The Effects of Different Input Excitation on the Dynamic Characterization of an Automotive Shock Absorber

Transcription

1 NVC- The Eects o Dierent Input Excitation on the Dynamic Characterization o an Automotive Shock Absorber Copyright Society o Automotive Engineers, Inc. Darin Kowalski, Mohan D. Rao Michigan Technological University, Houghton MI 99 Jason Blough, Scott Gruenberg Keweenaw Research Center, Michigan Technological University, Houghton MI 99 Dave Griiths Ford Motor Company, Dearborn MI 8 ABSTRACT This paper deals with the dynamic characterization o an automotive shock absorber, a continuation o an earlier work []. The objective o this on-going research is to develop a testing and analysis methodology or obtaining dynamic properties o automotive shock absorbers or use in CAE-NVH low-to-mid requency chassis models. First, the eects o temperature and nominal length on the stiness and damping o the shock absorber are studied and their importance in the development o a standard test method discussed. The eects o dierent types o input excitation on the dynamic properties o the shock absorber are then examined. Stepped sine sweep excitation is currently used in industry to obtain shock absorber parameters along with their requency and amplitude dependence. Sine-on-sine testing, which involves excitation using two dierent sine waves has been done in this study to understand the eects o the presence o multiple sine waves on the estimated dynamic properties. In an eort to obtain all requency dependent parameters simultaneously, dierent types o broadband random excitations have been studied. Results are compared with stepped sine sweep tests. Additionally, actual road data measured on dierent road proiles has been used as input excitation to obtain the shock absorber parameters or broad requency bands under realistic amplitude and requency conditions. These results are compared with both simulated random excitation and stepped sine sweep test results. INTRODUCTION The shock absorber is one o the most important elements in a vehicle suspension system. It is also one the most non-linear and complex elements to model. The current method o characterizing the dynamic properties o shock absorbers or CAE models involves testing at discrete requencies, displacements, and preloads using an MTS test machine. The dynamic stiness (K) and damping (C) are extracted by itting a linear model o the orm F(ω)=K*x(ω)+C*v(ω) to the measured input displacement (x), velocity (v), and output orce (F). The excitation technique is a pure sine excitation at the desired requency and amplitude. These harmonic excitations are then swept through all desired requency and amplitudes. Parametric and non-parametric models also exist or the shock absorber. A non-parametric model based on a restoring orce surace mapping has been developed [,,]. The model considers the orce to be a unction o displacement and velocity. Although, this model is more applicable to a single requency excitation, it serves as a useul tool or identiying the non-linearity s in the system. A comprehensive physical model was developed by Lang [], later condensed and validated by Morman [6]. Lang s model has more than 8 parameters, is computationally complex and is not suitable or comprehensive vehicle simulation studies. Morman s model has been shown to be useul or studying the eects o design changes or a particular shock. Reybrouck [7] has developed a physical model, which has parameters, valid or requencies up to Hz, but has limited appeal or the analysis o shock absorbers or NVH applications.

