation of the train with an MR damper demonstrates that the MR damper

can enhance the train critical speed. In this section, the secondary dampers of a train

are replaced by the MR dampers and then the train is tested in a roller rig test

platform to verify the simulation result and investigate the effect of MR damper on

train critical speed.

3.7.1 Experimental facilities

The railway vehicle Harmony is used to do the experimental research in this part. It

is installed onto the roller rig experimental platform, as shown in Figure 3.23, and it

contains the front and rear truck frames. Each truck frame built in this paper

incorporates the primary and secondary suspensions. The roller rig which is available

in the State Key Laboratory for railway is used as an experimental platform to test

the train installed with MR dampers. The roller rig can be viewed as a track

simulator which simulates an endless track by using rollers. It can test a train

operating at different speeds without field tests. The roller rig has six rollers which

can move in vertical and lateral directions independently under servo control. Of

these six rollers, four have the ability of gauge variation between 1000 and 1676 mm

and two rollers can run at different rotational speeds which allow the roller rig to

simulate six types of irregularities, including cross level, gauge, curve, and so on.

The MR dampers are installed between the bogie and the car body, as shown in

Figure 3.24. A current driver, MR damper controller, and accelerometers are also

included to run the experiment.

46

3.7.2 Setup of experiment system

The train whose passive secondary dampers are replaced by MR dampers is tested on

the roller rig experimental platform. The MR dampers are installed between the car

body and the bogie, as shown in Figure 3.24. The irregularity of the railway vehicle

mounted on the roller rig is excited by the vertical and lateral motion under servo

control. The accelerometers are attached to the bogie to measure the transverse

acceleration and characterize the vibration and critical speed of the train. The output

terminals of the accelerometers are connected with a charge amplifier. The data

measured by accelerometers are amplified by the charge amplifier and then

transferred to the computer. The MR damper controller is connected with the current

driver. The desired current signal generated by the damper controller is delivered to

the current drivers. The output terminal of the current drivers is connected with the

MR dampers such that, based on the current signal generated by the damper

controller, the current drivers can adjust the input current to control the magnetic flux

density of the MR damper. With this variation of the magnetic field, the damping

force is changed.

Figure 3.23 Railway vehicle

47

Figure 3.24 Installation of MR dampers

3.7.3 Results of experiment

In this test，control current is changed from 0 to 1.5A to realize the damping

variation of MR damper. The train runs at 350 km/h, 320 km/h, 240 km/h, and 200

km/h, respectively, to investigate the influence of the MR damper on the vibration

reduction at different train speeds. The result of the test is shown in Figure 3.25. It is

noticed that the acceleration of the bogie changes slightly from 10m/s2 to 11 m/s

2

when the train runs at 200km/h, 240km/h, and 320 km/h, indicating that the train

keeps stable. However, when the train with passive off MR damper runs at 350 km/h,

the bogie acceleration reaches a high level of 13.25 m/s2. In this case the train loses

its stability and reaches its critical speed. However, the bogie acceleration decreases

continuously when the suspension damping increases by enhancing the current of the

MR damper.

Based on above analysis, the train reaches its critical speed of 350km/s when the

current of MR damper varies from 0 to 0.6A. As the current increases to 0.8A, the

transverse acceleration of bogie will drop to 10.1 m/s2, which means the train would

be stable running at 350km/s and its critical speed will be higher than 350km/s. Upon

on the comprehensive analysis, it is naturally concluded that the MR damper

possesses the priority to improve the train’s stability and enhance train critical speed

compared to the passive dampers.

48

Figure 3.25 RMS of lateral acceleration of the bogie

3.8 Conclusion

In this chapter the governing equations of a 15 DOF train were developed. The

damping ratio of each train DOF and the critical speed of trains were calculated

based on the train dynamics equations. The results reveal that the train critical speed

is mainly dominated by the truck frame and the rear truck wheelsets. The sensitivity

of the critical speed with respect to the suspension parameters is calculated to analyse

the different effect of bogie parameters on the train critical speed. The results

indicate that the secondary lateral damping and the primary longitudinal stiffness are

the two most sensitive parameters impacting the critical speed. Then a train whose

secondary dampers are replaced by MR dampers was simulated by a combined

simulation of ADAMS and MATLAB. The simulation results indicate that the MR

damper significantly improve the train critical speed. The results of the experiment

also verify the semi-active dampers’ ability to improve the train’s stability and

critical speed.

49

4 INVESTIGATION OF THE MRE RUBBER JOINT FOR TRAIN

4.1 Introduction

Operating at high speed stably so as to improve the transportation efficiency is

always a critical issue for train. On the other hand, improving the curve line

trafficability when the train ran on curved track is of importance to achieve low

maintenance cost for both vehicles and tracks. Consequently, compatibility between

dynamic stability allowing train operating at high speed safely and good curve track

trafficability maintaining low maintenance is urgently required by modern railway

vehicles. The stability and the curve track performance of train, however, require

conflictive parameter design. The stability of the train running at high speed requires

hard wheelset positioning stiffness to resist the hunting motion of the wheelsets

while realization of good curve passing performance needs the train have soft

wheelset positioning stiffness. This leads to conflict requirement between stability

design and curve passing performance when design the wheelset positioning stiffness

of conventional train suspension. This conflict brings many difficulties when the

rubber joint are to be designed. A new method to overcome the conflict requirement

of high speed stability and curve trafficability is urgent to be found.

In this chapter, a MRE joint for train with variable stiffness property was designed

and tested to overcome this conflict. The proposed MRE joint mainly contains of two

sets of electromagnetic coil, MRE materials, and three iron flanks. To characterize

the proposed MRE joint, a MTS machine was used to test the field-dependent

property, the amplitude-dependent performance, and the frequency-dependent

response. After the characterization, the MRE joint was then applied on a train model

by simulation method using ADMS. In the simulation, different curve tracks and

different train speed were simulated to evaluate the effectiveness of the MRE joint on

reducing the angle of attack, lateral displacement, and lateral force. Additionally, the

critical speeds of the train model were tested and compared when the MRE joint was

working softened and stiffened, respectively. The simulation results demonstrated

that the MRE rubber joint can offer soft and hard wheelset positioning stiffness under

different requirements. Specifically, it can be softened for the train running on the

curve tracks so as to protect the wheelsets and track from wear and improve the

trafficability, and it can become stiffened when the train runs on the straight tracks so

that the critical speed and stability of the train can be improved.

50

4.2 The design and working mechanism of the MRE joint

Figure 4.1 shows the design diagram of the proposed MRE joint. It is mainly

composed of an electromagnetic coil, an iron flank, a cylinder, and a cylindrical

shaft. Two sets of electromagnetic coil and three steel flanks are assembled in

interlayer along the steel shaft. A MRE sheet is then used to cover the whole surface

of the flanks. The structure with MRE is finally housed by the steel cylinder. When

the electromagnetic coil is powered, a magnetic circuit is formed and the present of

the steel flanks can improve the conductivity of the whole structure. The detailed size

of the joint is shown in Table 4.1. For the purpose of easy installation to the testing

equipment (MTS), the assembled MRE joint is fixed to the testing attachment.

Figure 4.1 The structure of the MRE rubber joint

Table 4.1 value of the main size

Parameter Value Parameter Value

D1 52mm L2 10mm

D2 55mm L3 40mm

D3 63mm L4 100mm

L1 20mm

The MRE rubber joint is mounted in the rotational arm connecting the truck frame

and wheelset. It provides the primary longitudinal stiffness for the train. The

proposed MRE joint is supposed to change its stiffness depending on the variations

51

of the applied current. The MRE rubber joint is supposed to satisfy complicated

requirements, such as different rail conditions (curve track and straight track),

different train speeds, and different turning diameters. Specifically, when the train

runs on a curved line, as shown in Figure. 4.2, the wheelsets tend to rotate relatively

with the truck frame in order to keep parallel with the rail. In this case, soft

longitudinal stiffness is needed because hard longitudinal stiffness prevents the

relative motion between the wheelset and truck frame. On the other hand, hunting

motion or yaw motion of the wheelsets always exists and can even cause the train

unstable or derail, especially when the train runs at a high speed. In order to control

the hunting motion and keep the train stable, hard longitudinal stiffness is needed to

restrict the yaw motion of the wheelset. In summary, the proposed MRE rubber joint

should be adjusted to be softened for the turning train and stiffened for the high

speed running train.

(a)

52

(b)

Figure 4.2 The working mechanism of the MRE rubber joint: (a) Train runs on curve

line with soft longitudinal stiffness (b) Train runs on straight line with hard

longitudinal stiffness

4.3 Prototype

4.3.1 Fabrication and characterise of MRE

Fabrication of MREs

The MRE samples with iron particles mass fraction 70% were fabricated. Silicon

MRE (SELLEYS PTY.LIMITED, Australia) and silicon oil were chosen as matrix

and the dispersed particles were iron particles which has a diameter of 4.5-5.2 um

(SIGMA Company, USA). The mass fraction ratio of iron, silicon oil and silicone

MRE in the mixture was 7:1.5:1.5. First to put the iron particles in a container and

then pour silicon oil into it, mix them with silicone MRE and stir them until all the

materials were mixed thoroughly. Then put the mixture into a vacuum case to

remove the air bubbles inside it. Lastly, the mixture was poured into a mould. After

24 hours curing under room temperature, MRE sample are fabricated.

Characterization of MRE

A parallel-plate rheometer (Physica MCR 301, the Anton Paar Company, Germany)

was used to measure the MREs’ shear working mode properties. The

Magnetorheolgical Device is equipped with an electromagnetic kit which can

53

generate a magnetic field perpendicular to the direction of the shear flow.

Specifically, a 20mm diameter parallel-plate measuring system with 1 mm gap was

used. The samples were sandwiched between a rotary disk and a base placed in

parallel. The stress and strain signals are measured by the rheometer system.

The size of the MRE sample was about Ф20 mm×1.15 mm. The MRE sample was

tested under a sinusoidal rotary excitation with swept strain amplitude and frequency

of 5 Hz. The MRE modulus under magnetic field strength of 0mT, 110mT, 220mT,

330mT, 440mT, and 1100mT was obtained, respectively. The magnetic field strength

was adjusted through tuning the current. The storage modulus and loss modulus of

the prepared MRE with respect to different magnetic flux densities are shown in

Figure 4.3.

4.3.2 Assembly of MRE joint

After all the metal parts were machined, the two coils were wrapped around the

intervals between the three flanks first. Then the MRE sheet will be glued onto the

three flanks. At last, the assembling process can be finished after assembling the

cylinder to the rubber joint. The prototyped MRE rubber joint is shown in figure 4.4.

1 10 10010

3

104

105

106

Sto

rag

e m

od

ulu

s (

Pa

)

Strain (%)

Storage Modulus (0mT)






(a)

54

1 10 10010

3

104

105

106

Lo

ss m

od

ulu

s (

Pa

)

Strain (%)

Loss Modulus (0mT)

Loss Modulus (110mT)





(b)

Figure 4.3 The storage modulus and loss modulus of MRE under different magnetic

flux densities: (a) Storage modulus; (b) Loss modulus

Figure 4.4 The prototype of the MRE rubber joint

55

4.4 Dynamic testing of the MRE rubber joint

4.4.1 Testing

This MRE joint was tested by using a hydraulically driven MTS machine to obtain

its mechanical properties. As shown in Figure 4.5, the MTS machine has upper and

lower heads with grippers that can hold the device in place. The lower head is fixed

to the bottom base, while the upper head is excited by the hydraulic cylinder. A load

cell is mounted below the lower head to measure the force generated by the MRE

rubber joint. Then a predefined sinusoidal routine was programmed into the control

software in order to maintain consistency in the testing.

This experimental testing investigated the magnetic field-dependent properties, the

amplitude-dependent responses, and the performances under different frequencies, of

the proposed MRE joint. For the field-dependent responses under different currents

(0A, 1A, and 2A), the testing frequency was 1Hz and the amplitude was 0.2mm. The

force signal generated by the MRE joint was measured through the load cell and then

transferred to the computer for recording. The excitation signal under current of 0A

and frequency of 1Hz is used to evaluate the amplitude-dependent responses. In

terms of the frequency-dependent performances, the frequency was 1Hz, 1.5Hz, and

2Hz, respectively, with amplitude of 0.2mm. The following sub-section gives

detailed analysis and discussion according to the testing results.

Figure 4.5 Test of the MRE rubber joint

4.4.2 Testing results and discussion

Following the testing procedure designed in the above subsection, the testing results

under different current, different amplitude and different frequency were obtained. In

general, the increase of current leads to the increase of the stiffness while the effect

of the frequency on the performance of MRE joint is light. In terms of the amplitude,

56

the nonlinearity of the MRE joint becomes more obvious when the amplitude

increases. The details are presented in the following sections.

Different current

Figures 4.6 show the field-dependent performances of the MRE joint with different

current levels. It is seen that the slope of the force-displacement loop increase

obviously when the current was increased. Therefore, the increased current induced

an increment on the effective stiffness of the MRE joint. Figures 4.7 shows the

relationship between the effective stiffness and the current. The effective stiffness

increased from 0.87 MN/m to 1.52 MN/m with a relative change of 74.7% with the

current changed from 0A to 2A.

