Dynamic analysis of two wheeler chassis

Dynamic Analysis of a Two-wheeler Chassis 2007-08

PROJECT REPORT

On

“DYNAMIC ANALYSIS OF A TWO WHEELER CHASSIS”

Undertaken at

PESIT, BANGALORE.

Submitted in partial fulfilment of the requirement For the Award of Degree of

BACHELOR OF ENGINEERING IN

MECHANICAL ENGINEERING

Submitted by

PRAVEEN K S 1PI04ME066 SANDEEP SHARMA N V 1PI04ME081 VIKRAM K DESHPANDE 1PI04ME110

VINAY ANAND S 1PI04ME111

Under the guidance of

Mr. SHARANBASSAPPA S. PATIL Associate Professor,

Department Of Mechanical Engineering, P.E.S.I.T, Bangalore.

Department of Mechanical Engineering

P. E. S. Institute of Technology 100 Feet Ring Road, BSK III Stage, Bangalore - 560 085 Ph: 6721983

For the academic session Feb 2008 – June 2008

Department of Mechanical Engineering 1



PEOPLES EDUCATION SOCIETY I N S T I T U T E O F T E C H N O L O G Y 100 Feet Ring Road, BSK III Stage, Bangalore - 560 085.

DEPARTMENT OF MECHANICAL ENGINEERING

CERTIFICATE

Certified that the project entitled DYNAMIC ANALYSIS OF A TWO WHEELER CHASSIS is a bonafide work carried out by PRAVEEN K S, SANDEEP SHARMA N V, VIKRAM K DESHPANDE and VINAY ANAND S in partial

fulfillment for the award of degree of Bachelor of Engineering in MECHANICAL

of the Visveswaraiah Technological University, Belgaum during the year

2007-2008. It is certified that all corrections/ suggestions indicated for internal

assessment have been incorporated in the report in departmental library. The

project report has been approved as it satisfies the academic requirements in

respect of project work prescribed for the Bachelor of Engineering Degree. Signature of Internal Guide Signature of HOD Signature of Principal Mr. Sharanbassappa S. Patil Dr K Narasimha Murthy Dr K.N Balasubramanya Murthy Associate Professor, Professor & Head, Principal, Dept. of Mechanical Engg. Dept. of Mechanical Engg P.E.S.I.T P.E.S.I.T P.E.S.I.T

Name of Students USN

1. PRAVEEN K S 1PI04ME066 2. SANDEEP SHARMA N V 1PI04ME081 3. VIKRAM K DESHPANDE 1PI04ME110 4. VINAY ANAND S 1PI04ME111 EXTERNAL VIVA Name of Examiners Signature with Date

1.

2.


ACKNOWLEDGEMENT

The satisfaction and euphoria that accompany the successful completion of any

task would be incomplete without the mention of the people whose constant

guidance and encouragement crowned our effort with success.

We are grateful to Dr. K. Narasimha Murthy, Professor and Head, Department

of Mechanical Engineering, for his encouragement and the facilities extended by

the department. We are also thankful to our Principal, Dr. K. N. Balasubramanya Murthy.

We consider ourselves fortunate to have Mr.Sharanbassappa S. Patil, Associate Professor, Department of Mechanical Engineering, as our guide. We

are grateful to him for his useful guidance and encouragement throughout the

project period.

It is our pleasure to thank Mr. Shirish R. Kala, Lecturer, Department of

Mechanical Engineering, for his constant and valuable guidance.

We express our profound gratitude to Mr.Sanjay Patil, Geometric India

Solutions, for his support. We would like to thank Mr. Kannan, LMS India, for his

valuable guidance.

We would also like to thank all the teaching and non-teaching staff of the

Department of Mechanical Engineering, for their support.

This project would not have completed without the valuable support of our Family

and Friends.



ABSTRACT

A chassis serves as the basic foundation on which all the parts of a

machine rest. In an automobile, the chassis acts as a skeleton on which the

engine, transmission, driveshaft, differential, gearbox and suspension are

mounted.

In the two wheeler scenario, the ride comfort quality offered by the two

wheeler plays an important role in attracting the potential buyers. The comfort is

significantly affected by noise and vibration which is experienced by the rider

during the travel. These vibrations are caused by road roughness, mass

unbalance etc. and are transmitted to the occupants through the seat floor,

handle bar, foot rests etc, in totality through the frame skeleton of motorcycle

chassis. Hence a thorough understanding of the dynamic behavior of the chassis

is essential.

This work deals with numerical analysis of the chassis for its vibrations

and experimental modal testing. The numerical analysis involves 3D modeling of

the chassis and analyzing its behaviour under varying load conditions. For

experimental modal testing, the chassis is suspended to simulate the free - free

condition and excited by some means. The vibration pattern is recorded by an

FFT analyzer. The results are then extracted using a software. Ultimately, the two

results obtained are corroborated.



CONTENTS

ACKNOWLEDGEMENT ABSTRACT LIST OF FIGURES LIST OF TABLES Chapter 1: Introduction 1.1 Chassis 1 1.2 Types of chassis 3 Chapter 2: Literature Survey 2.1 Vibrations in motorcycles 7

2.2 Human Body Vibration 11 2.2.1 Vibration Exposure Criteria 13 2.3 Finite Element Analysis 16 2.3.1 Steps involved in FEM 17 2.4 Experimental Modal Testing 18 2.4.1 Procedure for modal testing 21 2.4.2 Modal Testing setup 24 2.4.3 Concept of frequency response system 26 2.4.4 Excitation methods 34 2.4.5 Exciting Modes with Impact Testing 35 2.4.6 Assumptions in modal testing 38

Chapter 3: Dynamic Analysis – FEM Approach 3.1 FEM analysis of the motorcycle chassis 41 3.2 Results 44

Chapter 4: Experimental Modal Testing 4.1 Procurement of the chassis 49 4.2 Dimensions of the chassis 49

4.3 Modal Testing Procedure Implemented 51 4.4 Setting up the modal test 51 4.5 Creating the geometry of the chassis 54 4.6 Documentation of the test 56



4.7 Experimental Results 60 Chapter 5: Comparison of Results 61 CONCLUSION 62 REFERENCES 63



LIST OF FIGURES

Figure Description

1.1 Typical model of Backbone frame 1.2 Typical model of a Perimeter Chassis 1.3 Typical model of Trellis frame 2.1 Different motions of a motorcycle 2.2 Forces produced by tyres 2.3 Human body as a mechanical system 2.4 Tolerance of humans to repetitive vertical impact 2.5 Rigid body modes 2.6 Types of curve-fit methods 2.7 Modal testing procedure 2.8 General measurement test setup for Modal testing 2.9 A typical FRF 2.10 Nyquist plot of frequency response 2.11 Frequency response-polar coordinates 2.12 Frequency response-rectangular coordinates 2.13 Typical Instrumentation for Accelerometer 2.14 Types of mounting – Stud mount and Fin mount pad 3.1 Part models of the chassis 3.2 Assembled chassis model 3.3 Meshed Finite Element model 4.1 Suzuki Zeus chassis 4.2 Chassis suspension, Accelerometer, Wax used 4.3 Impact Hammer 4.4 Eight channel FFT Analyzer 4.5 Line diagram and Solid model of the chassis