2 The goal o this study was to determine i the current excitation technique holds true when more than one requency is present. The irst task included standardizing the testing procedure. This is done because shock absorbers characteristics change with temperature and nominal length. Sine-on-sine testing, dierent types o broadband random excitations have been utilized. Results are compared with stepped sine sweep tests. Additionally, actual road data has been used as input excitation to obtain the shock absorber parameters or broad requency bands under realistic amplitude and requency conditions. Details o these are presented in the ollowing sections TEST PROCEDURE All o the testing or this project was done using the MTS 8 elastomer characterization machine located at the Keweenaw Research Center o Michigan Technological University. A picture o a shock absorber in the test ixture is shown in Figure. The hardware used to control the MTS 8 was TestStar II. In conjunction with TestStar II, TestWare-SX sotware was used to organize a test matrix and also to monitor and record the desired parameters throughout the test. TestWare-SX, however, is only capable o producing pure sine excitations. Thereore, Component RPCIII (CRPC) sotware was used to excite the test specimen with arbitrary time domain excitation. CRPC has the ability to generate pure sine waves, multiple sine waves, shaped random excitations, or any arbitrary time domain excitation. Figure : MTS 8 Machine with Shock Absorber Installed ANALYSIS - The analysis methodology that TestWare- SX uses in its stepped sine sweep is visualized in Figure [8]. Shown in the igure are the output orce vector ( A load ) and input displacement vector ( A disp ) plotted in a real and imaginary ormat. From this representation the stiness (K) and damping (C) parameters can be calculated. * K = A A load disp * * K K = K cos( Φ), and = sin( Φ) ω Φ = Φ Φ,, load disp C. This analysis method can be extended to all requencies by realizing that K* and φ are simply the magnitude and phase o the requency response unction between the output orce and input displacement. This analysis method is the current industry standard in the elastomer characterization. Thereore, it will be used to analyze all the new excitation methods presented in this paper. VALIDATION OF COMPONENT RPCIII TestWare-SX Figure : Force and Displacement Vectors is assumed to yield correct shock absorber parameter estimates, since it is currently the deacto industry standard. Both CRPCIII and TestWare-SX are capable o producing pure sine wave input excitations. For this reason TestWare-SX has been used to validate CRPCIII or pure sine wave input excitations. The requencies o interest are between and Hz. Figures and show that the estimates or the stiness and damping parameters, K and C, are quite comparable between the two sotware packages. The reason or the slight deviation between the two is due to the act that these estimates are not taken rom the same data set. The same data set cannot be recorded by both sotware packages simultaneously, this results in a slight dierence between data sets. Having validated the CRPC package, all urther results presented in this paper have been obtained with the CRPC approach. TEMPERATURE EFFECTS - It is widely know that shock absorber characteristics vary with temperature [9]. In an eort to eliminate temperature eects rom the rest o this study, the shock absorber was instrumented with a thermocouple located on the outside o the main body o the shock absorber. The shock was then excited at 8 Hz and zero to peak amplitude o.8 mm or minutes. The temperature, input displacement, and output orce were recorded. Temperature and output orce versus time is shown in Figure. It is clearly seen that the output orce decreases as temperature increases. Since the input displacement was held constant, K* decreases with temperature, as shown in Figure 6. It was determined that temperature would be

3 maintained between 7 and 8 F or all uture tests in order to limit errors due to temperature eects. To veriy this, the temperature was monitored and recorded in all subsequent tests. K(N/mm) K Vs. Frequency or Sine Waves o.mm Amplitude RPC III Results Test Star Results 6 8 Figure : Stiness Estimates rom Test Star II and CRPCIII C Vs. Frequency or Sine Waves o.mm Amplitude RPC III Results Test Star Results. 6 8 NOMINAL LENGTH EFFECTS - The nominal length o a shock absorber is deined here as the distance between the top o the shock body and the top o the piston rod, as shown in Figure 7. The standard nominal length o this particular shock absorber was mm. To determine the eects o nominal length on the estimated shock absorber parameters, sine excitations o and Hz with zero to peak Figure 7: Nominal Length amplitudes o. mm were used at nominal lengths o 9,,, and mm. The estimated parameters rom these tests are shown in Figure 8. It can be seen that the estimated parameters are eected by the change in nominal length. The exact eect, however, is diicult to determine rom such a small test matrix. This is because the Hz stiness estimations are eected dierently than the Hz stiness estimations, as the nominal length is changed. Due to the dependency o the estimated shock absorber parameters on nominal length, the nominal length was checked to ensure that it was at the standard length in all remaining tests. Figure : Damping Estimates rom CRPCIII and Test Star II K V s. N o m i n a l L e n g t H z H m m S in e Temperature (degrees) 8 Temperature Vs. Time Time (seconds) Force Vs. Time 7 Maximum o Output Force 9 N o m ) m in a l L e n g t h (m K V s N o m i n a l L e n g t H z H m m S in e 6 9 Force (N) 6. 9 N o m in a l L e n g t h ( m m ) C V s. N o m i n a l L e n g t h Time (seconds) C (N*s/mm) H m m S i n e H m m S i n e Figure : Output Force and Temperature or Temp Test. 6 6 K * V s. T e m p e r a t u r e. 9 N o m m m in a l L e n g t h ( ) Figure 8: Results o K and C rom Nominal Length Study K* (N/mm) T e m p e r a t u r e ( D e g r e s F ) Figure 6: Variation o Dynamic Stiness with Temperature PURE SINE SWEEP TESTS In order to understand the eects o multiple sine waves on K and C, a baseline or the shock absorber parameters was irst established. The baseline consisted o pure sine waves with zero to peak amplitudes o.,.,., and. mm. The requencies chosen or the pure sine waves were,,,,, 8,, and Hz. The maximum requency anti-alias

