ARTICLE IN PRESS

doi:10.1016/j.biosystemseng.2004.08.011PM—Power and Machinery

Biosystems Engineering (2005) 90 (2), 153–160

Design Optimisation for the Vertical Suspension of a Crop Sprayer Boom

Jan Anthonis1; Jorgen Audenaert2; Herman Ramon1

1Laboratory of Agricultural Machinery and Processing, Katholieke Universiteit Leuven, Kasteelpark Arenberg 30, 3001 Heverlee, Belgium;e-mail of corresponding author: jan.anthonis@agr.kuleuven.ac.be

2John Deere Fabriek Horst B.V., Energiestraat 16, 5961 PT Horst, The Netherlands

(Received 24 December 2003; accepted in revised form 10 August 2004; published online 30 November 2004)

The dynamics of a vertical suspension for a 39m wide boom on a John Deere crop sprayer was optimised. Theoptimisation was based on a mathematical model of the suspension with an existing non-linear Konis dampercharacteristic. During the optimisation, several tracks, which are based on power spectral densities ofmeasurements in different field conditions, are applied to the suspension. The objective function to beminimised is the standard deviation of the absolute boom rotation around the horizontal axis while applyingthe tracks. As the model is simple but accurate, computation time is small such that many different fieldsituations can be imposed during optimisation. By playing with the distance to the rotation point of thedamper and selection of the appropriate damping value, the optimum could be realised.r 2004 Silsoe Research Institute. All rights reserved

Published by Elsevier Ltd

1. Introduction

Over the past 10 yr, the width of field sprayers hasincreased drastically. Nowadays, sprayers having awidth of 45m are commercially available. Owing tolarge spray boom widths, flexible behaviour of spraybooms becomes important. Even small deformations ofthe structure can cause, by the large spray boom width,considerable displacements at the boom tips. However,there is not a clear correlation between boom width andthe amount of spray boom motion. Another importantfactor is whether it concerns a trailed or a mountedsprayer (Herbst & Wolf, 2001). As spray boom motionsplay a dominant role on the spray distribution pattern,spray boom stability is important. Theoretical studies,simulations and field experiments have indicated thatdue to spray boom vibrations, spray deposit distributionvaries between 0 and 800% (Ramon & De Baerdemae-ker,1997; Ramon et al., 1997; Sinfort et al., 1997; Oomset al., 2002).

The most important vibrations, affecting the spraydistribution pattern, are rolling (rotational motionaround an axis along the driving direction) causingspray boom motions in the vertical plane and two typesof vibrations in the horizontal plane, yawing and jolting

1537-5110/$30.00 153

(anti-symmetric and symmetric motions, respectively)(Fig. 1). Despite the fact that horizontal boom move-ments are much more critical for the spray depositdistribution (Wolf, 2002; Ramon & De Baerdemaeker,1997), this paper focuses on rolling, as practice showsthat proper tuning of the vertical suspension is stillproblematic. There are almost as many vertical suspen-sions as there are manufacturers. However, most ofthem can be classified in one of the following fewcategories: pendulum-based suspensions, trapezoidallinkage systems, suspensions in which the boom isallowed to roll or slide on a curved shape, and cablesuspensions. Although almost all of them can bedescribed as a second-order low pass filter (Anthoniset al., 1999), they differ significantly from a practicalpoint of view. The differences are the frequency rangesin which the cut-off frequency can be located and howthe damping of the boom can be controlled. The lowerthe cut-off frequency of the suspension, the lessvibrations are transmitted from the tractor to the boombut the slower the boom reacts when tilting it by theactuator, which is used to put the boom parallel to theslope of the field. Most of the suspensions are tunedthrough the experience of the manufacturer, but forsome types of suspensions, theoretical studies are

r 2004 Silsoe Research Institute. All rights reserved

Published by Elsevier Ltd

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Fig. 1. Most important motions affecting the spray distribution pattern (rolling, yawing and jolting)

Frame connected to the tractor

Boom

First pendulum rod

Rotation point

Second pendulum rod

Spring-damper

J. ANTHONIS ET AL.154

available (Deprez et al., 2002; Ramon & De Baerde-maeker, 1995; Frost & O’Sullivan, 1988; O’Sullivan,1988; Nation, 1987a and 1987b).

