(12) United States Patent (10) Patent N0.: US 7,778,809 B2 Miyashita Et A]
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US007778809B2
(12) United States Patent (10) Patent N0.: US 7,778,809 B2 Miyashita et a]. (45) Date of Patent: Aug. 17, 2010
(54) TIRE CHARACTERISTIC CALCULATION (56) References Cited METHOD, TIRE DYNAMIC ELEMENT PARAMETER VALUE DERIVATION U.S. PATENT DOCUMENTS METHOD, VEHICLE TRAVELING 5,880,362 A 3/1999 Tang et a1. SIMULATION METHOD, AND TIRE 5,944,082 A * 8/1999 Thompson et a1...... 152/2098 DESIGNING METHOD AND VEHICLE 6,754,615 B1 6/2004 Germann et a1. DESIGNING METHOD IN WHICH CONSIDERATION IS GIVEN TO TIRE (Continued) FRICTION ELLIPSE FOREIGN PATENT DOCUMENTS (75) Inventors: Naoshi Miyashita, KanagaWa (JP); EP 1 297 975 4/2003 Kazuyuki Kabe, KanagaWa (JP); (Continued) Masahiko Mizuno, Aichi (JP) OTHER PUBLICATIONS Assignee: The Yokohama Rubber Co., Ltd., (73) Pacejka, H. Non-Steady-State Out-of-Plane String-Based Tyre Mod Tokyo (JP) els, Sciencedirect, Tyre and Vehicle Dynamics, 2006, pp. 216-294.* (*) Notice: Subject to any disclaimer, the term of this (Continued) patent is extended or adjusted under 35 U.S.C. 154(b) by 412 days. Primary ExamineriRussell Frejd (74) Attorney, Agent, or FirmiKnobbe Martens Olson & (21) App1.No.: 11/842,883 Bear, LLP (22) Filed: Aug. 21, 2007 (57) ABSTRACT (65) Prior Publication Data Values of multiple tire dynamic element parameters are set for a tire dynamic model constructed using the tire dynamic US 2008/0059134 A1 Mar. 6, 2008 element parameters for calculating a tire axial force and a self-aligning torque under a given slip ratio. Next, the values (30) Foreign Application Priority Data of the tire axial force and the self-aligning torque are calcu Aug. 22, 2006 (JP) ...... 2006-225069 lated using the tire dynamic model and output. The tire Aug. 22, 2006 (JP) ...... 2006-225070 dynamic model alloWs a center position of a contact patch thereof against a road surface to move in accordance With a (51) Int. Cl. longitudinal force that occurs as the tire axial force When a G06F 17/10 (2006.01) slip ratio in a braking/driving direction is given so that a G06G 7/48 (2006.01) position of the contact patch moves in a longitudinal direction (52) US. Cl...... 703/2; 703/6; 703/8 due to the longitudinal force. When designing a vehicle or (58) Field of Classi?cation Search ...... 703/2, When designing a tire, the tire dynamic model is used. 703/6, 8; 73/146; 152/2098, 209.14, 209.23 See application ?le for complete search history. 18 Claims, 21 Drawing Sheets
