Parameterization of in-plane rigid ring tire model from instrumented vehicle measurements

Transcription

1 AVEC 1 Prmeteriztion of in-plne rigid ring tire model from instrumented vehicle mesurements Ari J. Tuononen 1,, Lssi Hrtikinen 1, Frnk Petry 1, Stephn Westermnn 1 1 Goodyer S.A. Colmr-Berg, L-775, LUXEMBOURG Phone: E-mil: lssi_hrtikinen@goodyer.com Vehicle Engineering Alto University Espoo, 76, FINLAND Phone: E-mil: ri.tuononen@lto.fi In-plne rigid ring tire model prmeters were extrcted using vehicle mesurements. Virtion modes of the tire were identified y driving over clet. These modes were then used for defining the rigid ring model prmeters. Additionlly, slow rke rmp, s well s cost-down test nd some simple mesurements on the tire itself were performed to define the remining model prmeters. The effect of the vehicle suspension verticl nd longitudinl movement on the oserved tire modes ws studied nd the suspension effect ws reproduced in the model. Finlly, the mesured nd simulted tire ehvior ws relted to ABS rking tests. Topics / Vehicle dynmics, Tire dynmics, ABS, rigid ring model 1. INTRODUCTION An ccurte representtion of tire force genertion in ABS rking simultions reuires n deute tire model [1]. A common pproch is n empiricl Mgic Formul [] model extended with the longitudinl relxtion length [e.g. 1]. Such n pproch cn e improved even more y defining the relxtion length for different operting conditions (such s force). However, the relxtion length model cnnot cpture some essentil tire virtion modes (when e.g. elt inerti is introduced), which might e of importnce in certin trnsient mneuvers such s ABS rking [3 4,1,16]. The significnce of this topic my even rise in the future, if the electricl motors with dded inerti nd flexiility in drive trin reformulte this complex virtion system [11]. Some of these virtion modes cn e descried e.g. with computtionlly efficient rigid ring model [3,7], which neglects the flexile elt modes ( recent study for more generl tire virtions cn e found in [15]). The rigid ring pproch cn e lso extended to comined slip conditions [6] nd for ritrrily uneven rod surfces [8]. The drwck of the rigid ring model compred to longitudinl relxtion length pproch is tht set of dditionl prmeters is needed. Moreover, these prmeters often depend on operting conditions such s velocity, lod nd force excittion [3,5]. This mkes the full prmeteriztion (including velocity nd mplitude dependency of sidewll stiffnesses) of the model very time consuming nd expensive. This pper studies how these rigid ring model prmeters cn e identified from stndrd vehicle mesurements with typicl instrumenttion used in nlyzing vehicle dynmics. The flexile wheel mounting used on vehicles poses chllenge in this pproch [8,14], ecuse chnge in the oundry conditions (rim is not fixed) influences the nturl freuencies nd virtion modes of the tire. Alterntive wys to derive the model prmeters re lortory test rig mesurements with fixed rim position [e.g. 13] nd using finite element nlysis [9].. RIGID RING MODEL (RRM) The version of RRM implemented in this study is minly from [3] nd used nottions re lso similr. This model is shortly reviewed in the following nd extended with simple suspension model. The RRM model consists of rigid rim nd rigid ring, which re connected with springs nd dmpers in verticl, longitudinl nd torsionl directions (z,x,θ). The rod is descried with n effective rod surfce. The model is shown in Fig. 1. The eutions of motion for the rigid ring re: m & x + kx ( x& x& ) + cx ( x x ) = cos β Fcx + sin β F (1) cn I + k (& θ & θ ) + c ( θ θ ) = r F + M () y θ m& z + kz ( z& z& ) + cz ( z z ) = (3) sin β Fcz + cosβ FcN m g where k is the dmping coefficient, c is the stiffness coefficient, F is the force, M is the moment, β is the effective rod surfce ngle, nd r l is the tire loded rdius. The suscript indictes the component ( for rim, for rigid ring, c for the contct ptch) nd the θ e cx cy