4 ilter on the CRPC III boards is 6 Hz; thereore, the upper requency limit was below this to eliminate possible ilter eects. The orce transducer established the lower requency limit on the MTS 8, which was determined to be approximately Hz. The results o the baseline testing are shown in Figures 9 and. It can clearly be seen that stiness increases as a unction o requency. However, no clear trend emerged or stiness as a unction o amplitude. Figure shows that the damping estimates decrease signiicantly as a unction o requency and amplitude at requencies below 8 Hz. Above 8 Hz damping does not appear to change much with an increase in requency. the carrier wave and the higher requency wave is reerred to as the rider wave. In order to understand this sine-on-sine excitation a test Amplitude Example o Carrier and Rider Waves Time (sec) Figure : Example o Combined Carrier and Rider Wave K(N/mm) 6 K or Vs. Frequency & Amplitude.mm Sine Waves.mm Sine Waves.mm Sine Waves.mm Sine Waves 6 8 Figure 9: Stiness Vs. Frequency Curves or Dierent Amplitudes matrix was determined as ollows. The requencies o,,, and Hz are the carrier wave requencies. These requencies were held at a constant amplitude o.mm. The requencies o, 8,, and Hz are the rider requencies. These requencies will be added to the carrier wave requencies at amplitudes o.,.,., and. mm. In summary, this results in our dierent rider requencies at our distinct amplitudes being added to each o the our dierent carrier wave requencies. This results in a total o 6 dierent test conditions C or Vs. Frequency & Amplitude 6 8 SINE-ON-SINE EXCITATION.mm Sine Waves.mm Sine Waves.mm Sine Waves.mm Sine Waves Figure : Damping Vs. Frequency Curves or Dierent Amplitudes Having established the baseline, this study ocussed on how these parameters change when two requencies are present simultaneously. The driving orce or this inquiry is that in practice, shock absorbers experience multiple requencies simultaneously. Beore the shock can be studied with many requency inputs it must irst be understood or two requencies. The hypothesis is that when a higher requency wave is superimposed on a lower requency wave, the lower requency wave breaks the static stiction o the shock resulting in a lower orce requirement to move the shock at the higher requency. Thereore, a lower stiness estimate would be obtained at the higher requency. An example o a sine-on-sine input is shown in Figure. It can be seen that the lower requency higher amplitude wave looks like it is carrying the higher requency lower amplitude wave. For this reason, the lower requency wave is reerred to as STIFFNESS ESTIMATES OF RIDER WAVES - Shown in Figures - are the results that the carrier wave requencies have on the rider wave stiness estimates. Each graph is or a rider wave amplitude and has plotted the rider wave stiness estimates versus requency. Each series on these plots is or a dierent carrier wave requency. Also plotted are the values o stiness, at the appropriate amplitude, or the rider waves as pure sine inputs. When the rider amplitude is.mm the variance on the estimations is the greatest. This is believed to be due to the act that.mm amplitudes are approaching the noise loor o the measurement system. At all o the higher amplitude rider waves the variance is less. The stiness estimates at the rider wave requencies seem to be independent o both the requency o the carrier wave and the existence o a carrier wave. In conclusion, the existence o a carrier wave has little eect on the estimates o stiness at the rider wave requencies. DAMPING ESTIMATES OF RIDER WAVES - Figures 6-9 show these results. The damping estimates below Hz, or the rider requencies, do not approximate the pure sine estimates as closely as the stiness estimates did. However, above Hz the rider wave damping estimates obtained with sine-on-sine input are approximately the same as the estimates obtained using pure sine input excitation. Another interesting result shown in these igures is that the damping estimates increase relative to the pure sine estimates, as the rider wave amplitude increases. Hence, at the lower amplitude rider waves the pure sine estimate is the highest estimate, and at the higher amplitude rider waves the pure sine estimate is the lowest estimate.