In this paper, a pendulum-based suspension for a39m spray boom of John Deere crop sprayer isoptimised. A similar optimisation has already beencarried out on the 27m of the 800 Series, John Deerecrop sprayer and turned out to be very successful(Hekkert, 2003), but has never been published by theauthors. The following issues are considered: modellingof the suspension, location of dampers, modelling ofcommercially available dampers and when and where touse springs. The theoretical optimisation was discussedwith design engineers of John Deere and a compromisehas been made between theory and practice. The modelsused for optimisation and the suspension itself arevalidated.

Boom

Hydraulic cylinder

Frame connected to the tractor

(a)

(b)

Fig. 2. Two possibilities to insert springs and dampers in thesuspension: (a) configuration A with vertical suspension linkages

and (b) configuration B with horizontal suspension linkages

2. Suspension configuration

Essentially, the suspension of the 39m crop sprayer ofJohn Deere consists of a double pendulum. The firstpendulum serves as a passive suspension. The secondpendulum is steered by a hydraulic cylinder and is usedto follow the slope of the field. This hydraulic cylinder iscontrolled by an on–off flow valve. In case the valve isnot activated, the second pendulum is blocked and thesuspension is a simple passive single pendulum system.

Whenever the addition of extra springs or dampers isrequired, several locations are possible. They can beconnected between the boom and the frame fixed to thetractor (Fig. 2 configuration A) or between the firstpendulum rod and the frame fixed to the tractor (Fig. 2

configuration B). Most manufacturers select for the firstoption (configuration A). Simulations, performed in thisstudy, indicated that configuration A is not the bestsolution. This can be understood intuitively. In the casewhere dampers are connected between the frame fixed tothe tractor and the boom, the dampers always workagainst the action of the actuator to put the boomparallel to the field. Suppose that the frame fixed to thetractor in Fig. 2(a) follows the slope of the field and theboom needs to turn to the left (indicated by the arrow

below the figure), then the dampers have to slide in andout, resulting in a force counteracting the motion of theactuator. In this situation, springs work cooperatively asthey exert a moment to the left. However, when the

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DESIGN OPTIMISATION OF A CROP SPRAYER BOOM 155

boom and the frame fixed to the tractor are parallel andthe boom needs to be rotated relative to the frame fixedto the tractor, both springs and dampers try to preventthe motion of the actuator.

On the contrary, when the springs and the dampersare connected between the first pendulum and the framefixed to the tractor, and the boom has to be turned tothe left (indicated by the arrow below the figure), thesprings have to work against the action of the dampersbut the dampers do not hamper the action of theactuator. When the boom has to be rotated relative tothe frame fixed to the tractor, again the springs and thedampers help the actuator as they deliver an extrareaction force to the actuator.

When the actuator is not steered, both placements ofsprings and dampers have the same effect.

Fig. 3. Detailed view of the double pendulum suspension

3. Mathematical modelling of the suspension

In a first step, a parameterised mathematical model ofa boom suspension is conceived. With this model,different spring and damper characteristics and loca-tions are determined in a more systematic way beforestarting an implementation in practice. Generally,despite the fact that spray boom motions are large, therotation angles of boom roll performed by a spray boomare small. Owing to the large boom widths, smallrotations cause large boom displacements. With theassumptions of small rotations, linear models can bederived, which has already been successfully performedby other authors (Deprez et al., 2002; O’Sullivan, 1988;Frost & O’Sullivan, 1988; Nation, 1987a and 1987b).The equations of motion of a double pendulumsuspension have already been determined by O’Sullivan(1988) or can be found in some textbooks on engineeringvibrations (Thomson, 1998). However, the John Deeresuspension (Fig. 3) is geometrically more complex, andfor optimisation, these structural details are important,especially when springs and dampers are introduced. Asa consequence of this requirement, the suspension wasmodelled in detail by applying the method of the virtualwork described by Ramon and De Baerdemaeker(1996). The boom itself is modelled as an undeformablebeam. This assumption is reasonable, as the resonantfrequency of vertical boom suspensions for long boomshas generally an order of magnitude of 0�1Hz and thefirst flexible vertical mode is located in a range between0�6 and 1�5Hz (Parloo et al., 2003; Clijmans et al., 2000;Langenakens et al., 1999). Owing to the suspensionsystem, the flexible modes are only softly excited.

