INFLUENCE OF SHOCK ABSORBER MODEL FIDELITY ON THE PREDICTION OF VEHICLE HALF ROUND PERFORMANCE Chris Masini Oshkosh Corporation Oshkosh, WI

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1 2010 NDI GROUND VEHICLE SYSTEMS ENGINEERING ND TECHNOLOGY SYMPOSIUM MODELING & SIMULTION, TESTING ND VLIDTION (MSTV) MINI-SYMPOSIUM UGUST DERBORN, MICHIGN INLUENCE O SHOC BSORBER MODEL IDELITY ON THE PREDICTION O VEHICLE HL ROUND PERORMNCE Chris Masini Oshkosh Corporation Oshkosh, WI Xiaobo Yang, PhD Oshkosh Corporation Oshkosh, WI BSTRCT Moel base esign techniques are being use increasingly to preict vehicle performance before builing prototype harware. Tools like DMS an Simulink enable very etaile moels of suspension components to be evelope so vehicle performance can be accurately preicte. In creating moels of vehicle systems, often there is a question about how much component etail or moel fielity is require to accurately moel system performance. This paper aresses this question for moeling shock absorber performance by comparing a low fielity an high fielity shock absorber moel. high fielity an low fielity mathematical moel of a shock absorber was evelope. The low fielity shock absorber moel was parameterize accoring to real shock absorber harware imensions. Shock absorber force vs. velocity curves were calculate in Simulink. The results from the low fielity an high fielity moel were compare to shock absorber force vs. velocity test results. New vehicle esigns must meet requirements for maximum river s seat acceleration uring half roun testing. These requirements have create a nee for preicting half roun performance. The low fielity an high fielity shock absorber moels were place in a 7 Degree-of-reeom vehicle moel. Maximum river s seat acceleration was calculate an simulation results were compare to half roun test results from a prototype vehicle for a 10mph, 8 half roun test. INTRODUCTION Suspension systems for a new vehicle esign must meet various performance requirements such as rie an hanling, etc. n efficient suspension esign is usually base on the ability to accurately preict suspension performance using computer simulation tools such as DMS or Simulink, where the fielity of the vehicle simulation moel is epenent on the fielity of various sub-component moels. In view of the critical contribution of shock absorbers to vehicle ynamic response uner half-roun events, in this stuy, the influence of shock absorber moel fielity on preiction of half roun performance of a four-wheele vehicle is investigate. etaile hyraulic moel of a shock absorber was create in Simulink an the calculate force-velocity profile was then compare to shock absorber test results to emonstrate the high fielity of the shock absorber moel. On the other han, a set of simplifie equations were then evelope to moel the force-velocity curve provie by the shock absorber manufacturer. The simulation results from the simplifie equations were compare to those from the Simulink moel an shock absorber test results. inally, vehicle half roun test results from a four-wheele vehicle were compare to vehicle simulation results. Half roun simulation results were calculate from a 7 egree-offreeom (DO) Simulink moel of a four-wheele vehicle. Simulation runs were mae with the simplifie shock absorber equations an the more complex hyraulic shock absorber moel. comparison of time omain traces an peak responses for half roun simulation results an test results was mae to show the influence of shock absorber moel fielity on preiction of vehicle half roun performance. ORCE VS. VELOCITY CURVES Shock absorber amping is one of the primary means to tune the rie an hanling of vehicle suspension systems. Vehicle esigners use shock absorber force vs. velocity curves to specify the appropriate shock absorber amping characteristics. n example force vs. velocity curve is shown in figure 1. The force vs. velocity curve shows how

