Wheel Slip Simulation For Dynamic Road Load Simulation
F eature ArticleFeature ArticleApplicationWheel Slip Simulation for Dynamic Road Load SimulationApplication Reprint of Readout No. 38Wheel Slip Simulationfor Dynamic Road Load SimulationBryce JohnsonIncreasingly stringent fuel economy standards are forcing automobilemanufacturers to search for efficiency gains in every part of the drive trainfrom engine to road surface. Safety mechanisms such as stability control andanti-lock braking are becoming more sophisticated. At the same time driversare demanding higher performance from their vehicles. Hybrid transmissionsand batteries are appearing in more vehicles. These issues are forcing theautomobile manufacturers to require more from their test stands. The test standmust now simulate not just simple vehicle loads such as inertia and windage,but the test stand must also simulate driveline dynamic loads. In the past,dynamic loads could be simulated quite well using Service Load Replication(SLR*1). However, non-deterministic events such as the transmission shifting orapplication of torque vectoring from an on board computer made SLR unusablefor the test. The only way to properly simulate driveline dynamic loads for nondeterministic events is to provide a wheel-tire-road model simulation in additionto vehicle simulation. The HORIBA wheel slip simulation implemented in theSPARC power train controller provides this wheel-tire-road model simulation.*1: Service load replication is a frequency domain transfer function calculation with iterativeconvergence to a solution. SLR uses field collected, time history format data.Introductionfrequency. The frequency will typically manifest itselfbetween 5 and 10 Hz for cars and light tr ucks. (seeTo understand why tire-wheel simulation is required, weshould first understand the type of driveline dynamicsthat need to be reproduced on the test stand. Figure 1 isthe speed and torque of the left wheel of a manualtransmission vehicle accelerating aggressively from restat the test track. The clutch is released quickly and thetire spins on the dry pavement creating large torque andspeed deviations at the vehicle axle shaft. The importantcharacteristics of the torque and speed response are thefrequency, the amplitude and the damping of the torqueand speed oscillations.Driveline response of the vehicleThe oscillatory response of the tire-wheel speed andtorque is caused by the numerous spring-mass-dampercomponents in the driveline. The predominant frequencyseen at t he clutch release is t he d r iveli ne nat u ral50English Edition No.42 July 201412 kphDamping8.33 Hz Drive lineNatural frequency7 kphspinFigure 1
Technical ReportsPropshaftEngineinertiaWheelInertiaAxle shaftDifferentialTire Spring-dampingRoad surfaceFigure 2Figure 2) It is highly dependent on the two inertias andthe driveline spring rates.Vehicle on the test standWhen the vehicle is moved to the test stand, the tires andwheels are removed and replaced with a dynamometer (seeFigure 3. yellow). To preserve the driveline response, thetire inertia, the tire damping, the tire spring rate and thetire-road surface must be simulated.Traditionally, the tire-wheel inertia must be replaced by adynamometer with inertia of identical value. That wasthe only way to get the correct driveline natural frequencyresponse. The problem is that a dynamometer motor ofsuch low inertia is very expensive to manufacture.HORIBA’s solution is to use a relatively inexpensivedynamometer and use special controls to simulate thetire-wheel inertia. The software and hardware Horibauses to simulate the wheel-tire-road is called “wheel slipsimulation”. An additional component is the “vehiclesimulation” that provides road loads based on the vehicledesign. The software executes on a SPARC controller andis an integral part of the HORIBA power Train controller.Vehicle SimulationVehicle simulation sof t ware k now n as Road LoadSimulation (RLS) has been used to provide loads to thedriveline via the dynamometers to simulate the vehicleloads. The most basic form of RLS includes vehicle masssimulation, frictional force simulation, windage force andhill incline simulation. The vehicle mass simulationassumed the mass was concentrated at the vehicle centerof gravity. Wheel slip simulation distributes this mass tothe individual tires depending on vehicle dynamics. Avehicle dynamics simulation in STARS *2 provides ameans to distribute the mass to each tire model in realtime to simulate steering, acceleration and braking weighttransfer. RLS is still used to provide vehicle simulation.Wheel slip is used in conjunction with vehicle simulationto support high dynamic torque events. The road loadforce is given by an equation that is a function of thevehicle speed.FRoad K A K B*v K C* (Speed Vehicle vHeadwind)X m*g*sin (Incline Hill)FVeh TMeasured / Radius WheelSpeed Vehicle 1/m Vehicle* (Fveh - FRoad) dt*2: STARS is the name of the software product and trademark thatprovides all test automation functions.The difference between vehicle force and road force is theforce used to accelerate the vehicle. If we integrate thisforce acting on the vehicle inertia, the result is simulatedvehicle speed. Figure 4 is a comparison of the realSparc eel SlipSimulationSoftwareDynoInertiaPropshaftFRoad 138 8.60V 0.478V2Axle shaftDifferentialFigure 3Figure 4English Edition No.42 July 201451
