Tyre Model Manual
Contents
1. Magic Formula Tyre model with Transient Properties Supplement to Vehicle System Dynamics Vol 27 pp 234 249 1997 Zegelaar P W A The Dynamic Response of Tyres to Brake Torque Variations and Road Unevenesses dissertation Delft University of Technology The Netherlands 1998 Maurice J P Short Wavelength and Dynamic Tyre Behaviour under Lateral and Combined Slip Conditions dissertation Delft University of Technology The Netherlands 1999 Schmeitz A J C A Semi Empirical Three Dimensional Model of the Pneumatic Tyre Rolling over Arbitrarily Uneven Road Surfaces dissertation Delft University of Technology Delft The Netherlands 2004 Besselink I J M H B Pacejka A J C Schmeitz S T H Jansen The SWIFT tyre model overview and applications Presented at the AVEC 2004 7th International Symposium on Advanced Vehicle Control 23 27 August 2004 A Riedel J J M van Oosten Standard Tyre Interface Release 1 4 Presented at 2nd International Colloquium on Tyre Models for Vehicle Dynamics Analysis February 20 21 1997 Issued by the TYDEX Working group TNO Automotive MF Tool 6 1 Users Manual TNO Automotive The Netherlands 2008 35 352. 0 3038 m 2locity 32 886 rad s slip 0 080 is information to set the correct angular velocity of the wheel when specifying the initial our model 32 35 5 3 LMS DADS MF Tyre MF Swift 6 1 is offered for DADS 9 6 To introduce the tyre model and to change the tyre model settings tyre property file scale factors etc in the DADS GUI select Force Tire STI in the DADS modelling panel Xx i iibe a deike Wa dah aena SE mie ibseriaf HE To plot the tyre model outputs after having performed a simulation open the DADSGraph menu and select tire element and the signal you want to plot 33 35 3 BGE Fri Feb 08 up 1 u 2 uD 3 MESSAGE New curve s nane optional LMS up 4 fun 5 up gimsh m File Operations Appearance Show Tools Help UD UD 8 UD q e X x EX x Draw curves ag MultiAxis along X p MultiAxis along Y Current binary file TYRE slipangl 5 4 Third party software MF Tyre MF Swift 6 x is also available in third party simulation software Some examples are Virtual Lab LMS SIMPACK INTEC MADYMO TASS CarSim BikeSim TruckSim MSC Please contact your simulation package supplier or TNO for more information Del ft Ty re 34 35 iy 6 References 1 2 3 4 5 6 7 8 Pacejka H B Tyre and Vehicle Dynamics Second Edition Butterworth Heinemann Oxford 2006 Pacejka H B I J M Besselink
3. Longitudinal slip stiffness Kfx Fz at Fznom Lateral friction Muy Maximum value of stiffness Kfy Fznom Load at which Kfy reaches maximum value The use of estimated combined slip possibly improves the performance of the tyre model when extrapolating to very low friction values Estimated combined slip can be turned on by setting the combined slip coefficients in the tyre property file to zero or by omitting them 13 35 3 2 Backward compatibility MF Tyre MF Swift 6 1 is backward compatible with MF Tyre 5 x MF MC Tyre 1 x SWIFT 1 x and MF Tyre MF Swift 6 0 x Tyre property files generated for these tyre models will work with MF Tyre MF Swift 6 1 and give the same simulation results as before passenger car tyres motorcycle tyres passenger car tyres handling handling ride MF Tyre 5 0 MF MCTyre 1 0 MF Tyre 5 1 ai 1 0 MF Tyre 5 2 MF MCTyre 1 1 SWIFT 1 1 h SWIFT 1 2 a MF Tyre MF Swift 6 0 MF Tyre MF Swift 6 1 Backward compatibility of tyre property files However some differences may occur at very low speeds when relaxation behaviour is included combined with a forward velocity below the value specified with the parameter VXLOW in the MODEL section Due to new formulations the tyre behaviour is much more realistic for these operating conditions In the case of MF Swift minor differences may occur between the 1 x 6 0 x and 6 1 versions due to a different formulation of the contact patch dy
4. ae x xX x VERTICAL_DAMPING Tyre vertical damping x x eee xX x x MC_CONTOUR_A Motorcycle contour ellipse A x MC_CONTOUR_B Motorcycle contour ellipse B x BREFF Low load stiffness of effective rolling radius x x ESRA xX x x DREFF Peak value of effective rolling radius x x EJEA x x FREFF High load stiffness of effective rolling radius x x EGEA xX x x Q_RE0 Ratio of free tyre radius with nominal tyre radius x x X xX x Q V1 Tyre radius increase with speed x x Bae x Q_v2 Vertical stiffness increase with speed x x Bee x Q_FZ2 Quadratic term in load vs deflection x x EaR x Q_FCX Longitudinal force influence on vertical stiffness x x Bax X Q_FCY Lateral force influence on vertical stiffness x x EAE x Q_CAM Stiffness reduction due to camber x PEZA Pressure effect on vertical stiffness x x BOTTOM_OFFST Distance to rim when bottoming starts to occur x xX Bae X BOTTOM_STIFF Vertical stiffness of bottomed tyre x x Bae X STRUCTURAL LONGITUDINAL_STIFFNESS Tyre overall longitudinal stiffness x x ax LATERAL_STIFFNESS Tyre overall lateral stiffness x x Bae YAW_STIFFNESS Tyre overall yaw stiffness x x ax FREQ_LONG Undamped frequency fore aft and vertical mode X K FREQ_LAT Undamped frequency lateral mode x x FREQ_YAW Undamped frequency yaw and camber mode x x FREQ_WINDUP Undamped frequency wind up mode x x DAMP_LONG Dimensionless damping fore aft and vertical mode x x DAMP_LAT Dimensionless damping lateral mode x x DAMP_YAW Dimensionless damping yaw and camber mod
5. by parameter LKZC 24 35 Delft Tyre 4 The road data file Besides the road surfaces that are available to the tyre model when implemented in a multibody package TNO offers several relatively simple road surface types that can be used with the tyre model e Flat Road ROAD_TYPE flat As the name already indicates this is a flat road surface e Plank Road ROAD_TYPE plank This is a single cleat or plank that is oriented perpendicular or in oblique direction relative to the X axis with or without bevel edges e Polyline Road ROAD_TYPE poly_line Road height as a function of travelled distance e Sine Road ROAD_TYPE sine Road surface consisting of one or more sine waves with constant wavelength These road surfaces are defined in road data files rdf Like the tyre property file the road data file consists of various sections indicated with square brackets Comments section UNITS LENGTH meter FORCE ANGLE degree MASS kg TIME sec newton MODEL ROAD_TYPE PARAMETERS In the UNITS section the units that are used in the road data file are set The MODEL section is used to specify the road type see listing above The PARAMETERS section contains general parameters and road surface type specific parameters The general parameters are listed below 25 35 General MU Road friction correction factor not the friction value itself to b
6. term in contact length equation x Q_RA2 Linear term in contact length equation X Q_RB1 Root term in contact width equation x Q_RB2 Linear term in contact width equation X ELLIPS_SHIFT Scaling of distance between front and rear ellipsoid x x x ELLIPS_LENGTH Semimajor axis of ellipsoid x x x ELLIPS_HEIGHT Semiminor axis of ellipsoid x x x ELLIPS_ORDER Order of ellipsoid x x x ELLIPS_MAX_STEP Maximum height of road step x x x ELLIPS_NWIDTH Number of parallel ellipsoids x x x ELLIPS_NLENGTH Number of ellipsoids at sides of contact patch x xX x Q_A2 Linear load term in contact length x x Q_A1 Square root load term in contact length x x ELLIPS_INC Discretisation increment of ellipsoid contour x x Q LBF Length of basic function x x Losi Basic function offset threshold K X Q_LOS2 Basic function offset scaling factor with basic function length x x Q_LIMP1 Linear contact length term in basic function shift x X Q_LIMP3 Scaling factor for quasi static longitudinal enveloping force x Q_LIMP4 Scaling factor for dynamic longitudinal enveloping force x Q_LIMP2 Quadratic contact length term in basic function shift x INFLATION_PRESSURE_RANGE PRESMIN Minimum allowed inflation pressure xX xX PRESMAX Maximum allowed inflation pressure x x VERTICAL_FORCE_RANGE FZMIN Minimum allowed wheel load x x xia x x xX FZMAX Maximum allowed wheel load xX x ee x x LONG_SLIP_RANGE KPUMIN Minimum valid wheel slip xX x EJEA x x x KPUMAX Maximum valid wheel slip x x EJ