Four degrees of freedom are considered, i.e. two forexcitation of the boom and the two degrees of freedomof the pendulum. The two degrees of freedom, exciting

the boom (Fig. 2), are the rotation and translation of thefixed frame connected to the tractor around the pivotpoint of the first pendulum rod to this frame. Withoutsprings between the first pendulum rod and the frame,rotation of the latter is unable to induce boom roll incase of a perfect pivot point. Only the translationalexcitation degree of freedom can do this. Therefore,inserting springs in the suspension is a bad solution forboom stability but enables the sprayer to followpartially the slope of the field (see later). The transla-tional excitation is often caused by rolling of the wholesprayer around its centre of gravity.

After modelling the suspension, according to theprocedure of Ramon and De Baerdemaeker (1996), anequation of the following form is obtained:

M s €q þ C s _q þ K sq ¼ Fsf (1)

in which Ms, Cs, Ks and Fs are, respectively, the mass,damping, stiffness and input distribution matrix, q, thevector of Lagrangian generalised coordinates, contain-ing the four degrees of freedom and f, the input forcevector. The force vector f contains the lateral force andtorque exerted on the frame fixed to the tractor, causingrespectively translational and rotational motion of thisframe and the force exerted by the hydraulic cylinder totilt the boom. For simulation purposes, Eqn (1) is notvery useful since it is difficult to evaluate the forces andtorques acting on the frame connected to the tractor inreal-field situations. Displacements or rotations of theframe connected to the tractor can better be estimatedmore readily or measured in the field by, for example,accelerometers. The hydraulic actuator is connected to aflow valve, imparting a velocity to the piston rod ratherthan a force. Therefore, the force inputs need to bereplaced by the motion of their point of action, i.e. the

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rotation and transversal motion of the frame connectedto the tractor and the motion of the actuator. In caseEqn (1) is already available, replacement of the inputforces f by the motion of the point of action is an easytask. A systematic procedure exists that can automati-cally convert Eqn (1) into an equation with the motionof the point of action of the forces f as inputs (Anthonis,2000; Anthonis & Ramon, 2003). By this operation, onlyone degree of freedom remains, i.e. the rotation of thefirst pendulum rod around the pivot point of the frameconnected to the tractor.

Figure 4 shows the ratio of the absolute boom rollover the different inputs in the case where springs areinstalled. The figure indicates the effect of a certaininput on the absolute boom roll, which frequencies areattenuated and which are amplified. If no springs areinstalled, the effect of tractor roll as input on boom rollis zero. The springs force the boom to follow themotions of the frame attached to the tractor up to theresonant frequency (highest peak on the figure) [Fig.

4(b)]. In case the latter frequency is not well damped, theboom over-reacts to the motion of the frame connectedto the tractor and the boom starts to roll. Beyond theresonant frequency, the boom is unable to follow tractorroll and the suspension acts like a low pass filter. FromFig. 4(b), it is clear that the boom only partially followsthe slope of the field as for frequencies below theresonant frequency, the amplitude or gain is below 0 dB.The gain is the ratio of the absolute boom roll over theinput rotation of the frame connected to the tractor. Asthe tractor crosses the field, it globally follows the slope

100 102

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10−2

Am

plit

ude,

dB

10

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−70

20

Am

plit

ude,

dB

Frequency, Hz

1010−2

Frequ(a) (b)

Fig. 4. Transfer functions for: (a) transversal input;

of the field, i.e. it will follow certainly the slow variationsof the field but not every unevenness. Whenever the gainis one, the tractor rotation and boom roll are equal. Ifthis happens in the low-frequency range, the boomfollows the slope of the field as it follows the tractor. Themore stiff the springs are made, the closer theamplitudes approach the 0 dB line.

Concerning transversal motions of the tractor, thesuspension seems to react like a high pass filter [Fig.

4(a)]. However, by considering transversal accelerationsinstead of transversal displacements, which is morenatural as structural vibrations are more associated witha certain acceleration, the shape of the transfer functionhas a similar lowpass characteristic as the transferfunction in Fig. 4(b).