LIST OF TABLES Table Description 2.1 Symptoms affecting humans at different frequencies

2.2 Forms of Frequency Response Function

3.1 Natural frequencies of the chassis at different modes

4.1 Co-ordinates of various points on the chassis

4.2 Experimental values of Natural frequencies

5.1 Comparison of Results



1.1 Chassis

A chassis serves as the basic foundation on which all the parts of a

machine rest. In an automobile, the chassis acts as a skeleton on which the

engine, transmission, driveshaft, differential, gearbox and suspension are

mounted. The chassis should be structurally sound in every way and support the

body panels over the expected life of the vehicle and beyond.

The engine generally sits inside the frame, the rear swing arm is attached

by a pivot bolt (allowing the suspension to move) and the front forks are attached

to the front of the frame. The frame can also help to protect the more sensitive

parts of the motorcycle in a crash.

Any good chassis must do several things:

1. Be structurally sound in every way over the expected life of the vehicle and

beyond. This means nothing will ever break under normal conditions.

2. Maintain the suspension mounting locations so that handling is safe and

consistent under high cornering and bump loads.

3. Support the body panels and other passenger components so that

everything feels solid and has a long, reliable life.

4. Protect the occupants from external intrusion.

5. Help the wheels align on a single straight line.



Different chassis designs have their own strengths and weaknesses.

Every chassis is a compromise between weight, component size, complexity,

vehicle intent, and ultimate cost. And even within a basic design method,

strength and stiffness can vary significantly, depending on the details. There is

no such thing as the ultimate method of construction for every vehicle, because

each vehicle presents a different set of problems.

Even though an aluminum chassis is the path to the lightest design, it is

not necessarily true. Aluminum is more flexible than steel. In fact, the ratio of

stiffness to weight is almost identical to steel, so an aluminum chassis must

weigh the same as a steel one to achieve the same stiffness. Aluminum has an

advantage only where there may be very thin sections where buckling is possible.

Chassis design works around three major aspects of the motorcycle, the

rider, engine and suspension. The suspension mounting points are fixed in

space and are determined by the geometry of the suspension. The engine is a

large component in the vehicle with a fixed size, and needs to be located as close

to the rear of the vehicle as possible for proper weight distribution. The rider is

the largest lumped mass in the vehicle, with special ergonomic requirements for

comfort and drivability.

These three items directly govern chassis design and must be accounted

for before any subsystem design can begin. A good chassis design

encompasses all of these aspects in an efficient way, providing a stable and

sound foundation for all vehicle components.



1.2 Types of Chassis

Single cradle frame: The single cradle is the simplest type of motorcycle

frame, and looks similar to the first ever motorcycle frames. It is made from

steel tubes that surround the engine with a main tube above and other,

smaller diameter tubes beneath.

If a single cradle becomes double at the exhaust, as frequently occurs, it is

referred to as a split single cradle frame. Single cradle frames are usually

found in off-road motorcycles. Double cradle frame: Double cradle frames are descended from single

cradle frames. They consist of two cradles that support the engine one

either side. Double cradle frames are commonly used in custom

motorcycles and simpler road bikes. They offer a good compromise

between rigidity, strength and lightness, though they have now been

technically surpassed by perimeter frames.

Backbone frame: Far from the most desirable frame around, the

backbone frame comprises a single, wide main beam from which the

engine is suspended.

The backbone frame allows for great flexibility in design, since it is

concealed inside the finished motorcycle. The engine just seems to hang

in mid air. It is simple and cheap to make, and is used mainly on naked

and off-road motorcycles.



1.1 Typical model of Backbone frame

Monocoque frame: The monocoque frame is used nearly exclusively on

competition bikes and is very rarely found on road-going bikes.

Monocoque frames act as a single piece unit that functions as seat

mounting, tank and tail section. Though they offer certain advantages in

terms of rigidity, monocoque frames are heavy and generally not worth the

effort.

Perimeter frame: Motorcycle racing research has shown that major

advantages are to be gained in terms of rigidity by joining the steering

head to the swing arm in as short a distance as possible. Flexure and

torsion are dramatically reduced. This is the concept behind the perimeter

frame. Two robust beams descend in the most direct way possible from

the steering head to the swing arm, passing around the engine.

The earliest perimeter frames were made from steel, but the need to

improve rigidity to weight ratios led most manufacturers to adopt aluminum

instead.



Aluminum is now by far the most common road bike frame material and

the aluminum perimeter frame is the most popular frame for modern super

sports motorcycles.

1.2 Typical model of a Perimeter Chassis

Trellis frame: The trellis frame rivals the aluminum perimeter frame for

rigidity and weight. A favorite of Italian and European manufacturers it has

proved a great success in racing and competition. The Trellis frame uses

the same principles as the perimeter frame, and connects the steering

head and swing arm as directly as possible.



1.3 Typical model of Trellis frame

The frame is made up of a large number of short steel (or aluminum) tubes

welded together to form a trellis. The trellis frame is not only easy to

manufacture but extremely strong as well. The frame picture is from the

Suzuki SV650S.



2.1 Vibrations in Motorcycles

The motorcycle is assumed to run straight on a flat, level road surface at a

certain velocity. The rider is thought to be a rigid body fixed to the rear frame,

which can exert no control on the motorcycle. For simplicity's sake, the

motorcycle is considered to have rigid suspension; from a kinematics point of

view it is a spatial system whose motion can be described by means of the

following four coordinates:

• the steering angle;

• the roll angle;

• the yaw angle;

• the lateral displacement of the mass centre.

2.1 Different motions of a motorcycle

The system "motorcycle" may be considered to consist of two parts:

• the rear frame including the rider, the engine, the petrol tank and the seat

and rear wheel;

• the front frame including the forks, the handlebars and the front wheel.



The rear frame and the front frame are hinged together at the steering axis by

means of a revolute pair. During the motion, the tyres are free to sideslip; so they

produce lateral forces which are a linear function of the sideslip angles and the

camber angle. These forces, from a practical point of view, may be considered to

be restoring forces like those produced by springs.

2.2 Forces produced by tyres

Keeping the above simplification in mind, the steering axis is considered to be

constrained so that it can't move laterally. So the motorcycle may be thought of

as two decoupled systems each having only one degree of freedom:

• The front frame oscillating around the steering axis on which the lateral

front tyre force (with the normal trail as a lever) acts as a restoring force;

• The rear frame oscillating around the steering axis on which the lateral

rear tyre force (with a lever proportional to the wheelbase) acts as a

restoring force.