7. user to manipulate and tune the tyre characteristics for example to get a better match between full vehicle tests and simulation model Another application of the scaling factors is that they may be used to eliminate some undesired offsets or shifts in the Magic Formula The most important scaling factors are e LMUX longitudinal peak friction coefficient Fx e LKX longitudinal slip stiffness Fx LMUY lateral peak friction coefficient Fy LKY cornering stiffness Fy LKYC camber stiffness Fy LTR pneumatic trail Mz LKZC camber moment stiffness Mz LMP parking moment at standstill Mz Normally when processing the tyre measurements these scaling factors are set to 1 but when doing a validation study on a full vehicle model they can be adjusted to tune the tyre behaviour The scaling factors are defined in the SCALING_COEFFICIENTS section of the tyre property file 16 35 3 4 Parameters i n the tyre property file The following table lists the required and optional parameters for each tyre model version For convenience a comparison is made with the previous model versions x required parameter x optional parameter r T o Stan j Tyre property file 2 a x FG egerk amp SE EEE amp MODEL FITTYP Magic Formula version number 61 61 60 60 6 21 52 TYRESIDE Position of tyre during measurements xX x EJEA x x x LONGVL Reference speed x x Eoaea x x x VXLOW Lower boundary velocity in s
8. x x xe xX x x QDZ4 Variation of peak Dpt with camber squared x x aea xX xk x QDZ6 Peak residual torque Dmr Dmr Fz RO x x ie x x QDZ7 Variation of peak factor Dmr with load xX x eee x x x QDZ8 Variation of peak factor Dmr with camber x x Rapea xX x x QDZ9 Variation of peak factor Dmr with camber and load x x ESEA x x x QDZ10 Variation of peak factor Dmr with camber squared x x EaR X QDZ11 Variation of Dmr with camber squared and load x x ERE x QEZ1 Trail curvature Ept at Fznom x x aea xX x x QEZ2 Variation of curvature Ept with load x x ex x x QEZ3 Variation of curvature Ept with load squared x x EJEA x x x QEZ4 Variation of curvature Ept with sign of Alpha t x x Bei x x x QEZ5 Variation of Ept with camber and sign Alpha t x x ee x x QHZ1 Trail horizontal shift Sht at Fznom x x ee xX x x QHZ2 Variation of shift Sht with load x x eaea xX x x QHZ3 Variation of shift Sht with camber x x ie xX x x QHZ4 Variation of shift Sht with camber and load x x ee xk x SSZ1 Nominal value of s RO effect of Fx on Mz x x eaea xX x x SSZ2 Variation of distance s RO with Fy Fznom x x xe xX x x SSZ3 Variation of distance s RO with camber x x gia xX x x SSZ4 Variation of distance s RO with load and camber x x el x x x PPZ1 Linear pressure effect on pneumatic trail xX x PPZ2 Influence of inflation pressure on residual aligning torque xX x QTZ1 Gyroscopic torque constant XIX X MBELT Belt mass of the wheel X X TURNSLIP_COEFFICIENTS PDX
9. 0 MF TYRE amp MF SwiFT 6 1 USER MANUAL 2008 Ren TRO Copyright 2008 TNO Automotive The Netherlands http www delft tyre nl http www automotive tno nl Document revision 20080208 Table of Contents 1 RIERA WV oo os ccc race eautesssceaveundaudsnsaadadeuuauud sess vauudeuusuldseacxuud dousdussdevecddduauaddeatiuuuu suaueedauebuewabenuessde 3 1 1 NIARO BU O3 H EA 3 1 2 UM YR Esc E E bead dees eacadeae EEE A EE ea etc alsa aanvooth eee eed 4 1 3 M IF Weucsccc ccnsssaectacscavansudasucatesctouwiuasancecctenaseessvancecctessssesGeseneccuesasesscussceeciesenedsdersbecsaeeuseatcede 4 1 4 NEW FEATURES IN MF TYRE MF SWIFT 6 1 ccccccccceccceeeeececcceeeeeeueeeueeceeeseeaueeuseseseseeuuaeaeeeeeeeeeees 6 1 5 LICENSING OF MF TYRE MF SWIFT 6 1 o ccccccceccecscceeeeececeeeeeseuueeeseeeeeseeuaaeaueseseeeseeuaaeaeeseeeeees 6 INNER SAG Ee os ces cc sess std vena concccouscddyacsveeusuousuvadsracuaduvanaedeesvucduusoauveddsevueususdseenes stueusteadsecssceuedsbe 7 2 1 OPERATING MODES cccccccccesceeeeeececeeeseeuueeeeececeeeseuueueueeceseceuuuesseseeeeceeauaausseeeeesseuaaeeseeeeseeeeanaeees 7 2 2 OAS SYSTEMS AND UNITS wicicet teed accrsiee cheat sdesvatesanceusafevecdadnct wevecindaridsteviacsistvanidesteedesesi ce eae teeos 9 2 3 TYRE MODEL OUTPUT oceccccccccceeececececesceeeeeecececeseeuueeeuescesseeauaeeusesseseseuuuaeussceeeeseeuaeeeseeeeeeseeanaeees 11 SHERE PROPERTY FILE 0 sccceccsssssssseesece
10. 04 0 0 0 0 0500 0 Sine Road HEIGHT Height of the sine wave START Distance along the X axis of the road to the start of the sine wave LENGTH Wavelength of the sine wave along X axis of the road DIRECTION Rotation of the bump about the Z axis with respect to the X axis of the road If the bump is placed crosswise DIRECTION 0 If the bump is along the X axis DIRECTION 90 N_BUMPS Number of consecutive sine bumps Finally sample road data files are provided with the installation 27 35 5 Application specific notes 5 1 ADAMS MF Tyre MF Swift 6 1 is offered as a user programmed tyre in ADAMS To use the TNO tyre model you need a customised ADAMS solver These are included in the delivery The next table gives an overview of supported ADAMS versions and operating systems ADAMS operating system version Windows Linux HP UX 2003 2005 2005r2 2007r1 under development property file format To use the tyre model in ADAMS make sure that the following statement is in the MODEL section of the tyre property file PROPERTY_FILE_FORMAT USER USER_SUB_ID 815 This ensures that the TNO MF Tyre MF Swift 6 1 tyre model is called This can also be checked in the ADAMS message file msg the following statement should appear TYR815 gt DELFT TYRE MF Tyre MF Swift 6 1 xxxxxxxx x introducing the tyre using ADAMS View To introduce MF Tyre MF Swift 6 1 in an A
11. DAMS model using ADAMS View commands create a road Tools gt Command navigator gt vpg_road gt instance gt create right click on instance name and select vpg_road gt create fill in the fields create a tyre Tools gt Command navigator gt vpg_tire gt instance gt create right click on instance name and select vpg_tire gt create fill in the fields You get a graphical representation of the tyre after closing the dialog box In this way a wheel body including tyre force element is created You will have to add a revolute joint between the wheel body and vehicle chassis component ADAMS Car it is sufficient to select a MF Tyre MF SWIFT 6 1 tyre property file 28 35 selecting an operating mode In ADAMS the operating mode is selected by setting the value of USE_MODE in the MODEL section of the tyre property file If you want to change the operating mode of the tyre model this has to be done by modifying the tyre property file As explained in section 2 1 a four digit number ABCD would be required to define the operating mode When defining a tyre in ADAMS via the graphical user interface the user has to identify a tyre as being left or right This information can be taken into account by the tyre model If A is not specified so USE_MODE is a three digit number MF Tyre MF Swift 6 1 will honour the ADAMS sideflag and adjust the value for A accordingly The user can overrule this by s