2 much force a shock absorber will generate for a given amount of velocity uring extension (REB) an compression (COMP). Shock absorbers are typically teste accoring to SE J1574-1, Measurement of Vehicle an Suspension Parameters for Directional Control Stuies [1]. The force vs. velocity curve is generate by applying a linear velocity or a sinusoial input to the shock absorber. The force vs. velocity curve is a primary communication tool between vehicle esigners an shock absorber manufacturers. There are several ifferent shock absorber esigns incluing position sensitive, ajustable amping an variable amping shock absorbers. These esigns form a amping envelope on the force vs. velocity curve. The work in this paper will focus on a shock absorber esign with a single force vs. velocity curve as shown in figure 1. m = && x = = m && x = sum of forces applie to the mass or mass or acceleration The an check have a force which is calculate using the linear equation: x = isplacement = x + = rate _ preloa _ preloa = preloa on (1) (2) Relief Valve 1 Relief Valve 2 DMPER ORCE (N) Check Valve 1 P1, V1 1=1*P1 P2, V2 2=2*P2 mass Check Valve 2 External Input Seal friction DMPER VELOCITY (m/s) COMP REB igure 1: Shock bsorber Measure orce vs. Velocity x=0 (+) x, (+) igure 2: Schematic of Shock bsorber Hyraulic Circuit HIGH IDELITY SHOC BSORBER MODEL high fielity numerical moel of the hyraulic circuit insie a shock absorber was create in Simulink. igure 2 illustrates a schematic view of the hyraulic amper. Dynamic equations for the amper valve, amper check valves, amper volume an were evelope. The governing equations for the moel are evelope below. The, an check mass ynamics are escribe by Newton s 2 n Law: The, an check have a force applie to them by the expose pressure area: P area = P opening _ pressure pressure _ area opening _ pressure to or = area of pressure _ area = pressure applie or (3) or the an check, flow area was calculate using a simple annular opening area as a function of position using the equations: INLUENCE O SHOC BSORBER MODEL IDELITY ON THE PREDICTION O VEHICLE HL ROUND PERORMNCE Page 2 of 7

3 D opening = π D _ iameter _ iameter = iameter x = isplacement x simple pi**x relationship was selecte for the an check because the shock absorber has a simple isc valves to relieve pressure in the amping. s the isc valve opens, it forms an annular area between the isc an the amping which is efine by equation (4). low through the an check was calculate using the orifice equation [2]: C _ flow = C opening = ischarge coefficient ρ = flui ensity 2 P ρ opening _ pressure ischarge coefficient of 0.62 an a flui ensity of 850kg/m^3 was use for the hyraulic flui in the shock absorber. (4) (5) P& Β = ( in out ) V Β = flui bulk moulus V = volume of shock absorber in out = sum flow into shock absorber = sum of flow out of shock absorber The bulk moulus for the selecte hyraulic flui was 1,000 MPa or 145,000psi [3]. The flow into the cyliner must take into account the motion of the. The time rate of change of volume in the shock absorber was calculate from velocity: x& _ flow _ area = = area of shock absorber amping = amping _ area x& velocity (7) (6) DMPER ORCE(N) 0 DMPER ORCE(N) 0 vance Simulink Test Data DMPER VELOCITY(m/s) Simple Simulink Test Data DMPER VELOCITY(m/s) igure 3: Shock bsorber Measure an High ielity Simulink orce vs. Velocity The pressure insie the hyraulic cyliners was calculate using the ynamic pressure / flow equation [2]: igure 4: Shock bsorber Measure an Low ielity Simulink orce vs. Velocity Damping velocity was calculate by integrating the acceleration of the or mass. To simulate the force vs. velocity curve in Simulink, the shock absorber moel was constraine an simulate accoring to SE J1574-1[1]. sinusoial input of +/- 150mm was applie to the shock absorber moel. The force applie to the shock absorber an the resultant velocity of the shock absorber moel was calculate an plotte in figure 3. igure 3 shows simulation results from the high fielity shock absorber compare with test results for the shock absorber. INLUENCE O SHOC BSORBER MODEL IDELITY ON THE PREDICTION O VEHICLE HL ROUND PERORMNCE Page 3 of 7