F eature ArticleApplicationWheel Slip Simulation for Dynamic Road Load Simulationvehicle and a simulated vehicle during a coast from 50mph to zero. This comparison shows how well thesimulation (green) matches the real vehicle (blue).Wheel slip simulationThere are 3 characteristics of the test stand that must becont rolled to get proper d r ivelive dy namics in thesimulation. First, the tire forces and tire slip must besimulated using a tire model. Second, the wheel-tireinertia must be simulated to get the proper drive linenatural frequency. Third, the damping of the oscillationsmust be controlled.The tire model, what is slip?Most of us are intimately familiar with tire spin eventswhen a tire spins on wet roads or ice. However, noteveryone understands that the tire is always slippingslig htly; even when a veh icle is mov i ng on a d r ypavement. Figure 5 is the data from a real vehicle at atest track on dry pavement. The vehicle speed is 39.4 kph,the front tire speed is 367 rpm and the rear wheel speed is383 rpm. This is a rear wheel drive vehicle whose reartires are transferring 4600 N of force. What is seen inthis graph is that the rear tires are rotating 16 rpm fasterthan the front tires. Saying another way, the rear tires areslipping at 16 rpm on the road surface when rotating at383 rpm while transferring 4600 N of force.What we find is that vehicle tires slip at a rate proportionalto the amount of force they transfer to the road surface.This slippage is what is referred to as wheel slip. If wecontinue to increase the tire force by accelerating thevehicle more aggressively, a maximum force will bereached and the tire will slip quite dramatically as the tireon ice. One often says the tire is spinning. The test standmust implement a tire model to reproduce this force-slipfunctionality. The definition of slip is: Slip (VTire-V Vehicle)/ V Vehicle. If we take vehicle speed as the front tire speedor 367 rpm and the tire speed as the rear tire speed or 383rpm, we get a slip of 4.4%.Simulation of tire forces and slip using PacejkaThe traditional way to simulate tire forces and slip is touse a tire model. The traditional tire model describes afunctional relationship between slip of the tire and theforce transferred through the tire. Although there are anumber of tire models in the literature, one of the mostwell known tire models is the Pacejka-96 longitudinal tiremodel. This is function that describes the tire force as afunction of tire slip. The Pacejka function is F D sin (b0tan-1 (SB E (tan-1 (SB) - SB))). “F” is tire force and “S”is tire slip. The parameters D, B, E and S are valuesbased on the tire normal force and the Pacejka parametersb0 to b10. The value Fz is the normal force applied to thewheel. By adjusting the normal force of each tire in realtime using STARS, the test engineer accounts for vehiclebody movements that change the weight distribution ofthe vehicle. (Figure 6)mup b1 Fz b2D mup FzB (b3 Fz b4) e -b5 Fz / (b0 mup)E b6 Fz2 b7 Fz b8S 100 Sfrac b9 Fz b10Simulation of tire forces and slipusing a simple modelQuite often, the test engineer does not have access to thePacejka parameters. In such a case, the customer can usea simple model to describe the tire forces and slip. TheVehicle speed 39.6 kphNon-drive front tire 367 rpmTorque producing rear tire 383 rpm0%-20 %NormalForce NFigure 552English Edition No.42 July 2014Figure 6Slip %TireForce Nb0 1.65b1 0b2 1688b3 0b4 229b5 0b6 0b7 0b8 -1020 % b9 0b10 0
Technical ReportsInertia simulation and dampingA tire model simulation as a requirement for proper wheelslip simulation has been describe as part of a three partsolution. Two other critical requirements for wheel slipsimulation are controlling the natural frequency andcontrolling the damping. The natural frequency is highlydependent on the wheel inertia. So it is crucial that theinertia of the tire-wheel combination is simulated. Thetypical problem is that the dynamometer inertia is greaterthan the tire-wheel inertia. So the simulation must apply aforce to the dyno inertia to compensate for the inertiadifference between the dyno and the tire-wheel. Theactual means by which Horiba does this is proprietary,but suff ice to say it is adjustable with a parameter.Likewise, damping is also controlled by a parameter.Road surface simulationActual road surface simulation is embodied in the Pacejkaparameters as mu p . This value represents the peaklo ng it u d i n a l f r ic t io n c o ef f ic ie nt . A r e a s o n a bleapproximation to the actual friction coefficient is tomultiply this value by a normalized coefficient of frictionmu n, which takes on values between 1/10 and 1. Below isa table that provides a reasonable approximation to theroad surface mun.10000Spin800060004000Tire forcesimple model consists of two numbers: the maximumforce and the force-slip gradient. These two numbers canbe calculated reasonably easy from road data. The tiregradient represents the region of operation where the tireslips as a f unction of torque. The maximum forcerepresents the region of operation where the tire spinsquite dramatically rather than slipping slightly. Themaximum force also represents the tire force given that aparticular normal force Fz exits. As the tire normal forcechanges, the maximum value changes proportional to thenormal force. (Figure 7)Force-slip 050100Wheel slipFigure 7function of road surface. The test engineer simulates achange in road surface by changing this value. A typicaltest might be to set both tires to dry pavement, then as thetest vehicle accelerates, change one of the tires to saysnow. A split mu test, as