2 AVEC 1 direction of the vrile. The mss is denoted y m, the moment of inerti y I, nd the grvittionl ccelertion y g. The stiffnesses c x, c θ nd c z re constnt in this study (velocity nd mplitude dependent in [3]), ecuse the focus is on studying the tire virtions t certin velocity nd t conditions relevnt for the eginning of ABS rking. The effective rod plne ws clculted with the tndem model with ellipticl cms introduced in [8]. Cr ody ~ 1 Hz Rim longitudinl ~ 1 Hz Wheel hop ~ 1 Hz M y Mss of urter cr Rim & Ring: In phse mode 35 Hz Anti-phse mode 7Hz Ring verticl 75Hz Fig. 1 Rigid ring model in urter cr model with longitudinl suspension stiffness The verticl spring c z connecting the rim nd the ring is tuned to descrie the tire verticl virtion mode, where the tire virtes verticlly s rigid ody. This verticl stiffness is fr from the overll stiffness, which is why Zegelr introduced residul stiffness ρ zr to chieve relistic overll tire stiffness. This is importnt in this study to get the wheel hop mode modeled correctly. The verticl contct ptch force reds: 3 Fcz = r 3ρ zr + r ρ zr + r1ρ zr + V 1Ω (4) where the s indicte the coefficients (more detiled in [3]) nd Ω is the rim rottionl velocity. The residul deflection reds: ρ zr = w z + V 1Ω (5) where w is the effective rod surfce height. The effective rolling rdius is third order polynomil s well: 3 r F + F + F + + (6) e = re3 cn re cn re1 cn re V1Ω The dely of the contct ptch response to chnge in slip is pproximted with first order filter: σ & κ + κ = V (7) c V cx s, x where the slip velocity reds: V = x& r ( Ω + & θ ) (8) s, x e The contct ptch relxtion length σ c euls hlf of the contct length, which reds: = FcN + 1 F (9) cn The friction model in the contct needs to descrie the longitudinl forces s function of the longitudinl slip. The most suitle options re the rush model nd the Pcejk model []. The dvntge of the rush model is its physicl nture. However, typiclly it does not give good prediction with physicl prmeters, minly ecuse the crcss nd tred stiffnesses re not seprted in the sic version of the rush model. To void physiclly motivted model with empiriclly fitted prmeters, we chose directly the empiricl Pcejk model. The sic version reds: Fcx = Fcz D sin( C rctn( Bκ E( Bκ rctn( Bκ )))) (1) where only four core prmeters (B,C,D,E) re considered in the model of this pper. The min drwck of this pproch is mye the ssumption of liner influence of wheel lod to the tire force, ut we prtly include this effect when estimting the prmeters from rking mneuver, where certin rking force induces certin wheel lod vi lod trnsfer. The rigid ring tire model rim ws connected to the vehicle ody with verticl suspension spring nd shock sorer. The eution of motion for the sprung mss m s is: ms& z s + ksz ( z& s z& ) + csz ( zs z ) = msg (11) nd for the rim verticl direction: m&& z + kz ( z& z& ) + cz ( z z ) + (1) ksz ( z& s + z& ) + csz ( zs + z ) = mg Here the unsprung mss is divided to rim mss m nd elt mss m. Grvity cts on these msses independently (E. 3 nd 1). The longitudinl elsto-kinemtics of the rim were modeled with spring-dmper element s well: m && x + kx( x& x& ) + cx ( x x ) + (13) kxx& + cxx = Wheel nd drive trin rottionl dynmics re very importnt fctors when nlyzing tire virtions. The rottionl eution of motion for the rim is: I & θ + k (& θ & θ ) + c ( θ θ ) = M (14) y θ θ where M y is the input torue y friction rke. 3. EXPERIMENTAL TESTS 3.1 Vehicle nd tire The vehicle used in this study ws front-wheel