The two oscillation modes are:

• An oscillation of the front frame around the steering axis called the wobble

mode.

• An oscillation of the rear frame around the steering axis called the weave

mode.

The frequency of the wobble mode is:

where:

α n is the normal trail;

If is the moment of inertia of the front frame around the steering axis;

k λ f is the front tyre stiffness;

ε is the steering head angle.

The frequency of the weave mode is:

where:

l is the lever of the rear tyre force with respect to the steering axis;

I r is the moment of inertia of the rear frame around the steering axis;

k λ r is the rear tyre slip stiffness.



In reality, the modes are different in view of the fact that the steer axis is

not blocked. The wobble mode is essentially a steering oscillation of the front

forks; this mode doesn't involve the rear frame in any significant way.

Typical values of the frequencies vary from 4 Hz, in the case of heavy

motorcycles, to 9 Hz, in the case of lightweight motorcycles.

The frequency of the wobble mode goes up as the trail increases and as

the front inertia decreases: this depends essentially on the sideslip stiffness of

the front tire and is also influenced by the lateral flexibility of the front fork. When

the speed of the motorcycle ranges from 10 to 20 m/s (40-80 km/h), the wobble is

only a little damped and can therefore become unstable: the adoption of a

damping steer increases the damping and consequently the degree of stability.

The weave mode is a side-to-side motion of the entire motorcycle

characterized by a coupling of the yaw and roll oscillations with a large lateral

displacement of the steering axis. The weave mode has a natural frequency

increasing from about 0.2 Hz at a low speed to about 3-4 Hz at a high forward

speed.

Its value depends on numerous factors:

• the position of the mass centre of the rear frame;

• the inertia of the wheels;

• the castor angle;

• the trail.

The mode may be unstable at a low speed; at a high speed it may be difficult

to control since its natural frequency may be too high to be controlled by the

driver.



It is well known that motorcycles, without the action of control exercised by

the rider, are unstable in roll, this motion is a non-oscillatory motion and consists

in the capsize of the two-wheel vehicle. In fact, the motorcycle in uniform

rectilinear motion will eventually fall laterally: the motorcycle is therefore an

intrinsically unstable system, above all in the low speeds range when the

stabilizing action of the gyroscopic effects turns out to be negligible.

The capsize motion is essential for driving the motorcycle; it is used and

controlled by the rider by means of the steering. The time of the vehicle's capsize

depends on numerous factors such as the speed of the vehicle; the inertia of the

wheels (gyroscopic effect); the height of the mass centre; the mass of the

motorcycle; the roll inertia of the vehicle; the castor angle; the trail.

Thus it is essential to have a good understanding of the behaviour of the

motorcycle under varying load conditions.

2.2 Human Body Vibration

Our ultimate aim is to isolate the vibrations and prevent them from

affecting the human body. For this purpose, a sound knowledge of both the

behaviour of chassis to vibrations and the human response to it is required. This

chapter deals about the effects of vibrations on human body.

The human body is both physically and biologically a "system" of an

extremely complex nature. When looked upon as a mechanical system it can be

considered to contain a number of linear as well as non-linear "elements", and

the mechanical properties are quite different from person to person.



Biologically the situation is by no means simpler, especially when

psychological effects are included. In considering the response of man to

vibrations and shocks it is necessary, however, to take into account both

mechanical and psychological effects.

Considering first the human body as a mechanical system it may, at low

frequencies and low vibration levels, be roughly approximated by a linear lumped

parameter system of the type shown in the figure 2.3.

2.3 Human body as a mechanical system

One of the most important parts of this system with respect to vibration

and shock effect seems to be the part marked "thorax-abdomen system". This is

due to a distinct resonance effect occurring in the 3-6 Hz range. This makes

efficient vibration isolation of a sitting or standing person very difficult.



A further resonance effect platform is found in the 20 to 30 Hz region and

is caused by the head-neck shoulder system.

Also in the region 60 to 90 Hz disturbances are felt which suggest eyeball

resonances, and a resonance effect in the lower jaw-skull system has been found

between 100 and 200 Hz.

Above 100 Hz, simple lumped parameter models are not very useful. It is

then necessary to apply continuous structural analysis methods which become

very complex. By such methods, however, it has been shown that for the skull

itself, the fundamental mode of vibration seems to be in the region of 300-400 Hz

with resonances for higher modes around 600 to 900 Hz.

At still higher frequencies use must be made of wave theory both in the

form of shear waves and of compression waves (sound waves).

2.2.1 Vibration Exposure Criteria

Apart from the mechanical responses mentioned above, both physiological

and psychological effects are observed. Psychological effects such as

perception, discomfort, and pain, have recently been studied in some detail. Most

of the studies have been carried out on vehicle drivers and aircraft pilots, whose

ability to perform complex tasks under adverse environmental conditions, in-

cluding vibration, is particularly important. The data available is therefore mainly

for sitting or standing subjects.

Vibration at frequencies below 1 Hz occurs in many forms of transport and

produces effects, e.g. Kinetosis (motion sickness), which are completely different

in character from those produced at higher frequencies. These effects cannot be

simply related to the three parameters of the exciting motion, intensity, duration,

and frequency, as has been possible in the range from 1 Hz to 80 Hz.



In addition, human reaction to vibration below 1 Hz is extremely variable

and seems to depend on a large number of external factors which have nothing

to do with the motion, e.g. age, sex, vision, activity, odours. Despite this variability

and the limited amount of data available, an attempt has been made to formulate

tentative standards for the frequency range from 1 Hz down to 0.

2.4 Tolerance of human subjects in the standing or supine position to

repetitive vertical impact pulses



Tolerance of human subjects in the standing or supine position to

repetitive vertical impact pulses representative of impacts from pile drivers, heavy

tools, heavy traffic etc. is as shown in the figure. Subjective reaction is plotted as

a function of the maximum displacement of the initial pulse and its rise time.

The numbers indicate the following reactions for the areas between the lines:

I a - threshold of perception;

I b - for easy perception;

I c - of strong perception, annoying;

11a - very unpleasant, potential danger for long exposures;

II b - extremely unpleasant, definitely dangerous.

Symptoms for vibration exposure at frequencies of 1 to 20 Hz are shown in

the table. The frequency ranges given are those where the symptoms are most

predominant.

Symptoms Frequency (Hz)

General feeling of discomfort 4-9

Head symptoms 13-20

Lower jaw symptoms 6-8

Influence on speech 13-20

Lump in the throat 12-16

Chest pains 5-7

Abdominal pains 4-10

Urge to urinate 10-18

Increased muscle tone 13-20

Influence on breathing movements 4-8

Muscle contractions 4-9

2.1 Symptoms affecting humans at different frequencies



Thus the design of chassis should be such that it does not transmit these

frequencies to the human body. The mass and the stiffness of the chassis are

modified in such a way that these frequencies remain isolated and are not

transmitted from the ground to the human body.