5 STIFFNESS ESTIMATES OF CARRIER WAVES - Plotted in Figures - are the results or stiness estimates or the carrier waves. These plots are shown in the same manner as the rider wave results. Each graph is or one rider wave amplitude. Each series on these graphs is or a single rider wave requency. It can be seen that the stiness estimates or the carrier waves are eected by the presence o a rider wave. With the exceptions o carrier waves o and Hz, with a rider wave requency o Hz and amplitude.mm, all o the carrier wave stiness estimates are below the pure sine stiness estimates. These graphs also show that the stiness estimates or the carrier waves decrease as the rider requency is increased. This is clearly evident in Figure where the amplitudes o the rider and carrier waves are equal. Following the Hz rider wave through all the amplitudes shows that the carrier wave stiness estimates decrease as the rider amplitude increases. This trend is clearly evident when the Hz rider amplitude is equal to the carrier amplitudes, because the stiness o the carrier waves approach zero. DAMPING ESTIMATES OF CARRIER WAVES - Figures -7 show the damping estimates or the carrier waves as a unction o requency. When comparing the damping results o the carrier waves to the damping results o the rider waves, the carrier wave estimates are eected greater than the rider estimates. The estimates are quite scattered with no clear trend emerging. CONCLUSIONS FROM SINE-ON-SINE TESTING - The overall outcome o adding two sine waves together is diicult to sort out. However, the estimates at higher requency waves are ar less eected by the presence o the lower requency wave than the opposite. This is evident by the stiness estimates or the higher requency waves alling much closer to the values obtained with pure sine inputs. It is also demonstrated by the damping estimate, which was much closer to the pure sine value or the higher requency waves. In general, the higher requency wave dominates the parameter estimates or the shock absorber. This is demonstrated by the highest requency rider wave, o Hz, at the largest amplitude o.mm. When this wave was added to the lower requency carrier waves the parameters estimated at Hz were almost the same as the Hz pure sine wave. While, the parameters estimated at the lower carrier requencies tend towards zero. These results have yielded little light on what may happen when many requencies are added together and the shock absorber characterized or all requencies simultaneously. However, due to the rider wave dominance, it is speculated that the higher requencies will hold closer towards the pure sine values while the lower requencies tend towards zero. 6 K or Rider Vs. Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrer Wave K or Rider Vs. Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrer Wave K or Rider Vs. Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrer Wave Figure : Eect o Carrier Wave Frequency on.mm Rider Wave Stiness Estimates Figure : Eect o Carrier Wave Frequency on.mm Rider Wave Stiness Estimates Figure : Eect o Carrier Wave Frequency on.mm Rider Wave Stiness Estimates K or Rider Vs. Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrer Wave Figure : Eect o Carrier Wave Frequency on.mm Rider Wave Stiness Estimates

6 .6.. C or Rider Vs. Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrer Wave K or Carrier Vs. Rider Hz Rider Wave 8 Hz Rider Wave Hz Rider Wave Hz Rider Wave C (N*s/mm) Figure 6: Eect o Carrier Wave Frequency on.mm Rider Wave Damping Estimates Figure : Eect o.mm Rider Waves on Carrier Wave Stiness Estimates C or Rider Vs. Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrer Wave K or Carrier Vs. Rider Hz Rider Wave 8 Hz Rider Wave Hz Rider Wave Hz Rider Wave Figure 7: Eect o Carrier Wave Frequency on.mm Rider Wave Damping Estimates Figure : Eect o.mm Rider Waves on Carrier Wave Stiness Estimates C or Rider Vs. Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrier Wave Hz Carrer Wave K or Carrier Vs. Rider Hz Rider Wave 8 Hz Rider Wave Hz Rider Wave Hz Rider Wave Figure 8: Eect o Carrier Wave Frequency on.mm Rider Wave Damping Estimates Figure : Eect o.mm Rider Waves on Carrier Wave Stiness Estimates.9 C or Rider W Vs. Carrier Wave Hz Carrier Wave Hz Carrier W ave Hz Carrier W ave Hz Carrer Wave Pure Sine W aves 6 K or Carrier Vs. Rider Hz Rider Wave 8 Hz Rider Wave Hz Rider Wave Hz Rider Wave C (N *s/ m m) Figure 9: Eect o Carrier Wave Frequency on.mm Rider Wave Damping Estimates Figure : Eect o.mm Rider Waves on Carrier Wave Stiness Estimates 6