drive VW Golf VI 1.4TSI. The vehicle ws euipped with pneumtic rke root nd one wheel force trnsducer t the front left wheel. Additionlly, the vehicle hd sensors mesuring the rke pressures nd wheel speeds t ech wheel, s well s GPS dt logger recording the vehicle speed. The tire used in this study ws pssenger cr summer tire in the size of 5/55R ABS-rking The ABS rking tests were performed y n emergency rking mneuver, where pneumtic rke root pplied n rupt rke pedl input until the cr ws stopped. During this mneuver, the driver held the clutch pressed with the mnul trnsmission set to neutrl. The rke pressure ws regulted y the vehicle s originl ABS rke system. The stility control ws switched on during ll test sessions. 3.3 Clet tests To introduce torsionl nd verticl excittion to the tire, the vehicle ws driven over rectngulr clets mm high nd 35mm wide. The clet tests were performed s cost-down tests, where the clutch ws pressed nd the ger set to neutrl efore the first clet. y

3 AVEC 1 The vehicle then rolled over four clets while slowing down, providing severl speed conditions. 3.4 Brke rmp Otining relistic slip-force mesurement dt is not trivil. The gol ws to otin the dt on surfce similr to the one used in vehicle rking tests, especilly in terms of surfce roughness. This excluded the usge of lortory tire test rigs. To e consistent with other dt used in this study vehicle rking test ws selected to otin the dt. The rking mneuver ws rke rmp, where the driver slowly increses the rke pressure. This wy stedy-stte tire ehvior is mintined nd rpid chnges in wheel lod nd longitudinl position of the wheel (rim velocity euls cr velocity) due to elsto-kinemtics of the suspension re voided. The model fit is shown in Fig.. Fig. Pcejk model fit curve nd sctter plot of three runs of mesured rke rmp dt As this study is focused on n in-plne tire model, lterl tire force genertion ws not estimted. Therefore, the cse of comined slip is not tken into ccount. It should e noted, however, tht the tire my generte significnt lterl forces even during stright rking. Conseuently, in detiled rking simultion, the lterl component nd comined slip hs to e included. However, sed on [1], the in-plne dynmics re not chnged due to the presence of lterl force. 3.5 Cost down test effective rolling rdius The effective rolling rdius nd its dependence on the vehicle speed were estimted using vehicle cost-down test. In this test, the vehicle ws ccelerted to 1km/h, fter which the clutch ws pressed nd the ger ws set to neutrl. After this, the individul wheel speeds nd the vehicle speed were recorded s the vehicle grdully slowed down. These signls were then used for clculting the effective rolling rdius: r e = V x / Ω (15) s function of velocity. The front nd rer xle tires served s different lod cses. The velocity dependency prmeter v1 ws clculted first y keeping the rest of the E. 4 constnt. The remining prmeters of E. 4 re fitted sed on mesurement points for r e, nd F cz re otined from front nd rer xle wheel lods. An dditionl mesurement point is otined from the tire circumference C when pproching zero velocity nd lod: r e = C / π (16) 3.6 Tire loded rdius nd contct length The tire loded rdius (distnce etween the spindle xis nd the rod surfce) ws mesured for sttic tire. The wheel lod ws vried nd the tire loded rdius ws mesured while cpturing the wheel lod with scles under the tire. The first three prmeters of E. 4 re the lest sures estimted when Ω=. It is ssumed tht the rottionl velocity hs similr effect on loded nd effective rdii (s in [3]), thus the V1 is ville from the effective rolling rdius mesurements. The sttic contct length ws mesured simultneously with the loded rdius. The contct ptch forces in our model re descried with Pcejk model. Therefore, the contct length hs influence only on the relxtion length of the contct ptch, which produces dely needed to pproximte the contct dynmics. This should not e confused with the longitudinl relxtion length of the complete tire, which is not prmeter of the RRM, ut rther result of the model [3]. 