12. EA x x SLIP_ANGLE_RANGE ALPMIN Minimum valid slip angle x x EIRA x x x ALPMAX Maximum valid slip angle x xX xX xX xX xX xX INCLINATION_ANGLE_RANGE CAMMIN Minimum valid camber angle x x EJEA xX x CAMMAX Maximum valid camber angle xX x EIRA xX x x SCALING_COEFFICIENTS LFZO Scale factor of nominal rated load x x ESRAS x x 19 35 Delft Tyre zegas Z Tyre property file e z o z 2 a F ege k amp EE ESE amp LCX Scale factor of Fx shape factor x x EJEA x x x LMUX Scale factor of Fx peak friction coefficient x x xia x x x LEX Scale factor of Fx curvature factor x x Be xX x x LKX Scale factor of slip stiffness x x Ee x x x LHX Scale factor of Fx horizontal shift xX x ee ox ox LVX Scale factor of Fx vertical shift xX xX Bee x x x LCY Scale factor of Fy shape factor x x axes x x x LMUY Scale factor of Fy peak friction coefficient x x Edea x x x LEY Scale factor of Fy curvature factor x x EJEA xx x LKY Scale factor of cornering stiffness x x ESEA x xx LKYC Scale factor of camber stiffness x x EaR LKZC Scale factor of camber moment stiffness x xX eae LHY Scale factor of Fy horizontal shift x x ESRA xT LVY Scale factor of Fy vertical shift x x Bei x x LTR Scale factor of Peak of pneumatic trail x x xe x x x LRES Scale factor for offset of residual torque x x gael x x x LXAL Scale factor of alpha influence on Fx xX xX Bee x x x LYKA Scale factor of alpha influence on Fx x x Bee x x x LVYKA Scale
13. ONS INERTIA VERTICAL STRUCTURAL CONTACT_PATCH Input limitations INFLATION_PRESSURE_RANGE VERTICAL_FORCE_RANGE LONG_SLIP_RANGE SLIP_ANGLE_RANGE INCLINATION_ANGLE_RANGE Magic Formula SCALING_COEFFICIENTS LONGITUDINAL_COEFFICIENTS OVERTURNING_COEFFICIENTS LATERAL_COEFFICIENTS ROLLING_COEFFICIENTS ALIGNING_COEFFICIENTS TURNSLIP_COEFFICIENTS units system used for the definition of the parameters parameters on the usage of the tyre model tyre dimensions operating conditions like inflation pressure tyre and tyre belt mass inertia properties vertical stiffness loaded and effective rolling radius tyre stiffness damping and eigenfrequencies contact length obstacle enveloping parameters minimum and maximum allowed inflation pressures minimum and maximum allowed wheel loads minimum and maximum valid longitudinal slips minimum and maximum valid sideslip angles minimum and maximum valid camber angles Magic Formula scaling factors see also section 3 3 coefficients for the longitudinal force Fx coefficients for the overturning moment Mx coefficients for the lateral force Fy coefficients for the rolling resistance moment My coefficients for the self aligning moment Mz coefficients for turn slip affects all forces moments Though at first sight the number of coefficients may seem extensive Delft Tyre has established two methods to significantly facilitate tyre model parameterisation 1 MF To
14. P1 Peak Fx reduction due to spin parameter x x aie PDXP2 Peak Fx reduction due to spin with varying load parameter x x X xX PDXP3 Peak Fx reduction due to spin with kappa parameter x x EaR PKYP1 Cornering stiffness reduction due to spin x x ax PDYP1 Peak Fy reduction due to spin parameter x x Bax PDYP2 Peak Fy reduction due to spin with varying load parameter x x aie PDYP3 Peak Fy reduction due to spin with alpha parameter x x Bex PDYP4 Peak Fy reduction due to square root of spin parameter x xX Bax PHYP1 Fy alpha curve lateral shift limitation xX xX XxX xX PHYP2 Fy alpha curve maximum lateral shift parameter Xx xX XxX xX PHYP3 Fy alpha curve maximum lateral shift varying with load parameter x x ex PHYP4 Fy alpha curve maximum lateral shift parameter Xx xX XxX xX PECP1 Camber w r t spin reduction factor parameter in camber stiffness x x ax PECP2 Camber w r t spin reduction factor varying with load parameter in camber stiffness x x ex QDTP1 Pneumatic trail reduction factor due to turn slip parameter x x Bax QCRP1 Turning moment at constant turning and zero forward speed parameter x x Bax QCRP2 Turn slip moment at alpha 90deg parameter for increase with spin x xX Bae QBRP1 Residual spin torque reduction factor parameter due to side slip x x Bex QDRP1 Turn slip moment peak magnitude parameter x x Ea 23 35 Delft Tyre Obsolete parameters which may be in a tyre property file but are ignored by MF Tyre MF Swift 6 x a z AR SEB descrip
15. Tyre of Pacejka s renowned Magic Formula tyre model With MF Tyre you can simulate validated steady state and transient behaviour making it a very suitable tyre model for vehicle handling control prototyping or rollover analysis With MF Swift you can simulate tyre dynamic behaviour up to about 100 Hz which is particularly useful for vehicle comfort durability dynamic vehicle control or vibration analysis Special attention has been paid to include behaviour necessary for special applications such as motorcycles regular and racing motorsport e g Formula 1 or aircraft tyres TNO Delft Tyre s MF Tyre and MF Swift are available for all major simulation packages TNO Delft Tyre makes sure that the tyre model implementation and simulation results are identical and that the same set of tyre model parameters can be used for all these packages Further MF Tyre and MF Swift are fully compatible with all previous official TNO Delft Tyre releases 3 35 1 2 MF Tyre MF Tyre is TNO Delft Tyre s implementation of the world standard Pacejka Magic Formula tyre model including the latest developments by TNO and Prof Pacejka 1 and 2 MF Tyre s semi empirical approach enables fast and robust tyre road contact force and moment simulation for steady state and transient tyre behaviour MF Tyre has been extensively validated using many experiments and conditions For a given pneumatic tyre and road condition the tyre forces and
16. b mdl is that SimMechanics is not supported The MATLAB command line functions mfread and mfeval have been replaced by the new function dteval The sequence of the signals in the output vector varinf in the Simulink tyre block has changed Please use the help function of this block to learn more about the new definition In addition a Bus Selector block may be used to select the appropriate output signals based on their names mass specification in the SimMechanics block In the Wheel and tyre block the complete wheel consisting of rim and tyre is modelled The wheel centre connection port should be connected via a revolute joint to an axle body In the mask of the Wheel and tyre block you specify the mass and inertia of the rim only the mass and inertia of the tyre is obtained from the tyre property file A detailed breakdown of the mass will be shown if Display debug messages is switched on For example 31 35 1 gt use_mode 1114 s 19 3 kg 1 391 kgm2 2 736 kgm2 9 3 kg belt mass 7 1 kg 0 391 kgm2 belt Ixx 0 326 kgm2 0 736 kgm2 belt Iyy 0 636 kgm2 itching on rigid ring dynamics the mass inertia distribution is adjusted in such a way and inertia properties of the complete wheel rim tyre remain unchanged gid ring initial statics the tyre model will give the following messages l rigid ring balancing yre force 4721 4 N rolling radius
17. cecsssnnceseseeceenonezsseeececeseoeseresexecennnnnnsesseneennanns 12 3 1 o ANAE E A A AA E O E SAE A A A AR EEE EEA E EEE 12 3 2 BSAOKWARD COMPATIBILITY cc cccccccsessecscscceesecneceeeeeseseacanneceaceesececeedeneeeeeeseneececaaeeeesaneauseseeeesenea 14 3 3 RSA ING FACTORS 00 0cccccccesccccsssceeeccsececnscensaeecuaeceeseeaaseeeeacensuceaseseaeusaaseesseeaeeenesecaaeseasaueaaes 16 3 4 PARAMETERS IN THE TYRE PROPERTY FILE 000ceecceccceseeeseeccecceeseeeueeeesceeesseauaeesseeeeeeseuaaeaseeess 17 n al Roy Ayur Na 25 5 APPLICATION SPECIFIC NOTES uu0 ccccssssssseseeececensseseeeueeeceenusseseueeeeeoouasseeeeuseeuonaugseseuseanaaaas 28 5 1 E Sc ctect caleba coets sete a caine estrada ee tcc clas ntact a 28 5 2 MATLAB SIMULINK SIMMECHANICS 0 ccececceeecceccceseseeeeeececeseseeuaeeeseseeseeeuaeeseeeseeeeauaeeaeeeeeseeees 31 5 3 AN Bs ee ee 33 5 4 THIRD PARTY SOFTWARE c00cccccccesesceeeeeececececceuueeeuecceseeseuaueuseeseuseeuueaeuseeeeeseuuaeueseeeeeeseeanaeees 34 SOSS L pI e ooo E E iienedsudayanades Gnundentuuacee tecwapsunsandaecenesans 35 2008 TNO Automotive All rights reserved MF Tool MF Tyre and MF Swift are part of the DELFT TYRE product line developed at TNO Automotive Helmond The Netherlands This document contains proprietary and confidential information of TNO No part of this publication may be reproduced and or published by print photoprint microfilm or any other means without the previous wr