-0.2 -0.1 0.0 0.1 0.2

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Fo

rce

(kN

)

Displacement (mm)

0.2mm-1Hz-0A

0.2mm-1Hz-1A

0.2mm-1Hz-2A

Figure 4.6 The response of the MRE rubber joint to different magnetic field

0.0 0.5 1.0 1.5 2.00.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Stiffn

ess (

MN

/m)

Current (A)

Figure 4.7 The stiffness variation under different currents

57

Different amplitudes

Figure 4.8 presents the influence on the joint properties of changing the loading

amplitudes. When changing the amplitudes, the current and the frequency remain

unchanged as 0A and 1Hz. The effects of changing the amplitudes are clearly

observed. On one hand, it is observed from Figure 4.8 that the maximum force gains

a large increase with the increasing amplitude. A closer observation on the hysteresis

loops reveals that the effective stiffness of the MRE joint, represented by the slope of

force-displacement loop, decreases slightly with ascending loading amplitudes. On

the other hand, it is noted that the nonlinear relationship between force and

displacement appears much more obvious when the amplitude is large, as shown in

Figure 4.8.

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Fo

rce

(kN

)

Displacement (mm)

0.2mm-1Hz-0A

0.4mm-1Hz-0A

0.6mm-1Hz-0A

Figure 4.8 The response of the MRE rubber joint to different amplitudes

Different frequency

The effects of changing frequencies on performance of the MRE joint are shown in

Figure 4.9. It is noticed that frequencies have a slight influence on the maximum

force and effective stiffness. The increase of the frequency leads to the increase of

the maximum force and effective stiffness of MRE rubber joint slightly.

58

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Fo

rce

(kN

)

Displacement (mm)

1Hz

1.5Hz

2Hz

Figure 4.9 The response of the MRE rubber joint to different frequencies

4.5 Simulation evaluation of the MRE joint on a train

4.5.1 Test the trafficability of the train on a curve track

Figure 4.10 The angle of the attack

To further verify the effectiveness of MRE joint on enhancing train’s dynamic

performance, a train model equipped with the variable stiffness MRE joint is built

with ADMS software. The parameter values of the train model are the same as the

values given in Table 3.2. Some important indexes for evaluating the joint, such as

59

the angle of attack, the lateral displacement, the lateral force, and the critical speed,

can be obtained with the train model. The angle of the attack is illustrated in Figure

4.10. The lateral force working on wheelsets means the friction force between

wheelsets and rail in lateral direction while the lateral displacement means the

relative displacement between the wheelset and rail in lateral direction. Basically, the

train’s speed is low when it runs on a curve track and high when it operates on a

straight line. Based on this regularity, the MRE joint can be controlled according to

the operating speed of the train.

0 5 10 15 20

-0.05

0.00

0.05

0.10

0.15

0.20

An

gle

of a

tta

ck (

de

gre

e)

Time (s)

soft

hard

Figure 4.11 The angle of attack on curve track with 600m radius

For the steering tests, two cases with different radius curve tracks and different train

speed were considered, as shown in Table 4.2. The radius of the curve track and the

train speed chosen for the first case were 600m and 150km/h, respectively. Likewise,

the radius of the curve line and the train speed for the second case were 3000m and

250km/h, respectively. Figures 11-13 present the testing results for the first case and

Figures 14-16 show the second case.

Table 4.2. The steering test cases

Cases Train speed Curve line radius

1 150km/h 600m

2 250km/h 3000m

60

The angle of attack, the lateral displacement, and the lateral force are the most

important indexes indicating the curve track trafficability. Smaller angel of attack

will help improve the trafficability and reduce the wear of both the train and rail.

Figure 4.11shows the angle of attack of the train when the MRE joint was soft and

hard, respectively. Generally, it is seen that the angle of attack under soft MRE

rubber joint is smaller than that under the hard MRE rubber joint, especially after the

train started turning at around the 8th

second. This means that the softened MRE

helps reduce the angle of attack. Similar to the angle of attack, smaller lateral

displacement and smaller lateral force can prevent the hit and wear between the train

and the rail so as to increase the trafficability and help prolong their lifespan. Figure

4.12 and Figure 4.13 present the lateral displacement and lateral force of a turning

train. Similarly, the MRE joint worked in softened mode and stiffened mode,

respectively. As expected, the instant values of the lateral displacement and the

lateral force under the soft MRE rubber joint are smaller than under the hard joint.

0 5 10 15 20-2.0x10

-3

-1.0x10-3

0.0

1.0x10-3

2.0x10-3

3.0x10-3

4.0x10-3

5.0x10-3

6.0x10-3

7.0x10-3

La

tera

l d

isp

lace

me

nt (m

)

Time (s)

soft

hard

Figure 4.12 The lateral displacement of the wheelset on curve track with 600m radius

Similar findings can be observed from Figure 4.14, Figure 4.15 and Figure 4.16 that

those three parameters are all smaller under the soft MRE rubber joint than under the

hard joint. Therefore, it is reasonably concluded that the utilization of the softened

MRE helps improve the trafficability, specifically, reduce the lateral force and angle

61

of attack. The above testing results for the two cases further demonstrate that this

proposed variable stiffness MRE rubber joint is suitable for the train turning on a

large radius or a relative small one with a fast speed or a relative slow one.

0 5 10 15 20-1x10

4

0

1x104

2x104

3x104

4x104

La

tera

l fo

rce

(N

)

Time (s)

hard

soft

Figure 4.13 The lateral force of the wheelset on curve track with 600m radius

0 5 10 15 20 25 30

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

An

gle

of a

tta

ck (

de

gre

e)

Time (s)

soft

hard

Figure 4.14 The angle of attack on curve track with 3000m radius

62

0 5 10 15 20 25 30-2.0x10

-3

-1.5x10-3

-1.0x10-3

-5.0x10-4

0.0

5.0x10-4

1.0x10-3

1.5x10-3

2.0x10-3

2.5x10-3

3.0x10-3

La

tera

l d

isp

lace

me

nt (m

)

Time (s)

soft

hard

Figure 4.15 The lateral displacement of the wheelset on curve track with 3000m

radius

0 5 10 15 20 25 30-1.0x10

4

-5.0x103

0.0

5.0x103

1.0x104

1.5x104

2.0x104

La

tera

l fo

rce

(N

)

Time (s)

soft

hard

Figure 4.16 The lateral force of the wheelset on curve track with 3000m radius

63

4.5.2 The stability evaluation of the train with MRE rubber joint

The above mentioned three important indexes (angle of attack, lateral displacement,

and lateral force) indicate the behaviours of train running on curve track. In this

subsection the critical speed indicating the stability of a running train on a straight

track will be investigated. The larger the critical speed, the running train tends to be

more stable. The effect of the longitudinal stiffness on the train’s critical speed can

be calculated by the dynamic model of the train presented in section 3.2. Based on

the model calculation results shown in Figure 3.11, the increase of the longitudinal

stiffness from 0.87 MN/m to 1.52 MN/m leads the critical speed of train increase

from 97m/s to 170m/s. This means when the effective stiffness of the joint stiffens

increases, the critical speed increases. The train will be more stable utilizing the hard

MRE rubber joint when running on a straight track. Combining the findings of this

subsection and the above subsection, it can be concluded that the controlled MRE

joint can offer both high speed stability and good curve track trafficability for train

while the passive soft and passive hard rubber joint only can satisfy one of them.

4.6 Conclusion

This chapter presented a variable stiffness MRE joint and its application on a train.

The mechanical property testing using a MTS machine has verified that this

proposed MRE rubber joint is capable of changing its effective stiffness when the

applied current was changed. In order to evaluate its effectiveness on train, a series

of simulation work using ADAMS was conducted. The simulated responses of the

angle of attack, the lateral displacement, and the lateral force were provided and the

analysis results indicate that the trafficability is improved and the wear can be

reduced when using the soft MRE rubber joint. The calculation results on the straight

track demonstrate that the train reaches a larger critical speed under the hard MRE

joint, which means the train is more stable with hard longitudinal stiffness. To

conclude, the proposed variable stiffness MRE joint is to be controlled hard when the

train is running straightly at high speed to keep the train stable and to be controlled

soft when the train is turning on a curve track to obtain good trafficability. Therefore,

MRE joint can provide the train both good curve track trafficability and high speed

stability.

64

5 COMPACT VARIABLE STIFFNESS AND DAMPING DAMPER FOR

VEHICLE SUSPENSION SYSTEM

5.1 Introduction

Speaking of the solutions to addressing the undesired vibrations, stiffness and

damping are fundamental yet important mechanical features to be controlled for

many technical systems to achieve a desired dynamic behavior. The variation of

damping will induce a change on the resonance magnitude through adjusting the

dissipated vibration energy, and the variable stiffness will change the vibration

transmissibility by changing the natural frequencies of the controlled system. Besides

pure damping or stiffness controllable system mentioned above, system capable of

changing both stiffness and damping is another advanced semi-active vibration

control method and performs better than pure damping controllable or pure stiffness

controllable system. Many studies have been carried out with the concept of dual

controllability of stiffness and damping. Although the better performance of the

variable stiffness and damping system on vibration control has been verified,

compact devices capable of varying both their stiffness and damping for practical

applications have rarely been developed.

Based on the above motivation and further enhance the vibration reduction

performance of the train, an innovative compact variable damping and stiffness

damper was fabricated and analysed in this chapter. The variable stiffness and

damping damper contains inside and outside damping cylinders which are the main

characteristics. The advanced damper is compact and can be easily installed into the

scaled train without any change to the original configuration. The performance of

train with variable stiffness and damping damper was evaluated numerically.

5.2 Variable stiffness and damping damper

5.2.1 Design and working principle of the advanced MR damper

Figure 5.1 shows the structure design and the prototype of the proposed advanced

MR damper. The advanced MR damper mainly consists of two coaxial damping

cylinders and two springs with different stiffness. The damping cylinders are

composed of an internal damping cylinder, which connects the top connector and

bottom connecter, and an outer damping cylinder, which links the two springs. The

internal damping cylinder is composed of a piston rod, electromagnetic coils, seals

65

and a reserve filled with MRF. The electromagnetic coils extend generally coaxially

around the piston. The solid lines in Figure 5.1 illustrate the magnetic circuit

generated by the coils in the internal damping cylinder. The damping force of the

internal cylinder is controlled by the applied magnetic field on the basis of MRF

properties. The outer damping cylinder consists of an electromagnetic coil, seals,

reserve, and in particular, it has the internal damping cylinder as its piston rod. The

electromagnetic coils of the outer damping cylinder are wrapped in a special

designed supporting structure at the outer house of the internal damping cylinder.

The magnetic circuits are shown by the dash lines in Figure 5.1. The two damping

cylinders may have relative sliding motions under the external excitations.

Figure 5.1 Design and photograph of the advanced MR damper

Figure 5.2 Scheme of Connection Mode

66

The working principles of the variable stiffness and damping MR damper can be

demonstrated by Figure 5.2 where different connection modes of this device are

shown. In terms of the stiffness variable mechanism, there are different working

modes. When the current applied to the outer damping cylinder (I2) is small enough

(mode1), the outer damping force will allow the relative motion between the two

damping cylinders. In this case, the advanced MR damper is working in connection

mode 1 where spring k1 and spring k2 work in series because both of the springs

deform when the outer cylinder slides along the internal cylinder. For this working

mode, the overall stiffness of the damper is soft. For the second working mode with

middle damping damper 𝑐2, the deformation of spring 𝑘1 is restricted to some extend

and as a result the spring 𝑘2 deforms more under external force compared with

working mode 1. This means the overall stiffness of the damper is harder than the

first scenario. For the last scenario (mode 3), when the outer damping force is large

enough to prevent the relative motion between the two damping cylinders, the

advanced MR damper is working in connection mode 3. In this case, the deformation

of spring 𝑘1 is totally blocked by damper 𝑐2 and only spring 𝑘2 has a deformation in

response to the external force and in this case the overall stiffness of the damper is

hardest. The determination of connection mode is controlled by the magnitude of the

outer damping force which is determined by the amount of the input current I2. The

stiffness variability, therefore, is realized by the switch between the connection

modes.

The damping variability is realized by adjusting the current applied to the internal

damping cylinder. As shown in the Figure 5.2, no matter which connection mode the

advanced MR damper is, the overall equivalent damping is represented by the

internal damping C1. C1 increases as the current (I1) applied to the internal damping

cylinder increases. In summary, the effective stiffness of the proposed advanced MR

damper is controlled by current I2 and the equivalent damping is controlled

independently by current I1.

5.2.2 Prototype of the advanced MR damper

Prototype

The first step in the assembly of the advanced MR damper was to prepare two sets of

electromagnetic coils for two damping cylinders, respectively. MRF (MRF-132DG,

67

LORD Corporation) was then poured into the reserve of the internal damping

cylinder after the piston rod was inserted into the internal cylinder. The piston rod

will seal the MRF inside a closed reserve. Then a small spring serving as the

accumulator with approximately 200N pre-load was mounted between the piston rod

and the bottom connector in order to provide enough pre-pressure on the MRF inside

the internal damper. As follow up, spring k1 was then mounted connecting the bottom

connector and the external damping cylinder. MRF was then poured into the reserve

and sealed between these two cylinders. In the last step, spring k2 connecting the

external cylinder and the top connector was assembled. Table 5.1 shows the details

of the two springs and the actual advanced MR damper prototype is shown in Figure

5.1.