4. RESULTS 4.1 Identifiction of virtion modes from clet tests The time responses of some of the cptured signls from the clet test re shown elow (Fig.3). The zero rke pressure signl is included for consistency with the rking test results shown lter. Brke pressure [r] [Nm] Wheel speed [deg/s] Fig. 3 Time response of the wheel force, moment nd speed signls when driving over clet. The clet impct cn e seen in the force signls s rerwrd force in the F x chnnel nd s n upwrd force in the F z. The virtions excited y the clet re then dmped, nd the signl is dominted y excittion from the rod unevenness nd the vrying wheel rottionl speed. The power spectrl density curves shown in Fig. 4 re clculted for the sme period s the time responses. However, the dt is filtered to rnge of 5-Hz to limit the spectrum to the re of interest. Severl cler modes re visile in the Power Spectrl Density (PSD) plots (Fig. 4). Strting from the lowest freuencies (sprung mss mode excluded y filtering), the first detected mode is round 1Hz, which is where the longitudinl nd verticl modes of the unsprung mss of the vehicle re expected to e. The second pek is round 34Hz. This is the freuency, where the in-phse rottionl mode is expected to e [3]. The mode is visile in the F x, M y, nd the wheel

4 AVEC 1 rottionl ccelertion signls, ut not in the F z signl. The third mode, t round 7Hz cn e seen in ll four signls. This is the rnge for the nti-phse rottionl mode of the tire, s well s the verticl mode of the elt. There re dditionl modes visile t higher freuencies, ut these re not needed for the model prmeteriztion. PSD [N/Hz] [Nm/Hz] [(rd/s )/Hz] 1 4 Power Spectrl Density Freuency (Hz) cc_fl Fig. 4 PSD of F x, F z, M y, nd wheel rottionl ccelertion when driving over clet. (.3r) In the next figure, the effect of the vehicle speed on the M y modes is shown. The clerest difference etween the curves is the sence of the 7Hz nti-phse mode on the lowest velocity step. Also, the dmping of the 35Hz in-phse mode is clerly lowest for the smllest velocity of 4km/h. This is lso oserved in [3]. Some of the higher modes seem to shift freuencies t higher speeds, ut otherwise the oserved freuencies re uite insensitive to velocity. PSD [Nm/Hz] 1 1 Power Spectrl Density _98 _78 _6 _ Freuency (Hz) Fig. 5 PSD of M y, from clet tests t different speeds. The pek freuencies were identified from the PSD plots, nd linked to the most prole corresponding virtion modes. The results re summrized in Tle 1, which includes results from tests with three different infltion pressures. An increse in the infltion pressure generlly increses the freuencies, s expected. Especilly the in-phse, nti-phse nd the verticl elt modes re sensitive to the infltion pressure. Tle 1 Identified nturl freuencies from clet tests for different infltion pressures t 78 km/h 78km/h [Hz] 1.8r.3r.3r.8r Note repet 1 st verticl 1.83Hz 1.85Hz 1.83Hz 1.87Hz Vehicle ody heve (). nd verticl 1.3Hz 11.Hz 1.6Hz 11.Hz Verticl movement of unsprung mss (). 1 st longitudinl 11.6Hz 11.4Hz 11.4Hz 1.4Hz Long. movement of unsprung mss (,) nd rim rottion. In-phse rottionl 3.3Hz 36.9Hz 34.8Hz 36.Hz In-phse rottion of the rim nd the elt (,,w_fl). Long. rim movement. 