I- — _ — _ — T T T T T T ______T _ T w ______~ T ______T “"l
I ______— _ — _ — _ _ __1 | l ' 20 24 I I l 10 : l | 2 4 i 13 l SMALL SLIP SMALL sLIP : I I VEHICLE I ANGLE CONDITION ANGLE OONDITION I I CPU MEMORY I TRAVELING INTEGRATION/ : PARAMETER Fx/Fy/MZ DATA I } I sIMuLATION MANAGEMENT I CALCULATION cALOuLATION I I : PROGRAM PROGRAM I PROGRAM PROGRAM :I I | l | l 1 I | I I I | | } I I SETTING "Magic Formula" : FX/Fy/Mz Fx/Fy/MZ TIRE DYNAMIC I I I PROGRAM DATA/PARAMETER , PARAMETER DATA OAL- MODEL I I { cALOuLATION I OALOuLATION cuLATION COMPUTATION I l I PROGRAM : PROGRAM PROGRAM PROGRAM
l _ _ I ______1
I ______\____L_\\______J 9 11 “ _ 22 26 14 8 1‘2 PROGRAM TIRE DYNAMIO MODEL GROUP PROGRAM GROUP US 7,778,809 B2 Page 2
US. PATENT DOCUMENTS Conference, 2000. Proceedings. Winter Orlando, FL, USA Dec. 10-13, 2000, Piscataway, NJ, USA, IEEE, US, vol. 1, pp. 1025-1034, 7,363,805 B2 * 4/2008 Jayakumar et al...... 73/146 XP010529378, ISBN: 0-7803-6579-8. 7,483,821 B2 * 1/2009 Miyashita et al. 703/8 Gafvert M. et al., “A novel semi-empirical tyre model for combined 7,680,610 B2* 3/2010 Miyashita et al. 702/34 slips”, Vehicle System Dynamics Swets & Zeitlinger Netherlands, 2007/0233352 A1* 10/2007 Miyashita et al...... 701/82 vol. 43, No. 5, May 2005, pp. 351-384, XP002459819, ISSN: 0042 3 1 14. FOREIGN PATENT DOCUMENTS Kabe, K. et al., “A new analytical tire model for cornering simulation. EP 1 516 751 3/2005 Part I: cornering power and self-aligning torque power”, Tire Science JP 2002-356106 12/2002 and Technology, XX, XX, vol. 34, No. 2, Jun. 2006, pp. 84-99, JP 2003-57134 2/2003 XP009092086. JP 2006-225069 8/2006 Partial European Search Report from EP 07 11 4754, dated Nov. 30, JP 2006-225070 8/2006 2007. Hans. B. Pacejka, “Tire and Vehicle Dynamics”, pp. 172-191, ISBN: OTHER PUBLICATIONS 0-7506-5141-5, Butterworth-Heinemann (Sep. 2002). Lugner, et al.., “Rcent advances in tyre models and testing proce Miyashita, N. et al., “A new analytical tire model for cornering dures”. Vehicle System Dynamics, Jun./Jul. 2005, Taylor and Francis simulation. Part II: cornering force and self-aligning torque”, Tire Ltd. GB, vol. 43, No. 6-7, Jun. 2005, pp. 413-436. Science and Technology, XX, XX, vol. 34, No. 2, Jun. 2006, pp. International Search Report for European Application No. EP 07 11 100-118, XP009092085. 4754 dated Jan. 26, 2010. Lacombe, J. Ed iJoines, J. A. et al., “Tire model for simulations of vehicle motion on high and low friction road surfaces”, Simulation * cited by examiner