it is called, exercises the tractioncontrol logic of the vehicle computer.Issues of dynamometer sizingDynamometers are often sized based on compromisesbet ween cost and perfor mance of the components.Typically, high dynamics require low inertia motors andl a r ge d r ive s. O n e mu s t d i s c u s s ex t e n sively t herequirements with the customer to determine the properdynamometer sizes. A good example is the test inFigure 1 requires a dynamometer which accelerates at8000 rpm/s. Such a test stand could be built with thefollowing: (Figure 8)223 kW, Dynas3 4000WH with 600 kW driveInertia 8.8 kgm 2Peak torque 8109 NmPeak acceleration rate 8800 rpm/secOr it could be built with a high performance PM4000The normalized coefficient of friction mu n is a dynamicvalue that can be changed in real-time by STARS as aTable 1Surface typeNormalized munPerfect surface1.0Asphalt and concrete (dry)0.8-0.9Concrete (wet)0.8Asphalt (wet)0.5-0.6Earth road (dry)0.7Earth road (wet)0.5-0.6Gravel0.6Snow (hard packed)0.3Ice0.1Figure 8English Edition No.42 July 201453
F eature ArticleApplicationWheel Slip Simulation for Dynamic Road Load Simulation8.33 HzFigure 9Figure 10motor and drive using the following: (Figure 9)the natural frequency. Shown below is a spin event onsnow created by a sudden acceleration by the engine. Itclearly shows the driveline natural frequency of 8.33 Hzt h a t we s a w i n F i g u r e 1 d u r i n g t h e a g g r e s s i veacceleration event of the vehicle on dry pavement at thetest track. (Figure 10)330 kW, Dyas PM4000 WH with 600 kW driveInertia 1.0 kgm 2Peak torque 4200 NmPeak acceleration rate 38,000 rpm/secIn this case, a less expensive Dynas3 provides theminimum acceleration rate required for the customerr e q u i r e m e n t s a t l e s s t h a n 5 0 % t h e c o s t . A l ldynamometers can provide wheel slip capability; however,t he dy n a m ic p e r for m a nc e for whe el sl ip w i l l b edetermined heavily by the torque-to-inertia ratio, whichdetermines the acceleration rate. As a trade off, thecustomer may elect to reduce his wheel slip events tolower amplitudes and/or frequency in an effort to reducethe dynamometer costs. Typically, low frequency testswith large vehicles and less aggressive wheel slip eventsare suit able for the Dy nas3 dy namometers. Highfrequency tests with smaller vehicles and very aggressiveslip events are suitable for the Dynas PM dynamometers.Wheel slip model checkAs a check to verify the wheel slip model, the slipgradient as calculated the slip gradient from the tire forceand slip. It should agree with the slip gradient for themodel of 101904 N/slip. Below, the measured slipgradient is 102,639 which is within 0.7% of the expectedvalue. This value is derived by first calculating the tireforce from the torque transducer. Then calculate the slipas the difference between the vehicle speed and themeasured tire speed. The gradient is calculated bydividing the tire force by the slip. (Figure 11)ResultsTire Force 886.8 NDriveline natural frequencyThe test stand was not able to reproduce the aggressiveacceleration event by the vehicle at the test track depictedin Figure 1 because the test stand dynamometers wererated to 6000 rpm/sec and the test required dynamometersrated to 8000 rpm/sec. However, the dynamometers wereable to excite the drive line natural frequency at loweramplitudes in other events.The drive line natural frequency is a function of theinertias and spring rates and is affected only slightly bythe damping. As a result, most any step event can excite54English Edition No.42 July 2014Slip 0.00864Gradient 102,639 886.8/0.00864Figure 11
Technical ReportsConclusionWheel slip is a current development at Horiba. Nearfuture development will provide correlation between thevehicle data and the wheel slip simulation data. Thecurrent test stand is limited by the dynamic capabilities ofthe current dynamometers at 6000 rpm/s compared to therequired acceleration rate of 8000 r pm /s, so someverification is yet to be done. Future development mightinclude sophisticated road surface simulation includingbumps. Yaw sensor simulation for vehicle computerswould provide inputs for onboard vehicle computers fortesting stability controls.Cur rently, the algorithm successfully recreates thedriveline natural frequencies, which means iner tiasimulation works correctly. This is an industry first indynamometer test stand simulation for wheel slip. Alsosuccessfully implemented are the two tire models aspresented. Testing included the slip-spin events workingcorrectly with proper wheel forces. Dynamic split mutests are possible. In addition, dynamic weight adjustmenton individual wheels is provided supporting varyingweight distribution caused by body roll, cornering andacceleration. The current implementation provides alongitudinal model which is expected to provide the 99%market requirement. Two tire models are provided asdiscussed. If the market demands change, the SPARCcontroller is f lexible enough that the models can beextended as required.Bryce JohnsonPrinciple EngineerAutomotive Test systemsHORIBA Instruments Inc.English Edition No.42 July 201455
dependent on the wheel inertia. So it is crucial that the inertia of the tire-wheel combination is simulated. The typical problem is that the dynamometer inertia is greater than the tire-wheel inertia. So the simulation must apply a force to the dyno inertia to compensate for the inertia difference
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