66.4Hz 69.7Hz 68.4Hz 7.3Hz Anti-phse rottion of the wheel nd the elt (, w_fl, no ). Anti-phse rottionl 3 rd verticl 71.Hz 75.9Hz 75.Hz 81.Hz Belt verticl movement (,) nd 87.1Hz 86.8Hz 93.3Hz nd, not rigid ring mode longitudinl (wek) 3rd 88.1Hz 97.74Hz 97.7Hz 15.9Hz nd, not rigid ring mode longitudinl The corresponding stiffness nd inerti prmeters cn e rther esily fitted, when e.g. the tire elt inerti nd mss re defined y weighing the components. The dmping properties of ruer components, on the other hnd, re often difficult to determine. The PSDs were not used for determining the dmping prmeters, ecuse the spectrum of the clet input is not exctly known. The solution ws to simulte the RRM rolling over the clet nd to fit the dmping prmeters sed on the time domin response (Fig. 6). The rottionl velocity nd the longitudinl force give good correltion. The verticl force virtes t the correct freuency, ut in n incorrect phse proly due to the effective rod surfce prmeters. However, the intention ws to use this comprison only to fit the dmping prmeters. The longitudinl nd verticl elt dmping prmeters were kept eul due to the ssumed symmetry of rolling tire in this regrd (trnsltionl stiffness). Rottionl velocity [rd/s] Longitudinl force Verticl force Model Mesured Time [s] Fig. 6 Comprison of mesured nd simulted tire ehvior over the clet 4. Identifiction of virtion modes from ABS rking To provide n overview of rking event on dry sphlt, the time response of the F x signl is shown in Fig. 7. This is followed y the spectrogrm of the sme signl to show the occurrence of the different freuency components during rking. For the spectrogrm, the dt is gin filtered to rnge of 5-Hz. F x Time [s] Fig. 7 Longitudinl force F x nd its spectrogrm during ABS rking on dry sphlt (.3r)

5 AVEC 1 Two freuencies re highlighted in the spectrogrm: one t round 15Hz, nd nother t round 75Hz. The higher freuency oscilltion cn e seen in the time signl just efore the force drop-offs, which re cused y dropping the rke pressure (Fig. 8). During these periods the tire typiclly opertes t high longitudinl slip, when the in-phse mode is well dmped. The lower freuencies, on the other hnd, cn e found fter these events, when the force hs lredy dropped significntly, which cuses longitudinl movement of the rim due to suspension complince. To provide more detiled view, shorter section of the ABS rking mneuver is shown in Fig. 8. The section depicts the end of the fourth ABS control loop nd the eginning of the fifth loop. The vehicle speed during the section is etween 5 nd 3km/h. Brke pressure [r] [Nm] Wheel speed [deg/s] Time [s] Fig. 8 Time response of the rke pressure, s well s F x, F z, M y, nd wheel speed signls during ABS rking (pressure drop, hold nd rise cycles). As shown in the rke pressure signl, the pressure drop rte is much higher compred to the pressure rise rte. However, the F z signl shows virtion lredy efore the pressure drop. A similr virtion is lso seen in the F x. During these virtions the wheel speed hs lredy strted to drop leding to high wheel slip vlues. These two virtions cn lso e seen in the power spectrl densities in Fig. 9, which re clculted for the sme time period (filtered for rnge 5-Hz). PSD [N/Hz] [Nm/Hz] [(rd/s )/Hz] 1 5 Power Spectrl Density ABS Brking Dry Asphlt cc_fl Freuency (Hz) Fig. 9 Power spectrl density of F x, F z, M y, nd wheel rottionl ccelertion during ABS rking The in-phse mode is not clerly present in the force signls nd the F x virtion freuency is rther high to e the nti-phse freuency in this prticulr exmple. The virtion freuency seen in the F z, however, mtches uite closely the verticl elt mode detected during the vehicle clet tests (75.9Hz in Tle 1). A PSD comprison of the F x from different mesurements nd simultions is shown in Fig. 1. The clet simultion nd mesurements (dt immeditely fter the clet) oth clerly excite ll three modes expected in F x nd