US. Patent Aug. 17, 2010 Sheet 2 0f 21 US 7,778,809 B2
FIG.2
r/TREAD MODEL 'VBELT MODEL
US. Patent Aug. 17, 2010 Sheet 5 0f 21 US 7,778,809 B2
FIG . 5A FIG . 5B CONTACT PATCH CONTACT PATCH
DIRECTIONMOVEMENT OF -_ I 1
SURFACEON ROAD ii' : , “ b‘ / 1n } DIRECTIONI I’ t'tanol *5 —(E-|)-F y OF WHEEL (1—S)t(1-(1—S)t) SURFACE (8-D-Fy-(1-s)t(1-(1—s)t)
FIG . 5C CONTACT PATCH
FIG . 5D "—-- BRAKING 4 Z[Cm]
\ ------DRIVING , \‘\ 3 I’ \\ I, \:\ 2 z’ // \\\ I, / \\\\\\ 1 I,’ //
Vr vs SLIP B ANGLE 01;
US. Patent Aug. 17, 2010 Sheet 8 0f 21 US 7,778,809 B2
F IG . 8
LATERAL BENDING DEFORMATION _ OF BELT ‘ —(<‘:-l)-Fy
—_>ROLLING SPEED V AMENDED SLIP SLIP ANGLE a ANGLE +‘ Page-“p87? H Fy: BRAKING/DRIVINGSLIP RATIO 8 IN a'e: a -(G1 )-M2 “_'_+ (5%)R $3 HMZFX I DIRECTION m2
1 CHANGE OF CON TACT PRESSURE DISTRIBUTION AND CENTER POSITION OF CONTACT PATCH
TORSIONAL DEFORMATION OF TIRE 1 _ (Gm) ' ""1 US. Patent Aug. 17, 2010 Sheet 9 0f 21 US 7,778,809 B2
FIG.9
( START )
V ~STEP S100 ACQUIRE FX, F , M2, F2, I AND w
V SET INITIAL vALuES OF NSTEP 5102 NONLINEAR PARAMETERS
, V PERFORM LINEAR STEP S104 LEAST SQUARE REGRESSION
STEP CALCULATE COMBINED SuM “STEP S106 5110 OF SQUARED RESIDUALS 2 STEP S108 ADJUST VALUES OF NONLINEAR ' CONVERGED ? PARAMETERS Yes. DETERMINE VALUES OF ~STEP $112 NONLINEAR PARAMETERS AND LINEAR PARAMETERS
I END US. Patent Aug. 17, 2010 Sheet 10 0f 21 US 7,778,809 B2
F IG . l 0
( START )
ACOUIRE CHARACTERISTIC “STEP S202 CURvES OF FX, Fy AND M2
V INITIALIZE NONLINEAR NSTEP S204 PARAMETERS
PERFORM LINEAR ~STEP S206 LEAST SQUARE REGRESSION
STEP CALCULATE COMBINED SUM~STEP S208 8212 OF SOUARED RESIDUALS 3 STEP S210 ADJUST VALUES NO OF NONLINEAR ' PARAMETERS Yes. DETERMINE VALUES OF ~STEP S214 NONLINEAR PARAMETERS AND LINEAR PARAMETERS
V US. Patent Aug. 17, 2010 Sheet 11 0f 21 US 7,778,809 B2
FIG. 11
I START )
SET LINEAR PARAMETERS AND ~STEP S300 NONLINEAR PARAMETERS
SET INITIAL VALUES (SET STEP S302 VALUES) OF FX, Fy AND MZ UNDER APPLIED LOAD F2
, CALCULATE CALCULATED ~STEP S304 VALUES OF FX', R,’ AND M2’
CALCULATE COMBINED SUM NSTEP S306 OF SQUARED RESIDUALS OF SET VALUES AND STEP CALCULATED VALUES S310 STEP S308
ADJUST SET ' CONVERGED ? VALUES Yes. DETERMINE FX', R,’ AND MZ' ~STEP S312 UNDER APPLIED LOAD FZ STEP S314 STEP S316 Yes. IS FZ SMALLER Ff» FZ+ A F2 HAN PREDETERMINED LOAD? US. Patent Aug. 17, 2010 Sheet 12 0f 21 US 7,778,809 B2
FIG. 12
I START I
SET LINEAR PARAMETERS ~STEP S400 AND NONLINEAR PARAMETERS
SET INITIAL VALUES (SET ~STEP S402 VALUES) OF Fx, Fy AND MZ