4 The high fielity shock absorber moel force vs. velocity profile showe goo correlation with test results. The governing equations selecte for the hyraulic components provie an accurate preiction of the force vs. velocity behavior of the shock absorber. There were some isavantages to the high fielity moel. The high fielity shock absorber moel was teste with an DMS moel of the vehicle. The DMS moel woul not run using cosimulation with the high fielity Simulink shock absorber moel because the high fielity shock absorber moel ha high frequency components that stalle the co-simulation. simplifie representation of the shock absorber was neee to run the co-simulation with DMS. LOW IDELITY SHOC BSORBER MODEL simplifie set of governing equations for the behavior of the hyraulic valve insie the shock absorber was evelope. The simplifie moel was neee for use with DMS an to spee simulation times in Simulink. The simplifie governing equations for the shock absorber were evelope base on an algebraic relationship between pressure an flow through the shock absorber. The ifference between the low fielity moel an the high fielity moel is the low fielity moel oes not inclue the secon orer mass ynamics of the shock absorber,, an check. The mass ynamics are efine by equation (1). lso, the low fielity moel oes not inclue the first orer pressure ynamics of the shock absorber flui volumes efine by equation (6). ll other equations are similar between the low fielity an high fielity moels. The flow through the valves in the low fielity shock absorber amping was calculate using external velocity inputs to the shock absorber. The source of external velocity input for the force vs. velocity simulation was a sinusoial velocity input. The shock absorber velocity input for the half roun simulation was calculate from the relative motion between the suspension an the boy of the vehicle in the 7 egree-of-freeom moel escribe below in the section title 7 DO Vehicle Moel. The velocity inputs to the Simulink shock absorber moels were moele after the real test inputs from the force vs. velocity test an from the half roun test. The following equations were evelope for the low fielity shock absorber moel. The force vs. velocity performance of the shock absorber was parameterize using an algebraic relationship between pressure an shock absorber velocity. The moel parameters represent real shock absorber component imensions. or the low fielity moel, the orifice flow equation was use to calculate the flow through the amping. This is the same as equation (5) which was use for the high fielity moel [2]: C P = C = = orifice coefficien t ρ = = flui area ensity flow 2 P ρ = pressure rop across The equation for valve opening area is the same as equation (4): D opening = π D _ iameter _ iameter = iameter x = isplacement x or a loae, the opening height is relate to pressure by the equation: x P = preloa _ = = rate preloa _ = pressure area preloa (8) (9) (10) low through the amping is relate to the amping pressure by the equation: x where : = C P = π D * x preloa _ 2 P ρ (11) INLUENCE O SHOC BSORBER MODEL IDELITY ON THE PREDICTION O VEHICLE HL ROUND PERORMNCE Page 4 of 7

5 inally, flow through the amping is relate to the shock absorber velocity by the equation: x& = _ area / _ area = area of shock absorber amping (12) vehicle moel to stuy the influence of shock absorber moel fielity on preiction of river s seat acceleration uring a half roun event. 7 DO VEHICLE MODEL One of the requirements for a new vehicle esign is to meet river s seat acceleration limits on a half roun test. During the half roun test, a test vehicle is riven over half roun cyliners with pre-efine iameters ranging from 2 to 12. The half roun test simulates riving over a log, obstacle or spee bump in the roaway. This test is repeate igure 5: Test Vehicle 8 Half Roun Test Equation (12) efines the pressure vs. velocity relationship for the shock absorber. It is parameterize accoring to equation (11) with the actual valve imensions. Equation (11) was entere into a Simulink lookup table to calculate the force generate by the shock absorber in response to velocity inputs. Calculation an test results for the force vs. velocity of the shock absorber were plotte in figure 4. Goo correlation was achieve between the low fielity shock absorber moel an test results. The low fielity Simulink shock absorber moel was also teste with DMS an a solution coul be calculate using cosimulation. The isavantage of the low fielity moel was the hysteresis associate with the bulk moulus of the shock absorber hyraulic flui an the masses of the valve components was not calculate. The secon orer mass ynamics of the an check s an the first orer pressure ynamics associate with the volumes in the shock absorber cause the hysteresis of the high fielity moel which is shown in figure 