MODELLING OF ROAD VEHICLE SUSPENSIONSYSTEMS FOR PERFORMANCE EVALUATION

Damien Maher and Paul Young,

School of Mechanical and Manufacturing Engineering, Dublin City University, D9, Irelanddamien.maher3@mail.dcu.ie, paul.young@dcu.ie

Abstract

The suspension of a road vehicle is a non-linear system that poses significant challenges tothe designer. One particular area of road vehicle suspension analysis which has taken ona greater significance in recent years is the reduction of noise and vibration transmittedthrough the suspension into the vehicle. In designing a suspension, the interaction of eachof the components with the vehicle must be understood together with both individual andsystem characteristics. While gross simplifications can be made to provide rough estimates ofthe system behaviour, only a complete analysis of individual components and then assemblyinto a system model can provide a proper understanding of the implications of design changesfor stability and vibration isolation.

This paper will present work recently started on the simulation of vehicle suspension systems.Preliminary testing was carried out on a purpose built quarter-car laboratory suspensionrig. Results will be presented which compare the operational response of the system to thecomputer simulation response. The use of operational modal analysis on suspension systemswill also be examined with the goal of using results from testing to further the developmentof the suspension mathematical model.

1 Introduction

A vehicle suspension is a non-linear system that poses significant challenges to the designer.Its main purpose is to ensure the safe, controlled movement of the car. This requires differentresponses depending on the characteristics of the road surface encountered. In addition, itmust cushion the driver from the more severe shocks, while transmitting enough informationto give confidence that the vehicle will perform as expected to driver inputs. A lower priority,but more obvious to the driver, is the reduction of noise and vibration in the vehicle.

In designing a suspension, the interaction of each of the components with the vehicle mustbe understood together with both individual and system characteristics. The complexity ofthe system arises in the non-linear characteristics of the individual elements - Tyre, hub,bushes, links, spring and shock absorber. Simulation plays an important part in the designprocess. The most widely used suspension simulation is the Quarter Car model [3]. Itconsists of sprung and unsprung masses connected by spring and damper elements. The tyreis modelled as a linear spring and its damping is neglected.

This work will focus on the MacPherson Strut suspension, a popular system in cars today.Findings presented in this paper are part of ongoing research into the use of the quarter carmodel for the development of suspension simulations.

2 Background

The quarter car model is the most widely used suspension system model [3]. Many pub-lications use the quarter car model as the basis for suspension simulations. The authorsfound little dedicated research on the validity of the relatively simple quarter car model atpredicting the movement of complex suspension systems. A number of authors includingKim et al. [5] have cast doubts over the effectiveness of the quarter car model in predictsuspension movement in certain circumstances, especially when suspension kinematics arecomplex. Turkay and Akcay stated that the quarter car model is ‘too simple for performinga comprehensive analysis of the ride motion of the vehicle’ [7]. Verros et al. however statedthat the quarter car model is used due to its simplicity and due to the qualitatively correctinformation it provides for ride and handling studies in the initial stages of design. [8].

Kim and Ro wrote that the two mass quarter car model is effective in predicting the twodominant modes, sprung mass bouncing and wheel hopping [4]. They did however have somereservations about the component data used in such simulations. The authors constructed anaccurate complex model in ADAMS, a commercial multibody dynamic analysis software, andused it to produced a reduced order model. They estimated the component parameters forthe reduced order model and found them to be very far from the measured component data.They also referred to work carried out by Kim et al. [5], in which it was shown that suspensionkinematic structure has an influence on the effectiveness of this simple model. This studyshowed that the quarter car model with component data taken from real components hada different response to the real system. They termed parameters owing to the suspensionstructure as ‘invisible’ uncertainties. A set of revised component parameters were calculatedto improve the accuracy of the results. This may be a case of fitting the results to themeasurements, and may be missing the important underlying problem that the quarter carmodel cannot predict complex kinematic structures.