Table 5.1 The parameters of the two springs

Parameter Spring 1 Spring 2

Stiffness 7420N/m 24583N/m

Free Length 11cm 15cm

Inside Diameter 48cm 50cm

Outside Diameter 60cm 68cm

5.2.3 Test and result discussion

The properties of stiffness variability and damping variability were first tested

separately. The excitation signal chosen was a sinusoidal wave with a single

frequency of 0.1 Hz and amplitude of 10 mm. To obtain the performance in terms of

the variable stiffness of the device, the current applied to the outer damping cylinder

was varied from 0A to 1.5A with a step of 0.5A whilst the current applied to the

internal damping cylinder was set as 0A. On the other hand, the current applied to the

internal damping cylinder was set to 0A, 1A, and 2A, respectively, with the external

current maintained as a constant to demonstrate the performance of variable

damping. In addition to studying the field-dependent properties, the effectiveness of

changing loading frequency on the device performance is also investigated. In this

test, the loading frequency was changed from 0.1Hz to 0.5Hz, then to 2Hz with a

step of 0.5Hz and the internal and external currents were set as a constant value.

Stiffness Variability Testing

68

Figure 5.3 shows a series of stable force-displacement loops under the condition of

I1=0A and I2=0A, 0.5A, and 1A, respectively. For each case, two cycles were

provided to show the accessible repeatability and uniformity of the device

performance. The experimental results in Figure 5.3 clearly show that the output

force is a piecewise function of the input displacement in a clockwise direction. In

order to give a clear explanation of how the force-displacement loop progresses, the

response under the condition of I1=0A and I2=0.5A was taken as an example. It is

seen that letters are placed clock wisely as indicators of each inflection. For the

reason that there exists an initial damping force from the internal damping cylinder

although no current applied to it, an external force large enough to overcome the

internal damping force so as to allow the relative motion between the piston rod and

the internal cylinder is requested, which explains segment AB where the

displacement is nearly unchanged even though the absolute force continues to grow.

The same rule applies to the external damper, which means that the relative motion

between the internal and the external damping cylinders will happen only if the

pressure from spring k2 is large enough to overcome the external damping force. As

the external force increases to overcome the internal damping force, the piston rod

begins to move into the internal cylinder and spring k2 begins to be compressed,

generating an elastic force applied to the external damping cylinder. During this

process, only spring k2 works and spring k1 remains undeformed because there is no

movement between these two cylinders. This means that the effective stiffness of this

process can be represented by the stiffness k2, which is indicated by segment BC in

Figure 5.3. The elastic force increases as spring k2 is more compressed until it is

large enough to overcome the external damping force, which is indicated by the

critical inflection C. After inflection C, the external cylinder begins to slide along the

internal cylinder, which means that k1 is also compressed. In this stage, k1 and k2 can

be considered as working in series, therefore, the effective stiffness of this stage can

be represented by 𝑘1𝑘2 (𝑘1 + 𝑘2)⁄ . This process is described by segment CD. We

can see that the slope of segment CD is much smaller than that of segment BC.

69

-20 -15 -10 -5 0-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

Fo

rce

(K

N)

Displacement (mm)

I1=0A, I

2=0A

I1=0A, I

2=0.5A

I1=0A, I

2=1A

A

B

C

D

E

F

Figure 5.3 Force displacement relationship under I1=0A

This process is reversed when the piston rod moves out of the internal damping

cylinder. As shown by segment DE, when the piston rod intends to move in a

different direction, the internal damping force prohibits its movement. That is why in

segment DE the absolute force decreases but the displacement remained unchanged.

In segment EF, the compressed spring k2 begins to restore as the piston rod starts to

move out of the internal cylinder. In this case, only spring k2 is working and the

effective stiffness of the device is presented by the stiffness k2. As spring k2 restores,

the elastic force generated by spring k2 becomes smaller. When it reaches the critical

point at which the elastic force of spring k2 plus the external damping force is not

strong enough to resist the elastic force generated by spring k1, the external damper

begins to slide along the internal damper in the opposite direction and spring k1

begins to restore as well. At this point, the springs work in series again and this

process is described by segment FA.

The results observed from the figure matches well with the above analysis because

segments AB, BC and CD are parallel to segments DE, EF and FA, respectively.

This means that the force-displacement relationship of this device consists of

symmetrical loops. Accordingly, the overall effective stiffness of the MR damper can

be represented by the slope of the solid line which encloses segments BC and CD, as

shown in Figure 5.4.

70

From an overall respect in terms of these three testing cases in Figure 5.3, segment

BC is longer and segment CD is shorter than those corresponding segments in the

loop under I1=0A and I2=0A. This means that the critical absolute displacement

where the segment BC (only spring k2 is working) is changed to segment CD (spring

k1 and spring k2 are working in series) increases. It is because a larger external

damping force is generated when a larger external current (I2=0.5A) is applied,

which means that spring k2 must be compressed much more in order to produce an

much bigger elastic force to overcome the external damping force. The force-

displacement response under I1=0A and I2=1A is shown as a parallelogram. This is

because the external damping force under I2=1A is large enough to overcome the

elastic force generated by spring k2 and spring k1 remains undeformed during this

whole test. Despite of the difference, it can still be seen that the corresponding

segments in the different curves are parallel. It is worth noting that the overall

effective stiffness increases as the current (I2) applied to the external damping

cylinder increases. The effective stiffness versus current I2 is shown in Figure 5.4,

which illustrates that the increase of I2 from 0A to 1A enhances the stiffness from

8.7kN/m to 24.5kN/m.

0.0 0.2 0.4 0.6 0.8 1.08

10

12

14

16

18

20

22

24

26

Effe

ctive

stiffn

ess (

KN

/m)

Current (A)

Figure 5.4 Effective stiffness as a function of the current applied to the external

damper

71

Damping Variability Testing

Figure 5.5 shows the variable damping characteristic of the advanced MR damper

under different currents of I1 =0A, 1A, and 2A, respectively. It is seen that the

enclosed area of the force-displacement loops increases with the increase of

current 𝐼1. This means that the increasing I1 leads to the increase in the equivalent

damping of the advanced MR damper, which can be evidenced by Figure 5.6 where

the equivalent damping coefficient is shown. The equivalent damping coefficient

𝐶eand energy consumption shown in Figure 5.6 is calculated by equation (5.1) and

(5.2) reported in [121].

The equivalent damping coefficient:

𝐶e = 𝐸d/(π𝜔𝑋02) (5.1)

where 𝑋0 is the displacement amplitude, 𝜔 is the excitation frequency, The energy

dissipated by advanced MR damper in one cycle, 𝐸d , is represented by the area

enclosed within the hysteresis loop, which is given as:

𝐸d = ∮ 𝐹d𝑥 = ∫ 𝐹�̇�d𝑡2π/𝜔

0 (5.2)

where F is the force generated by the advanced MR damper, x is the piston

displacement. It can be clearly seen from Figure 5.6 that the increase in current I1

from 0A to 1A leads to the equivalent damping coefficient being increased from

16.24 KN/(m/s) to 29.72 KN/(m/s). As the thermodynamic analysis is important to

develop damper [122], Figure 5.6 also shows the energy consumption as a function

of the current during the test. It is seen that the consumed energy grows as the current

(I1) increases. However, the MRF used herein is the commercialized product from

LORD Corporation. It is stable even under different temperature. Thus the effect of

temperature on the dynamic performance of the new advanced MR damper is light.

72

-20 -15 -10 -5 0-0.5

-0.4

-0.3

-0.2

-0.1

0.0

Fo

rce (

kN

)

Displacement (mm)

I1=0A, I

2=0.25A

I1=1A, I

2=0.25A

I1=2A, I

2=0.25A

Figure 5.5 Variable damping performance under various currents

Frequency dependent response

This part gives an analysis of the effectiveness of changing the loading frequency on

the damper performance, as shown in Figure 5.7. In this test, the loading frequency

was chosen as 0.1Hz, 0.5Hz, 1Hz, 1.5Hz, and 2Hz, respectively. It is seen that the

force generated by the advanced MR damper increases slightly though the loading

frequency increases, and that the effective stiffness and equivalent damping are

almost independent of the loading frequency. The loop shape, however, tends to be

more smooth as the frequency grows.

73

0.0 0.5 1.0 1.5 2.0

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Energy consumption

Effective stiffness

Current (A)

En

erg

y c

on

su

mp

tio

n (

J)

16

18

20

22

24

26

28

30

Eff

ective

stiff

ne

ss (

KN

/(m

/s))

Figure 5.6 Equivalent damping and energy consumption as a function of the applied

current to the internal damper

-20 -15 -10 -5 0-0.5

-0.4

-0.3

-0.2

-0.1

0.0

Fo

rce

(kN

)

Displacement (mm)

0.1 HZ

0.5HZ

1HZ

1.5HZ

2HZ

Figure 5.7 Force-displacement loops under different frequency

5.2.4 Modelling and parameter identification

Modelling

74

Figure 5.8 Phenomenological model for the advanced MR damper

Figure 5.8 illustrates a schematic model for the advanced MR damper which

incorporates two Bingham components to represent the two cylinders, respectively.

In this model, a coulomb friction element 𝑓1 in parallel with a viscous dashpot 𝑐1 is

used to characterize the internal damping cylinder. Similarly, the paralleled structure

of the coulomb friction element 𝑓2 with the viscous dashpot 𝑐2 models the external

damping cylinder. The outer damping cylinder is parallel with spring 𝑘1 and then in a

series with spring 𝑘2 . In this model, the working principle of the advanced MR

damper can be summarised as follows. When the damping of the outer damping

cylinder is small, the two springs 𝑘1, 𝑘2 can be considered as working in series. Thus

the total stiffness of the system is 𝑘eff = 𝑘1𝑘2/(𝑘1 + 𝑘2). Otherwise, the effective

stiffness of the advanced MR damper can be represented by only spring 𝑘2 .

Therefore, the stiffness of the proposed advanced MR damper can be varied between

the minimum value of 𝑘1𝑘2/(𝑘1 + 𝑘2) and the maximum stiffness of spring 𝑘2. For

the damping variation case, the damping of the advanced MR damper can be

controlled by varying the current applied to the internal cylinder. In this model, 𝑥2 is

the relevant displacement between the top connecter and the bottom connector. x1 is

the relative displacement between the top connecter and the outer housing of the

external MR damper. The equations for the model can be written as:

𝐹 = 𝑐1�̇�2 + 𝑓1 + 𝑘2𝑥1 (5.3)

75

where F is the force generated by the advanced MR damper; the relationship between

𝐹 and 𝑥2 is needed to describe the advanced MR damper. 𝑥2 is determined by:

𝑖𝑓: 𝑓2 ≥ 𝑘2𝑥1

𝑥2 = 𝑥1 (5.4)

𝑖𝑓: 𝑓2 + 𝑐2(�̇�2−�̇�1) < 𝑘2𝑥1

𝑓2 + 𝑐2(�̇�1−�̇�2) + 𝑘2𝑥1 + 𝑘1(𝑥1 − 𝑥2) = 0 (5.5)

The inputs of the new advanced MR damper are current 𝐼1 and 𝐼2. To give explicit

function relationships between the field-dependent parameters (f1, f2, C1, and C2) and

the applied currents, four polynomials are given and these functions are assumed as

third-order polynomial.

𝑓1 = 𝑓1a𝐼23 + 𝑓1b𝐼2

2 + 𝑓1c𝐼2 + 𝑓1d (5.6)

𝑓2 = 𝑓2a𝐼13 + 𝑓2b𝐼1

2 + 𝑓2c𝐼1 + 𝑓2d (5.7)

𝐶1 = 𝐶1a𝐼23 + 𝐶1b𝐼2

2+ 𝐶1c𝐼2 + 𝐶1d (5.8)

𝐶2 = 𝐶2a𝐼13 + 𝐶2b𝐼1

2 + 𝐶2c𝐼1 + 𝐶2d (5.9)

Parameter identification

In this section, both the theoretical and the experimental results are used to verify the

effectiveness of the proposed model on predicting the behaviour of the advanced MR

damper. Above all, the parameters in the model must be first identified according to

the experimental data. For this reason, this section proposed an enhanced

identification method, called the ‘intergeneration projection genetic algorithm (IP-

GA) [123], which is more accurate and faster than traditional GA.

IP-GA was proposed based on μGA. It not only takes advantage of the μGA avoiding

premature convergence but also has a faster global convergence speed than

traditional GA. A heuristic operation operator, intergeneration projection (IP)

operator, is also employed to further improve the performance of the GAs. The IP

operator is obtained by the following method. 𝑃𝑗𝑏 and 𝑃𝑗−1

𝑏 represent the best

individuals in the parent and the grandparent generations, respectively. Then three

different IP operators, new1, new2, new3 can be obtained by the following method:

𝑛𝑒𝑤1 = 𝑝𝑗𝑏 + 𝛼(𝑝𝑗

𝑏 − 𝑝𝑗−1𝑏 )

𝑛𝑒𝑤2 = 𝑝𝑗−1𝑏 + 𝛽(𝑝𝑗

𝑏 − 𝑝𝑗−1𝑏 ) (5.10)

𝑛𝑒𝑤3 = 𝑝𝑗𝑏 + 𝛾(𝑝𝑗

𝑏 − 𝑝𝑗−1𝑏 )

76

where α, β, γ are control parameters and 0 < 𝛼 < 1, 0 < 𝛽 < 1, 0 < 𝛾 < 1. Then

the fitnesses of new1, new2, and new3 are calculated. If the fittest individual

performs better than the worst individual in the current generation, the worst

individual will be replaced by the best performing individual among new1, new2,

and new3.