2.3 Finite Element Analysis

Finite Element Analysis consists of a computer model of a material or

design that is stressed and analyzed for specific results. It is used in new product

design, and existing product refinement. Modifying an existing product or

structure is utilized to qualify the product or structure for a new service condition. In case of structural failure, FEA may be used to help determine the design

modifications to meet the new condition.

There are generally two types of analysis that are used: 2-D modeling, and

3-D modeling. While 2-D modeling conserves simplicity and allows the analysis to

be run on a relatively normal computer, it tends to yield less accurate results. 3-D

modeling, however, produces more accurate results while sacrificing the ability to

run on all but the fastest computers effectively.

FEA uses a complex system of points called nodes which make a grid

called a mesh .This mesh is programmed to contain the material and structural

properties which define how the structure will react to certain loading conditions.

Nodes are assigned at a certain density throughout the material depending

on the anticipated stress levels of a particular area. Regions which will receive

large amounts of stress usually have a higher node density than those which

experience little or no stress.



Points of interest may consist of: fracture point of previously tested

material, fillets, corners, complex detail, and high stress areas. The mesh acts

like a spider web in that from each node, there extends a mesh element to each

of the adjacent nodes. This web of vectors is what carries the material properties

to the object, creating many elements.

2.3.1 Steps involved in FEM

In general, there are three phases in any computer-aided engineering task:

• Pre-processing – defining the finite element model and environmental

factors to be applied to it

• Analysis solver – solution of finite element model

• Post-processing of results using visualization tools

Pre-processing

The first step in using FEA, pre-processing, is constructing a finite element

model of the structure to be analyzed. The input of a topological description of the

structure's geometric features is required in most FEA packages. This can be in

either 1D, 2D, or 3D form, modeled by line, shape, or surface representation,

respectively, although nowadays 3D models are predominantly used.

Once the finite element geometric model has been created, a meshing

procedure is used to define and break up the model into small elements. In

general, a finite element model is defined by a mesh network, which is made up

of the geometric arrangement of elements and nodes. Nodes represent points at

which features such as displacements are calculated. FEA packages use node

numbers to serve as an identification tool in viewing solutions in structures such

as deflections.



Elements are bounded by sets of nodes, and define localized mass and

stiffness properties of the model. Elements are also defined by mesh numbers,

which allow references to be made to corresponding deflections or stresses at

specific model locations.

Analysis (computation of solution)

The next stage of the FEA process is analysis. The FEM conducts a series

of computational procedures involving applied forces, and the properties of the

elements which produce a model solution. Such as structural analysis allows the

determination of effects such as deformations, strains, and stresses which are

caused by applied structural loads such as force, pressure and gravity.

Post-processing (visualization) These results can then be studied using visualization tools within the FEA

environment to view and to fully identify implications of the analysis. Numerical

and graphical tools allow the precise location of data such as stresses and

deflections to be identified.

2.4 Experimental Modal Testing

Modal Analysis is a well-defined technique, which defines the inherent

dynamic properties of the structure. Modal analysis gives the modal parameters

especially natural frequencies, mode shapes & damping values of the structure.

The main objective here is to obtain the natural frequencies at various modes of

the chassis, thereby predicting any possibility of resonance. In addition, the

corresponding mode shapes are also obtained.



In the two wheeler scenario, the ride comfort quality is significantly

affected by noise and vibration which is experienced by the rider during the

travel. These vibrations are caused by road roughness, mass unbalance etc. and

are transmitted to the occupants through the seat floor, handle bar, foot rests etc,

in totality through the frame skeleton of motorcycle chassis. Hence to isolate

these vibrations, the understanding of the dynamic behavior of the chassis is

essential.

Modal analysis can be used as a means for visualizing, and thereby

increasing our understanding of the motions which occur when the structure or

system vibrates. Modes are used as a simple and efficient means of

characterizing resonant vibration. That is, under the proper conditions, a structure

can be made to vibrate with excessive, sustained, oscillatory motion.

Resonant vibration is caused by an interaction between the inertial and

elastic properties of the materials within a structure. To better understand any

structural vibration problem, the resonances of a structure need to be identified

and quantified. A common way of doing this is to define the structure’s modal

parameters. Resonant vibration occurs when one or more of the resonances or

natural modes of vibration of a machine or structure is excited. It typically

amplifies the vibration response far beyond the level deflection, stress, and strain

caused by static loading.

What are Modes?

Modes (or resonances) are inherent properties of a structure. Resonances

are determined by the material properties (mass, stiffness, and damping

properties), and boundary conditions of the structure.



Each mode is defined by a natural (modal or resonant) frequency,

modal damping, and a mode shape. If either the material properties or the

boundary conditions of a structure change, its modes will change. For instance, if

mass is added to a vertical pump, it will vibrate differently because its modes

have changed. At or near the natural frequency of a mode, the overall vibration

shape (operating deflection shape) of a machine or structure will tend to be

dominated by the mode shape of the resonance.

Two Kinds of Modes

Modes are further characterized as either rigid body or flexible body

modes. All structures can have up to six rigid body modes, three translational

modes and three rotational modes. If the structure merely bounces on some soft

springs, its motion approximates a rigid body mode. Many vibration problems are

caused, or at least amplified by the excitation of one or more flexible body

modes.

2.5 Rigid body modes Why are Modes Dangerous?



Modes cause structures to act as “mechanical amplifiers”. At certain

natural frequencies of the structure (its modal frequencies), a small amount of

input force can cause a very large response. (When a peak is very narrow and

high in value, it is said to be a high Q resonance.)

If the structure is excited at or near one of the peak frequencies, the

response of the structure per unit of input force will be large. On the other hand, if

the structure is excited at or near one of the anti-resonances (zeros or inverted

peaks), the structural response will be very small per unit of input force.

2.4.1 Procedure for modal testing

The general procedure for performing a modal test is

• To select test points on the structure

• To collect frequency response function (FRF) data for each of these points

• To curve fit the data and obtain the modal model of the test structure

Selecting the points on the structure

In order to excite the structure, various points have to determined. These

points must be chosen such that they form the major part of the structure which

vibrates with reasonably high amplitude.



Frequency response function (FRF)

FRF is defined as the ratio of the Fourier transform of an output

response divided by the Fourier transform of the input force that causes the

output. Experimental modal parameters (frequency, damping, and mode shape)

are also obtained from a set of FRF measurements. The FRF describes the

input-output relationship between two points on a structure as a function of

frequency.

Curve-fitting the data obtained

Curve-fitting processes the data to extract the modal parameters from the

FRF measurements. At the end of Curve-fitting, tables giving frequencies and

damping factors are obtained.