The work carried out in references [5] and [4] used ADAMS instead of a real experimentalsystem. This paper will assess the usefulness of the quarter car model using a purposebuilt test rig subject to a range of excitations. The rig mimics the MacPherson strut typesuspension. This was one identified by Kim et al. to be only slightly affected by suspensionlayout. There is clearly a grey area surrounding the quarter car model in terms of whenit can be used and for what types of simulations it can be used. This paper will look at anumber of different excitations and discuss the usefulness and accuracy of the quarter carmodel in predicting suspension behaviour.

This work will also look at the use of operational modal analysis methods for suspension sys-tem identification. A number of papers have looked at the use of operational modal analysisas a means of identifying vehicle suspension systems. Successful validations of operationalmodal results using classical modal testing techniques have been achieved. Hermans andVan Der Auweraer used operational modal analysis methods to solve a noise problem in apassenger car [2]. The rear suspension system was identified as the problem and operationalmeasurements were made. Operational modal analysis found the problem to be relate toa bending mode at 73 Hz. This compared favourably with the 74.6 Hz measured underlaboratory conditions. Moller et al. looked at operational modal analysis of mechanical sys-tems in general [6]. In this paper they compared traditional modal analysis and operationalmodal analysis of a plate structure with electric motor attached. The results showed that itwas possible to extract all modes in the frequency range of interest using operational modalanalysis.

3 Testing Apparatus and Methodology

Figure 1a shows the laboratory test rig purpose built for this research. It was designed tomimic a MacPherson Strut type car suspension and is approximately half full size. A variablespeed motor drives CNC machined cams which provided the input to the system. The rigincludes an optical sensor which measures the frequency of rotation of the cam. This allowsthe frequency of the input to the simulation to be matched to the frequency of the cam inputto the rig. The rig also has interchangeable steel and rubber bushings. This will allow theflexure of bushing to be taken into consideration. The inputs applied during preliminarytesting included sine waves and step inputs. Measurements taken were accelerations of thesprung and unsprung masses allowing displacements to be calculated.

Figure 1: Testing Apparatus

A one degree of freedom shaker system was also developed for this rig. This can also beseen in figure 1b. Figure 1c shows the layout of the shaker system. It consists of a plate onwhich the tyre sits. Weak springs under the plate take the weight of the rig and the shakeris then attached to the plate via a stinger. This setup allows for operational measurementsand modal analysis to be carried out on the same rig. A shaker system based on similarprincipals was developed by Anthonis et al. to enable mobile evaluation of the vibrationcharacteristics of agricultural and off-road machinery [1].

Figure 2: Quarter Car

Simulations were carried out in Matlab and Simulink. The quar-ter car model was used as the basis for the simulations. Figure 2shows the Quarter Car model. It consists of sprung and un-sprung masses connected by spring and damper elements. Thetyre is modelled as a linear spring and its damping is neglected.The use of the suspension rig allowed for the measurement ofparameters which could be used in the simulation. The pa-rameters measured were, Unsprung Mass, Sprung mass, SpringStiffness, Tyre Stiffness and Shock Damping. The spring wascustom made for the rig. The tyre stiffnesses were measuredusing a compression testing machine. The tyre was compressed30mm and the measured stiffness was found to be linear in thisrange. The custom spring stiffness was also verified using thecompression tester.

Rig Measurements were carried out using Pulse. The Pulse hard-

ware/software family is Bruel & Kjærs platform for noise and vibration analysis. A com-puter based simulation tool was developed for the purpose of quickly carrying out time andfrequency analysis on Experimental measurements and Simulation Results. Experimentalmeasurements are setup and run using Visual Basic control of Pulse. Visual Basic exportsmeasurement data to Matlab which reads this outputted data into a graphical user interface.In Matlab simulations can be run to compare experimental data with simulation data in thetime and frequency domains. This simulation tool provided the basis for a validation of thequarter car model as a means of simulating vehicle suspension systems.

4 Verification of the Quarter-Car Model

Comparisons were made between the experimental results taken from the suspension rig andsimulated results taken from the Matlab model. A profile of how well the quarter car modelsimulates the movement of the suspension rig was then developed over a range of differentfrequencies and excitations.