Figure 5.9 presents a flow chart describing the process of parameter identification.

First, the displacement data was collected. Then the data series was incorporated into

the mathematical model expressed by Equation (5.4) to (5.5). Based on the proposed

model, the simulated force can be calculated. In order to minimise the error between

the simulated force and the measured force, the objective function was defined as the

mean square error, which is presented below.

error(C) = √1

𝑛∑ (𝑢𝑗

𝑚 − 𝑢𝑗𝑐𝑛

𝑗=1 )2 (5.11)

where ujm and uj

c are the measured and calculated forces generated by the advanced

MR damper at the jth sampling point. Control parameters of IP-GA, α, β, γ, were set

as 0.2, 0.6, 0.2 during the GA phase. Thus, it can be concluded that the best

individual chromosome can be obtained when the objective function reaches the

lowest value.

Identification results

Figure 5.9 The flow chart of parameter identification using IP-GA

The identified parameters by using IP-GA for the variable stiffness and variable

damping cases are shown in Table 5.2. The input data for identifying these

parameters was obtained by driving the advanced MR damper using a sinusoidal

wave with a single frequency of 0.1Hz and amplitude of 12mm. It can be seen that

77

only equation 5.6 is a third order polynomial while the rest three functions are second

order polynomials because their third-order coefficient is 0. Figure 5.10 shows the

fitting results between the predicted responses and the measured responses. It can be

seen that the proposed model captures the damping variability property very well

(Figure 5.10 (a)) and predicts the performance of variable stiffness favourably

(Figure 5.10 (b)).

In order to further verify the capability of the proposed model to predict the

performance of the advanced MR damper, different data set is used to evaluate the

effectiveness of the identified parameters. As shown in Figure 5.11, the testing

condition of advanced MR damper is similar with Figure 5.11 except the testing

amplitude. Thus, the identified parameter in Table 5.2 should be able to describe the

new testing result. It can be seen from Figure 5.11 that the predicted responses match

well with the measured data, which means the parameters identified by other data set

can also precisely describe the new testing result. All of the fitting results indicate

that the proposed model is appropriate for the description of the dynamic

performance of the advanced MR damper.

Table 5.2 The identified parameters

Parameters 𝑓1𝑎 𝑓1𝑏 𝑓1𝑐 𝑓1𝑑

value 26.74 -129.85 223.28 71

Parameters 𝑓2𝑎 𝑓2𝑏 𝑓2𝑐 𝑓2𝑑

value 0 506.03 81.4 62.95

Parameters 𝐶1𝑎 𝐶1𝑏 𝐶1𝑐 𝐶1𝑑

value 0 -0.269 3.436 1

Parameters 𝐶2𝑎 𝐶2𝑏 𝐶2𝑐 𝐶2𝑑

value 0 -5.8 15.3 2.675

78

-25 -20 -15 -10 -5 0

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

Experiment (I1=0A, I2=0.25A)



Model (I1=0A, I2=0.25A)

Model (I1=1A, I2=0.25A)

Model (I1=2A, I2=0.25A)

Fo

rce (

kN

)

Displacement (mm)

a

-25 -20 -15 -10 -5 0-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

Experiment (I1=0A, I2=0A)



Model (I1=0A, I2=0A)

Model (I1=0A, I2=0.5A)


Fo

rce/k

N

Displacement/mm

b


(a) Variable damping property (b) Variable stiffness property

79

-20 -15 -10 -5 0

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

Fo

rce

(kN

)

Displacement (mm)

Experiment ( I1=0A, I

2=0.25A)


2=0.25A)


2=0.25A)

Model ( I1=0A, I

2=0.25A)

Model ( I1=1A, I

2=0.25A)

Model ( I1=2A, I

2=0.25A)

a

-20 -15 -10 -5 0-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

Fo

rce (

KN

)

Displacement (mm)





Model (I1=0A, I2=0.5A)


b


(a) Variable damping property (b) Variable stiffness property

80

In summary, an innovative variable stiffness and damping damper is developed and

analysed. The test results verified its capability to change both stiffness and damping.

The proposed model also can predict the dynamic performance of the device.

5.3 Simulation of railway vehicle with variable stiffness and damping damper

In order to verify the effectiveness of the advanced damper on vibration control, a

train mounted with the damper is evaluated in this section. As the developed variable

stiffness and damping damper presented in the above section is a scaled damper for

the train, the force generated by the advanced damper is amplified by 5 times in the

simulation conducted in this section. The variable stiffness and damping suspension

including a control system is presented in Figure 5.12. ADAMS/RAIL is used to

establish the dynamic model of the train. The model established in this study is a

two-axle railway vehicle containing a front truck and a rear truck frame. The primary

suspension consists of four primary vertical dampers and four primary vertical

springs while the secondary suspension consists of four secondary vertical dampers,

four secondary vertical springs, and four secondary lateral dampers. Four secondary

lateral dampers are replaced by the variable stiffness and damping MR dampers.

Accelerometers are mounted on the car body and the truck frame to measure their

lateral accelerations. The measured acceleration signals are transferred to the

damping controllers and the stiffness controllers to control the secondary lateral

damping and stiffness, respectively.

81

Figure 5.12 Control system of variable stiffness and damping suspension

5.3.1 Control strategy

The control strategy involved in this study contains two parts. The first part is the

damping control algorithm. The main purpose of the damping controller is to

determine the desired damping. The control strategy adopted in this article is sky-

hook. Details of the sky-hook control strategy are as follows:

𝐼𝑑 = {2𝐴 �̇�(�̇� − �̇�𝑜) ≥ 00𝐴 �̇�(�̇� − �̇�𝑜) < 0

(5.12)

82

Figure 5.13 Car body response in time domain

The second item is the stiffness controller. The control method is also sky-hook

control and the details are expressed as:

𝐼𝑠 = {1𝐴 �̇�(𝑥 − 𝑥𝑜) ≥ 0

0𝐴 �̇�(𝑥 − 𝑥𝑜) < 0 (5.13)

where 𝐼𝑑 and Is are the currents controlling damping and stiffness items,

respectively, x and �̇� are the displacement and velocity of the car body while x0 and

�̇�𝑜 are displacement and velocity of track frame.

0 1 2 3 4 5-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

Accele

ratio

n (

m/s

2)

Time (s)

Passive

Only Damping control

Only stiffness control

Damping stiffness control

2 3-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

Accele

ratio

n (

m/s

2)

Time (s)

Passive




83

The control strategies are built in MATLAB/SIMULINK. Since ADAMS and

MATLAB are compatible, the semi-active train can be established by inserting the

control algorithm developed in Matlab/SIMULINK to the railway vehicle built by

ADAMS.

5.3.2 Simulation results and discussions

In this section, four different types of suspensions are simulated. The four

suspensions are passive suspension, stiffness variable suspension, damping variable

suspension, and variable stiffness and damping suspension. In this simulation, the

train runs on random irregular track. The simulation results of the lateral vibration of

the car body in time domain and frequency domain are shown in Figure 5.13 and

Figure 5.14, respectively. As a compare, the performances of the railway vehicle

with other three kind suspensions are also evaluated and plotted in the two figures.

From the two figures, it can be seen that semi-active suspensions perform better on

train’s vibration attenuation than the passive suspension. It also can be seen that the

train mounted with variable stiffness and damping suspension performs best

compared with passive suspension, stiffness variable suspension, and damping

variable suspension.

Figure 5.15 shows the root mean square (RMS) of the lateral acceleration of the car

body. It shows that variable damping suspension and variable stiffness suspension

decrease the lateral vibration by 23% and 11%, respectively, while the variable

stiffness and damping suspension can improve the vibration attenuation effectiveness

by 31%.

84

Figure 5.14 Car body response in frequency domain

Figure 5.15 Acceleration RMS of car body

5.4 Conclusion

An advanced MR damper with variable stiffness and damping characteristics that can

be practically applied to railway vehicle was designed, developed, and tested. The

analysis and test results verified that both the stiffness and the damping properties of

0 2 4 6 8 100.0

2.0x10-3

4.0x10-3

6.0x10-3

8.0x10-3

1.0x10-2

1.2x10-2

1.4x10-2

1.6x10-2

PS

D (

(m/s

2)2

/Hz)

Frequency (Hz)



Passive


Passive S control D control D+S control0.00

0.02

0.04

0.06

0.08

0.10

Acce

lera

tio

n R

MS

(m

/s2)

Different suspension

85

the damper can be controlled. The stiffness of the damper can vary from 8.7kN/m to

24.5kN/m while the equivalent damping coefficient has the ability to change from

16.24 KN/(m/s) to 29.72 KN/(m/s). An innovative model was established and

identified to describe the proposed MR damper. The successful development of the

compact variable stiffness and damping damper proves that the concept of variable

stiffness and damping suspension system for train is feasible.

By replacing the conventional secondary lateral dampers by the variable stiffness and

damping dampers, the railway vehicle with variable stiffness and damping

suspension is established. ADAMS/rail and Matlab/Simulink software are used to

evaluate the performance of the semi-active railway vehicle. The simulation results

illustrate that the variable stiffness and damping suspension performs the best on

train’s vibration attenuation and offers higher level of ride comfort compared with

passive suspension, stiffness variable suspension and damping variable suspension.

86

6 HORIZONTAL VIBRATION REDUCTION OF A SEAT SUSPENSION

USING MRE ISOLATORS

6.1 Introduction

Up to date, various MRE isolator structures, especially laminated structure, have

been reported in existing literature. As the laminated structure can provide the

required vertical support and horizontal flexibility, it has been used to develop the

MRE isolator for the seat suspension in this study. The stiffnesses of existing MRE

isolaters can only be increased, however, when the applied current is increased. This

means that in order to keep the seat stable and avoid collision, the MRE isolators

should be powered on in most of the time to offer harder initial stiffness, which

consumes a lot of power. Thus, developing an energy efficient MRE isolator with

harder initial stiffness and capable of providing controllable stiffness is very

important. In this chapter, a magnetic system that consists of a pair of permanent

magnets and an electromagnetic coil is incorporated into the manufacture of the

MRE isolator. The permanent magnets can provide a stable magnetic field to

energize the MRE layers without powering the electric coil, giving the MRE isolator

a hard lateral stiffness without power consumption. When the electric coil generates

the electromagnetic field that is opposite to the permanent magnetic field, the overall

magnetic field is reduced so that the MRE isolator shows a negative changing

stiffness effect. Subsequently, a smart seat suspension employing four controllable

MRE isolators with negative changing stiffness was developed. In section 6.2, the

structure and working principle of the multilayer MRE isolator is discussed. In

section 6.3, the proposed MRE isolator is prototyped and tested and its natural

frequency shift property is evaluated. Subsection 6.4 reports the vibration isolation

performance of the MRE isolator-based seat suspension. The conclusions are drawn

in the last subsection.

6.2 Structure and working principle of the MRE isolator

Figure 6.1 illustrates the controllable MRE isolator with a laminated structure. The

laminated structure is composed of 10 layers of the MRE sheets bonded onto 11

layers of the steel sheets. The thicknesses and diameter for the MRE sheets and steel

sheets are 1mm and 35mm, respectively. A clear advantage of the laminated

structure is that it prevents horizontal bulging and malfunctioning of the MRE. This

87

structure can also further strengthen the vertical stiffness and enhance the vertical

load capacity of the MRE isolator. Another advantage is that the laminated structure

does not affect the shearing deformation of the MRE sheets, and this means that this

structure allows high horizontal flexibility which can be controlled by the excitation

current. It should be noted that the laminated MRE structure is placed between two

permanent magnets before it is placed inside of a solenoid. The permanent magnets

produce a permanent vertical magnetic field to energize the MRE layers while the

solenoid generates an electromagnetic field the direction of which can be changed by

changing the direction of the applied current. As shown in Figure 6.1, the solenoid is

constructed by winding the electromagnetic coil around the thin non-magnetic

support which was made of plastic with a wall thickness of 2 mm. The copper wire

used is of 1 mm diameter and a total of 1000 turns of coils are tightly wrapped

around the plastic support. The inner diameter of the cylindrical solenoid is 50 mm,

which is larger than the diameter of the MRE sheet, allowing the isolator to have a

maximum deformation of 7.5 mm, and the outside diameter of the cylindrical

solenoid reaches 75 mm. In order to overcome the low magnetic conductivity of the

MRE, a cylindrical steel yoke with a thickness of 5 mm is designed and installed

outside of the cylindrical solenoid. In this way, an enclosed magnetic circuit can be

formed to further enhance the magnetic strength inside the MRE layers. A gap of 5

mm between the top plate and the steel yoke is designed to allow movement between

the top plate and the steel yoke. When the MRE isolator works properly, the top

plate, steel yoke, bottom plate, permanent magnets, and the laminated MRE form a

closed magnetic circuit. As shown in Figure 6.1, the yellow line illustrates the

magnetic circuit generated by the permanent magnets while the blue one denotes the

electromagnetic circuit generated by the solenoid. It can be seen that these two

magnetic fields are in opposite directions. In this case, the permanent magnetic field

will be reduced or even eliminated by the electromagnetic field once the coil is

powered on. The overall stiffness of the MRE isolator decreases steadily with the

increase of the coil current, which exhibit a negative change in stiffness.

