1、SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirelyvoluntary, and its applicability and suitability for any particular use, including any patent infringement arising therefro
2、m, is the sole responsibility of the user.”SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions.QUESTIONS REGARDING THIS DOCUMENT: (724) 772-8512 FAX: (724) 776-0243TO PLACE A DOCUMENT
3、 ORDER; (724) 776-4970 FAX: (724) 776-0790SAE WEB ADDRESS http:/www.sae.orgCopyright 1994 Society of Automotive Engineers, Inc.All rights reserved. Printed in U.S.A.SURFACEVEHICLE400 Commonwealth Drive, Warrendale, PA 15096-0001RECOMMENDEDPRACTICESubmitted for recognition as an American National Sta
4、ndardJ1988ISSUEDAUG94Issued 1994-08RESIDUAL ALIGNING MOMENT TESTForewordThis Document has not changed other than to put it into the new SAE Technical Standards Boardformat.1. ScopeThis SAE Recommended Practice describes the determination of tire pull force properties for anuninclined tire (SAE J670e
5、) on a laboratory flat surface tire force and moment machine. It is suitable foraccurately determining pull forces and residual aligning moments for passenger and light-truck tires. Theseproperties are important determinants of vehicle trim (See section 2.1.2). They describe steady-state, free-rolli
6、ng pull effects ascribable to tires.The test method described in this document is suitable for comparative evaluation of tires for research anddevelopment purposes. The method is also suitable for modeling when followed carefully.2. References2.1 Applicable PublicationsThe following publications for
7、m a part of this specification to the extent specifiedherein. The latest issue of SAE publications shall apply.2.1.1 SAE PUBLICATIONAvailable from SAE, 400 Commonwealth Drive, Warrendale, PA 15096-0001.SAE J670eVehicle Dynamics Terminology2.1.2 TIRE SCIENCE AND TECHNOLOGYAvailable from The Tire Soci
8、ety, P.O. Box 1502, Akron, OH 44309-1502Tire/Vehicle Pull: An Introduction Emphasizing Plysteer Effects, M.G. Pottinger, TSTCA, Vol 18, No 3, July-September, 19903. DefinitionsThe definitions which follow are of special meaning in this document and may be wordedsomewhat differently from those in SAE
9、 J670e for instructional reasons. Other definitions which are used,including the tire axis system, are found in SAE J670e.The symbology used in this document was chosen for convenient use in computer programming.3.1 Aligning Moment Characteristics3.1.1 AL0Aligning Moment at Zero Slip Angle for the S
10、traight Free Rolling Tire Operating in Left Rotation.SAE J1988 Issued AUG94-2-3.1.2 APPlysteer Aligning Moment is an Aligning Moment for the Straight Free Rolling Tire. It is the average ofthe Aligning Moments at Zero Slip Angle in Left and Right Rotations. It does not change direction withrespect t
11、o the Tire Axis System when the Tire Direction of Rotation is reversed.3.1.3 AR0Aligning Moment at Zero Slip Angle for the Straight Free Rolling Tire Operating in Right Rotation.3.1.4 ASAligning Stiffness is the average of the Aligning Stiffnesses of the Free Rolling Tire in Left and RightRotations.
12、3.1.5 ASLAligning Stiffness in Left Rotation is the first derivative of the Aligning Moment of the Free Rolling Tirewith respect to Slip Angle determined at Zero Slip Angle, Zero Inclination Angle, and Zero Path Curvaturewith the Tire rotating in Left Rotation.3.1.6 ASRAligning Stiffness in Right Ro
13、tation is the first derivative of the Aligning Moment of the Free RollingTire with respect to Slip Angle determined at Zero Slip Angle, Zero Inclination Angle, and Zero PathCurvature with the Tire rotating in Right Rotation.3.1.7 CRATConicity Residual Aligning Moment (Torque) is the Residual Alignin
14、g Moment Component in RightRotation which separates the tires Residual Aligning Moment from that due to Plysteer alone. CRATchanges sign with respect to the Tire Axis System when the direction of Tire Rotation is reversed.3.1.8 PRATPlysteer Residual Aligning Moment (Torque) is the Aligning Moment of
15、 a tire without Conicity existingwhen the Lateral Force of a tire without Conicity is zero. PRAT does not change sign with respect to the TireAxis System when the direction of Tire Rotation is reversed.The Aligning Moment curve of a tire without Conicity is obtained by averaging the Left and Right R
16、otationcurves for Aligning Moment.3.1.9 RATLResidual Aligning Moment (Torque) in Left Rotation is the Aligning Moment of the tire operating inLeft Rotation which exists when the tires Left Rotation Lateral Force is zero.3.1.10 RATRResidual Aligning Moment (Torque) in Right Rotation is the Aligning M
17、oment of the tire operating inRight Rotation which exists when the tires Right Rotation Lateral Force is zero.3.2 Lateral Force Characteristics3.2.1 CLFConicity Lateral Force is the Lateral Force at Zero Slip Angle in Right Rotation minus the PlysteerLateral Force. Conicity Lateral Force changes dir