4.1 Sine Input

Sine excitation was used to begin with due to its simplicity and the rig was setup with steelbushings. The rig was excited at different frequencies using 2 node, 4 node and 8 node camsup to a maximum frequency of 14Hz. The 2 and 4 node cams had amplitudes of 5mm whilethe 8 node cam had an amplitude of 2.5mm. The measurements taken were accelerations ofthe sprung and unsprung masses. Displacements were calculated from these accelerations.

Table 1 shows the percentage error between measured and simulated, sprung and unsprungmass, acceleration and displacement values. This table was calculated using RMS values.Negative values indicate that the simulation under estimated the measured value.

Table 1: % Error in Simulation Results for Sine Excitations

Mass Measurement 2Hz 4Hz 6Hz 8Hz 10Hz 12Hz 14HzUnsprung

Acceleration -41 -15.7 -14.2 -17.1 -27.0 -45.4 -59.2Displacement 33.0 41.4 20.9 16.2 -19.7 -42.5 -55.2

SprungAcceleration 44.8 72.0 76.6 32.8 19.7 3.8 -24.9Displacement 70.8 84.8 90.9 35.4 5.2 -23.3 -43.3

4.1.1 Sprung Mass

Table 1 shows sprung mass displacements to have large percentage errors. The RMS valuesat higher frequencies are misleading. Figure 3 is a typical output produced by the Matlabsimulation comparison tool. It shows very good correlation between measured and simulateddisplacements for a simulation time between 10 to 10.25 seconds. Lengthening of the obser-vation time to 14 seconds revealed a beat pattern to the sprung mass movement as shown infigure 4. Although the quarter car model was unable to predict this beat pattern, it predictedthe higher frequency movement of the sprung mass with good accuracy. This beat patternwas observed at 12 and 14 Hz and to a lesser extent at 10 Hz. The simulation over predicts

Figure 3: Measured (- -) and Simulated (—) displacements at 14Hz

sprung mass accelerations in all cases except at 14 Hz. The simulation does however predictthe acceleration of the sprung mass accurately at 12 Hz. This can be seen in figure 5

4.1.2 Unsprung Mass

The unsprung mass displacements at 10, 12 an 14 Hz also showed a beat pattern, resultingagain in misleading RMS amplitudes. The simulation in this case however still under predictsthe higher frequency component but not to the extent suggested by RMS values.

Figure 4: Sprung Displacement 14Hz

Looking at the unsprung acceleration errors, it canbe seen that the simulation under predicts the mea-sured accelerations at each frequency. The errorsare greatest at the higher frequencies. Figure 5shows accelerations at 12 Hz. In this case notethe considerably higher peak and RMS accelera-tions of the measured unsprung mass compared tothe simulated unsprung mass. A possible reasonfor the higher measured accelerations may be dueto the tyre momentarily leaving the surface of thecam at the higher frequencies. This is the reasonthe 8 node cam was designed with an amplitudeequal to half that of the other cams. This is some-thing which cannot be predicted by the quarter carmodel simulation. Lateral movement of the wheelwas also noticed at higher frequencies and particularly when using the 8 node cam. This typeof movement would also be present in actual car suspensions and is not taken into accountin the quarter car simulation. Wheel imbalance may also be a source of error in this caseand may explain the increasing percentage error with increasing frequency.

Figure 5: Measured (- -) and Simulated (—) accelerations at 12Hz

4.2 Step Input

The second type of excitation used was a step input. The step size used was 25mm, 10% ofthe wheel height. This would be equivalent to approximately 50mm in a full size car. Theaccelerations produced for the sprung and unsprung masses can be seen in figure 6(a). Asimilar pattern to the peaks produced can be seen for the simulated and measured accel-erations. The simulation does however predict lower peak accelerations than the measuredvalues. Figure 6(b) shows the displacements of the sprung and unsprung masses for the25mm step input. Again the simulation is in good agreement with measured values in termsof the pattern to the peaks. The peak displacements in this case are over predicted by thesimulation.