18. citly will have to select smooth road contact with circular cross section B 2 to get the same results using MF Tyre 6 1 with their MF MCTyre datasets Former SWIFT Tyre 1 x users will have to select 2D road contact using basic functions B 4 and rigid ring dynamics C 3 to get the same results as before Note 3 The camber angle scaling factors LGAX LGAY and LGAZ are not supported anymore The camber influence in MF Tyre MF Swift 6 x can now be more conveniently controlled by the new parameters LKYC Fy and LKZC Mz These parameters allow explicit scaling of the camber stiffness and camber moment stiffness These new parameters also have to be used in combination with MF Tyre 5 x and MF MCTyre 1 x datasets 15 35 3 3 Scaling factors Tyre force and moment testing is often done in a laboratory environment e g using a flat track tyre tester or a drum The artificial road surface on the tyre test machine may be quite different from a real road surface Combined with other factors like temperature humidity wear inflation pressure drum curvature etc the tyre behaviour under a vehicle may deviate significantly from the results obtained from a test machine Differences of up to 20 in the friction coefficient and cornering stiffness have been reported in literature for a tyre tested on different road surfaces compared to lab measurements For this purpose scaling factors are included in the tyre model which allow the
19. e multiplied with the LMU scaling factors of the tyre model Default setting MU 1 0 OFFSET Vertical offset of the ground with respect to inertial frame ROTATION ANGLE _XY_PLANE Rotation angle of the XY plane about the road Z axis i e definition of the positive X axis of the road with respect to the inertial frame DRUM_RADIUS Radius of the drum The road surface type specific parameters are explained in the next sections Plank Road HEIGHT Height of the cleat START Distance along the X axis of the road to the start of the cleat LENGTH Length of the cleat excluding bevel along X axis of the road BEVEL _EDGE_LENGTH Length of the 45 deg bevel edge of the cleat DIRECTION Rotation of the cleat about the Z axis with respect to the Y axis of the road If the cleat is placed crosswise DIRECTION 0 If the cleat is along the X axis DIRECTION 90 DIRECTION LENGTH START ia y V Polyline The PARAMETERS block must have a XZ_DATA subblock The subblock consists of three columns of numerical data e Column one is a set of X values in ascending order e Columns two and three are sets of respective Z values for left and right track Example 26 35 PARAMETERS MU 1 0 peak friction scaling coefficient OFFSET 0 vertical offset of the ground wrt inertial frame ROTATION _ANGLE_XY_PLANE 0 definition of the positive X axis of the road wrt inertial frame X road Z left Z_right XZ_DATA 1 0e
20. e x x DAMP_WINDUP Dimensionless damping wind up mode x x DAMP_RESIDUAL Residual damping proportional to stiffness Xx xX X xX DAMP_VLOW Additional low speed damping proportional to stiffness Xx xX xX xX Q_BVX Load and speed influence on in plane translation stiffness x x x Q_BVT Load and speed influence on in plane rotation stiffness x x x PCFX1 Tyre overall longitudinal stiffness vertical deflection dependency linear term x x PCFX2 Tyre overall longitudinal stiffness vertical deflection dependency quadratic term x x PCFX3 Tyre overall longitudinal stiffness pressure dependency x X PCFY1 Tyre overall lateral stiffness vertical deflection dependency linear term x x PCFY2 Tyre overall lateral stiffness vertical deflection dependency quadratic term x x PCFY3 Tyre overall lateral stiffness pressure dependency x x PCMZ1 Tyre overall yaw stiffness pressure dependency xX xX C_BX0 In plane belt translation stiffness x C_RX Longitudinal residual stiffness x C_BTO In plane belt rotation stiffness x Cc BY Out of plane belt translation stiffness x C_RY Lateral residual stiffness x C_BGAM Out of plane belt rotation stiffness x C_RP Yaw residual stiffness X K_BX In plane belt translation damping x 18 35 Delft Tyre gle ga Z Tyre property file e z o z 2 a Eeee EE ESESE K_BT In plane belt rotation damping X K_BY Out of plane belt translation damping X K_BGAM Out of plane belt rotation damping X CONTACT_PATCH Q_RA1 Square root
21. factor of kappa induced Fy xX x Bee x x x LS Scale factor of Moment arm of Fx x x eaea xX x x LMX Scale factor of overturning moment x x ESEA xX x x LVMX Scale factor of Mx vertical shift x x EJEA x x x LMY Scale factor of rolling resistance torque x x aes x x x LMP Scale factor of parking moment x xX eae LKC Scale factor of camber stiffness x LCC Scale factor of camber shape factor x LEC Scale factor of camber curvature factor x LSGKP Scale factor of Relaxation length of Fx x x x LSGAL Scale factor of Relaxation length of Fy x x amp LGYR Scale factor gyroscopic moment X X xX LONGITUDINAL_COEFFICIENTS PCX1 Shape factor Cfx for longitudinal force x x xa x x x PDX1 Longitudinal friction Mux at Fznom xX x EJEA x x x PDX2 Variation of friction Mux with load xX x EIRA x x x PDX3 Variation of friction Mux with camber x x a x x x PEX1 Longitudinal curvature Efx at Fznom xX x EaEa x x x PEX2 Variation of curvature Efx with load xX xX axel x x PEX3 Variation of curvature Efx with load squared x x ee xX x x PEX4 Factor in curvature Efx while driving x x xe x xX x PKX1 Longitudinal slip stiffness Kfx Fz at Fznom xX x ESEA x x x PKX2 Variation of slip stiffness Kfx Fz with load x x EJEA x xX x PKX3 Exponent in slip stiffness Kfx Fz with load xX x exe x xX x PHX1 Horizontal shift Shx at Fznom xX x eae xix PHX2 Variation of shift Shx with load xX x Egea x x PVX1 Vertical shift Svx Fz at Fznom xX x ERA x x x PVX2 Variation of s
22. features in MF Tyre MF Swift 6 1 With respect to MF Tyre MF Swift 6 0 the following changes have been made e Introduction of tyre pressure dependency on the tyre characteristics This includes the Magic Formula tyre stiffness rolling resistance and other properties e Improved motorcycle tyre road contact e Replacement of the 2D road contact method using basic functions by the more robust and accurate ellipse contact method The ellipse parameters can be used for both 2D and 3D road contact Backward compatibility is maintained so older tyre property files with basic function parameters will keep on working e A parameter DRUM_RADIUS has been added to the TNO road surfaces to allow simulations on a drum surface The tyre model automatically adjusts tyre properties to account for the global road curvature 1 5 Licensing of MF Tyre MF Swift 6 1 The licensing system of MF Tyre and MF Swift 6 1 depends on the multibody simulation package in which it is used and the used operating system Please read the license manual license agreement and terms of use that are supplied with the Delft Tyre and or multibody simulation software If things are unclear please contact TNO Automotive http www delft tyre nl The operating modes that are supported by MF Tyre and MF Swift licenses are discussed in section 2 1 6 35 2 Model usage 2 1 Operating modes MF Tyre MF Swift 6 1 is set up in a modular way and allows a user to independently se