88

Figure 6.1 Structure of the MRE isolator

6.3 Prototype and testing of the MRE isolator

6.3.1 Fabrication of the MRE isolator

The MRE material with mass fraction ratios of 80:10:10 of iron, silicon oil, and

silicone rubber was used to fabricate the laminated MRE isolator. The MREs were

prepared as follows. First, iron particles, silicon rubber, and silicon oil were mixed

thoroughly. Then the mixture was placed inside a vacuum case to remove the air

bubbles before it was poured into a mold. After curing for 5 days at room

temperature, the MER samples were ready for fabricating the MRE isolator with the

laminated structure. After the permanent magnets were mounted on each end of the

laminated MRE pillar, the whole core structure was fixed to the bottom plate of the

isolator. Then the outer cylinder that includes the solenoid and the steel yoke was

mounted onto the bottom plate. Finally, the top steel plate was fixed to the top

permanent magnet.

6.3.2 Experimental testing

An experimental platform was setup to test the performance of the MRE isolator. As

shown in Figure 6.2, the bottom steel plate of the MRE isolator was connected to a

horizontal shaking table which was excited by a shaker (Vibration Test Systems,

89

AURORA, Model No.: VG 100-8). The shaker was excited by the signal from the

amplifier (YE5871), the signal of which was provided by Data Acquisition (DAQ)

(Type: LabVIEW PCI-6221, National Instruments Corporation U.S.A) and a

computer. A force sensor was mounted between a fixed rig and the top plate of the

MRE isolator to measure the elastic force generated by the MRE isolator. The signals

were amplified by the charge amplifier (YE5851A from SINOCERA Piezotronics,

Inc) and then transferred to the computer through the DAQ board to be processed. A

laser sensor (MICRO-EPSILON Company) was employed to monitor the movement

of the bottom steel plate of the MRE isolator. This displacement signal was

transferred to the computer after it was measured. One DC power supply (GW

INSTEK GPC-3030D) was used to tune the currents of the coil to control the

strength of the magnetic field produced by the electromagnets and the stiffness of the

MRE. Through these equipment the relationship between the displacement of the top

plate and the relevant elastic force under different magnetic field could be obtained.

Figure 6.2 The experiment setup for testing the dynamic performance of MRE

isolator

To obtain the magnetic field-dependent performance, five different currents (0A, 1A,

2A, 3A, 4A) were used to energize the MRE isolator. Figure 6.3 presents the

magnetic field-dependent characteristic of the MRE isolator. It can be seen that

increase in the applied currents leads to an obvious decrease in the lateral stiffness

(indicated by the slope of the force-displacement loop), which verifies the negative

changing stiffness effect of the proposed MRE isolator. The field dependence of

overall stiffness can be seen in Figure 6.4, where the lateral stiffness of the MRE

isolator has a considerably large decrease from 23903 N/m at 0A to 11442 N/m at

4A. It can also be seen that the damping varies little with the coil current. The

response of the MRE isolator to different amplitudes was also evaluated. Figure 6.5

shows the amplitude-dependent characteristic of the MRE isolator. The testing

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amplitude to the MRE isolator was controlled by adjusting the input voltage levels of

the shaker. The enhancement of the input voltage increases the vibration amplitude

of the shaker, which results in a larger relative displacement between the top plate

and the bottom plate of the MRE isolator. From Figure 6.5, it can be seen that the

increase in the amplitude slightly decreases the stiffness of the MRE isolator. It

should also be noted that the force-displacement loops tend to be non-linear as the

amplitudes increase.

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

-10

-8

-6

-4

-2

0

2

4

6

8

10

Fo

rce

(N

)

Displacement (mm)

0A

1A

2A

3A

4A

Figure 6.3 Relationship between force and displacement under different currents

0 1 2 3 4

12000

14000

16000

18000

20000

22000

24000

Eq

uiv

ale

nt stiffn

ess (

N/m

)

Current (A)

Figure 6.4 Relationship between equivalent stiffness and current

91

-3 -2 -1 0 1 2 3-30

-20

-10

0

10

20

30

Fo

rce

(N

)

Displacement (mm)

0.2mm

0.5mm

1 mm

1.5mm

2.4mm

Figure 6.5 Relationship between force and displacement with different amplitudes

6.3.3 Frequency shift property evaluation

In order to further characterize the isolator’s negative changing stiffness property, its

natural frequency shift is evaluated in this section. The proposed MRE isolator with a

small mass attached on the top plate can be considered as a single-degree-of-freedom

(SDOF) vibration system. This system is mounted onto a horizontal shaking table

excited by a shaker. Thus the transmissibility presented in (Zhang and Li, 2009) is

also adapted to this SDOF system. The magnitude transmissibility of the negative

changing stiffness MRE isolator is expressed as:

T = √1+⟨2ζλ⟩2

⟨1−λ2⟩2+⟨2ζλ⟩2 (6.1)

where ω0 = √k

mO , λ =

ω

ω0 , ζ =

CO

2mOω0 . ω is the vibration frequency. mO is the

masses mounted on the isolator and top plate, k is the stiffness of the spring, and CO

is the damping coefficient. When the magnitude transmissibility, T, reaches its

maximum value, the corresponding exciting frequency is determined as the

resonance frequency.

The frequency shift test platform is similar to the test setup in subsection 6.3.2. The

difference is that the force sensor was removed. As a result, the top plate is free from

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the fixed rig. Two accelerometers were used to replace the laser sensor to measure

the accelerations of the top and bottom plates of the MRE isolator.

Five currents, 0A, 1A, 2A, 3A, 4A, were applied to the MRE isolator in this

experiment. Figure 6.6 illustrates the transmissibility of the MRE isolator. This

figure shows that as the current varies from 0A to 4A, the natural frequency of the

negative MRE isolator decreases from 32Hz to 21Hz. The test result shows that the

increase in current decreases the natural frequency of the MRE isolator, which means

that the stiffness declines when the current increases.

10 20 30 40 500.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Tra

nsm

issib

ility

Frequency (Hz)

0A

1A

2A

3A

4A

Figure 6.6 Transmissibility of the MRE isolator under different currents

6.4 Vibration suppression evaluation of seat suspension mounted with four

MRE isolators

6.4.1 Structure of the seat suspension mounted with MRE isolators

The structure of the seat suspension is illustrated in Figure 6.7. This seat suspension

consists of two parts: the vertical vibration control part and the horizontal vibration

control part. The structure of the vertical part is the same as a commercial seat

suspension which has leaf springs and dampers. The leaf springs are mainly used to

support the weight of the driver while the dampers are used to further suppress the

vibration of the seat in the vertical direction. In the horizontal part, four MRE

isolators are mounted between the vertical part and the cushion. In this way, the

horizontal vibration can be controlled by adjusting the stiffness of the MRE isolators.

93

Figure 6.7 Structure of the MRE seat suspension

6.4.2 Experimental testing system

(a) (b)

Figure 6.8 Experiment setup for seat vibration testing: (a) Schematic diagram (b)

Experimental setup

A vibration isolation experiment was conducted to evaluate the effectiveness of the

MRE isolators in attenuating horizontal vibration. As the main purpose of the MRE

isolators is to attenuate the horizontal vibration of the seat suspension, the vertical

part is not involved in this test. As illustrated in Figure 6.8, the seat was mounted

onto a horizontal shaking table and one person was seated on this seat serving as the

driver. Two different excitations (constant frequency excitation and sweep frequency

excitation) were employed to evaluate the vibration control effectiveness of the

proposed MRE isolators. In this testing system, the control algorithm was developed

in Matlab/Simulink and a HILINK (Zeltom) board was used as the interface between

the physical plants and Matlab/Simulink. Based on this system, the relative

displacement of the top and bottom plates of the MRE isolators measured by a laser

sensor were transferred to Simulink via the HILINK board. After the relative

94

displacement was processed by the controller developed in Simulink, the desired coil

excitation current was then obtained. The current signal was passed to the power

amplifier via the HILINK board. The amplified current signal was delivered to the

MRE isolator in order to control its lateral stiffness.

6.4.3 Control algorithm

As shown in Figure 6.9, the above testing system was simplified as the SDOF

system, where the driver and the seat were considered as one mass, m; and the

shaking table produces excitation to the mass via the spring and damping systems.

The sky-hook control algorithm was used in this study and is shown as follows:

𝐼 = {0, 𝑥𝑟�̇�𝑟 > 0 𝐼𝑀𝐴𝑋 , 𝑥𝑟�̇�𝑟 ≤ 0

(6.2)

where 𝑘MRE and 𝑐 are the lateral stiffness and the damping coefficient of the MRE

isolator, respectively; 𝑥𝑟 and �̇�𝑟 are the relative displacement and velocity of the top

and bottom plates of the MRE isolator, respectively.

Figure 6.9 The equivalent SDOF system

6.4.4 Experimental results

In this study, three different constant frequency excitations (5Hz, 7Hz, and 10Hz)

were used to evaluate the vibration isolation effectiveness of the MRE isolators under

constant frequency excitations. Figure 6.10(a), Figure 6.10(b) and Figure 6.10(c)

present the acceleration and displacement responses of the seat suspension under

95

different sinusoidal excitations at 5Hz, 7Hz, and 10Hz, respectively. These results

demonstrate that the seat vibration was clearly attenuated when the sky-hook control

algorithm was applied. The relative decreases in the acceleration under different

excitations were 44.6% (5Hz), 44.4% (7Hz), and 27.4% (10Hz), respectively, which

clearly indicates that the presented MRE isolator performs well on seat vibration

control.

0 2 4 6 8 10-1.5x10

-2

-1.0x10-2

-5.0x10-3

0.0

5.0x10-3

1.0x10-2

1.5x10-2

Dis

pla

cem

ent

(m)

Time (s)

(a)

0 2 4 6 8 10-1.2x10

-2

-8.0x10-3

-4.0x10-3

0.0

4.0x10-3

8.0x10-3

1.2x10-2

Dis

pla

cem

ent

(m)

Time (s)

(b)

0 2 4 6 8 10-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Acce

lera

tio

n (

m/s

2)

Time (s)

0 2 4 6 8 10-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Acce

lera

tio

n (

m/s

2)

Time (s)

Control applied

Control applied

Control applied

Control applied

96

0 2 4 6 8 10 12-0.02

-0.01

0.00

0.01

0.02

Dis

pla

ce

me

nt (m

)

Time (s)

(c)

Figure 6.10 Acceleration and displacement responses of seat suspension under

different sinusoidal excitations: (a) 5Hz. (b) 7Hz. (c) 10Hz

In order to further assess the vibration attenuation performance of MRE isolators in

wider frequency domains, a swept sinusoidal signal with a frequency band from 4Hz

to 15Hz was selected as the excitation signal. The reason why 4Hz to 15Hz is

selected is because human is sensitive to the vibration frequency range from 4Hz to

8Hz. The second reason is the horizontal stiffness cannot be as soft as vertical

stiffness because of stability concern. The case where no control logic was applied to

the MRE isolators is defined as the passive seat suspension while the one with sky-

hook control is considered as the semi-active seat suspension.

0 2 4 6 8 10 12-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Acce

lera

tio

n (

m/s

2)

Time (s)

Control applied

Control applied

97

Figure 6.11 Responses of seat under sweep frequency sinusoidal excitation

Figure 6.11 illustrates the comparison of the acceleration responses between the

passive seat suspension and the semi-active seat suspension. It can be seen that the

vibration of the seat system is significantly suppressed under sky-hook control logic

compared to the passive case. Specifically, the vibration reduction percentages under

some representative frequencies are given in Table 6.1.

Table 6.1 The reduction percentage under different frequencies

Frequency 4 Hz 7 Hz 10 Hz 12 Hz 15 Hz

Reduction percentage 37.5% 44.4% 28% 30% 27.4%

6.5 Conclusions

This chapter presents the design, prototyping, and testing of a negative changing

stiffness MRE suspension for train’s seat vibration control in lateral direction. The

dynamic testing results of the MRE isolator, which consist of the current-dependent

and amplitude-dependent responses, show that the isolator can vary its stiffness from

23903 N/m at 0A to 11442 N/m at 4A, verifying the negative changing stiffness

property of the isolator. Accordingly, its natural frequency shift property shows a

decreasing trend with the increasing coil currents applied. The effectiveness of the

isolator-based seat vibration control was experimentally verified. The vibration test

0 10 20 30-5

-4

-3

-2

-1

0

1

2

3

4

5

Accele

ratio

n (

m/s

2)

Time (s)

Passive

Semi-active

98

result of a real seat suspension employing four MRE isolators clearly demonstrates

that negative changing stiffness MRE suspension can suppress the seat vibration

more effectively and offer better ride comfort than the passive isolation suspension.