5 Discussion

The results show that the quarter car model was not particularly effective in predictingthe quarter car rig movement. This is a surprising result considering that only simple sineexcitation was used. Table 1 does however show some trends in the predictions made bythe quarter car model. In general it under predicted unsprung mass accelerations and overpredicted sprung mass accelerations. Lateral movement of the wheel was observed duringsimulations, especially at higher frequencies. This type of wheel movement would be observedin actual car suspensions due to bushing and suspension arm deflection. The idea behindusing steel bushings in this work was to simplify the movement of the rig as much as possible.New steel bushings will be manufactured to tighter tolerances and a stiffer A-arm setup willbe used in an effort to eliminate this lateral movement. As the analysis of the systemprogresses and the simulation complexity increases this lateral movement of the wheel willbe introduced using flexible rubber bushings and the simulation will be adjusted accordingly.

Sprung and unsprung displacements were over predicted in most cases. The beat patternidentified in the displacement time plots will be investigated further. An interesting findingwas how accurately the quarter car simulation predicted the high frequency component ofthe displacement time plots at 10, 12 and 14 Hz.

(a) Acceleration (b) Displacement

Figure 6: Measured (- -) and Simulated (—) Step Results

Kim et al. [5] showed that complex suspension kinematic structure has an influence on theeffectiveness of the quarter car model. This may not be a major source of error in thiscase due to the simple layout of the quarter car rig. The shock is mounted vertically and thesprung mass is constrained to move in the vertical direction. Furthermore no rubber bushingswere used during this analysis. Kim et al. also highlighted concerns about using measuredcomponent data in the presence of complex suspension geometries. Measured componentdata was used in this simulation as Kim et al. also noted the fact the the MacPherson strutsystem was only slightly affected by changes in suspension geometry.

The step input provided some interesting results. Although the peak accelerations are lowerfor the simulated than for the measured, a similar pattern to the peaks can be seen. The inputapplied to the simulation in this case was not a true step input. The tyre acts as a geometricfilter and this was taken into account in developing the input for the simulation. Protrusionof the step into the tyre would be a source of error for two reasons. Firstly deflection of thetyre as it impacts the step will result in incorrect inputs to the simulation as the tyre wasassumed rigid in the development of the simulation input. Secondly vibrations induced inthe tyre due to impacting the step are not accounted for in the quarter car simulation. Ahigh speed camera will be used to examine these phenomenon and quantify their effects.

One assumption made during this work is that the cams input pure sine waves. The camswere CNC machined ensuring high tolerances. The actual profiles were developed in a 2DCAD package to ensure there rotation provided a sine input to the wheel. Errors may arisefrom cam drive shaft flexure during high frequency operation. The rig is currently beingredesigned to minimise such occurrences.

6 Future Work

Sources of errors identified during this work will be examined in an effort to eliminate them.Work is under way to upgrade the motor and gearbox system of the suspension rig. With theupgraded motor, the rig will be capable of simulating vehicle velocities close to 100km/hr.This will facilitate the use of circular cams with small bumps to simulate the random inputwhich would be encountered due to asperities on a road profile. The motor will also be

capable of ramping up in speed allowing a sine input cam to input a swept sine wave profile.The upgraded system will ensure better correlation between cam inputs and simulated inputsdue to a more rigid design.

The shaker system which has been recently developed will also be used in the testing ofoperational modal analysis methods on the rig. Pseudo random inputs provided by therotating cam will be used to simulate driving conditions. Operational modal results collectedunder these conditions will be compared to traditional modal results collected using theshaker system.

7 Conclusion

The experiments used a ‘Quarter Car’ Rig which was built and tuned for the purpose ofthis study. Operational analysis and modal analysis can both be carried out on this rig.The rig was excited using sine waves and step inputs using rotating cams. Results from theexperimentation were compared with simulated values obtained from a quarter car simulationrun in Matlab. Although results showed large percentage errors between the simulated andmeasured values for both the sine and step inputs, trends in the results have been identifiedand will be examined further. A number of issues with the rig have also been identified andwill be rectified.

References

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