2.6 Types of curve-fit methods

The above classification is based on the accuracy and the computing

resources needed. The groups employing single mode methods are usually

concerned with time and require a fast medium quality curve fitter. The groups

employing multi mode methods are more serious about quantitative parameter

estimates for use in a modal model. They require more accuracy and are willing

to spend more time obtaining results. For the groups using multi measurement

techniques, accuracy rather than time is of paramount importance.



The phases involved in the experimental modal testing are shown in the figure

2.7 Modal testing procedure

2.4.2 Modal Testing setup



2.8 General measurement setup for Modal testing

Excitation device

This provides a measurable input of mechanical force into the structure which

sets it into vibratory motion. Excitation may be provided by an electro dynamic

exciter or an impact hammer. A source for the excitation signal will depend on the

type of the test being undertaken and can be any one of the following:

i. Sinusoidal (from an oscillator)

ii. Random (from a noise generator)

iii. Transient (by applying an impact with a hammer)

iv. Periodic (from a special signal generator capable of producing a specific

frequency content)

The best choice of the excitation function depends on several factors which are:

a) Available signal processing equipment

b) Characteristics of the structure

c) Excitation system and General measurement considerations

Power amplifier



The function of the power amplifier is to amplify the generated signal from

analyzer or any other signal generating devices. The signals coming from the

analyzer or any other signal generating devices will be weak and hence may not

be able to drive the exciter. The power amplifier raises these signals to a

sufficient level to drive with minimum distortion.

Force transducer

The input time history of the excitation force is measured by means of a

force transducer, usually piezoelectric transducer.

Accelerometer

The dynamic response of an excited test structure is normally detected by

one or more piezoelectric transducers attached to the structure. Strain gauges

are often found to be convenient because of their minimal interference with the

test object.

Analyzer

The function of the analyzer is to simply measure the various signals

developed by the transducers in order to ascertain the magnitudes of the

excitation forces and responses. It transforms both the excitation and response

time histories into frequency spectra and calculates the ratio of these two

functions. This ratio is called the FRF.

2.4.3 Concept of frequency response system



2.9 A typical FRF

Every structure has inherent dynamic properties that determine how the

structure responds to its environment. By subjecting a structure to a known

excitation and measuring the resulting responses, its dynamic properties can be

determined. Conceptually, this can be shown by considering a structure as a

“black box” with dynamic properties h (t), as shown in the diagram.

Excitation Response

f (t) x (t)

Any arbitrary set of time

structure’s dynamic properties

the dynamic characteristics h

excitation.

This type of description

in the analysis of control syste


Structure

h (t)

varying excitations or inputs f (t) are filtered by the

h (t) to yield responses x (t). Obviously, if we know

(t), we can predict the response caused by any

of the input / output relationship is in common use

ms and electrical circuits.

34


Describing the dynamic properties of the “black box” is easier in the

frequency domain, i.e., instead of describing the excitation, responses and

dynamic properties as functions of time, they are transformed into functions of

frequency, using the Laplace transformation:

∞ -st F (s) = ∫ f (t) e dt

0

The black box diagram now becomes

F (s) X (s)

The input / output relationship can no

F (s) * H (s) = X(s)

H (s) is called the transfe

characteristics of the structure as a

measuring the excitation f (t) and re

transforms, the transfer function is ob

For practical applications, the

prohibitive. Therefore Fourier transfo

Laplace transform, is made use of to

the dynamic properties. This is known

FRFs can be measured directly with m

The physical interpretation of

frequency ω, will produce a sinusoida

output amplitude will be multiplied by

input will be shifted by θ (ω).


Structure h (t)

w be written as a simple algebraic equation

i.e. X(s) / F (s) = H (s)

r function and expresses the dynamic

function of the complex variable “s”. By

sponse x (t), and computing their Laplace

tained from the equation X (s) / F (s).

effort in computing Laplace transform is

rm (evaluated at s = jω), a special case of

obtain the frequency domain description of

as the Frequency response function (FRF).

odern dual channel spectrum analyzers.

FRF is that a sinusoidal input force, at a

l output motion at the same frequency. The

I H (ω) I and the phase between output and

35


The various forms of Frequency Response Function based on the type of

response variable are given in the table.

Response parameter R Standard R/F Inverse F/R

DISPLACEMENT RECEPTANCE

ADMITTANCE

COMPLIANCE

FLEXIBILITY

DYNAMIC STIFFNESS

VELOCITY MOBILITY MECHANICAL IMPEDANCE

ACCELERATION INERTANCE

ACCELERANCE

APPARENT MASS

2.2 Forms of Frequency Response Function

One cannot easily define the mobility of the structure as a whole; one has

to define the mobility of every point as a function of frequency. For modeling, the

FRF most commonly used is Compliance. The FRF generally used for

measurements is Accelerance, since the most convenient motion transducer is

the Accelerometer. Since the FRFs are a complex quantity, they cannot be fully

displayed on a single two dimensional plot. It can, however, be presented in

several formats, each of which has its own uses.

Coherence is related to the FRF and shows the degree of correlation of

one signal with a second signal. Coherence varies from zero to one and is a

function of frequency. In modal analysis, this function shows the quality of a

measurement.



A good impact produces a vibration response that is perfectly correlated

with the impact, indicated by a coherence plot that is near one over the entire

frequency range. If there is some other source of vibration, or noise, or the

hammer is not exciting the entire frequency range, the coherence plot will drop

below one in some regions.

Getting good measurements from an analyzer requires careful selection of

the measurement settings for the averaging, triggering, and windowing

parameters.

Triggering is a technique for capturing an event when you do not know

exactly when it will occur. A trigger can start data acquisition and processing

when a user-specified voltage level is detected in an input channel. For example,

you can set up a trigger to capture a hammer impact. After you arm the trigger,

the analyzer will wait until the impact occurs before it starts acquiring data.

Averaging improves the quality of the measurement. It applies to both the

frequency and time domains. Frequency domain averaging uses multiple data

blocks to "smooth" the measurements. You can average signals with a linear

average where all data blocks have the same weight; or you can use exponential

weighting. In this case, the last data block has the most weight and the first has

the least. Averaging acts to improve the estimate of the mean value at each

frequency point; it reduces the variance in the measurement. Time domain

averaging is useful in measuring repetitive signals to suppress background noise.

An impact test is good example of repetitive signals. Both the force and

acceleration signals are the same for each measurement. This assumes that the

trigger point is reliable. The presence of high background noise may adversely

affect the reliability of the trigger.



Windowing is a processing technique used when computing FFTs.

Theoretically, the FFT can only be computed if the input signal is periodic in each

data block(it repeats over and over again and is identical every time). When the

FFT of a non-periodic signal is computed, the FFT suffers from 'leakage.'