3. igure 4 shows there is no hysteresis with the low fielity moel because the force vs. velocity characteristics of the low fielity moel are efine by a table create from equation (11). The low fielity moel has no first or secon orer system ynamics. With these observations, the low fielity an high fielity shock absorber moels were place insie a 7 DO Simulink igure 6: 7 DO Simulink Vehicle Moel at increasing vehicle velocities until the peak acceleration of the river s seat excees 2.5 G s. The velocity at which the vehicle excees 2.5 G s is reporte. igure 5 shows a photograph of the prototype test vehicle approaching the half roun. 7 DO moel of a test vehicle was create in Simulink to simulate the half roun performance of a prototype vehicle. igure 6 shows the schematic from the 7-DO Simulink vehicle moel. The boy or sprung mass of the vehicle was efine to have 3 egrees of freeom, pitch, roll, an vertical motion. The other 4 egrees of freeom were efine as the vertical movement of the four un-sprung masses comprise of the suspension linkage, wheels, s, shocks, an tires at each of the 4 corners of the vehicle. Two 7 DO moels were create. One vehicle moel was create with the high fielity shock absorber moel at each of the four corners of the vehicle. secon vehicle moel was create with the simplifie shock absorber moels at each corner of the vehicle. Both vehicle moels were run in parallel in the same Simulink moel to eliminate errors associate with using ifferent moel set-ups. INLUENCE O SHOC BSORBER MODEL IDELITY ON THE PREDICTION O VEHICLE HL ROUND PERORMNCE Page 5 of 7

6 The response of the test vehicle to half roun roa inputs was calculate. The roa input was phase from front to rear to account for the longituinal spacing of the axles. The lag to the rear axle was calculate by iviing the wheel base by the velocity of the vehicle. ll river s seat acceleration simulation an test results were post-processe using a 30Hz low-pass Butterworth filter to remove high frequency components from the ata. COMPRISON O SIMULTED ND MESURED HL ROUND RESULTS Half roun tests were performe on a test vehicle with all simulation runs recore on vieo. The test vehicle was instrumente with an accelerometer uner the river s seat an with front an rear wheel position sensors. igure 5 shows a picture of the test vehicle approaching an 8 inch half roun obstacle at 10mph. Time omain river s seat acceleration results are shown in figure 7. igure 7 inclues measure river s seat roun event, aitional testing woul nee to be complete to unerstan the influence of the low fielity moel on simulating fast repeating events such as an RMS course simulation or a rumble strip simulation. When comparing the river s seat acceleration test ata to simulation results in igure 7, the measure peak Wheel Position (%) 100% 80% 60% 40% 20% 1 (+)Z VERTICL MOTION UP TEST DT SIMPLE MODEL DVNCED MODEL 0% Time (sec) cceleration (g`s) igure 8: Measure vs. Simulate ront Wheel Vertical Motion for 8 Half Roun at 10mph 100% 80% 30Hz ilt TEST DT SIMPLE MODEL (-)Z VERTICL MOTION DOWN DVNCED MODEL Time (sec) igure 7: Measure vs. Simulate Driver s Seat cceleration for 8 Half Roun at 10mph acceleration ata (30Hz ilt TEST DT). igure 7 also inclues the simulate river s seat acceleration from the 7 DO vehicle moel. Low fielity (SIMPLE MODEL) an high fielity (DVNCED MODEL) shock absorbers simulation results were overlai on top of the measure river s seat acceleration. igure 7 shows goo correlation between the low fielity an high fielity shock absorber moels for calculate river s seat acceleration. Eliminating hysteresis associate with the bulk moulus of the flui in the shock absorber ha a minor influence on simulate river s seat acceleration for the half roun event. lthough this was true for the half Wheel Position (%) 60% 40% 20% TEST DT SIMPLE MODEL DVNCED MODEL 0% Time (sec) igure 9: Measure vs. Simulate Rear Wheel Vertical Motion for 8 Half Roun at 10mph acceleration of the river s seat was significantly higher than the simulate peak acceleration. The simulate peak acceleration response of the river s seat was 0.6 g s. The measure response of the river s seat was 1.3 g s. The simulate response was 54% low for preiction peak river s seat acceleration response. INLUENCE O SHOC BSORBER MODEL IDELITY ON THE PREDICTION O VEHICLE HL ROUND PERORMNCE Page 6 of 7