99

7 A SEAT SUSPENSION WITH A ROTARY MR DAMPER FOR VERTICAL

VIBRATION CONTROL

7.1 Introduction

Seat suspension for lateral vibration control has been investigated in last chapter.

This chapter will develop an innovative seat suspension for vertical vibration control.

Semi-active seat suspensions founded on MR dampers have begun to be investigated

and have achieved certain expectations for vertical vibration control. The current MR

dampers applied on seat suspensions have all been linear dampers with inherent

drawbacks which need to be addressed: 1) In principle, high pressure inside damper

is always needed to avoid the force lag performance, which require advanced sealing

technology for the avoidance of fluid leakage; 2) With respect to the usage of MRF,

the reserve of the linear damper must be totally filled up, which results in higher

consumption of the MRF material and high cost. For the above reasons, there is great

possibility to advance the current seat suspension design by overcoming the above-

mentioned requirements.

Based on the above motivations, this chapter proposes a new seat suspension

structure using a rotary MR damper. By applying the rotary MR damper to the seat

suspension, the configuration and operation will be much easier with low cost and

sealing requirement. The development of a rotary MR damper based seat suspension

for vehicle aims at upgrading the current seat suspension technology and hence the

ride comfort of drivers can be levelled up. The specific contents of this chapter are

introduced as following. Following the instruction, the structure and design of the

innovative seat suspension will be presented. The property test of the seat suspension

will be conducted in section 7.3 and the test results will be discussed. Section 7.4 and

7.5 present the vibration attenuation performance of the seat suspension numerically

and experimentally, respectively. The conclusion is drawn in section 7.6.

7.2 The structure and design of the seat suspension

7.2.1 The structure of the innovative seat suspension with rotary MR damper

Figure 7.1 shows the structure of the proposed innovative seat suspension system

which is mainly composed of the scissors structure with rotary MR damper installed.

One beam of the scissors structure is fixed with the shaft of the damper and the other

is fixed with the outside cylinder. When this seat intends to vibrate vertically, the

100

relative motion of these two crossed beams will drive the rotary damper to work. In

this way, the vertical linear movement is transformed into rotational motion of the

rotary dampers. Subsequently, the damping variation of the rotary MR damper will

induce the overall damping variation of the seat suspension.

(a)

(b)

Figure 7.1 The structure of the innovative seat suspension: (a) working mechanism

(b) photograph of the suspension system

7.2.2 The design of the rotary MR damper based seat suspension

The design of the rotary MR damper, including its structure and peak torque, is very

import for the seat to achieve better ride comfort. The relationship between the

torque and the vertical force is very important to guide the design as well. This

subsection presents the design procedure of the rotary MR damper based seat

suspension.

Figure 7.2 shows the structure design of the proposed rotary MR damper. In general,

it is seen that this rotary MR damper consists mainly of a cylinder, a coil, a shaft, a

rotor, and the enclosed reservoir filled with MRF. Unlike the linear MR damper with

101

single shaft, the rotary MR damper does not need a spring or gas chamber to provide

the initial pressure in the damper. The rotor is made of low-carbon steel and the shaft

is made of aluminium. The choice of material for different parts is under the

consideration of magnetic circuit design. The coil is composed by winding the

copper wire around the rotor. When the coil is energized, two sets of magnetic circuit

are formed as is shown in Figure 7.2. This magnetic circuit design guarantees that the

magnetic flux passes through MRF.

Figure 7.2 The structure of the rotary MR damper

The peak torque is the most important index for the rotary MR damper design and

directly determines the ride comfort of the seat suspension. The calculation method is

shown as following [124]:

𝑇𝜏 =4𝜋𝜇𝑒𝑞𝑅𝑜

4

(𝑛𝑒 + 3)𝑑[1 − (

𝑅𝑖

𝑅𝑜)𝑛𝑒+3] 𝛺 +

4𝜋𝜏𝑦𝑒

3(𝑅𝑜

3 − 𝑅𝑖3)

+2𝜋𝑅𝑜2𝐿𝑎(𝜏𝑦𝑎 + 𝐾𝑎(

𝛺𝑅𝑂

𝑑𝑜)𝑛𝑎) (7.1)

𝑇𝜏𝑜 =4𝜋𝜇𝑒𝑞𝑜𝑅𝑜

4

(𝑛𝑜 + 3)𝑑[1 − (

𝑅𝑖

𝑅𝑜)𝑛𝑜+3] 𝛺 +

4𝜋𝜏𝑜

3(𝑅𝑜

3 − 𝑅𝑖3)

+2𝜋𝑅𝑜2𝑤𝑑(𝜏𝑜 + 𝐾𝑜(

𝛺𝑅𝑂

𝑑𝑜)𝑛𝑜) (7.2)

where 𝑇𝜏 is the torque with magnetic field and 𝑇𝜏𝑜 is the torque without magnetic

field. 𝜏𝑦𝑒, 𝐾𝑒, and 𝑛𝑒, are yield stress, the consistency and the behaviour index of the

MRF in the end-face duct. 𝜇𝑒𝑞 , governed by 𝜇𝑒𝑞 = 𝐾𝑒 (𝑅𝑜𝛺

𝑑)𝑛𝑒−1, is the equivalent

102

viscosity of the MRF in the end-face duct. La ≅ 𝑤d − 𝑤c is the effective length of the

annular duct. The meanings of d, D, L, do, Ro, Ri, wc and wd have been given in

Figure 7.2. The detailed size of the rotary damper is shown in table 7.1. According to

the size, the MRF usage for the rotary damper can be calculated, which is 13.87mL.

As a comparison, the MRF usage in a representative paper [105] using linear MR

damper for seat suspension is approximately 126.24mL. Obviously, the MRF usage

in the rotary damper designed in this paper significantly reduced.

Table 7.1The size of the rotary MR damper

do 1.5mm wc 22mm

Ro 34mm wd 12mm

Ri 20mm L 45mm

D 100mm d 1.5mm

Based on the reference [125], the rheological properties of the MRFs can be

estimated by the following equation:

Y = 𝑌∞ + (𝑌𝑜 − 𝑌∞)(2𝑒−𝐵𝛼𝑆𝑌 − 𝑒−2𝐵𝛼𝑆𝑌) (7.3)

where Y represents rheological properties of MRF including post-yield viscosity,

yield stress, fluid consistency, and flow behavior index. The value of the MRF

rheological properties Y has a range of 𝑌𝑜 (zero applied field) to 𝑌∞ (saturation

value). B is the applied magnetic flux density and can be calculated by finite element

analysis method. 𝛼𝑆𝑌 is the saturation moment index. Based on the curve fitting

results with experimental results, the values of Y, 𝑌∞ and 𝛼𝑆𝑌 corresponding to

different rheological properties of MRF (LORD MRF-132DG) can be determined

and they are given in table 7.2.

Table 7.2 The parameters for the MRF-132DG

𝐾𝑂 0.22 Pa sn 𝜏𝑦∞ 30000 Pa

𝐾∞ 3900 Pa sn 𝛼𝑠𝑡𝑦 2 T

-1

𝛼𝑠𝑘 5 T-1

𝑛𝑂 0.917

𝜏𝑦𝑂 10 Pa 𝑛∞ 0.25

𝛼𝑠𝑛 32

As a gear box (ratio is 8) is mounted between the rotary damper and the scissors

structure, the torque working on the scissors structure will be:

𝑇 = {8𝑇𝜏 𝑖𝑓 𝐵 ≠ 08𝑇𝜏𝑜 𝑖𝑓 𝐵 = 0 (7.4)

103

The relationship between the MR damper torque and the vertical damping force

working on seat suspension is essential to guide the seat suspension design. Figure

7.1 shows the geometry of the seat suspension and the relationship between the MR

damper torque T and vertical damping force 𝑓𝑀𝑅𝐹 can be obtained as:

𝑓𝑀𝑅𝐹 = 2𝑇/w = 2𝑇/ √𝐿𝑜2 − H2 (7.5)

where Lo is the length of the beam of scissor structure, H is the height of the

suspension. Lo is a constant value of 0.287 m, and H can be measured in real-time.

Thus the overall force generated by the seat suspension can be obtained by:

Fz = 𝑘𝑥 + 𝑓r + 𝑓𝑀𝑅𝐹 (7.6)

where k is the stiffness of the seat suspension, x is the displacement of the seat

suspension, fr is the friction force.

In summary, the above section provides the design principle which will offer useful

guideline for the seat suspension design with rotary MR damper. The comparison of

the calculation pick force with the tested peak force is shown in Figure 7.4.

7.3 The property test of the seat suspension and results discussion

7.3.1 Testing method

The dynamic properties of the seat suspension system is tested and evaluated in this

section in terms of its field-dependent responses, amplitude, and frequency-

dependent performances. The seat suspension was fixed onto a computer-controlled

MTS machine (Load Frame Model: 370.02, MTS Systems Corporation). A DC

power with two channels was ready to energize the magnetic fields of the specimen

whenever needed. Once the testing started, the specimen moved in accordance with

the preprogramed sinusoidal routine.

7.3.2 Test results

A series of experimental tests were conducted to evaluate and characterize the

performance of the innovative seat suspension using the above described

experimental setup. For field-dependent tests, various harmonic inputs under

different current levels, which are used to energize the magnetic field working on the

MRF, were chosen to load this seat suspension. The properties of variable damping

can be observed in Figure 7.3(a). It is seen that the force-displacement relationships

104

form different parallelograms and the slopes of the parallelograms increase with the

increasing current. It is also observed in Figure 7.3(a) that the area of the force-

displacement loops increases obviously before saturation arises when the current

level increases from 0A to 2A with a step of 0.5A. As the variation of damping is

usually indicated by the area change of the enclosed force-displacement loops, the

results demonstrate that this innovative seat suspension shows controllable damping

variations.

-10 -5 0 5 10-1400

-1300

-1200

-1100

-1000

-900

-800

-700

Fo

rce

(N

)

Displacement (mm)

0A (Experiment)

0.5 (Experiment)

1 (Experiment)

1.5 (Experiment)

(a)

105

-15 -10 -5 0 5 10 15

-1200

-1150

-1100

-1050

-1000

-950

-900

-850

Fo

rce

(N

)

Amplitude (mm)

1mm

5mm

10mm

15mm

(b)

-10 -5 0 5 10-1200

-1150

-1100

-1050

-1000

-950

-900

Fo

rce

(N

)

Amplitude (mm)

1Hz

2Hz

3Hz

(c)

Figure 7.3 The test results of the seat suspension :(a) different currents (b) different

amplitudes (c) different frequencies

106

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

120

140

160

180

200

220

240

260

280

Pe

ak fo

rce

(N

)

Current (A)

Experiment

Calculation

Figure 7.4 The comparison between the experimental peak force and calculated peak

force

Figure 7.3(b) shows the responses of force-displacement when the seat suspension

was loaded with sinusoidal signals with different amplitudes (1 mm, 5mm, 10mm,

and 15mm) at constant frequency (1 Hz) and current (0 A). The effects of changing

the amplitudes are clearly observed that the maximum force gain a large increase

with the increasing amplitude. This set of results show the amplitude-dependent

properties of the tested seat suspension. Likewise, the effects of changing frequencies

on performance of the seat suspension are presented in Figure 7.3(c). It is noticed

that frequency variations have slight influence on the maximum force, the area of the

loops, and the slopes of parallelograms. In order to verify the correctness of the

calculation in section 2.2, the comparison of the tested peak force and calculated

peak force is presented in Figure 7.4, where the tested peak force is obtained by

using the peak force in Figure 7.3(a) minus the preload force of 1045N. The fitting

result shown in Figure 7.4 demonstrates the calculation method in section 2.2 predict

the dynamic performance of seat suspension well.

The above experimental results sufficiently verify that this proposed rotary MR

damper has the required properties as the linear MR dampers do and meanwhile it

has some advantages that linear MR dampers do not possess. The compact design

107

enables the rotary MR damper to be installed without any modifications to the

original seat suspension structure. Furthermore, its advantages of weight reduction,

smaller installation space, easy sealing and maintenance should be highlighted.

Additionally, the rotary damper design improves the cost efficiency because it

requires smaller quantity of MR fluid than linear MR damper does.