Leakage is the effect of the signal energy smearing out over a wide frequency

range. If the signal were periodic, it would be in a narrow frequency range. Since

most signals are not periodic in the data block time period, windowing is applied

to force them to be periodic.

A windowing function should be exactly zero at the beginning and end of

the data block and have some special shape in between. This function is then

multiplied with the time data block, and this forces the signal to be periodic.

Accept/Reject

Because accurate impact testing results depend on the skill of the one

doing the impacting, FRF measurements should be made with spectrum

averaging, a standard capability in all modern FFT analyzers. FRFs should be

measured using 3 to 5 impacts per measurement. Since one or two of the

impacts during the measurement process may be bad hits, an FFT analyzer

designed for impact testing should have the ability to accept or reject the result of

each impact. An accept/reject capability saves a lot of time during impact testing

since you don’t have to restart the measurement process after each bad hit.

One method of presenting the FRF is to plot the real plot versus the

imaginary plot. This is often called the Nyquist plot or a Vector response plot.This

graph emphasizes the area of frequency response at resonance and traces out a

circle, as shown in the figure 2.10

Another method of presenting the data is to plot the polar coordinates,

magnitude and phase versus frequency as illustrated in the figure 2.11. At

resonance, the magnitude is a maximum and is limited only by the amount of

damping in the system.



The phase ranges from 0° to 180° and the response lags the input by 90°

at resonance.

A third method of presenting the data is to plot the rectangular

coordinates, the real part and the imaginary part versus the frequency. For a

proportionally damped system, the imaginary part is maximum at resonance and

the real part is zero, as shown in the figure 2.12

2.10 Nyquist plot of frequency response



2.11 Frequency response-polar coordinates



2.12 Frequency response-rectangular coordinates



2.4.4 Excitation methods The excitation mechanisms mainly fall into two categories:

1. Shaker testing

2. Impact testing

Shaker testing

The most useful shakers for modal testing are the electro dynamic and

electro hydraulic types.

In the electro dynamic shaker, force is generated by an alternating current

that drives a magnetic coil. The maximum frequency limit varies from 5 kHz to 20

kHz depending on the size. Smaller shakers have higher operating range.

Hydraulic shakers can provide much higher force levels. A hydraulic

shaker has the ability to apply a large static preload to the structure. This is useful

for massive structures such as grinding machines that operate under relatively

high preloads which may alter their structural characteristics.

Impact testing

Impact testing is a simple means of exciting the structure into vibration. An

impact hammer is a specialized measurement tool that produces short duration

vibration levels by striking the structure at some point. The hammer incorporates

a sensor (called a load cell) that produces a signal proportional to the force of

impact. This enables precise measurement of the excitation force.

An impact hammer is often used for modal analysis of structures where

use of a mechanical vibrator is not convenient; examples are in the field or with

very large structures.



Different impact tip materials allow tailoring of the frequency content of the

impact force. For low frequency measurements, a soft rubber tip concentrates the

excitation energy in a narrow frequency range.

Impact testing has two potential signal processing problems associated with it.

1. Noise can be present in either the force or response signal as a result

of a long time record.

2. Leakage can be present in the response signal as a result of short time

record.

Compensation for both these problems can be accomplished with Windowing

technique.

2.4.5 Exciting Modes with Impact Testing

With the ability to compute FRF measurements in an FFT analyzer, impact

testing was developed during the late 1970’s, and has become the most popular

modal testing method used today. Impact testing is a fast, convenient, and low

cost way of finding the modes of machines and structures.

The following equipment is required to perform an impact test,

• Impact hammer

• Accelerometer

• FFT Analyzer

• Post-processing Modal software

I. An impact hammer with a load cell attached to its head to measure the input

force.



II. An accelerometer is used to measure the response acceleration at a fixed

point & direction. Structural vibration is commonly measured with electronic

sensors called accelerometers. These sensors convert an acceleration signal to

an electronic voltage signal that can then be measured, analyzed and recorded

with electronic hardware. There are many types of accelerometers. The most

common requires a power supply connected by a wire to the accelerometer as

shown in Figure 2.13.

Some accelerometers have internal circuitry that allows the analyzer to

provide the power, eliminating the need for a power supply. The signal analyzer

includes a calibration setting that allows the voltage signal to be converted back

into a measurement of acceleration.

2.13 Typical Instrumentation for Accelerometer

The normal method of MOUNTING accelerometers in intrinsically safe

environments is to drill, spot face, and tap a threaded hole in the machine. This

allows the accelerometer to be stud mounted and have direct metal to metal

contact insuring conductivity between the sensor and the machine.

As shown in the figure 2.14, a small circular flat is machined on the

surface of the machine. A hole is drilled and tapped in the center of the machined

surface. The accelerometer is then attached to the machine by a threaded stud

and tightened with a mounting torque.



(A) (B)

2.14 (A) Stud mount (B) Fin Mount Pad for mounting Accelerometer

The Fin Mount Pad is a universally accepted method of mounting

accelerometers on motors and is available in various sizes as shown in the figure

The Fin Mount Pad is seated in the valley between two cooling fins on the motor,

and by applying an epoxy held in place as shown in the figure.

The accelerometer is then stud mounted or magnet mounted to the Fin

Mount Pad to measure the vibration of the motor. A typical epoxy used in this

case is the Devcon Plastic Welder. Although it has very good adhesive

properties, it is an insulator and will not meet the requirements for intrinsic safety.

III. A multi channel FFT analyzer to compute FRFs - the input signal is digitized

at a high sampling rate, similar to a digitizing oscilloscope. Nyquist's theorem

says that as long as the sampling rate is greater than twice the highest frequency

component of the signal, the sampled data will accurately represent the input

signal.

The FFT is simply a clever set of operations which implements Fourier's

theorem. The resulting spectrum shows the frequency components of the input

signal. The original digital time record comes from discrete samples taken at the

sampling rate.



The corresponding FFT yields a spectrum with discrete frequency

samples. The advantage of this technique is its speed.

One of the most common applications of FFT analyzers is to measure the

transfer function of a mechanical or electrical system. A transfer function is the

ratio of the output to the input. Single-channel analyzers cannot measure transfer

functions. Single-channel analyzers with integrated sources can measure transfer

functions but only by assuming that the input spectrum of the system is equal to

the spectrum of the integrated source.

In general, to measure a general transfer function, a two-channel analyzer

is required. One channel measures the spectrum of the input, the other measures

the spectrum of the output, and the analyzer performs a complex division to

extract the magnitude and phase of the transfer function. Because the input

spectrum is actually measured and divided out, you’re not limited to using a

predetermined signal as the input to the system under test—any signal will do.

IV. Post-processing modal software for identifying modal parameters and

displaying the mode shapes in animation.

2.4.6 Assumptions in modal testing

The basic assumptions concerning any structure that are made in order to

perform an experimental modal analysis:

1. The structure is assumed to be linear i.e., the response of the

structure to any combination of forces, simultaneously applied, is the sum of the

individual responses to each of the forces acting alone.



