A Handling Quality Metric12A Given: Instability is A Bad ThingInstability implies response is unbounded withtime; invehicle control terms, an uncommanded spinSpins not preferred because they may lead to trippedrollover by presenting the vehicle sideways toobstacles/terrainFour states possible for systems generally[1,2]:Asymptotic StabilityNeutral StabilityDivergent InstabilityOscillatory Instability[1] Fundamentals of Vehicle Dynamics, Gillespie, p402[2] The Multibody Systems Approach to Vehicle Dynamics, Blundell & Harty, p172[3] Race Car Vehicle Dynamics, Milliken & Milliken, p245Understeer/Oversteer and StabilitySAE Understeer guarantees oscillatory asymptoticstability in absence of driver input[3]SAE Oversteer does not predict instability (below)From Fundamentals of Vehicle Dynamics, Gillespie, p403rVehicleDynamics,Milliken&Milliken,p245Divergent Instability Better Surrogate for Tripped Rollover RiskA Given: Instability is A Bad ThingHandling Metric Context3Lateral Acceleration Very NoisyMeasurement noise veryhigh on luggedtires with non-deformable terrainPolynomial Fit ArbitraryVehicle motion is the combination of tireforces divided by reluctance of vehicleto move (mass, inertia)[4]Tires are often represented with socalled “Magic Formula”[5]:There is no good reason to fit apolynomial to the data[4] Newton’s 2ndLaw[5] Tyre Modelling for Use in Vehicle Dynamics Studies, SAE 870421, Bakker, Nyborg,PacejkaDiscerning Turning Point Unsatisfactory ExperimentallyL t l A l ti VNMeasurement Noise> @^ `sin arctan arctanY X D C Bx E Bx Bxa o¬ 1⁄44The Fixed Steer TestExtremely repeatable and requires nospecial facilities other than a consistentsurfaceUnlike constant radius test, it is not atest of the steeringrobot quality, driverskill, etcWhile not directly comparable to othertests (none are directly comparable witheach other), will nevertheless expose avehicle that seeks to spin (“divergent”)Yaw Rate Gives Clean SignalYaw rate is rotation viewed in planData not so susceptible to vibration(magenta) when compared to lateralacceleration (green)Mount location insensitive (identicalreadings anywhere on vehicle)Fixed Steer is Repeatable, Driver-Independent and gives Clean DataThe Fixed Steer TestYaAnother Possible Test ProtocolD t t tibl t ib ti5Yaw Rate is Directly Connected to Lateral AccelerationA Geometric Connection“Non Spin” (aka No-Slip, Steady State) Yaw rate connects to Lateral Acceleration simply:A“geometric” vehicle will have a yaw ratewhich is identical to a neutral steer vehicle[3][3] Race Car Vehicle Dynamics, Milliken & Milliken, p159UδrLA = rUY6Visually a Strong Difference–No Filtering/Processing RequiredDivergent Spin ConditionInstability is shown by a large change in the character(slope) of the plot for a small speed change–it“goesvertical”Detecting Divergence–Fixed Steer Results0.5g HyperbolaMeasuredYaw Ratevs VehicleSpeedExtrapolated line fromon-center fit–5seconds after 2m/s(5 repeats)No Spin ConditionPlotting yaw rate against vehicle speed will show itscharacter compared to a “geometric” vehiclePlotting0.5g*9.81ms-2/Vehicle Speed(ms-1)gives a “0.5gHyperbola”to determine test endConvergent vehicles typically keep a “substantiallyconstant” slope of yawrate with speed7•Divergent response–trace “becomes steep”below0.5g Hyperbola–divergence obvious•Extremely convergent vehicle–trace goeshorizontal•Both vehicles very consistent in fixed steer testProposed Test Shows Large Difference•Divergent responsetrace“becomes steep”Extremely conbecomvergen200ft Fixed Steer–Divergent/ConvergentLeft TurnRight Turn8•Shows loss