For the effect of the actuator displacement on theboom roll, Fig. 4(c) shows that the boom can only reacton actuator displacements with a frequency contentbelow the resonant frequency of the boom. Contrary toFig. 4(b), Fig. 4(c) has a horizontal asymptote beyondthe resonant frequency at about �35 dB, which impliesthat for an actuator motion with a frequency contentbeyond the resonant frequency, the boom also respondsbut with an attenuation of �35 dB. By consideringdisplacements and rotational inputs instead of forcesand torques; however, it is assumed implicitly that thereis always enough force and power available to realise themotion of the actuator. In practice, the power of theactuator is limited, such that in practical cases, from acertain frequency and amplitude of motion, the effect ofthe actuator on boom roll drops to zero.

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ency, Hz

100 10210−2

Frequency, Hz(c)

(b) roll input; and (c) and actuator displacement

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DESIGN OPTIMISATION OF A CROP SPRAYER BOOM 157

4. Model validation

All parameters were supplied by John Deere. Theweight, moment of inertia, and locations of the centre ofgravity were determined from a virtual prototypedesigned in Pro-Engineer. As a first validation, theresonant frequency could be measured by tilting theboom and measuring the time for one back and forthmotion. However, a resonant frequency does notcompletely characterise the transfer function of thedifferent inputs to boom roll (Fig. 4). It turns out thatthe transfer function from the actuator motion to boomtilt [Fig. 4(c)] contains the most parameters. Further-more, if this transfer function is known, the othertransfer functions of Fig. 4 can be calculated. Therefore,the model of the suspension is validated by measuringthe transfer function from the actuator displacement tothe absolute boom rotation. To determine this transferfunction experimentally, i.e. the frequency responsefunction (FRF), the motion of the actuator is measuredby a linear variable displacement transducer (LVDT)and two ultrasonic sensors, measuring the distance tothe ground level. From the ultrasonic sensor signals, theabsolute rotation of the boom can be calculated.

For the determination of the FRF, the boom shouldbe persistently excited. As the valve steering the actuatoris an on–off valve, no continuously varying voltage canbe sent to the valve. Therefore, the frequency content ofthe boom excitation must be controlled by controllingthe timing the actuator is left or right pressurised. Todetermine the frequency range in which the boom mustbe excited, a simple pendulum experiment was per-formed to determine the resonant frequency, which isaround 0�06Hz. The lowest frequency is selected at0�01Hz and the highest 1Hz. For the lowest frequency,a compromise must be made. The lower the lowestexcitation frequency, the longer one side of the actuatoris pressurised, with the risk that the boom hits theground. In case the boom touches the ground, the boomreceives input from another source which disturbs themotion of the boom and the measurement. By hittingthe ground, the causality between actuator motion andboom roll is lost such that the calculated FRF fromthese measurements does not represent the one-to-onerelationship between actuator displacement and boomroll. On the other hand, the lowest excitation frequencyshould be low enough to be able to measure theamplification factor of the transfer function in staticconditions (0Hz).

Another issue, directly related to the lowest excitationfrequency is the length of the input signal. It must besuch that enough periods in the response of the systemare available to estimate the points of the FRF at thelowest frequencies. As the actuator is a single rod

cylinder, it displaces more in the case when the rod sideis activated than when the piston side is pressurised. It isvery difficult to incorporate this effect in the excitationsignal because the amount of motion for a certainactivation time is not proportional to the difference inarea between piston and rod side. At the rod side, ahigher pressure is required to move the cylindercompared to the piston side, causing a longer reactiontime at the rod side. The difference in dynamics of bothsides of the actuator cannot compensate the effect of thedifference in area. Therefore, during the experiment, theboom will drift slowly to one side. To compensate thiseffect, the boom is tilted to one direction before startingthe measurements. Even so, after some time, the boomwill hit the ground on the other side. To prevent this, thelength of the input signal must be restricted. By selectingthe input signal time 204�8 s, hitting the ground couldjust be prevented and only two periods of the lowestfrequency can be measured.

The excitation signal, which is a binary sequence, iscalculated by making use of the Frequency DomainToolbox in Matlab (Kollar, 1995). This excitation signalhas approximately a uniform spectrum, containing 4096points, which are sampled at 20Hz.