23. fines the step size of the local integrator too big values may result in instability and generally 0 25 ms is a safe value TIME_SWITCH_INTEG defines the time when the switch is made from global to local integration It is possible to have ADAMS calculate static equilibrium for the tyre model and at a later stage during the simulation switch to local integration to speed it up Switching between local and global integration is only possible if a sufficient states are available in the ADAMS model The ADAMS message file will provide additional information on this Some examples e GLOBAL integration of tyre dynamics 0 4 0 states required 4 available e GLOBAL integration of tyre dynamics 6 30 6states required 30 available e GLOBAL integration of tyre dynamics 30 30 30 states required 30 available e LOCAL integration of tyre dynamics 30 4 30 states required 4 available e LOCAL integration of tyre dynamics 30 30 30 states required 30 available Delf T yre 29 35 ion is only possible when the first number is smaller than or equal to the second one states available is defined by the tyre GSE using local integration the maximum step size HMAX of the ADAMS integrator has to or smaller otherwise the simulation results may become inaccurate or unstable e global integration if possible comment out the line defining HMAX_LOCAL from the le by using a or character 30 35 5 2 MATLAB Simuli
24. he static equilibrium of the tyre belt rigid ring body at the start of the simulation We may select one of the following values for C Steady state evaluation lt 1 Hz Transient effects included tyre relaxation behaviour lt 10 Hz linear Transient effects included tyre relaxation behaviour lt 10 Hz nonlinear Rigid ring dynamics included lt 100 Hz nonlinear Rigid ring dynamics initial statics same as 3 but with finding static equilibrium OND O Delf Tyre 8 35 Slip forces Magic Formula evaluation number D When evaluating the Magic Formula it is possible to switch off parts of the calculation This is useful when e g debugging a vehicle model or if only in plane tyre behaviour is required The following values may be selected for D no Magic Formula evaluation Fz only longitudinal forces moments only Fx My lateral forces moment only Fy Mx Mz uncombined forces moment Fx Fy Mx My Mz combined forces moment Fx Fy Mx My Mz combined forces moment Fx Fy Mx My Mz turnslip akWNM Oo NOTE In principle all combinations are possible although some make more sense than others Typically you do not use road contact for 2D or 3D roads without activating rigid ring dynamics On the other hand you may want to use rigid ring dynamics on a flat road surface e g in case of ABS ESP or shimmy analysis Obviously the choice of the operating mode will affect the calculation times MF Tyre and MF Swif
25. hift Svx Fz with load xX x aR x x x RBX1 Slope factor for combined slip Fx reduction xX x Bee xX x x RBX2 Variation of slope Fx reduction with kappa x x ESES x x x 20 35 Delft Tyre gle ga Z Tyre property file e z o z 2 a F ege k amp SE EEE amp amp RBX3 Influence of camber on stiffness for Fx combined x xX eae x RCX1 Shape factor for combined slip Fx reduction x x Bex x x REX1 Curvature factor of combined Fx x x Be xX x x REX2 Curvature factor of combined Fx with load x x Bai x x x RHX1 Shift factor for combined slip Fx reduction xX x ee xX x x PPX1 Linear pressure effect on slip stiffness xX x PPX2 Quadratic pressure effect on slip stiffness xX xX PPX3 Linear pressure effect on longitudinal friction xX x PPX4 Quadratic pressure effect on longitudinal friction xo X PTX1 Relaxation length Sigkap0 Fz at Fznom Xx EX PTX2 Variation of SigKap0 Fz with load x xX xX PTX3 Variation of Sigkap0 Fz with exponent of load XI Xe AX OVERTURNING_COEFFICIENTS Qsx1 Overturning moment offset x x eae x x x QSX2 Camber induced overturning couple x xX Bee x x x QSx3 Fy induced overturning couple x x eae x x x QSX4 Mixed load lateral force and camber on Mx x x EAR QSX5 Load effect on Mx with lateral force and camber x x EaR QSX6 B factor of load with Mx x x EE QSX7 Camber with load on Mx x xX XxX xX QSX8 Lateral force with load on Mx x x a QSX9 B factor of lateral force with load on Mx x x E QSX10 Vertical force with camber on M
26. itten consent of TNO The terms and conditions governing the licensing of MF Tyre consist solely of those set forth in the document titled License conditions of MF Tyre software The terms and conditions governing the licensing of MF Swift and MF Tool consist solely of those set forth in the document titled License Maintenance and Support conditions of DELFT TYRE software Delf Tyre 2 35 1 Overview 1 1 Introduction The contact interaction between tyres and the road largely affects the driving performance of vehicles Automotive engineers are optimising the tyre road interaction so that the vehicle handles well and operates both safely and comfortably under any circumstance To analyse the influence of tyre properties on the dynamic behaviour of vehicles the engineer requires an accurate description of the tyre road contact phenomena TNO Delft Tyre provides a complete chain of tools and services for detailed assessment and modelling of vehicle tyre road interaction tyre measurement data J MF Tool tyre model parameters VEHICLE SIMULATION MODELLING TNO Delft Tyre chain of tools for tyre analyses The tyre models MF Tyre and MF Swift can be used in vehicle dynamics simulations in all major simulation packages to efficiently and accurately represent tyre behaviour for applications ranging from steady state to complex high frequency dynamics MF Tyre and MF Swift contain the latest implementation by Delft
27. lip calculation x xX Bei xX x x ROAD_INCREMENT Increment in road sampling x x x ROAD_DIRECTION Direction of travelled distance x x x PROPERTY_FILE_FORMAT Tyre model selection ADAMS only xX x EIRA x x x USE_MODE Tyre use mode switch ADAMS only x xX Bae x x x HMAX_LOCAL Local integration time step ADAMS only x x x TIME_SWITCH_INTEG Time when local integrator is activated ADAMS only x x x DIMENSION UNLOADED_RADIUS Free tyre radius x xX xe xX x x WIDTH Nominal section width of the tyre xX x EIRA xX x x RIM_RADIUS Nominal rim radius x x EEx x x RIM_WIDTH Rim width x x EEA x XxX xX ASPECT_RATIO Nominal aspect ratio x x ERRA x xX x OPERATING_CONDITIONS INFLPRES Tyre inflation pressure xX x NOMPRES Nominal pressure used in MF equations x x INERTIA MASS Tyre mass x x EaR x IXX Tyre diametral moment of inertia Xx xX XxX xX RAK Tyre polar moment of inertia x x EJE BELT_MASS Belt mass x x BELT_IXX Belt diametral moment of inertia x x BELT_IYY Belt polar moment of inertia x x GRAVITY Gravity acting on belt in Z direction x x M_B Portion of tyre mass of tyre belt part x L_BY Normalized moment of inertia about Y of tyre belt part X I1_BXZ Normalized moment of inertia about XZ of tyre belt part x C_GRV Gravity constant x VERTICAL FNOMIN Nominal wheel load x x Eee x x x 17 35 Delft Tyre gle ga Z Tyre property file e z o z 2 a F ege k S EE EEE amp amp VERTICAL_STIFFNESS Tyre vertical stiffness x x
28. mass and inertia properties 2 Residual stiffness amp damping These have been introduced between contact patch and rigid ring to ensure that the total quasi static tyre stiffnesses in vertical longitudinal lateral and yaw directions are modelled correctly The total tyre model compliance is made up of the carcass ring suspension compliance the residual compliance in reality a part of the total carcass compliance and the tread compliance 3 Contact patch model This part features horizontal tread element compliance and partial sliding On the basis of this model the effects of the finite length and width of the footprint are approximately included 4 Generic 3D obstacle enveloping model This part calculates effective road inputs to enable the simulation of the tyre moving over an uneven road surface with the enveloping behaviour of the tyre properly represented The actual three dimensional profile of the road is replaced by a set of four effective inputs the effective height the effective forward and camber slopes of the road plane and the effective forward road curvature that is largely responsible for the variation of the tyre effective rolling radius 5 Magic Formula steady state slip model This part MF Tyre 6 1 describes the nonlinear slip force and moment properties This enables an accurate response also for handling manoeuvres For more details on the MF Swift tyre model please refer to 1 and 6 5 35 1 4 New