7 .8.6 C or Carrier Vs. Rider Hz Rider Wave 8 Hz Rider Wave Hz Rider Wave Hz Rider Wave Figure : Eect o.mm Rider Waves on Carrier Wave Damping Estimates.6 Figure : Eect o.mm Rider Waves on Carrier Wave Damping Estimates C or Carrier Vs. Rider Hz Rider Wave 8 Hz Rider Wave Hz Rider Wave Hz Rider Wave C or Carrier Vs. Rider Hz Rider Wave 8 Hz Rider Wave Hz Rider Wave Hz Rider Wave Figure 6: Eect o.mm Rider Waves on Carrier Wave Damping Estimates C or Carrier Vs. Rider Hz Rider Wave 8 Hz Rider Wave Hz Rider Wave Hz Rider Wave. Figure 7: Damp Eect o.mm Rider Waves on Carrier Wave Damping Estimates MULTIPLE FREQUENCY INPUT EXCITATION Now that sine-on-sine input excitation has been examined, the next step is to determine these parameters when all requencies o interest are present in the input excitation. It was decided to use random signals with the same envelope as the previously tested sine waves. For this study the peak-to-peak values o the random excitation was mm. This value was decided because there are pure sines with the same peak-to-peak values and because it yields the best signal to noise ratio o the available sine input amplitudes. Random signals are generated in three dierent ways or this study. The irst random signal generated has constant amplitude or all requencies. The second type o random signal generated weights the amplitudes at. The inal type o random signal weights the amplitudes at. It is important to remember that the peak to peak values o all three o these random signals is mm. This does mean however, that the amplitude at a given requency changes rom drive ile to drive ile. The power spectral densities o the input displacement and the output orce o these three signals can be seen in the Figure 8. The analysis o these signals is done spectral line by spectral line. The results o stiness and damping estimates are shown in Figures 9 and. Examining the damping estimate irst, it is noticed that above 6 Hz the damping estimates resulting rom the input signals o and all very close to the pure sine estimates. The estimates rom in the same region are higher than PSD o Displacement, mm /Hz PSD o Force, N /Hz Filtered Displacemet Spectrum or Random Input Signals o mm-pp - - Random (/ ) Random (/ ) -6 Random (/ ) Frequency, Hz Filtered Force Spectrum or Random Input Signals o mm-pp 6 Random (/ ) Random (/ ) Random (/ ) Frequency, Hz Figure 8: Power Spectral Densities o Input Displacement and Output Force or Random Input Signals 7

8 the pure sine estimates. Below 6 Hz none o the random signals show a good agreement with the pure sine values. One other thing noted is the act that the estimates rom and weighted random excitations are about the same throughout the entire requency range. This phenomenon holds true or the stiness estimates as well. Just like the damping estimates, the results rom weighting are higher than the other two, while the and weighted results are very close to one another. The results o stiness or seem to be an accurate estimator o the pure sine values above 7 Hz and below Hz. Between and 7 Hz the estimates are higher than the pure sine estimates. One alarming thing shown in the stiness graphs is that the estimates resulting rom and, below 6 Hz, all below zero. Having a negative stiness in a shock absorber is not a possible situation. As can be seen in Figure, the phase below 6 Hz rises above 9 degrees. This results in the stiness estimates in these areas to be negative. The reason is * that K = K cos( Φ), and the cosine unction changes Phase (degrees) Phase Random / Random / Random / K Vs. Frequency or mm-pp Inputs Figure : Phase between Input Displacement and Output Force or Random Inputs - Random (/ ) Random (/ ) Random (/ ) Figure 9: Stiness Vs. Frequency or Random Input Signals compared to Pure Sine Values sign at 9 degrees. It was hypothesized that the phase jumps were being caused by the shock absorber being over driven, by the amount o energy input at the higher requencies. This was speculated because the amplitude, or random weighting, is the same at all requencies. It is known that this is not the case when the shock absorber is in operation. In order to test this hypothesis the random input excitation o was iltered to contain only requencies below 6 Hz. The shock absorber was then excited using this lower requency limited random signal. As can be seen in Figure, the phase angle between input displacement. C Vs. Frequency or mm-pp Inputs Random (/ ) Random (/ ) Random (/ ) Phase Random (/ ) Random (/ ) below 6 hertz C (N*s/mm).. Phase (degrees) Figure : Damping Vs. Frequency or Random Input Signals Compared to Pure Sine Values Figure : Comparison between Phase Values o /^ Random Signals 8