7.4 Numerical effectiveness evaluation of the rotary MR seat suspension

7.4.1 The dynamic model of the seat suspension

Figure 7.5 shows the semi-active seat suspension model with stiffness k, friction fr

and the Bouc-Wen model for the MR damper. The suspension upper and base

displacements are 𝑧𝑠 and 𝑧𝑣, respectively. The governing equation of motion for the

seat suspension is

𝑚𝑧�̈� + 𝑘(𝑧𝑠 − 𝑧𝑣) + 𝑓r + 𝑓MRF = 0 (7.7)

where 𝑚 is the total mass of a driver’s body, seat suspension top platform and

cushion. In this dynamic model, the overall force working on the seat suspension can

be calculated by:

Fz = 𝑘(𝑧𝑠 − 𝑧𝑣) + 𝑓r + 𝑓MRF (7.8)

Based on the phenomenological model for magnetorheological dampers proposed by

Spencer[126], the damping force 𝑓MRF can be obtained by the following equations:

𝑓MRF = 𝑐1�̇� + 𝑘1(𝑥 − 𝑥0)

�̇� =1

𝑐𝑜 + 𝑐1

[𝛼𝑧 + 𝑘𝑜(𝑥 − 𝑦) + 𝑐𝑜�̇�]

�̇� = −𝛾|�̇� − �̇�||𝑧|𝑛−1𝑧 − 𝜇(�̇� − �̇�)|𝑧|𝑛 + 𝐴(�̇� − �̇�)

x=Zs – Zv (7.9)

y=Zm– Zv

α = αa + αbI + αcI2

𝑐𝑜 = 𝑐𝑜𝑎 + 𝑐𝑜𝑏𝐼 + 𝑐𝑜𝑐𝐼2

𝑐1 = 𝑐1𝑎 + 𝑐1𝑏𝐼 + 𝑐1𝑐𝐼2

where I is the current applied to the MR damper. The parameters

𝜇, 𝛾, 𝑥𝑜 , 𝑘1, 𝑘𝑂 , 𝑐𝑜𝑎, 𝑐𝑜𝑏 , 𝑐𝑜𝑐, 𝐴, 𝑛, 𝛼𝑎, 𝛼𝑏 , 𝛼𝑐 , 𝑐1𝑎, 𝑐1𝑏 , and 𝑐1𝑐 are used to characterize

the MR damper. The optimized values for the parameters are determined by fitting

the model to the experimental data obtained in the experiments. The least-square

method in combination with the Trust-region-reflective algorithm available in

108

MATLAB (R2013b) can be used for the parameter identification[127]. Figure 7.6

illustrates the tracing performance of the modelling results and experimental results

and the identified parameters are shown in the Table 7.3. It can be seen that the

predicted data matches the experimental data very well.

Figure 7.5 The mathematic model of seat suspension

-10 -5 0 5 10-1400

-1300

-1200

-1100

-1000

-900

-800

-700

Fo

rce

(N

)

Displacement (mm)

0A (Experiment)

0.5 (Experiment)

1 (Experiment)

1.5 (Experiment)

0A (Theory)

0.5 (Theory)

1 (Theory)

1.5 (Theory)

Figure 7.6 The fitting result of the mathematic model

Table 7.3The identified model parameters

𝑘𝑂 1500 𝐴 2

𝑘1 700 𝑛 2

𝑥𝑜 0 α𝑎 89839.1

𝛾 6e+5 α𝑏 205322.1

μ 3e+6 α𝑐 -65841

109

𝑐𝑜𝑎 198.1 𝑐1𝑎 155679.6

𝑐𝑜𝑏 635.6 𝑐1𝑏 9.04705E+6

𝑐𝑜𝑐 -221.4 𝑐1𝑐 -375621.5

7.4.2 Control algorithm

It is commonly recognized that the MR suspension system is difficult to be modelled

accurately because of its nonlinear and complicated nature. For this reason, an MR

seat suspension fuzzy control system was chosen herein since a fuzzy controller does

not rely on the analysis and synthesis of the mathematical model of the full system.

The parameters of the seat dynamic model, shown in equation 7.7, are m=90 kg,

k=4100 N/m. The input variables to the fuzzy controller are seat mass velocity Vs

and relative velocity Vrel while the desired current is its output. The fuzzy subsets of

input variables (Vs, Vrel) have five membership functions (NB, NS, ZE, PS, PB)

while the fuzzy subset of output variable is with seven membership functions (NB,

NM, NS, ZE, PS, PM, PB). The fuzzy control rules are based on sky-hook strategy

and are shown in Table 4 [128].

Table 7.4 The rules of the Fuzzy controller

Vrel

Vs NB NS ZE PS PB

NB PB PM PS ZE ZE

NS PM PS ZE ZE ZE

ZE PM PS ZE NS NM

PS ZE ZE ZE NS NM

PB ZE ZE NS NM NB

7.4.3 The numerical simulation results

The simulation results under harmonic excitation

In this test, the excitation, Zv, is a sweep frequency signal with 10mm amplitude. Its

frequency linearly varies from 0.1Hz to 2.5 Hz in 25 seconds. The simulation results

are shown in Figure 7.7. Passive-off means that the rotary MR damper is out of

control because no control current was applied to it in this case. Passive-on refers to

the situation where a certain current signal was chosen (1.5A) to energize the rotary

damper, and semi-active case means the rotary damper was under control of the

fuzzy logic. It can be seen that the seat suspension with off state MR damper

performs the worst and the resonance happens at around 13s. On the contrary, the

resonance can be barely seen for the seat suspension with passive-on or controlled

110

MR damper but it still can be observed that the semi-active seat suspension performs

better than the passive-on seat suspension.

0 5 10 15 20 25-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Am

plit

ud

e (

cm

)

Time (s)

Off

On

Semi-active

Figure 7.7 The simulation response of seat under harmonic excitation

The simulation results under random excitation

The random excitation is generated by the following method. Firstly, the road

displacement of the random ground surface [129, 130] can be defined as:

𝑧�̇�(𝑡) + 𝜌𝑉𝑧𝑟(𝑡) = 𝑉𝑊𝑛 (7.10)

where 𝜌 is the road roughness parameter, 𝑉 is the vehicle speed, and 𝑊𝑛 is white

noise with intensity 2𝛿2𝜌𝑉 in which 𝛿2 is the covariance of road irregularity. When

the random ground profile is being generated, 𝜌 = 0.45𝑚−1, 𝛿2 = 300𝑚𝑚2 , and

𝑉 = 20 𝑚𝑠⁄ are chosen. Then, a quarter car model is excited by this random ground

surface and the response of the sprung mass will be used as the excitation for the seat

suspension.

The simulation results are shown in Figure 7.8 and it can be seen that the seat

suspension with passive-off MR damper performs the worst and the controlled semi-

active seat suspension performs the best.

111

Figure 7.8 The simulation response of seat under random excitation

7.5 Experimental effectiveness evaluation of the rotary MR seat suspension

7.5.1 Test system

The vibration isolation experiment was conducted to evaluate the effectiveness of the

rotary MR damper to attenuate the vertical vibration. Two different excitations

(constant frequency harmonic excitation and random road profile) were employed to

evaluate the vibration reduction effectiveness of the proposed MR seat suspension.

The experimental testing system is shown in Figure 7.9. A normal commercial

vehicle seat (GARPEN GSSC7) was fixed to the suspension system which was

equipped with the innovative rotary MR damper. The seat suspension system was

driven to vibrate vertically by a vibration platform, as shown in Figure 7.9. This

vibration platform is controlled by NI CompactRio 9076. One displacement sensor

(Micro Epsilon ILD1302-100) is installed on the bottom base of seat to measure the

suspension relative displacement while the other displacement sensor (Keyence LB-

11) was used to measure the seat’s absolute displacement. Two accelerometers

(ADXL203EB) were used to measure seat acceleration and excitation acceleration,

respectively. Those measured signals were feedback to the seat suspension controller

through a NI CompactRio 9074. The suspension controller then output a desired

current signal. The current signal will be amplified by a power amplifier and then

used to control the rotary damper.

0 5 10 15 20-4

-3

-2

-1

0

1

2

3

4

Accele

ratio

n (

m/s

2)

Time (s)

Off

On

Semi-active

112

(a)

(b)

Figure 7.9 The effectiveness evaluation system for the seat vibration control: (a)

Sketch (b) Experiment

7.5.2 Test results

The test results under harmonic excitation

113

(a)

0 5 10 15 20 25 30 35 40-3

-2

-1

0

1

2

3

Accele

ratio

n (

m/s

2)

Time (s)

Passive-onSemi-activePassive-off

(b)

Figure 7.10 The test results of the MR seat suspension under harmonic excitation: (a)

1.3Hz (b) 1.75Hz

In this test, different harmonic signals with different frequencies were used to excite

the seat suspension. The responses of the seat suspension under two frequencies,

1.3Hz and 1.75Hz, are given as representatives. Figure 7.10(a) and Figure 7.10(b)

present the acceleration responses of the seat suspension under 1.3Hz and 1.75Hz,

0 5 10 15 20 25 30 35-5

-4

-3

-2

-1

0

1

2

3

4

5

Passive-onSemi-active

Acce

lara

tio

n (

m/s

2)

Time (s)

Passive-off

114

respectively. And the performance of the seat suspension under passive-off, passive-

on and semi-active control cases were considered for each frequency testing. The

comparison results between these three cases are persuasive in terms of the

performance of the semi-active rotary MR damper. Based on the testing results

shown in Figure 7.10, the semi-active case, obviously, holds the minimum amplitude

of the seat acceleration. The passive-off case performs worst when the excitation

frequency is 1.3 Hz, however, it is comparable to passive-on case when the excitation

frequency is 1.75 Hz.

0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.250.5

1.0

1.5

2.0

2.5

3.0

3.5

Tra

nsm

issib

ility

Frequency (Hz)

Semi-active (simulation)

On (simulation)

Off (simulation)

Semi-active (experiment)

0n (experiment)

Off (experiment)

Figure 7.11 The transmissibility of the MR seat suspension under different

frequencies

In order to further verify the vibration reduction effectiveness of the semi-active seat

suspension, transmissibility was measured under those three control cases. The

transmissibility is defined as the ratio of the seat acceleration to the excitation

acceleration. The smaller the ratio is, the more effective the suspension is. The

simulation transmissibility of the seat suspension with different control cases is

presented in Figure 7.11 as well. The simulation results and experimental results

match well. Both experimental and simulation results verified that the semi-active

case can effectively reduce the transmissibility and performs the best over a large

frequency range.

115

The test results under random excitation

Apart from the constant frequency excitation, random excitation was also used to test

the seat suspension. Figure 7.12 shows the comparison of seat acceleration under

passive-on case, passive-off and semi-active control case. The acceleration amplitude

under semi-active case is largely reduced compared to both passive-off and passive-

on cases. A more direct comparison is given by calculating the RMS under those

three control cases. Both the RMS values from the simulation and experimental

results are given in Table.7.5. Clearly, the semi-active control case has the smallest

RMS value, indicating that the rotary MR damper under fuzzy logic control has the

most effective vibration reduction capability.

0 2 4 6 8 10 12 14 16 18 20-5.0

-2.5

0.0

2.5

5.0

Acce

lera

tio

n (

m/s

2)

Time (s)

Passive-off

Passive-on

Semi-active

Figure 7.12 The performance of MR seat suspension under random excitation

Table 7.5 The acceleration RMS values

Passive-off Passive-on Semi-active

Experiment 1.006 0.795 0.695

Simulation 1.206 0.882 0.671

7.6 Conclusion

This chapter proposes an innovative seat suspension design using a rotary MR

damper, which can reduce not only the usage amount of MRF but also the sealing

requirements. The testing results on the MTS machine show that it has the capability

116

to vary damping in response to the current change. Then an evaluation system is

constructed, including the semi-active vehicle seat suspension, the control loop and

vibration platform providing the excitations to this system. The vibration reduction

effectiveness of the seat suspension is evaluated under two kinds of excitations, i.e.

constant frequency excitation and random excitation. For both of the situations, the

seat acceleration under fuzzy logic control holds the minimum value, which verified

the semi-active rotary MR damper based seat suspension performs the best regarding

the vibration attenuation effectiveness.

117

8 CONCLUSIONS AND FUTURE WORK

8.1 Improving the stability of railway vehicles

8.1.1 Analysing the mechanism of the vibration and stability of railway vehicles

This thesis established a dynamic model of a railway vehicle with 15 degrees-of-

freedom to investigate the mechanism used to stabilise trains. The damping ratio of

each degree-of-freedom of the train, and the index of its stability with respect to its

speed was carefully analysed. The results indicated that the lateral motions of the

leading and trailing wheelsets of the front truck, as well as the yaw motions are

stable, but the stability of the wheelsets on the rear truck is poor. The lateral and yaw

motions of the leading wheelsets of the rear truck become unstable as the train speed

increases while the stability of the lateral and yaw motions of the trailing wheelsets

of the rear truck is worse. This means the front truck frame and car body of the

railway vehicle are stable under different operating speeds, but not the rear truck

frame. Therefore, based on the damping ratio analysis, the rear truck wheelset and

the rear truck frame are more unstable than the other components of the train and

should receive more attention during the design process.

Based on an analysis of the damping ratio, the critical speeds of each DOF with

regards to suspension stiffness and damping were further calculated and analysed.

The sensitivity of the critical speed was studied by analysing the influence of

different suspension parameters, and it was concluded that the secondary lateral

damping and primary longitudinal stiffness are the most sensitive suspension

parameters.

8.1.2 Application of the MR damper for railway vehicles

Because the secondary lateral dampers play a significant role in stabilising trains, the

secondary lateral dampers were replaced with MR dampers. A train model with MR

dampers was simulated by a combined simulation of ADAMS and MATLAB and

tested in a roller rig test platform to investigate how the MR damper affected the

train’s stability and critical speed. The results showed that the semi-active suspension

installed with an MR damper substantially improved the stability and critical speed

of the train. This pioneer research provides a way to guarantee the operation safety of

118

railway vehicle and has the potential to further improve the operation speed of the

commercialised trains.

8.1.3 Investigation of the MRE rubber joint for train

The conflicting stiffness requirements of the bogie’s rubber joint to keep the curve

passing performance and strain stability have plagued rail designers for decades.