29. moments due to slip follow a typical characteristic These steady state and transient characteristics can be accurately approximated by MF Tyre F N K Steady state tyre lateral force as function of longitudinal and lateral slip calculated using MF Tyre MF Tyre calculates the forces Fx Fy and moments Mx My Mz acting on the tyre under pure and combined slip conditions on arbitrary 3D roads using longitudinal lateral and turn slip wheel inclination angle camber and the vertical force Fz as input quantities MF Tyre is valid for large slip angles typically over 30 degrees longitudinal slip 100 large load variations including truck tyre loads and large camber angles including motorcycle camber angles MF Tyre 6 x includes the functionality of MF MCTyre It can handle road undulations that have a wavelength larger than the tyre circumference and is typically applied for vehicle handling simulation 1 3 MF Swift In addition to the Magic Formula description in the MF Tyre part of the model MF Swift uses a rigid ring model in which the tyre belt is assumed to behave like a rigid body This means that the model is accurate in the frequency range where the bending modes of the tyre belt can be neglected which depending on the tyre type is up to 60 100 Hz MF Swift has been validated using measurements of a rolling tyre 7 to 40 m s containing frequencies up to 120 Hz The model includes essential gyr
30. namic behaviour These differences can be observed in the tyre contact forces and slip values whereas at wheel axle level the differences remain small Due to the built in estimation procedure it is possible to use for example an existing MF Tyre 5 2 tyre property file and perform simulations including turn slip rigid ring dynamics and tyre enveloping behaviour thus already benefiting from the new functionality available in MF Tyre MF Swift 6 1 14 35 Note 1 the selection of the appropriate set of Magic Formula equations is based on the parameter FITTYP in the MODEL section of the tyre property file The following conventions apply e FITTYP 5 MF Tyre 5 0 5 1 Magic Formula equations e FITTYP 6 MF Tyre 5 2 Magic Formula equations e FITTYP 21 MF Tyre 5 2 Magic Formula equations e FITTYP 51 MF MCTyre 1 0 Magic Formula equations e FITTYP 52 MF MCTyre 1 1 Magic Formula equations e FITTYP 60 MF Tyre 6 0 Magic Formula equations e FITTYP 61 MF Tyre 6 1 Magic Formula equations MF Tyre MF Swift 6 1 accepts all these values for the parameter FITTYP It is recommended not to change the value of the parameter FITTYP unless you are sure that the model parameters in the tyre property file are meant for that specific Magic Formula version Note 2 As described in section 2 1 the modular approach of the tyre model allows a user to select various combinations of Magic Formula equations contact methods and dynamics Former MF MCTyre users expli
31. nk SimMechanics MF Tyre MF Swift 6 1 is offered for MATLAB Simulink 6 5 and up The command dteval can be used to evaluate the Magic Formula model for series of input variables For more information on dteval please type help dteval on the MATLAB command line For simulation model development in MATLAB 2006a and up blocks are available from the library TNO_ditlib mdl in Simulink lLibrary TNO_dtlib 10 x File Edit View Format Help TALEE Lz TNO Delft Tyre library for MATLAB Simulink amp SimMechanics version 2006a and up f position roaa vel local dis p Moving road Non moving road local2global Scaling factors body sensor VR p SimMechanics VR sensor Wheel tyre CPI tyre STI tyre 100 Locked TNO Delft Tyre library In addition to the normal functionality the Simulink and SimMechanics blocks allow a user to change tyre scaling factors as a function of time or any other signal available in the model Further some blocks are provided to easily model moving and non moving road surfaces coordinate system transformation and animation of the wheel using the Virtual Reality Toolbox See the help function of the blocks and the Simulink and SimMechanics demos for more information backward compatibility For older versions of MATLAB 6 5 and up the library TNO_ditlib_v65 mdl in Simulink can be used The only difference with respect to the latest library TNO_dtli
32. ol this is an automated fitting tool to determine the tyre model parameters and manipulate the resulting characteristics 8 Fitting Magic Formula coefficients is a well established process within the vehicle industry Furthermore MF Tool features a generic method for identifying MF Swift parameters from standardised measurements such as loaded radius contact length and cleat drum tests 2 Reduced input data requirements if no or limited measurement data is available it is also allowed to omit coefficients in the tyre property file Built in procedures will be used to provide a reasonable estimate for the missing data and only a small number of coefficients are needed The next table gives the minimum required coefficients When using this reduced parameter file detailed effects such as combined slip tyre relaxation effects and enveloping behaviour on short wavelength road obstacles are included although the related parameters are not explicitly specified 12 35 coefficient meaning FITTYP UNLOADED_RADIUS MASS GRAVITY FNOMIN VERTICAL_STIFFNESS VERTICAL_DAMPING LONGITUDINAL_STIFFNESS LATERAL_STIFFNESS PDX1 PKX1 PDY1 PKY1 PKY2 Tip Magic Formula version number Free tyre radius Tyre mass Gravity acting on belt in Z direction Nominal wheel load Tyre vertical stiffness Tyre vertical damping Tyre overall longitudinal stiffness Tyre overall lateral stiffness Longitudinal friction Mux at Fznom
33. on file applies to all parameters in the tyre property file The tyre model expects SI units to be passed via the interface between tyre model and the multibody simulation program as defined in the specification of the Standard Tyre Interface STI 8 However many multibody codes do not use units internally and leave the choice of a consistent set of units to the user In many cases this implies that the vehicle model has to be defined using SI units to avoid unit conversion problems Please contact TNO if you have special non standard requirements with respect to units 10 35 2 3 Tyre model output Various signals are available for post processing Depending on the implementation they are selected by means of a keyword signal number or other methods tyre contact forces moments in the contact point Fx Fy Fz Mx My 6 Mz oa ARUN slip quantities 7 kappa 8 alpha 9 gamma 10 phi additional tyre outputs 11 Vx 13 Re 14 defl 15 contact_length 16 tp 17 mux 18 muy 19 sigma_x 20 sigma_y 21 Vsx 22 Vsy 23 Vz 24 psidot 28 s tyre contact point 31 xcp 32 ycp 33 zcp 34 nx 35 ny 36 nz 37 w 38 beta_y 39 longitudinal force Fxw lateral force Fyw vertical force FZy overturning moment Mxy rolling resistance moment Myy self aligning moment MZ longitudinal slip kappa sideslip angle alpha inclination angle turn slip wheel contact centre forward velocity effective rolling radius t