CALCULATE CALCULATED *VSTEP S404 V VALUES OF B’, R,’ AND M,,_' ACCORDING TO FORMULAE (6) TO (8) OR FORMULAE (16) TO (18)
CALCULATE COMBINED SUM ~STEP S406 OF SQUARED RESIDUALS OF STEP SET VALUES AND S410 CALCULATED VALUES 2 STEP S408 ADJUST SET VALUES
DETERMINE B’, R,’ AND MZI ~STEP S412 AT SLIP ANGLE oz STEP STEP S416 S434 Yes. IS a/ SMALLER THAN PREDETERMINED SLIP ANGLE? US. Patent Aug. 17, 2010 Sheet 13 0f 21 US 7,778,809 B2
F IG . l 3
I STEP S600 STEP S602 SET DATA OF SET VALUE OF TIRE VEHICLE llMagic Formula" SPECIFICATION PARAMETERS l STEP S604 LCREATE VEHICLE MODEL
4 SET TRAVELING ~STEP S606 SIMULATION CONDITION STEPQSGIG I STEP S608 AMEND DATA PERFORM SPEFCYFTEII’TTEN SIT/BETTER EXTRACT VALUES OF PERRIET‘IICE TIRE DYNAMIC EVALUATION DATA ELEMENT PARAMETERS STEP S612 PERFORMANCE —/ EVALUATION DATA
STEP S618 / No. AMENDMENT OF Yes. AMEND VALUES OF EHICLE SPECIFICATIO HMagic Formula" IMPOSSIBLE? PARAMETERS ‘DETERMINE DATA NSTEp 5622 OF VEHICLE SPECIFICATION ‘DETERMINE VALUES OF HMagic Formula" PARAMETERS AND TIRE DYNAMIC ELE MENT PARAMETERS l STEP S624 PLACE ORDER TO MANUFACTURER US. Patent Aug. 17, 2010 Sheet 14 0f 21 US 7,778,809 B2
F I G . 1 4
‘7 STEP S700 STEP S702 SET TIRE DESIGN SET DATA OF VALUES (DYNAMIC VEHICLE ELEMENT PARAMETERS) SPECIFICATION STEP S708 STEP S704 CALCULATE TIRE CREATE VEHICLE CHARACTERISTIC CURVE MODEL
v STEP S710 ‘ STEP S706 CALCULATE "Magic SET TRAVELING Formula" PARAMETERS SIMULATION CONDITION ‘ STEP S712 PERFORM VEHICLE TRAVELING STEP S720 SIMULATION STEP S714 CALCULATE VALUES v OF DYNAMIC ELEMENT CALCULATE PARAMETERS PERFORMANCE EVALUATION DATA STEP S718 STEP S716 {AMEND VALUE?’ OF No. IS TARCET Mag‘c F°rmula PA" VALUE ACHIEVED RAMETERS B TO E ? STEP S722 DETERMINE TIRE DESIGN SPECIFICATION (DYNAMIC ELEMENT PARAMETERS)
I END US. Patent Aug. 17, 2010 Sheet 15 0f 21 US 7,778,809 B2
FIG. 15
TIRE A ; (DRIVING) -—s=0.10 - _ s=0.05 - -- s:0.02
(BRAKING) - -- s=—0.02 - - s=-0.o5
n —10
TIRE B : (DRIVING) S=O.10 - —- S=0.05 — — — S=0.02 (BRAKING) - - - 82-002 — — 81-005 -—S=—O.I 0
-10 US. Patent Aug. 17, 2010 Sheet 16 0f 21 US 7,778,809 B2
FIG .16
TIRE A :
__ a:
0135 M: [kNm]
TIRE B :
__ a:
.VIII US. Patent Aug. 17, 2010 Sheet 17 0f 21 US 7,778,809 B2
FIG. 17A
i1
(DRIVING SIDIE) 1
FIG. 17B US. Patent Aug. 17, 2010 Sheet 18 0f 21 US 7,778,809 B2
F IG . l 8
4 t . . . . . Fy TIRE SIZE: 315/80R22.5 [kN] ' (NEGATIVE) APPLIED LOAD: 11 kN ' GRADIENT CAMBER ANGLE: Odeg SEEM - EDUDUEDD Etlqltu DDE'EIU 2“ (GRADIENT)NEGATIVE E1 DUE‘
6. El
‘0. Q U 1 .0... D SLIP ANGLE "5' a = 1° ‘3 ‘ ( BRAKING SIDE ) . o. U‘. 0 ...... 9.53.9‘ . 0 2 4 6 8 10