of path following ability–“path error”(vehicle is less predictable)Shows Both Divergence and Path Error PlainlyShows loss ofpath fof path200ft Fixed Steer–Divergent/Convergent•Note very large increase in yaw rate for 1mphspeed change (~0.5 m/s)Left TurnRight Turn9•Difference still clear - divergent configuration isobvious (vehicle tips onto outriggers on rightturn)•Excellent repeatability alwaysRobust against Test Radius•Difference stcleardivillergconfigurationiscent50ft Fixed Steer–Divergent/Convergent•Convergence remains clear visually at0.5g hyperbolafor 50ft diameter•Path following less compromised at low speedLeft TurnRight Turn10Numerically Robust With Typical Data (20 Vehicle Sample)Plot 5 repeats in each directionFor each repeatFit on-center slopeFit limit slopeAverage on-center slopes betweenrepeatsAverage limit slopes between repeatsEvaluate relationship of averaged limitslope to averaged on-center slopePass-fail criterion?Ratio preferred over arithmetical difference–less sensitive to radiusPlot 5 repeats in each directionSuggested Detail - Provisional0.5g HyperbolaMeasured Yaw Rate vsVehicle SpeedExtrapolated Linefrom on-center fit(5 repeats)Fitted line in limitregion–0.4g to 0.5gFitted line on-center5 seconds of databeyond 2 m/s11Divergent Response Stands Out in Blind, Automated ProcessingSample Metric–Fleet Review (40/50ft)•200ft circle data shows aneven stronger response -ratio of13.8:1(Vehicle 2)•100ft circle expected to besomewhere between thetwo•100ft probably reflects agood compromisebetween space requiredand quality of results•All vehicles convergeexcept Vehicle 2 (spins)•Not all vehicles areundersteer0123412•Test end detection–characteristic goesthrough 0.55g hyperbola or significantdecelerationProcess Automates Well•Test end detectioncharacteristic gristicProcess Automation•Limit identification–0.5g Hyperbolacrossing or maximum inferred LateralAcceleration (some vehicles don’t make0.5g)•Fit window controllable–uses 0.1g inexamples so farTest end autodetectedWllexamples sofar13100ft Data ComparisonExpand Vehicle seteg HistoricTest robustness of processingRefine Pass/Fail criteriaFormalize ProcessReceive Inputs from othersEarly Promise Needs Verification & Formalization100ft D t CNext Steps14Method developed on first principles/best-practicesBetter Surrogate for Tripped Rollover RiskRepeatable methods with minimal test errorsDrives predictable vehicle handling designsDiscriminates and identifies unpredictable behaviorsSuperior Alternative to Understeer BiasM th d dlSummary15•What other signatures can the data show?•Fails to reach 0.5g•Convergent oversteerOther Numerical Measures of Interestto Manufacturers are Possible•What other signatures can the datashow?Broad Picture of Vehicle•Lack of symmetry left-to-right“Club-like” thickening of dataassociated with tire saturation16•Vehicle 1Appendix–Real Vehicle Data–50ft•Vehicle 1Appendix–Real Vehicle Data–50ft•Vehicle 217•Vehicle 3Appendix–Real Vehicle Data–50ft•Vehicle 3Appendix–Real Vehicle Data–50ft•Vehicle 418•Vehicle 5Appendix–Real Vehicle Data–50ft•Vehicle 5Appendix–Real Vehicle Data–50ft•Vehicle 619•Vehicle 7Appendix–Real Vehicle Data–50ft•Vehicle 7Appendix–Real Vehicle Data–50ft•Vehicle 820•Vehicle 9Appendix–Real Vehicle Data–50ft•Vehicle 9Appendix–Real Vehicle Data–50ft•Vehicle 1021•Vehicle 11Appendix–Real Vehicle Data–50ft•Vehicle 11Appendix–Real Vehicle Data–50ft•Vehicle 1222Appendix–Real Vehicle Data–50ftAppendix–Real Vehicle Data–50ft•Summary•Ratio and Delta measurestell the same story(ratio plot shown)•All vehicles converge except Vehicle 2