34. oscopic effects The tyre model functionality is primarily based on 1 6 TNO has made several crucial changes and enhancements in cooperation with Prof Pacejka to the models as described in 1 in order to improve functionality robustness calculation times user friendliness and compatibility between various operating modes MF Swift uses an efficient single point contact for slip calculation which results in full compatibility with MF Tyre Due to the introduction of a so called phase leading network for the pneumatic trail MF Swift is suitable for path curvature with a wavelength in the order of two times the contact length For braking traction applications wavelengths as small as half the contact length are well described The Delf Tyre 4 35 transient slip behaviour is well described up to full sliding due to modelling of decrease in relaxation length for increased slip levels Enveloping model with elliptical cams Rigid ring 6 DOF ra Cleat a Sidewall stiffness Rim amp damping HHH Cy Residual eng stiffness amp gt Ons Effective road plane damping Slip model Graphical representation of the MF Swift model Five main elements of the model structure can be distinguished 1 Rigid ring with 6 degrees of freedom The primary vibration modes of the tyre belt are described by an elastically suspended rigid ring representing the tyre sidewalls and belt with its
35. pecifying the value A in the tyre property file so USE_MODE is then a four digit number Furthermore if ADAMS encounters an old SWIFT 1 2 tyre property file USE_MODE 24 is automatically replaced by USE_MODE 434 So existing models using MF Tyre 5 2 or SWIFT 1 2 will run without modifying the tyre property file In any case the user will get a clear feedback on the operating mode of the tyre model in the ADAMS message file msg A typical message would look like this TYR815 tyre number 1 USE_MODE 1434 tyre side left contact 2D short wave length basic functions dynamics rigid ring slip forces combined using a local integration scheme MF Tyre MF Swift 6 1 provides two methods for time integration with ADAMS e global integration the tyre differential equations are solved in the ADAMS solver together with the multibody equations e local integration the tyre differential equations are solved locally inside the tyre model independent of the multi body model Local integration can significantly speed up the simulation time when using rigid ring dynamics on an uneven road surface For calculations on a level road surface without rigid ring dynamics a global integration will be faster and more accurate The parameters for this local integrator inside the tyre model are set in MODEL section of the tyre property file for example HMAX_ LOCAL 0 00025 TIME _SWITCH_INTEG 0 1 HMAX_LOCAL de
36. re side Magic Formula mirroring number A A Magic Formula tyre model may show offsets and asymmetric behaviour caused by conicity and or plysteer In the tyre property file MODEL section there may be a keyword TYRESIDE which can be either LEFT or RIGHT when missing LEFT is assumed This indicates how the tyre measurement was executed Using the same characteristics on the left and right hand side of a vehicle may result in undesired asymmetrical behaviour of the full vehicle If TYRESIDE is LEFT and the tyre is mounted on the right side of the vehicle A 2 mirroring will be applied on the tyre characteristics and the total vehicle will behave symmetrically It is also possible to remove asymmetrical behaviour from an individual tyre A 3 We may select one of the following values for A 0 1 tyre is mounted on the left side of the car 2 tyre is mounted on the right side of the car 3 symmetric tyre characteristics Contact Method number B Various methods are available to calculate the tyre road contact point Smooth road contact should only be used on a smooth road surface profile containing a minimum wavelength larger than twice the tyre radius For short obstacles e g cleats bumps discrete steps potholes or road surfaces containing wavelength smaller than twice the tyre radius either the road contact for 2D or 3D roads should be selected The road contact for 3D roads works on both 2D and 3D road s
37. t The next table lists the operating modes that are supported by MF Tyre and MF Swift licenses ME Tyre 6 1 MF Swift 6 1 Slip forces Magic Formula evaluation number D 0 1 2 3 4 0 1 2 3 4 5 Dynamics number C 0 1 2 0 1 2 3 4 Contact Method number B 0 1 2 3 0 1 2 3 4 5 Tyre side Magic Formula mirroring number A 0 1 2 3 0 1 2 3 2 2 Axis systems and units Axis systems MF Tyre MF Swift 6 1 uses the ISO sign conventions as shown in the figure below reference sidewall position left direction of WHEEL velocity ISO sign conventions 9 35 The longitudinal slip and sideslip angle are defined as k a note x 1 is braking at wheel lock V tanla gt V x In these equations V is the x component in the wheel centre plane of the wheel contact centre horizontal i e parallel to road velocity V Vs is the wheel slip velocity with components V and Vsy which is defined as the horizontal velocity of the slip point that is thought to be attached to the wheel at a distance that equals the effective rolling radius below the wheel centre in the wheel centre plane Units The output of the tyre model is always in SI units m N rad kg s The tyre property file uses SI units by default m N rad kg s this is always the case when it is generated by MF Tool It is allowed to use a different set of units e g mm or inch for length The specification in the UNITS secti
38. t the operating mode of the Magic Formula tyre dynamics and contact method In some software packages this is done by defining a four digit value for the parameter ISWTCH in the GUI DADS for some other packages the selections can be made from a menu e g SIMPACK MATLAB Simulink In ADAMS changes to the operating mode can be made by setting the parameter USE_MODE in the MODEL section of the tyre property file For details on various implementations see chapter 5 cy Function Block Parameters STI tyre x STI_tyre mask link Tyre model using the standard tyre interface STI as developed by the TYDEX workgroup Inputs to the tyre model are the motions at the wheel centre The outputs force and torque should also be applied to the wheel centre Tyre model version MF Tyre MF Swaift 6 1 0 1996 2008 TNO Automotive Helmond The Netherlands Parameters Tyre ID integer 1 Tyre property file string TNO_car205_60R1 5 tir Road data file may be empty string TNO_PlankRoadidf Tyre side Jymmetic amp f Contact method 3D short wavelength road contact v Dynamics f rigid ring initial statics 0 Slip forces combined o amp Optional use mode overrides pop up integer 168 I Display debug messages Cancel Help Apply Example operating mode selection Simulink interface 7 35 Basically USE_MODE or ISWTCH ABCD e g 1134 the following choices can be made Ty
39. tion A MODEL TYPE 1 X x X MFSAFE1 1 x x x MFSAFE2 1 X X x MFSAFE3 1 x x x SHAPE The complete shape section is obsolete 2 x x INERTIA MA Portion of tyre mass of tyre part fixed to rim 3 x LAY Normalized moment of inertia about Y of tyre part fixed to rim 3 x LAXZ Normalized moment of inertia about XZ of tyre part fixed to rim 3 x M_R Normalized residual mass 4 x LR Normalized moment of inertia about Z of residual mass 4 x STRUCTURAL K_RX Longitudinal residual damping x K_RY Lateral residual damping x K_RP Yaw residual damping x VERTICAL BOTTOM_TRNSF Transition range of bottoming 6 x CONTACT_PATCH FLT_A Filter constant contact length x Q_KC1 Low speed tread element damping coefficient x Q_KC2 Low speed tread element damping coefficient 8 x SCALING_COEFFICIENTS LGAX Scale factor of camber for Fx 9 Xo XxX X LGAY Scale factor of camber for Fy 10 x x x LGAZ Scale factor of camber for Mz 11 P S ex 1 parameter was not used 2 used in combination with ADAMS durability contact replaced by motorcycle contact and basic functions ellipsoid contact 3 replaced by new mass inertia defintions 4 in MF Swift 6 0 and 6 1 a new formulation is used without residual mass 5 replaced by parameter DAMP_RESIDUAL 6 parameter deleted 7 parameter set internally in the software 8 replaced by parameter DAMP_VLOW 9 parameter deleted adjust PDX3 directly 10 camber force stiffness is controlled by parameter LKYC 11 camber moment stiffness is controlled