During the experiments no extra springs or dampersare installed. The FRF G( jo) is estimated by

Gð joÞ ¼YD

(2)

in which o the angular frequency (frequency multipliedby 2p), Y the fast Fourier transform (FFT) of theabsolute rotation of the boom (y) and D the FFT of thedisplacement of the actuator d. Figure 5 shows goodcorrespondence between the model and the measure-ments and justifies the use of a linear model. The FRF isdisplayed up to 0�16Hz. At higher frequencies, poorFRF estimates were obtained because of low signal-to-noise ratio. This is caused by the small reaction of theboom at higher frequencies within the order ofmagnitude of the accuracy of the ultrasonic sensor. Asthe FRF is measured without damping devices, thedamping of the suspension is caused by friction. FromFig. 5, a viscous damping coefficient has been estimated,which is 10 800Ns/m.

5. Optimisation

Previous discussion pointed out that by incorporatingsprings into the suspension, tractor roll is more easilytransmitted to the boom. Furthermore, by insertingsprings in the suspension, the resonant frequency of theboom increases, giving rise to a more unstable boom ashigher frequencies can enter the boom more easily.

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0

5

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Am

plitu

de, d

B

Frequency, Hz

Fig. 5. Validation of the linear model: solid line, measured;dashed line, predicted

J. ANTHONIS ET AL.158

Based on this, John Deere design engineers decided toincorporate only springs in the suspension whenever thesprayer is used in hilly conditions. As the springs aresupporting boom rotations, with the same actuator(hydraulic cylinder), higher inclinations of the boom canbe attained. John Deere decided that the slope of thefield should be followed for 70%, which means that incase the slope of the field is 20%, the boom inclination is14%. By this the resonant frequency increases to0�11Hz.

From the theory of vibrations (Thomson, 1998), it isknown that the optimal damping ratio for a second-order system is 0�7. This implies that a linear dampershould be found and located in the suspension such thata damping ratio of 0�7 can be achieved. However, inpractice no standard dampers are available providinglinear damping. A practical damper has an S-shapeforce–velocity characteristics instead of a straight linegoing through the origin. Generally, this S-shape isapproximated by a piecewise linear function (curveconsisting of pieces of straight lines) (Naude & Snyman,2003a). One reason to approximate the S-shape functionby a piecewise linear function is that the dampermanufacturer only provides force velocity values for alimited amount of points. In order to study the effect ofcommercially available dampers, the suspension modelneeds to be extended such that non-linear dampers canbe incorporated. This is performed by defining twoadditional outputs, which are the speed of change of the

connection points where the dampers are integrated inthe suspension, i.e. the speed of the change in length ofthe dampers if they would have been incorporated,and providing two extra inputs, i.e. the internalforces exerted by the dampers on the suspension.Between the newly created inputs and outputs of themodel, non-linear damper characteristics can be easilyinserted. The complete model is programmed inSimulink (2001).

Several optimisations can be performed with thismodel. A first possibility is to determine the optimalforce–velocity characteristics of the damper (Naude &Snyman, 2003a, 2003b), which is as such an interestingstudy but the problem is the commercial availability ofthe desired damper. In this research, a commerciallyavailable damper force–velocity curve is selected whichbest suits the application. Konis is the dampersupplier of John Deere, such that characteristicsof their gamut should be selected. In a very early stage,the optimisation revealed that a set of damperswith high damping value should be selected. As thedamping value is directly related to damper cost, it isclear that the dampers should be placed as far aspossible from the rotation point of the pendulum inorder to achieve a large lever arm. The largest lever armscan be achieved by placing the dampers horizontally.Therefore, a gas damper needs to be selected as they canbe placed horizontally. Gas dampers have a parasiticspring effect. The spring effect can be modelled as alinear spring.