7 One explanation for the ifference between calculate an measure rivers seat response is the measure acceleration response of the river s seat shows a short uration(less than 100ms) peak acceleration event at 6.3 secons. It is possible that the rear suspension on the test vehicle hit the reboun har stop uring the test, causing the acceleration spike. The response of the vehicle to impacting a har stop was not simulate in etail in the 7 DO Simulink moel. Har stops were use in the moel, but a spike in acceleration similar to the test results coul not be replicate in the simulation moels. igure 7 also shows goo time omain correlation between simulate an measure river s seat acceleration. The timing of peaks an valleys for measure an simulate river s seat acceleration is similar. The time omain correlation inicates that the stiffness an amping in the simulation moel accurately moel the prototype test vehicle. igures 8 an 9 show a comparison of the measure an simulate time omain response of the front an rear wheels to the 8 half roun roa input at 10mph. Wheel position was measure using string pots mounte to the test vehicle frame an attache near the wheel spinles. The timing of the simulation events shows goo correlation to the measure time omain response of the wheels. igures 8 an 9 show a significant amount of error between simulation an test results uring the front suspension compression event at 5.2 secons an rear compression event at 6.1 secons. This is the time at which the tire strikes the half roun an suspension motion is initiate. Static friction of suspension components, nonlinear tire rate behavior, an the ynamic response of the string potentiometer are all variables that coul influence the suspension travel. lso, the jounce bumpers are not fully moele in Simulink an have an influence on wheel travel. nother theory is that the simulation moel is issipating the same amount of energy as the vehicle, but the istribution of energy issipation between the tire an the shock absorber is ifferent for simulation an test. itional work nees to be one to stuy the source for this error in wheel travel. CONCLUSIONS The low fielity shock absorber moel was selecte to calculate the force vs. velocity behavior of a shock absorber. The force vs. velocity curve from the low fielity shock absorber moel is parameterize accoring to the actual imensions of the valve harware insie the shock absorber amping. This makes it possible to optimize the amping by changing actual amping valve imensions in the simulation moel. Test harware can be fabricate base on the final optimize shock absorber parameters erive from simulation results. or the half roun event, the low fielity shock absorber moel provie nearly ientical results to the high fielity shock absorber moel when comparing the acceleration response of the river s seat as shown in figure 7. Wheel travel was also calculate with a similar response for the high fielity an low fielity moels as shown in figures 8 an 9. The low fielity shock absorber moel coul also be run with DMS in co-simulation of half roun events. The timing of acceleration an wheel travel events was accurately moele in simulation when compare to test results. There was significant error in the magnitue of simulate river s seat peak acceleration an wheel travel when compare to test results. The measure peak acceleration of the river s seat for the 8 10 mph half roun was 1.3 g s. The calculate peak response was 0.6 g s, which is 54% error between simulation an test. Other than the one spike at 6.3 secons, the simulation moel provie a goo estimate of river s seat acceleration. The 7 DO moel i not accurately preict the short uration high magnitue acceleration spike at 6.3 secons, most likely cause by the suspension impacting the jounce an reboun bumpers. itional work nees to be one to moel the response of the vehicle response to suspension har stop impacts. REERENCES [1] SE J MR2000, Measurement of Vehicle an Suspension Parameters for Directional Control Stuies, Ch. 10 [2] itch an Hong, Hyraulic Component Design an Selection, BarDyne Inc, 1997 [3] George an Barber Lubrizol Corp., What is bulk moulus an why is it important?, INLUENCE O SHOC BSORBER MODEL IDELITY ON THE PREDICTION O VEHICLE HL ROUND PERORMNCE Page 7 of 7