the freuencies re comprle. The clet simultion with the RRM does not show 1Hz mode, which indictes tht it is not rigid ring mode. The PSDs of ABS rking do not show n in-phse mode, ut the nti-phse mode is ctive. However, the oserved freuency vries slightly. During the simultions, the model ws given mesured rke pressure signl s n input. To chieve good time-domin fit, detiled models for the verticl force vrition nd the rod plne re needed. PSD [N/Hz] 1 5 Power Spectrl Density of Clet Simultion Clet Mesurement 1 1 Dry Brking Simultion Dry Brking Mesurement Wet Brking Mesurement Freuency (Hz) Fig. 1 Power spectrl densities of F x from simultions nd mesurements for clet nd ABS rking tests. 4.3 Otined Prmeters The finl RRM prmeters for the.3r condition re shown in Tle. The tire elt mss ws estimted nd then used for determining the elt inerti together with the elt rdius. Verticl stiffness nd contct length were mesured in sttic conditions. The Mgic Formul nd effective rolling rdius prmeters were determined s descried in chpters 3.4 nd 3.5, respectively. The vehicle prmeters were fitted to otin the correct sprung mss, wheel hop mode, nd the longitudinl rim virtion mode. After these prmeters were fixed, the trnsltionl sidewll stiffness ws determined y fitting the verticl elt mode for 75.9Hz (Tle 1). The remining two prmeters, moment of rim inerti nd rottionl sidewll stiffness, were djusted to reproduce the correct in-phse nd nti-phse freuencies. This is rther simple tsk, ecuse the rim inerti hs similr influence on oth modes, ut the rottionl stiffness minly influences the nti-phse mode only. 5. DISCUSSION Looking t the PSDs tken from the vehicle tests nd compring the detected modes to literture nd the model, it seems cler tht the peks re cused y the following virtion modes. The lowest mode round 1.8Hz is the heve of the vehicle ody. The second

6 AVEC 1 verticl mode round 11Hz is the verticl mode of the suspension. Tle RRM prmeters for tire of the size 5/55R16 t 78 km/h nd.3r Rigid ring mss of rigid ring 6.15 kg Mesured moment of rigid ring.546 kg m Mesured inerti mss of the rim (unsprung mss) =48.5 kg Suspension + force hu rim + tire contriution moment of rim inerti.417 kg m Clet response (freuency domin) (inc. driveline clutch disengged) rottionl sidewll stiffness Nm/rd Clet response (freuency domin) rottionl sidewll Nms/rd Clet response (time domin) dmping trnsltionl sidewll N/m Clet (from verticl) stiffness trnsltionl sidewll 3 Ns/m Clet response (time domin) dmping Effective rolling rdius Cost-down re.3164 m N re1 re m / N m / re3 3 N Verticl tire stiffness V e-8 m s Mesured V s From [3] N/m Sttic mesurement N/m Sttic mesurement Contct length Sttic mesurement m / N m/n Mgic Formul Brke rmp B.937 C D 1.54 E.8613 Cr prmeters Front xle Suspension spring rte N/m Suspension dmper rte Ns/m Suspension longitudinl 3,4 1 5 N/m spring Suspension longitudinl Ns/m dmper Sprung mss of urter cr 41 kg Front left The first longitudinl mode is the longitudinl movement of the unsprung mss coupled to the rottion of the rim (s in [8]). This mode cn e seen in oth the clet nd the ABS rking tests. The mode t 35Hz is the in-phse rottionl mode coupled with the longitudinl movement of the rim (s in [8]). This mode is well dmped during ABS-rking (Fig. 9), ecuse locl slip stiffness is decresed t high slip levels. The RRM model cn cpture this phenomenon s oserved erlier in [3]. The mode t 68Hz is the nti-phse rottionl mode. The mode t 75Hz is the verticl movement of the elt nd cn e seen during oth clet nd ABS rking tests. The peks t 87Hz nd 97Hz my originte from flexile tire modes or elt longitudinl modes. 