40. urfaces but it is computationally more expensive than the road contact for 2D roads that works only with 2D road profiles The moving road is to be used for simulation of a four poster test rig It is available in a limited number of simulation packages e g MATLAB Simulink SIMPACK 8 700 and up The following values may be selected for B 0 1 smooth road contact single contact point 2 smooth road contact circular cross section motorcycle tyres 3 moving road contact flat surface 4 road contact for 2D roads using travelled distance 5 road contact for 3D roads Dynamics number C Depending on the frequency range of interest more details on the dynamic behaviour of the tyre may be included In the case of a steady state evaluation no dynamic behaviour is included Linear transient effects indicates that the tyre relaxation behaviour is included using empirical relations for the relaxation lengths In the Nonlinear transient effects mode a physical approach is used in which the compliance of the tyre carcass is considered to determine the lag This approach correctly accounts for the tyre property that the lag in the response to wheel slip and load changes diminishes at higher levels of slip This approach is fully compatible with the MF Swift theory Rigid ring dynamics refers to a detailed dynamic model MF Swift where the tyre belt is modelled as a separate rigid body Finally initial statics refers to finding t
41. x x exe x x PVY2 Variation of shift Svy Fz with load x x Eae x x PVY3 Variation of shift Svy Fz with camber x x EEA x x PVY4 Variation of shift Svy Fz with camber and load x x EaEa x x RBY1 Slope factor for combined Fy reduction xX x ee xX x x RBY2 Variation of slope Fy reduction with alpha xX x Bee x x x RBY3 Shift term for alpha in slope Fy reduction xX x Bei xX x x RBY4 Influence of camber on stiffness of Fy combined Xx x X xX x RCY1 Shape factor for combined Fy reduction x x eee x x ox REY1 Curvature factor of combined Fy x x EJEA x x x REY2 Curvature factor of combined Fy with load x x Be x x x RHY1 Shift factor for combined Fy reduction xX xX ee xX x x RHY2 Shift factor for combined Fy reduction with load x x Bea xk xk x RVY1 Kappa induced side force Svyk Muy Fz at Fznom x x Bei xX x x RVY2 Variation of Svyk Muy Fz with load xX x ee xX xX x RVY3 Variation of Svyk Muy Fz with camber x x ee xX x x RVY4 Variation of Svyk Muy Fz with alpha x x QRS x xX xX RVY5 Variation of Svyk Muy Fz with kappa x x Bee x x x RVY6 Variation of Svyk Muy Fz with atan kappa x x Eee x x x PPY1 Pressure effect on cornering stiffness magnitude xX x PPY2 Pressure effect on location of cornering stiffness peak x x PPY3 Linear pressure effect on lateral friction x x PPY4 Quadratic pressure effect on lateral friction x x PPY5 Influence of inflation pressure on camber stiffness xX x PCY2 Shape factor Cfc for camber forces x PHY3 Variation of shift Sh
42. x x x EE QSX11 B factor of vertical force with camber on Mx x x ix QSx12 Camber squared induced overturning moment x x QSX13 Lateral force induced overturning moment x x QSx14 Lateral force induced overturning moment with camber xk xX PPMX1 Influence of inflation pressure on overturning moment xX X LATERAL_COEFFICIENTS PCY1 Shape factor Cfy for lateral forces x x ee x ex x PDY1 Lateral friction Muy x x Qa x x PDY2 Variation of friction Muy with load xX x EJEA x x x PDY3 Variation of friction Muy with squared camber x x Bei xX x x PEYI Lateral curvature Efy at Fznom x x Bo x x x PEY2 Variation of curvature Efy with load xX xX Bee x x x PEY3 Zero order camber dependency of curvature Efy x x EJEA x x x PEY4 Variation of curvature Efy with camber x x eee xX x x REVS Camber curvature Efc x x eae x PKY1 Maximum value of stiffness Kfy Fznom x x ESEA xX x x PKY2 Load at which Kfy reaches maximum value x x EJEA x x x PKY3 Variation of Kfy Fznom with camber xX x xe x x x PKY4 Peak stiffness variation with camber squared Xx xX XxX xX x PKY5 Lateral stiffness depedency with camber x x ax x PKY6 Camber stiffness factor x xX ei x PKY7 Load dependency of camber stiffness factor x x ex x PHY1 Horizontal shift Shy at Fznom xX x EJEA x x x PHY2 Variation of shift Shy with load x xXx ESES x x 21 35 Delft Tyre zega Z Tyre property file e z o z 2 a Fae ge ES EE EEE amp amp PVY1 Vertical shift in Svy Fz at Fznom
43. y with camber X xX PTY1 Peak value of relaxation length SigAlp0 RO XX X PTY2 Value of Fz Fznom where SigAlp0 is extreme XX ax PTYs Value of Fz Fznom where Sig_alpha is maximum x ROLLING_COEFFICIENTS QSY1 Rolling resistance torque coefficient x x Bee x x x QSY2 Rolling resistance torque depending on Fx x xX Bee x x x Qsy3 Rolling resistance torque depending on speed x x ee x x x Qsy4 Rolling resistance torque depending on speed 4 x x ee x x x QSY5 Rolling resistance torque depending on camber squared x x QSY6 Rolling resistance torque depending on load and camber squared x X QSY7 Rolling resistance torque coefficient load dependency xX x QSY8 Rolling resistance torque coefficient pressure dependency x x ALIGNING_COEFFICIENTS QBZ1 Trail slope factor for trail Bpt at Fznom x xX Ea xx QBZ2 Variation of slope Bpt with load x x ex x x QBZ3 Variation of slope Bpt with load squared xX x ee x x x QBZ4 Variation of slope Bpt with camber x x eRe xX x x QBZ5 Variation of slope Bpt with absolute camber x x eae x x x QBZ9 Slope factor Br of residual torque Mzr x x ee x x x QBZ10 Slope factor Br of residual torque Mzr x x ia x x x QCZ1 Shape factor Cpt for pneumatic trail x x Bee x xl 22 35 Delft Tyre zegas Z Tyre property file e z o z 2 a Fae ge k amp SEES Ee amp QDZ1 Peak trail Dpt Dpt Fz Fznom RO0 x x EJEA x x x QDZ2 Variation of peak Dpt with load x x aea x x x QDZz3 Variation of peak Dpt with camber
44. yre deflection tyre contact length pneumatic trail longitudinal friction coefficient lateral friction coefficient longitudinal relaxation length lateral relaxation length longitudinal wheel slip velocity lateral wheel slip velocity tyre compression velocity tyre yaw velocity travelled distance global x coordinate contact point global y coordinate contact point global z coordinate contact point global x component road normal global y component road normal global z component road normal effective road height effective forward slope effective road curvature N N N Nm Nm Nm rad rad 1 m m s m m m m m m m s m s m s rad s m m m m m rad 1 m not always available not always available not always available not always available not always available not always available Note that the wheel spindle forces and moments are in general obtained from the multibody package 11 35 3 The tyre property file 3 1 Overview The tyre property file tir contains the parameters of the tyre model Sample tyre property files are provided with the installation The file is subdivided in various sections indicated with square brackets Each section describes a certain aspect of the tyre behaviour The next table gives an overview General and Swift parameters UNITS MODEL DIMENSION OPERATING_CONDITI
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