18、ection with respect to the Tire Axis System, but not the TireFace, due to a change in Tire Direction of Rotation.3.2.2 CSCornering Stiffness is the average of the Cornering Stiffnesses of the tire in Left and Right Rotations.3.2.3 CSLCornering Stiffness in Left Rotation is the absolute value of the
19、first derivative of the Lateral Force withrespect to Slip Angle determined at Zero Slip Angle, Zero Inclination Angle, and Zero Path Curvature with theTire rotating in Left Rotation.3.2.4 CSRCornering Stiffness in Right Rotation is the absolute value of the first derivative of the Lateral Forcewith
20、respect to Slip Angle determined at zero Slip Angle, Zero Inclination Angle, and Zero Path Curvaturewith the Tire in Right Rotation.3.2.5 LL0Lateral Force at Zero Slip Angle for the Straight Free Rolling Tire Operation in Left Rotation.3.2.6 LR0Lateral Force at Zero Slip Angle for the Straight Free
21、Rolling Tire Operating in Right Rotation.SAE J1988 Issued AUG94-3-3.2.7 PLFPlysteer Lateral Force is the Lateral Force for the Straight Free Rolling Tire which is the average of theLateral Forces at Zero Slip Angle, Zero Inclination Angle, and Zero Path Curvature in Left and RightRotations. It chang
22、es direction with respect to the Tire Face, but not the Tire Axis System, when the directionof Tire Rotation is reversed.The Lateral Force curve of the tire without Conicity is obtained by averaging the Left and Right Rotationcurves for Lateral Force.3.2.8 PRLFPlysteer Residual Lateral Force is the
23、Lateral Force of a tire without Conicity existing when theAligning Moment of a tire without Conicity is zero.3.3 Rotation Sense3.3.1 LRLeft Rotation is operation of the Tire in counterclockwise rotation when the Tire Face is being viewed. Anormally mounted tire on the left side of a vehicle moving f
24、orward operates in Left Rotation.3.3.2 PRRight Rotation is operation of the Tire in clockwise rotation when the Tire Face is being viewed. Anormally mounted tire on the right side of a vehicle moving forward operates in Right Rotation.3.3.3 TFTire Face is the outwardly directed side of a tire mounte
25、d on a vehicle in accordance with the vehicle ortire manufacturers specification or general practice.In the case of directional tires, the side facing outward on the right side of the vehicle with the tire operating inthe proper sense of rotation is taken as the Tire Face.3.4 Table 1SymbolsTABLE 1SY
26、MBOLSSAE J1988 Defined TermAL0 Aligning Moment at zero Slip Angle in Left RotationAP Plysteer Aligning MomentAR0 Aligning Moment at zero Slip Angle in Right RotationAS Aligning StiffnessASL Aligning Stiffness in Left RotationASR Aligning Stiffness in Right RotationCLF Conicity Lateral ForceCRAT Coni
27、city Residual Aligning MomentCS Cornering StiffnessCSL Cornering Stiffness in Left RotationCSR Cornering Stiffness in Right RotationFx Longitudinal ForceFy Lateral ForceFz Normal ForceIA () Inclination AngleLL0 Lateral Force at zero Slip Angle in Left RotationLR Left RotationLR0 Lateral Force at zer
28、o Slip Angle in Right RotationMx Overturning MomentMz Aligning MomentPLF Plysteer Lateral ForcePRAT Plysteer Residual Aligning MomentSAE J1988 Issued AUG94-4-4. Apparatus4.1 Description of Test EquipmentThe laboratory flat surface tire force and moment machine consists of threebasic components: a be
29、lt type flat surface simulated roadway with drive mechanism, a loading and positioningsystem, and a measuring system.4.1.1 SIMULATED ROADWAYThe simulated roadway shall be a continuous flat surface, coated with a stablenonpolishing material. The roadway shall be maintained free of loose material or d
30、eposit. The roadway shallbe wide enough to support the entire tire footprint.4.1.1.1 The supporting structure shall be rigid enough to insure that specifications can be met.4.1.1.2 The surface shall be periodically checked for friction characteristics and flatness.4.1.1.3 The bearing supporting the
31、simulated roadway shall be maintained at 24 C 2.5 C and flat to less than0.5 mm.4.1.1.4 The drive system shall be capable of operating the roadway at the speed specified by the test engineerwith an accuracy of 1 km/h.4.1.2 LOADING AND POSITIONING SYSTEMA fixture is provided to load and position the
32、tire with respect to thesurface of the simulated roadway at the Normal Force, Inclination Angle, and Slip Angle specified by the testengineer. It is important that angle positioning be consistent and free of bias. Results from machines whichprovide consistent data can be correlated. In a practical s
33、ense, it is not feasible to obtain the precise samedata from two different test machines.NOTE Every test machine and all wheels DEFLECT by a small amount under load, therefore, theoperating Inclination and Slip Angles existing during testing do not precisely equal the angles setby the load and posit