2. The structure is time invariant i.e., the parameters that are to be

determined are constants. In general, a system which is not time invariant will

have components whose mass, stiffness, or damping depend on factors that are

not measured or are not included in the model.

For example, some components may be temperature dependent. In this

case the temperature of the component is viewed as a time varying signal and

hence, the component has time varying characteristics. Therefore, the modal

parameters that would be determined by any measurement and estimation

process would depend on the time (by this temperature dependence) that any

measurements were made. If the structure that is tested changes with time, then

measurements made at the end of the test period would determine a different set

of modal parameters than measurements made at the beginning of the test

period. Thus, the measurements made at the two different times will be

inconsistent, violating the assumption of time invariance.

3. The structure obeys Maxwell’s reciprocity i.e., a force applied at

degree-of-freedom p causes a response at degree-of-freedom q that is the same

as the response at degree-of-freedom p caused by the same force applied at

degree-of-freedom q.

With respect to frequency response function measurements, the frequency

response function between points p and q determined by exciting at p and

measuring the response at q is the same frequency response function as found

by exciting at q and measuring the response at p.

4. The structure is observable i.e., the input-output measurements that

are made contain enough information to generate an adequate behavioral model

of the structure. Structures and machines which have degrees-of-freedom of

motion that are not measured are not completely observable.



5. The other assumption can be made regarding the system being analyzed. Commonly, the modal parameters are assumed to be global. For

example, this assumption means that, for a given modal frequency, the frequency

and damping information is the same in every measurement. Since

measurements are taken at different times and with slightly different test

conditions, this is often not true with respect to the measured data. This condition

is referred to as inconsistent data. Theoretical models do not attempt to

recognize this problem.

6. Another assumption is made relative to repeated roots. Repeated

roots refer to the situation where one of the complex roots (modal frequency,

Eigen value, pole, etc.) occurs more than once in the characteristic equation.

Each root with the same value has an independent modal vector or eigenvector.

This situation can only be detected by the use of multiple inputs or references.

The basic assumptions are never perfectly achieved in experimental test

situations involving real structural systems. Generally, the assumptions will be

approximately true. The important thing to remember is that each assumption can

be evaluated experimentally, either during the testing or after the testing is

completed and the data analysis has been performed. It is inexcusable to perform

a test without some measure of the validity of the assumptions involved.



3.1 FEM analysis of the motorcycle chassis

Modal analysis of the motorcycle frame was carried out using ‘ANSYS 11’

FEM package. The FEM analysis comprised of the following steps:

Model Preparation - The motorcycle frame is the assemblage of main

stem tube, steering tube, chassis back tubes, handle bar, steering column, foot

rests engine brackets, seat mount assembly, etc. Among these parts only main

stem tube of chassis is undertaken for the study.

We made use of AUTODESK INVENTOR to create the part models.

These were created by initially creating 2D models in the sketch mode and later

converting these 2D models to 3D by employing the “EXTRUDE” and the

“SWEEP” commands. A few part models are as shown:

3.1 Part models of the chassis



All these individual part models are assembled to get the model of the

chassis. The final assembled chassis is as shown in the figure.

3.2 Assembled chassis model Importing to ANSYS - This assembled model was imported to ANSYS

11.0 to conduct the analysis. The element type defined was SHELL 181. The

structural material properties were defined by the Young’s modulus, Poisson’s

ratio and Density.

Meshing the model - After defining all the material properties and

entering the values of required parameters, the model was meshed using MESH TOOL command. In this tab, quad mesh and free option was selected to mesh

the entire model. The figure shows the model after meshing.



.3.3 Meshed Finite Element model

Boundary Conditions - The analysis was carried out to predict and

analyze the vibrations induced in the chassis frame. The suspension and shock

absorber elements (road tyre interactions) were not considered. The condition

employed to conduct the test was Free-Free condition.

In the solution stage, the new Analysis type was chosen and the modal

option was selected. Among the different algorithms available on ANSYS for

Modal analysis, Block Lanczos method was used to extract the natural

frequencies and mode shapes of the motorcycle frame. The mode shapes

required for the study of dynamic behavior, were generally the lower mode

shapes of the structure.

After selecting Block Lancoz analysis option, the number of modes

required to extract was entered. A window appeared asking the bandwidth of the

natural frequency. For our analysis, we selected the bandwidth to be between 0 –

150 Hz.



After solving, the following results are obtained using READ RESULTS option in

the general post processor stage.

3.2 Results The natural frequencies obtained from modal analysis of motorcycle chassis

frame by FEM are given in the table.

Mode No. Natural Frequency in Hz

1 0

2 0

3 0

4 0

5 1.5e-4

6 4.95e-4

7 35.015

8 74.426

9 104.91

10 130.26


Some of the first modes were of very low frequency due to rigid body

motions of the chassis and the unsprung masses. These were followed by the

suspension modes showing bouncing and pitching of the whole body. Then in

higher frequency range, the modes of elastic deflection of the chassis and the

steering column were obtained.



Mode 7- 35.015 Hz

Contour plot

Deformed and undeformed plot



Mode 8- 74.426 Hz

Contour plot




Mode 9-104.91 Hz

Contour plot




Mode 10-130.26 Hz

Contour plot




4.1 Procurement of the chassis

The first stage of our project comprised of procuring the right kind of

chassis to conduct the analysis on. For this, we had to survey various

manufacturers who could provide us with the right chassis.

After enquiring with various manufacturers like HERO HONDA,

SUZUKI, BAJAJ AUTO and HONDA, we finally decided on the SUZUKI ZEUS

chassis.

Shown below is a picture of the chassis we procured.

4.1 Suzuki Zeus chassis 4.2 Dimensions of the chassis

Most manufacturers do not provide the dimensions of the chassis and

so also was the case with Suzuki. A sketch of the chassis also could not be

obtained. Hence we had to begin from scratch.



By making use of a measurement tape and a plumb line, we managed

to obtain the lengths of all the individual links. The angles i.e. the orientations

of each link with respect to the others were calculated by using simple

trigonometric ratios. To measure the diameters of each link a screw gauge

was employed.