Specifically, the rubber joint is required to be able to provide hard wheelset

positioning stiffness to maintain high speed stability when the train runs on straight

line at high speed and be soft to improve the train’s curve passing performance when

the train runs on curve track at a lower speed. The stiffness controllability of MRE

makes it a potential option to solve this conflict. However, how to embed the MRE to

the bogies to achieve the aim has been a big challenge. This thesis innovatively

proposed and designed an MRE based rubber joint which was capable of providing

variable primary longitudinal stiffness. To be exact, this thesis has successfully

designed, prototyped, and analysed a variable stiffness MRE joint to satisfy the

conflicting requirements. The result proved that the proposed MRE joint could

change its effective stiffness when the applied current was changed. A model train

built with ADMS software was used to evaluate how effectively it could maintain

high speed stability on straight track and good trafficability on a curved track. The

simulated responses of the angle of attack, lateral displacement, the lateral force of

the train running on curved track and the critical speed of train operating on a straight

line indicated that trafficability on a curved track had improved and its high speed

stability was maintained when an MRE joint was used. With the MRE joint

developed in this thesis, the wear between the rail and the wheelset will be mitigated

and subsequently the maintenance cost of the train operation will be reduced.

8.2 Reduced vibration and improved ride comfort of railway vehicles

8.2.1 Compact variable stiffness and damping damper for railway vehicles

According to the literature, the superiority of the variable stiffness and damping

system over the pure stiffness variable or pure damping variable system has been

verified experimentally and numerically. However, it still remains a big challenge to

design such a compact variable stiffness and damping system which is suitable for

railway vehicle. Based on this motivation, an innovative compact MRF damper with

119

variable stiffness and damping was designed, prototyped, tested, and analysed in this

thesis. The shape and size of this advanced MR damper are similar to those of the

traditional damper. In addition, this new damper can easily replace the original bogie

damper. The damper testing has verified that the stiffness and damping properties of

the advanced MRF damper can be controlled; indeed its stiffness and damping can

vary from 8.7kN/m to 24.5kN/m and from 16.24 KN/(m/s) to 29.72 KN/(m/s),

respectively. A mathematical model was then established. These results showed that

the proposed model can accurately predict the dynamic performance of the compact

advanced MR damper, and therefore this successful development makes the variable

stiffness and damping suspension feasible for railway vehicles.

The ability of the variable stiffness and damping suspension system to reduce

vibration was then evaluated numerically. ADAMS/Rail and Matlab/Simulink

software were used to build the train model as well as the control loop to evaluate the

property of the semi-active railway vehicle. The results showed that the variable

stiffness and damping suspension performed better than the passive suspension,

variable stiffness suspension, and variable damping suspension in terms of

attenuating vibrations and improving ride comfort. Furthermore, the application of

the advanced MRF damper developed in this thesis is not limited to railway vehicles.

It is also a good option to be used in many other areas such as automotive vehicle

and building protection from earthquake. It is believed that this proposed variable

stiffness and damping technology has potential to lead a breakthrough in vibration

control field.

8.2.2 Advanced seat suspensions with MR technology

Investigating the advanced seat suspension, as another feasible strategy to improve

ride comfort, also constitutes an important part in this research. Since vibration exists

laterally and vertically, two different seat suspensions used to control lateral and

vertical vibrations were developed, respectively. Regarding the seat suspension for

lateral vibration attenuation, rare research work has been done. The seat suspension

proposed in this thesis for lateral vibration attenuation contained four laminated

MRE isolators. The MRE isolators were tested and found that their stiffness variation

could reach to 109% when the current increased from 0A to 4A. This proved that the

120

MRE isolator can improve ride comfort in a lateral direction better than passive seat

suspension.

As for the seat suspension for vertical vibration, linear MR damper based seat

suspension has been widely studied. However, linear MR damper requires large

amount of MRF to fill up its reservoir, which subsequently increases the suspension

cost. It has always been a priority to reduce the cost. This thesis proposes a new seat

suspension structure using a rotary MR damper. The rotary damper based seat

suspension only utilizes a smaller quantity of MRF because the reservoir of the

rotary MR damper is much smaller than that of a linear one. This advantage

significantly reduces the cost of the seat suspension. An MTS machine was used to

test the seat suspension and verified its damping controllability. After that, a

vibration platform was used to evaluate its vibration attenuation performance and the

testing results demonstrated its excellent capability on vibration control.

In summary, the most important aspect to be considered for developing railway

vehicle is safety and ride comfort as the operating speed is now much closer to the

critical speed. At the critical speed the current system for mitigating vibration may

not function, which is an unavoidable challenge in the development of train

techniques. The development and application of innovative MR technology in this

thesis are believed to significantly contribute to improving the stability and ride

comfort of the railway vehicle and potentially increase the speed of commercial

trains in the future. In addition, the maintenance cost of the train and rail is another

important consideration. The rubber joint developed in this thesis definitely can

reduce the rail and wheelset wear when the train runs on curve track, which

subsequently lower the maintenance cost. In conclusion, the innovation MR

technology developed in this thesis can critically improve train’s dynamic

performance, including its stability, ride comfort and curve passing performance.

There is great chance to commercialise all the achievements in this thesis to further

improve train’s operation speed and reduce its maintenance cost.

8.3 Recommendation for future work

8.3.1 Optimisation of the design of variable stiffness and damping dampers

The result of testing variable stiffness and damping damper verified its capability,

but the damping variation range is approximately 2, which is lower than a mature

121

MR damper even though it can satisfy the requirements for trains. This narrow

damping range is due to the magnetic field being saturated in the shaft of the internal

piston, so the design of the internal damping unit must be improved and optimised.

That means the size of the shaft, the gap between the piston and the cylinder, and the

number of turns in the coil within a certain volume must be optimised to improve the

maximum magnetic flux density in MRF.

8.3.2 Optimise the stiffness variation range of the MRE rubber joint

The stiffness variation range of the MRE joint presented in section 4 is 74.7%, which

satisfies our needs at this stage. But it must be broadened because the storage

modulus of the MRE varied approximately10 times when the magnetic field

increased from 0 mT to 440 mT. There are two methods for carrying out this

optimisation; the first is to optimise the structure of the MRE joint to enhance the

magnetic flux density in MRE, and then use a finite element to optimise the magnetic

field. Another method is to consider other possible structures to change the working

mode of the MRE. The MRE in present design is working in squeeze mode, so

changing it to shear mode with a different structure may improve its stiffness

variation range.

8.3.3 Experimental investigation of a train mounted with variable stiffness and

damping damper or an MRE rubber joint

This thesis has already investigated the use of a conventional MR damper on railway

vehicles. A full scale train mounted with MR damper was tested and analysed, but a

train with variable stiffness and damping dampers or an MRE joint has not been

tested because it is difficult to gain access to a full scale test rig. This would be a

very worthwhile experiment in the author’s opinion.

122

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134

PUBLICATIONS DURING MY PHD STUDY

Book Chapter

1. J. Yang, S. S. Sun, H. Du & W. Li, (2015). A novel magnetorheological elastomer

isolator with achievable negative stiffness for vibration reduction. Smart Materials

Actuators: Recent Advances in Characterization and Applications (pp. 79-100).

United States: Nova Science Publishers.

Refereed Journal Articles

2. S. S. Sun; J. Yang; W. Li, H. Deng; H. Du; G. Alici; T. Yan, Development of a

compact isolator working with magnetorheological elastomers and fluids,

Mechanical Systems and Signal Processing (Accepted).

3. S. S. Sun; D. Ning, J. Yang; H. Du; S. Zhang, W. Li, A seat suspension with a rotary

magnetorheological damper for heavy duty vehicles, Smart Materials and Structures

(Accepted).

4. S. S. Sun, J. Yang, W. Li, H. Deng, H. Du, G. Alici, T. Yan, An innovative MRE

absorber with double natural frequencies for wide frequency bandwidth vibration

absorption, Smart Materials and Structures 25, 055035, 2016.

5. S. S. Sun, H. X. Deng, H. Du, W. H. Li, J. Yang, G. P. Liu, G. Alici, and T. H. Yan,

“A Compact Variable Stiffness and Damping Shock Absorber for Vehicle

Suspension”, IEEE-ASME Transactions on Mechatronics, 20, 2621-2629, 2015.

6. S. S. Sun, H. Deng, J. Yang, W. H. Li, H. Du, and G. Alici, “Performance evaluation

and comparison of MRE absorbers working in shear and squeeze modes”, Journal of

Intelligent Material Systems and Structures, 26, 1757-1763, 2015.

7. S. S. Sun, J. Yang, W. H. Li, H. X. Deng, H. Du, and G. Alici, “Development of an

MRE adaptive tuned vibration absorber with self-sensing capability”, Smart

Materials and Structures, 24, 095012, 2015.

8. S. S. Sun, J. Yang, W. H. Li, H. Deng, H. Du, and G. Alici, “Development of a novel

variable and damping magnetorheological fluid damper”, Smart Materials and

Structures, 24, 085021, 2015.

9. S. S. Sun, J. Yang, H. Du, W. H. Li, G. Alici, H. X. Deng, and M. Nakano

“Horizontal vibration reduction of a seat suspension using negative changing

135

stiffness magnetorheological elastomer isolators”, International Journal of Vehicle

Design, 68, 104-118, 2015.

10. S. S. Sun, H. X. Deng, H. Du, W. H. Li, G. Alici, and M. Nakano, “An Adaptive

Tuned Vibration Absorber Based on Multilayered MR Elastomers”, Smart Materials

and Structures, 24, 045045, 2015.

11. S. S. Sun, Y. Chen, T. F. Tian, H. X. Deng, W. H. Li, H. Du, and G. Alici, “The

Development of an Adaptive Tuned Magnetorheological Elastomer Absorber

Working in Squeeze Mode”, Smart Materials & Structures, 23, 075009, 2014.

12. S. S. Sun, H. X. Deng, W. H. Li, H. Du, Y. Q. Ni, and J. Yang, “Improving the

critical speeds of high-speed train using magnetorheological technology”, Smart

Materials and Structures, 22, 115012, 2013. (featured article, issue cover, 2013

Highlight)

13. M. Przybylski, S. S. Sun, W. Li, Development and characterization of a multi-layer

magnetorheological elastomer isolator based on a Halbach array, Smart Materials

and Structures (Accepted)

14. N. Jiang, S. S. Sun, Y. Ouyang, M. Xu, W. Li, S. Zhang, A Highly Adaptive

Magnetorheological Fluid Robotic Leg for Efficient Terrestrial Locomotion, Smart

Materials and Structures (Accepted)

15. D. Ning, S. S. Sun, H. Li, H. Du, W. Li, Active control of an innovative seat

suspension system with acceleration measurement based friction estimation, Journal

of Sound and Vibration. (Accepted)

16. G. Hu, Y. Lu, S. S. Sun and W. Li, Performance analysis of a magnetorheolgical

damper with energy harvesting ability, Shock and Vibration (Accepted)

17. D. Ning, S. S. Sun, J. Zhang, H. Du, W. Li and X. Wang, An active seat suspension

design for vibration control of heavy duty vehicles, Low Frequency Noise, Vibration

& Active Control (Accepted).

18. J. Yang, S. S. Sun, T. F. Tian, W. H. Li, H. Du, G. Alici, and M. Nakano,

“Development of a novel multi-layer MRE isolator for suppression of building

vibrations under seismic events”, Mechanical Systems and Signal Processing, 70,

811-820, 2016.

19. Z. Xing, M. Yu, S. S. Sun, J. Fu, and W. H. Li, “A hybrid magnetorheological

elastomer-fluid (MRE-F) isolation mount: development and experimental

validation”, Smart Materials and Structures, 25, 015026, 2015.

136

20. J. Yang, S. S. Sun, W. H. Li, H. Du, G. Alici, and M. Nakano, “Development of a

linear damper working with MR Shear Thickening Fluids”, Journal of Intelligent

Material Systems and Structures, 26, 1811-1817, 2015.

21. H. X. Deng, L. J. Zhou, S. Y. Zhao, W. H. Li, S. S. Sun, J. Zhang, and L. D. Yu,

“The dynamic behavior of high speed train using magnetorheological technology on

the curve track”, Applied Mechanics and Materials, 782, 210-218, 2015.

22. J. Yang, S. S. Sun, H. Du, W. H. Li, G. Alici, H. X. Deng, “A novel

magnetorheological elastomer isolator with negative changing stiffness for vibration

reduction”, Smart Materials and Structures, 23, 105023, 2014.

23. J. Yang, S. S. Sun, H. Du, G. Alici, T. Yan, and W. Li, “Fabrication and

characterization of magnetorheological shear-stiffened elastomers”, Front. Mater.

1:22. doi: 10.3389/fmats.2014.00022

24. J. Yang, H. Du, W. H. Li, Y. C. Li, J. C. Li, S. S. Sun, and H. X. Deng,

“Experimental study and modeling of a novel magnetorheological elastomer”, Smart

Materials and Structures, 22, 117001, 2013.

25. S. Zhao, H. Deng, J. Zhang, L. Yu, S. S. Sun, W. Li, and L. Zhou, “A novel MR

device with variable stiffness and damping capacity”, International Journal of

Aerospace and Lightweight Structures, 3, 325-335, 2013.

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