34、ioning system. It is the responsibility of the test engineer to be aware of andaccount for system flexibility induced effects.4.1.2.1 The loading mechanism shall have the ability to set the Normal Force on the tire to the commandedNormal Force with an accuracy equivalent to that specified for the No
35、rmal Force Load Cell throughout therange of the Normal Force Load Cell.4.1.2.2 The goal of the positioning system is the ability to set the Inclination and Slip Angles to the commandedvalues with a target accuracy equivalent to the recommended accuracy specified for the Inclination andSlip Angle mea
36、surements in Table 2 over the range from 1 degree.PRLF Plysteer Residual Lateral ForceRI Loaded RadiusRATL Residual Aligning Moment in Left RotationRATR Residual Aligning Moment in Right RotationRR Right RotationSA () Slip AngleTF Tire FaceTABLE 1SYMBOLS (CONTINUED)SAE J1988 Defined TermSAE J1988 Is
37、sued AUG94-5-4.1.2.3 The system shall accept the rim diameter and width required by the user.4.1.3 MEASURING SYSTEMThe measuring system shall minimally measure the following variable according to theaccuracies noted in Table 2. The ranges quoted for the measurement channels are minimum requiredrange
38、s and are not to be taken as design limits for equipment. Further, the accuracies quoted are for singlesamples of a measurement channel and do not represent the ultimate accuracy of the results which aredetermined by the amount of sampling (averaging) chosen by the test engineer as a compromise of t
39、est timeand precision. All reported data are to be matrix corrected for interactions.5. TestThe test procedure can be divided into three parts: tire preparation, tire selection, and test procedure.5.1 Tire SelectionThe principal concern is that the tire be warmed up to equilibrium operating temperat
40、ure atthe inflation pressure prior to the test. It is the duty of the test engineer to insure that equilibrium thermalconditions have been reached prior to the execution of the test procedure. The maintenance of the originalwear state is important to the measurements to be made so conditioning invol
41、ving Inclination and Slip Angleswhich will induce new wear is discouraged.5.2 Test ProcedureIn Residual Pull testing, the tire is tested at a sequence of small Slip Angles chosen toaccurately represent its behavior in the region from approximately 1 to 1 degree Slip Angle, for example, SlipAngles of
42、 1.0, 0.8, 0.6, ., 0.6, 0.8, 1 degree with the tire operating in both Right Rotation and in LeftRotation.Inclination Angle is set to zero in the method of this document, but may be set at a small angle simulatingsuspension alignment in some test cases. In the case of a small nonzero Inclination Angl
43、e, the data analysisgiven in this document is not truly correct and the engineer becomes responsible for his own data analysis.5.3 Machine PreparationThis assumes that routine calibrations have been conducted and are correct. Inaddition to these, the Inclination and Slip Angle calibrations should be
44、 checked and a control test run before thestart of Residual Pull testing to confirm that the machine is performing in correspondence to its statisticalhistory. Rerunning a control tire several times within a test day is advised in order to track small machinedeviations with time.TABLE 2RECOMMENDED M
45、INIMUM MEASURING SYSTEM RANGES AND ACCURACIESChannelRangeAbsolute Value AccuracyFx, Longitudinal Force 1 kN 1%Fy, Lateral Force 15 kN 1%Fz, Normal Force 25 kN 1%Mx, Overturning Moment 10 kNm 1%Mz, Aligning Moment 1 kNm 1%IA, Inclination Angle 01 degree 0.01 degree110 degrees 0.05 degreeRI, Loaded Ra
46、dius 200450 mm 1.0 mmSA, Slip Angle 01 degree 0.01 degree115 degrees 0.05 degreeNOTE: Force and Moment channel accuracies are stated as a percent of fullscale. Angle measurement accuracies are noted in angle units andLoaded Radius measurements in millimeters. Required machinemodifications and proces
47、s controls are the responsibility of the testengineer and are not covered in this document.SAE J1988 Issued AUG94-6-6. Data Processing and PresentationTo aid in clarity, real data were used to prepare the illustrations becausethey show the typical quality of the fits, etc., which are involved.Equati
48、ons 1 through 8 are the formulae required to determine all the items required in a minimum report oncethe basic fitting in 6.1.1 is complete.The example data processing emphasizes Residual Aligning Moment determination.(Eq. 1)(Eq. 2)(Eq. 3)(Eq. 4)(Eq. 5)(Eq. 6)(Eq. 7)(Eq. 8)6.1 Data Processing6.1.1
49、The Right- and Left-Rotation Lateral Force (Fy) and Aligning Moment (Mz) data Equation 9, Equation 10,Equation 11 and Equation 12 are fit with straight lines producing curve fits typically of the quality seen inFigure 1. 1(Eq. 9)(Eq. 10)(Eq. 11)(Eq. 12)6.1.2 For the study of tire residuals and vehicle pull behavior the region encompassing the intersection of allcurves with both axes, Figure 2, is critical.6.1.3 Figure 2 shows the critical region and two additional linear fits which are derived from the data fits in Figu