9 and output orce, o this abbreviated random does not contain any jumps in phase like the broader requency excitation. This supports the hypothesis that when all the requencies are excited with the same, or close to the same amplitude, it is not a realistic situation and the shock absorber is being over driven. As shown in Figure, the stiness estimates became realistic or the abbreviated random signal as expected. The stiness estimates rom this iltered input signal all close to the pure sine estimates. The two almost lie on top o each other below 6 Hz. The stiness estimates looked very promising or obtaining the same parameter estimates with broadband noise as pure sine waves. However, when examining the damping estimates, in Figure, the same phenomenon does not hold true. The damping estimates obtained rom the random signal, below 6 Hz, do not have the same estimates as obtained rom the pure sine waves. The estimates rom the abbreviated random signal have higher damping estimates than the pure sine estimates. C (N*s/mm) K Vs. Frequency Random Figure : Comparison o Stiness Estimates rom Pure Sines and /^ Randoms C Vs. Frequency Random Random (/ ) Random (/ ) below 6 Hz Random (/ ) Random (/ ) below 6 Hz Figure : Comparison o Damping Estimates or Pure Sines and /^ Random Input CONCLUSIONS FROM BROADBAND RANDOMS - What has been learned rom the random noise excitation study o the shock absorber? I the shock absorber is not being over driven, the random excitation will result in believable estimations or both stiness and damping. The results vary somewhat with the values obtained rom pure sine excitation. However, there is no reason to assume that the baseline o the pure sine excitation yields the best estimations because in practice shock absorbers see broad band requency inputs. ROAD EXCITATION In an eort to obtain a true shock absorber response in operation, a midsize sedan was instrumented with two 6 B8 PCB accelerometers. One accelerometer positioned on the top o the shock and one positioned was on the bottom o the shock. The automobile was then driven down a smooth highway, a semi rough paved road, and a rough dirt road, while the time traces o the accelerometers were recorded using the LMS Road Runner acquisition system. The dierence between acceleration signals was integrated twice in the requency domain, to get displacement. The signals were iltered below. Hz and above 6 Hz. The roughest dirt road proile is shown in Figure. Displacement (mm) Displacement (mm) - Rough Road Time Trace o Shock Displacement - 6 Time (sec) Frequency Spectum o Shock Displacement Figure : Measured Rough Road Proile The time trace shows maximum displacements o about mm. The requency domain representation o the road proile is quite interesting. The maximum displacements are about. mm and occur around Hz. The displacement inputs, above 8 Hz, are miniscule compared to the displacement inputs at the lower requencies. Due to dynamic range limitations on the MTS 8 machine these higher requency lower amplitude signals are diicult to reproduce. This results in a low conidence level in the parameters estimated above 8 Hz. Shown in Figures 6 and 7, are the estimated shock absorber parameters rom a road proile excitation. It is seen that the estimations do not look very realistic. The estimations or stiness drop below, and the damping estimates are all over the place. The reason these estimates look like this may be due to the 9

10 reproduction o the road proiles in the MTS 8 machine K Vs. Frequency Random Semi-Rough Road Rough Road Smooth Road Figure 6: Stiness Estimates Using the Road Data as Input C Vs. Frequency Random Semi-Rough Road Rough Road Smooth Road the time signal is a random signal with the same spectral content as the measured road data. Shown in Figures 9 and are the estimated parameter results rom the shaped road requency spectrum random excitation. It is important to keep in mind that there is little conidence in these results above 8 Hz, due to the low amplitudes. The stiness and damping curves are much more realistic or an automotive shock absorber using this method as opposed to the pure road response excitation. In the area in which conidence is held the parameter estimations are very close to the estimations rom pure sine wave excitation. There are slight deviations between the two methods, but one must keep in mind that the road parameters are estimated at many more requencies than the pure tones. Due to the realistic displacement conditions during this test, the results are as close to how the shock acts in operation as can be done at this time. In an eort to smooth these graphs out, they have been curve it in Matlab. 7 6 Semi-Rough Road Rough Road Smooth Road K Vs. Frequency Random Figure 7: Damping Estimates Using the Road Data as Input It is also possible that a dierent averaging scheme should be used when calculating the requency response between the input displacement and the output orce o the road excitations. The reason has not yet been determined. However, what has been done is to copy the requency displacement spectrum and add a random phase to it. This yields a shaped random signal with the same requency spectrum as the original road data. This is illustrated in Figure 8, where it is seen that the requency spectrum is the same as Figure. However, Displacement (mm) Displacement (mm) Random Noise with Duplicated Frequency Spect Time (sec) Random Noise with Duplicated Frequency Spect Figure 8: Duplicated Frequency Spectrum with Random Phase Figure 9: Stiness Estimates using road data with random phase C Vs. Frequency Random Semi-Rough Road Rough Road Smooth Road Figure : Damping Estimates using road data with random phase The results are shown here in Figures and. It is seen that the stiness and damping estimate are airly close to those o pure sine waves. In the case o stiness the estimates are a little lower than those obtained with pure sine excitation. The smooth road stiness estimations all well below the pure sine