The optimisation starts from a certain Konis damperpair located at both sides of the pendulum. Initially it isplaced as far as possible from the rotation point of thefirst pendulum with the frame connected to the tractor.During optimisation, the distance and number ofdampers will be varied. Simulations are performed withthis suspension configuration for different simulatedfield conditions. The authors have a large experienceconcerning field measurements on sprayers in differentsituations. Based on power spectral densities (PSD)measured at the frame to which the vertical suspensionis attached, field signals are generated as follows

f ik ¼ real FFT�1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPi � nið Þ

p� e jrik

� �� �(3)

in which fik is a sequence representing an excitation of afield signal generated based on PSD Pi for field situationi and a sequence of random phases rik, ni is the length ofthe PSD Pi, j is the complex number and ‘real’ is thefunction taking the real part of a complex variable. Inthis way, different time signals are generated withthe same PSD. The different sequences of timesignals fik are applied to the mathematical model, givingrise to absolute boom rotations b

pik for one particular

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0

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0.1

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0.2

0.25

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0.35

0.4

0.45

Abs

olut

e bo

om r

otat

ion,

rad

ians

Time, s

Fig. 6. Validation of the simulation model for the optimisedsuspension: solid line, measured; dashed line, simulation

DESIGN OPTIMISATION OF A CROP SPRAYER BOOM 159

suspension configuration p. For every boom responsesignal, two measures are defined for the quality of thesuspension, i.e. standard deviation s

pik and the maximum

deviation mpik:

spik ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

ni � 1

Xni

l¼1

ðbpikðlÞ � b

p

ikÞ2

s(4)

mpik ¼ max

ljb

pik lð Þj (5)

in which bp

ik is the mean value for a sequence and maxthe maximum over all points l in the sequence. For everysuspension configuration p, two measures are calculated,reflecting the quality of the suspension:

sp ¼ mean spik

� �(6)

mp ¼ mean mpik

� �(7)

where the function mean calculates the mean value.Criteria (6) and (7) are similar indicators; therefore only(6) is used as a decision variable. As dampers of aparticular series of Konis will be used, the optimisationvariable is a multiplication factor by which the forcevalues of the damper characteristic are multiplied. Amultiplication factor larger then one implies that thedamper should be placed further away from the rotationpoint, and that a damper with higher damping value ormore dampers need to be installed. By playing with thedistance to the rotation point and different dampers, theoptimum can be realised. It turns out that the optimalsolution from an economic and dynamic point of view isrealised by placing two dampers on the left and right asin Fig. 2(b) at a distance of 0�65m from the verticalrotation point.

Note that the suspension is optimised for a largenumber of field situations. This implies that for aparticular field situation, probably a more optimalsuspension exists. However, overall the suspensionshould be the most optimal. The fact that a big numberof field situations could be taken into the optimisation isbecause of the simple model, requiring only a smallamount of computation time. Five field signals gener-ated according to Eqn (3) which take in reality 400 s canbe simulated in approximately 28 s by a 2�6GHzpersonal computer.

To ensure the quality of the simulation model andthus the quality of the optimisation, the optimisedmodel is validated. This is performed by an experimentin which the boom is tilted and released. The boomrotation is measured by two ultrasonic sensors mountedsymmetrically with respect to the centre of the boom. Inthe simulation, the boom is released from the same angleand both time signals are compared (Fig. 6). Goodcorrespondence is noted between the simulation and the

real boom motion. As previously mentioned, the gasdampers introduce a parasitic spring effect increasingthe natural frequency of the boom from 0�058 to0�074Hz.

The same procedure could be repeated for the casewhere springs are inserted in the boom. John Deeredesign engineers decided that the dynamic improvementof the boom does not countervail against the economiccosts.

6. Conclusions

A double pendulum vertical suspension for a 39mboom of a John Deere crop sprayer has been optimised,based on a mathematical model of the suspension. Priorto the actual optimisation, a good conceptual study ofthe placement of dampers and possible springs is a pre-requisite to obtain a high-performance suspension. Thebehaviour of the pendulum suspension is basicallylinear, such that a linear model can be employed. Thedampers have a non-linear behaviour and their forcevelocity characteristics are inserted in the model.Optimisation is performed by applying vehicle pathsfrom different field situations and by minimising aquadratic criterion, which is a measure for boomvibrations. The optimisation variable is a multiplicationfactor, determining the number of dampers and the leverarm of the dampers. A large number of vehicle paths canbe taken into the optimisation as the model is simpleand fast to simulate. Despite its simplicity, the modelcaptures the dominant dynamics and non-linearities.Comparing the behaviour of the suspension with theoptimal damper settings to the simulations shows goodcorrespondence between theory and practice.

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J. ANTHONIS ET AL.160

Acknowledgements

Jan Anthonis is funded as a Post-doctoral Fellow bythe Fund for Scientific Research—Flanders (Belgium).

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