The co-ordinates of various points on the chassis are given in the table

below. These coordinates were used to build the chassis on the software:

NODES X-COORDINATE Y-COORDINATE Z-COORDINATE

1 0 0 0

2 -5 -16 0

3 18 -42 0

4 18 -57 0

5 20 -57 -5

6 29 -63 -7

7 43 -63 -5

8 43 -63 5

9 29 -63 7

10 20 -57 5

11 48 -60 0

12 48 -50 0

13 37 -15.5 0

14 21 -7 0

15 26 -12.5 0

16 57 -13 -6

17 57 -13 6

18 68 -13 -7.5

19 68 -13 7.5

20 75 -11 -8



NODES X-COORDINATE Y-COORDINATE Z-COORDINATE

21 75 -11 8

22 89 -8 -8

23 89 -8 8

24 103 -5 -8

25 103 -5 8

26 114 4 -8

27 114 4 8

28 53 -33 -5

29 53 -33 5

30 61 -33 -8

31 61 -33 8

4.1 CO-ORDINATES OF VARIOUS POINTS ON THE CHASSIS 4.3 Modal Testing Procedure Implemented

Our experimental modal testing procedure consists of the following steps:

1. Setting up the modal test

2. Creating the geometry of the chassis

3. Documentation of the test

4.4 Setting up the modal test This involves

a) Structure preparation

b) Suspension of the chassis

c) Connection of exciter and force transducer

d) Transducer conditioning and calibration

e) Setting up the analyzer



The initial step was to prepare the structure which involved identification

of the points at which impact was to be made. The chassis was then

suspended as shown in the figure. Three elastic chords were used to suspend

the chassis from the ceiling. The accelerometer was mounted using wax on

one of the pre-determined points.

(A) (B)

(C)

4.2 (A) Chassis suspended by elastic cords (B) Uni-Axial Accelerometer (C) Wax used for mounting



Setting up the software The software employed to carry out the modal testing was LMS TestXpress

and LMS TestLAB.

LMS TestXpress is a software used for data acquisition. The

methodology we employed was to excite the chassis at several points by

means of an impact hammer (fig 4.3) and obtain the time domain curves. We

could either ACCEPT or REJECT these curves depending on their

smoothness, thus ensuring that only the best excitations were selected. An

average of five trials further ensured that the results obtained were optimal.

4.3 Impact Hammer along with the various tips used for excitation



Setting up the analyzer The figure below shows the 8-channel FFT analyzer provided by LMS.

Channel 1 is connected to the impact hammer.

Channel 2 is connected to the accelerometer.

4.4 Eight channel FFT Analyzer 4.5 Creating the geometry of the chassis

In this phase, a set of FRF measurements between the excitation DOF

and all the other defined DOF are made and stored.

In order to obtain the mode shapes, the geometry of the chassis was

required. On entering the coordinates, the software created the model as

shown in the figure.



4.5 Line diagram and Solid model of the chassis



4.6 Documentation of the test

LMS TestLAB was employed to extract the data from TestXpress.

To obtain the various mode shapes and to plot the required FRFs, the

following procedure was adopted.

1. In the NAVIGATOR column, choose a node point. Here select the FRF

option to view the frequency response characteristics.

2. In modal data selection, select SWITCH option which will display all the

created key points.

3. For selecting individual FRFs, just drag the required key point on to the

workspace. This displays the FRF for that particular point.

4. In the display option select sum of all the included FRFs. The following

window will appear.



The above graphs show the plots of Amplitude v/s Frequency and Phase v/s Frequency. There is an option to view the real and imaginary parts

against the frequency as well.



5. Next select the Time MDOF tab. Again in the display option select SUM.

The following window appears.

Also the bandwidth is specified as required. For our project, the bandwidth

selected was 0 – 177 Hz. This enables us to easily identify the peaks, which

represent the Natural Frequencies in the summed FRF.



6. Select stabilization. Here the most stable peaks in the summed FRF

are chosen. This gives the Natural Frequency at various modes.

Upon entering the shapes Tab, select all mode shapes in the ‘poles’ column

and say calculate. Drag the various modes to the workspace to view the

respective mode shapes.



4.7 Experimental Results Performing the ROVING HAMMER IMPACT test on the chassis, using the LMS software, the following results were obtained.

Mode Shape Natural Frequency in Hz

1 32.4534

2 74.2329

3 115.2834

4 120.8307




The natural frequency for the first four modes was calculated by both

Finite Element Analysis approach and Experimental Modal testing method.

The values for the respective modes are given in the table below.

MODE NUMBER

FREQUENCIES OF ANSYS RESULTS

( Hz)

FREQUENCIES OF

EXPERIMENTAL RESULTS (Hz)

DIFFERENCE PERCENTAGE DIFFERENCE

1 35.015 32.453 2.562 7.89

2 74.426 74.232 0.194 0.26

3 104.910 115.283 10.373 8.99

4 130.260 120.830 9.430 7.80

5.1 Comparison of Results

It can be seen that the results obtained through FEM (ANSYS) i.e. the

theoretical results are in excellent agreement with those obtained by the

experimental approach, done using the modal testing method.

To calculate the percentage difference between the two sets of results,

the experimental approach was set as the reference.



Successful attempt has been made to predict the vibrations induced in

motorcycle chassis by using Modal analysis. Also the Finite Element method

is made use of to predict the behavior of the chassis at different modes.

The present study was an attempt to find out modal parameters like

natural frequencies, mode shapes and amplitude of vibrations of chassis of a

two wheeler.

Here the modal analysis was done by treating the chassis as a freely

suspended structure. In future, the same work can be carried further to

analyze the chassis, subjecting it to different types of constraints.

The structure can be excited to dynamic harmonic forces and the

responses at handle bar, footrest and seat mount locations can be observed.

Same responses can be obtained using finite element method and further

they can be correlated with each other.

From the results and discussion we come to the conclusion that the

Experimental Modal analysis is very useful tool to find out the vibration

sources correctly and reduce the overall vibration level.

From the comparison of engine excitation frequencies with the FE

Modal analysis results, it was found that the possibility of resonance of the

chassis and the engine were remote.

The finite element vibration analysis not only predicts the natural

frequencies of chassis but also shows the scope for structural modification to

be carried out to minimize the vibration level of the motorcycle.



Technical Papers 1. Modal analysis of Motorcycle Chassis Frame by Finite Element Method P. S. Shinde, S. R. E. S. C. O. E., Kopargaon.

2. Experimental Modal analysis- A Non Mathematical Presentation - Peter Avitabile, University of Massachusetts, Lowell, USA 3. Basics of Structural Vibration testing and analysis - LDS

4. Applications of Conductive Mounting Pads for Vibration Analysis - Jack D Peters, CTC, Inc, Victor, New York.

5. Human Body Vibration Exposure and its measurement – G. Rasmussen.

6. Fundamentals of Modal Testing - Agilent Technologies

7. Dynamic Analysis - Markus Mock, University Of Pittsburgh, Pittsburgh, USA Internet Sources 1. www.google.co.in/ Dynamic analysis 2. www.Howstuffworks.com/ Motorcycle chassis

3. www.Diseno-art.com/Motorcycle Frames

4. www.Wikipedia.com/ the free encyclopedia/Modal Analysis.html

Text Books

1. Motor Cycle Dynamics, by Vittore Cossalter

2. Modal Analysis, Theory and practice, by D J Ewins


Dynamic analysis of two wheeler chassis

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