11 estimations and the other road proile estimations. This is believed to be a result o the reproduction o the small displacements seen on the smooth road. Thereore, this series is disregarded because the data is approaching the noise loor o the measurement system. The two other road proiles are very close to one another and are o higher amplitudes, so these results are meaningul. The damping estimates using the shaped road spectrum all almost on top o the estimated damping rom pure sine excitation. C(Ns/mm) Figure : Stiness Vs. requency rom copied road spectrum curve it Figure : Damping Vs. Frequency rom copied road spectrum curve it CONCLUSIONS Curve Fit K Vs. Frequency or Copied Spectrum Smooth Road Semi-Rough Rough Road Curve Fit C Vs. Frequency or Copied Spectrum Smooth road Semi-Rough Rough Road The results o these studies have proven a number o things. First it has proven that when a comparison study is being done on an automotive shock absorber the temperature o the shock absorber must be maintained and monitored throughout the test. Another thing that must be monitored is the stroke length o the shock absorber rom test to test, i the estimated parameters are going to be compared. Secondly, when two sine waves are added together and used to actuate a shock absorber, the parameters estimated at each requency are dependent on one another. The dependency is a unction o the amplitude o the two waves and a unction o how ar apart the two requencies are. In the case where one requency is quite a bit higher in requency than the other, the higher requency maintains its parameters where as the lower requency parameter estimations are very low. The parameters estimated using sine-on-sine testing were not the same as the parameters estimated using pure sine waves. This iners that maybe pure sine excitation does not yield good parameter estimations. However, when broadband excitation was used the parameters estimated were very close to the estimations using pure sine waves. This means that the pure sine excitation produces realistic estimated parameters. It has been shown in the discourse o this paper that all the estimated parameters can be ound at once when using a shaped random signal. The best type o shaped random is one that has the same requency spectrum that the shock absorber sees in practice. When using this type o shaped random signal, the parameters estimated are close to those estimated using pure sine excitation. Using this type o excitation has a couple o big advantages. First the actual test takes ar less time than the stepped sine sweep. Also, due to the short test time, the temperature o the shock absorber does not change signiicantly during the test. The biggest advantage is that the dynamic parameters or all amplitudes and requencies are obtained simultaneously. At this time some o the higher requency and very small amplitude road responses cannot be reproduced, but this problem is sure to be addressed and solved in the not too distant uture. REFERENCES. Rao, M. D., Gruenberg, S., and Torab, H., Measurement o Dynamic Properties o Automotive Shock Absorbers or NVH, Proc. O SAE 999 Noise and Vibrations Con. 999, pp Caerty, S., Worden, K., Tomlinson, G., "Characterization o Automotive Shock Absorbers Using Random Excitation," Proc. Instn. Mech Engrs, Vol 9, 99.. Belingardi, G. and Camoanile, P., Improvement o the Shock Absorber Dynamic Simulation by the Restoring Force Surace Mapping Method, Proc. O the th International Seminar on Modal Analysis and Structural Dynamics, Leuven, Belgium, pp.-, 99.. Duym, S., Schoukens, J., Guillaume, P., A Local Restoring Force Surace Method, Proc. th IMAC, Nashville, Tennessee, pp. 9-99, 99.. Lang, H. H, A Study o the Characteristics o Automotive Dampers at High Stroke Frequencies, Ph.D. Thesis, University o Michigan, Morman, K., A Model or the Analysis and Simulation o Hydraulic Shock Absorber Perormance, Part I- Theoretical development (SR-8-), Part II- Parameter Identiication and Model Validation Studies (SR-86-6), Ford Motor Company Research Sta Reports. 7. Reybrouck, K., A Non Linear Parametric Model o an Automotive Shock Absorber, SAE Paper No. 9869, Vehicle Suspension ans System Advancements, SP-, pp , MTS TestStar II Control Manual, 79. Dynamic Characterization. 9. Surace, C., Storer, D., Tomlinson, G. R., "Characterizing an Automotive Shock Absorber and the Dependence on the Temperature," Proc. o th IMAC, 99, pp. 7-6.

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