6. CONCLUSION Bsed on the model nd the experiments performed, it seems tht it is possile to derive prmeters for n in-plne rigid ring tire model from vehicle mesurements. It is, however, very importnt to include the effect of the vehicle suspension into the model, ecuse dding the dditionl degrees of freedom to the model not only dds the suspension nd vehicle ody virtion modes, ut lso chnges the oserved tire virtion modes. The virtions modes oserved from clet tests re similr to those oserved during ABS-rking with some discussed exceptions. It is very difficult to drw ny generl conclusion when these virtions occur during ABS-rking, ut they certinly hve influence on locl sliding speed in the tire contct ptch nd to wheel speed signl noise. It seems tht nti-phse virtions re much stronger on wet thn dry, thus offering potentil to improve wet rking without trditionl trde-off with rolling resistnce. ACKNOWLEDGEMENTS This project ws supported y the Europen Community under the Mrie Curie Industry-Acdemi Prtnership nd Pthwys (PIAP-GA ), s well s the Fonds ntionl de l Recherche (Luxemourg) under the AFR grnt numer These contriutions re gretly pprecited. REFERENCES [1] A. T. vn Znten, W. D. Ruf, nd A. Lutz, Mesurement nd Simultion of Trnsient Tire Forces, in SAE Technicl Pper Series 8964, [] H.B. Pcejk & R.S. Shrp, Sher Force Development y Pneumtic Tyres in Stedy Stte Conditions: A Review of Modelling Aspects, Vehicle System Dynmics, :3-4, , 1991 [3] P. W. A. Zegelr, The Dynmic Response of Tyres to Brke Torue Vritions nd rod unevennesses, Delft University of Technology, 1998 [4] S. Gong, A Study of In-Plne Dynmics of Tires, Delft University of Technology, 1993 [5] J.P. Puwelussen, L. Gootjes, C. Schröder, K.-U. Köhne, S. Jnsen, nd Schmeitz, Full vehicle ABS rking using the SWIFT rigid ring tyre model, Control Engineering Prctice, vol. 11, no., pp , Fe. 3. [6] J. P. Murice, P. W. A. Zegelr, nd H. B. Pcejk, The Influence of Belt Dynmics on. Cornering nd Brking Properties of Tyres, Vehicle System Dynmics, vol. 9, no. S1, pp , 1998 [7] A. J. C. Schmeitz, I. J. M. Besselink, nd S. T. H. Jnsen, TNO MF-SWIFT, Vehicle System Dynmics, vol. 45, no. S1, pp , Jn. 7. [8] A. J. C. Schmeitz, A Semi-Empiricl Three-Dimensionl Model of the Pneumtic Tyre Rolling over Aritrrily Uneven Rod Surfces, Technische Universiteit Delft, 4. [9] N. Blrmkrishn nd R. K. Kumr, A study on the estimtion of SWIFT model prmeters y finite element nlysis, Proceedings of the Institution of Mechnicl Engineers, Prt D: Journl of Automoile Engineering, vol. 3, no. 1, pp , Oct. 9. [1] M Jiswl, G Mvros, H Rhnejt nd P D King, Influence of tyre trnsience on nti-lock rking, Proceedings of the Institution of Mechnicl Engineers, Prt K: Journl of Multi-ody Dynmics 1 4: 1 [11] M. Rosenerger, R. A. Uhlig, T. Koch, nd M. Lienkmp, Comining Regenertive Brking nd Anti-Lock Brking for Enhnced Brking Performnce nd Efficiency, in SAE Interntionl, 1, p. 1 [1] T. Rhyne, S. Cron, nd M. Knuf, Interction of ABS with Tire Torsionl Dynmics, in The Thirtieth Annul Meeting nd Conference on Tire Science nd Technology, 11. [13] S. Bruni, F. Cheli, nd F. Rest, On the Identifiction in Time Domin of the Prmeters of Tyre Model for the Study of In-Plne Dynmics, Vehicle System Dynmics, vol. 7, no. S1, pp , [14] R. S. Shrp nd D. J. Allison, In-plne Virtions of Tyres nd their Dependence on Wheel Mounting Conditions, Vehicle System Dynmics, vol. 9, no. S1, pp. 19-4, [15] P. Kindt, Structure-Borne Tyre / Rod Noise due to Rod Surfce Discontinuities, Ktholieke Universiteit Leuven, Leuven, 9. [16] S. T. H. Jnsen, P. W. A. Zegelr, nd H. B. Pcejk, The Influence of In-Plne Tyre Dynmics on ABS Brking of Qurter Vehicle Model The Influence of In-Plne Tyre Dynmics on ABS Brking of Qurter Vehicle Model, Vehicle System Dynmics, vol. 3, no. 3, pp , 1999.