Study of Tyre Damping Ratio and In-Plane Time Domain Simulation with Modal Parameter Tyre Model (MPTM)

Transcription

1 Sudy o Ty Damping aio and In-Plan Tim Domain Simulaion wih Modal Paam Ty Modl (MPTM D. Jin Shang, D. Baojang Li, and Po. Dihua Guan Sa Ky Laboaoy o Auomoiv Say and Engy, Tsinghua Univsiy, Bijing, China 1 4h Innaional Ty Colloquium Apil -1, 15

2 Oulin Inoducion o Modal Paam Ty Modl (MPTM Modling o In-Plan Tim Domain Simulaion Modling o Damping aio Conclusions

3 Inoducion o MPTM An analyical y modl by using xpimnal modal paams 3 In pas wo dcads, usd in a sis o publicaions and xpimns o addss y mchanics modls und din condiions Modal paams lcing y mchanics naual bhavios: y yp, pssu Modling y mchanics popis wih modal paams und din xnal inpus and consains:.g, vlociy, load, conac suac, c. Expimns o h spciic woking cass no quid a xacing y modal paams 3

4 MPTM: Ty Modal Expimns F-suspnding whl 3-D modal xpimns and idniicaion und 3-D xciaion 4 4

5 Sl-aligning oqu (NM MPTM: Ty Modls Saic vical popis: SAE 1998 Sady-sa coning: VSD Dynamic coning: VSD In-plan sady-sa and dynamic und din condiions: cla (TMPT, spds Oh modls =.7 =.9 =1. HM, / H M, Expimn Calculaaion.1 1 s a Slip Angl (dg Fig.7 Sl-aligning oqu und h loads,

6 MPTM: Modling Mhodology 3-D -suspnding modal xpimns Ty physical paams, and discizaion a y pim Consain quaions Ty mchanics consain quaions wih modal analysis hoy Ty gomic consain quaions wih o wihou oaion Exnal inpu consains such as olling vlociy, acclaion, conac suac, load, c. Solving consain quaions o ach im sp in al nvionmns o obain oc and domaion disibuion in im sis 6 6

7 Fz (N Modling o In-Plan Tim Domain Simulaion: Saic Cas Ty mchanics quaions Gomic moion consains Exnal inpus and consains Calculaion sul D A D A θ D Fz o z θ x 7 H D = + s + c D = + s + c c c H 7 H H ji N k1 H H jk K k ik x ( z ( D D sin D cos D z H Fz z Fx x cos sin AX=b, X={ z, x, H, L}, (n+ dimnsions Calculad Expimns in TMPT Vical domaion (mm

8 Modling o In-Plan Tim Domain Simulaion: olling (Dynamic Cas v 8 ω o V= Fx Fz o F z F x H ( +D D=- A Gomic olling moion consains D cos ( D sin D cos D H cos D sin cos 8

9 , Modling o In-Plan Tim Domain Simulaion: olling Ty mchanics quaions d d ji ji N V 1 ( jk jk cos( k( jd k1 k 1 k k ( sindk( dk N V ( hk ( cos( k( jd Sady-sa in olling: qual o a hamonic inpu 9 d ji X k N k 1 X k cos( b jk jk k V ( k bk ( kkbk k j kv bk λ k = an 1 ξ kω k b k ω k b k 9

10 , Modling o In-Plan Tim Domain Simulaion: olling Ty mchanics dynamic ansin quaions: dcay + ansin spons,.g, d ji N V 1 ( jk jk cos( k( jd k1 k k ( sindk( dk 1 k k 1 jk 1 pk1 pk1 cos pk1 j cos k ( n n k dk kk pk1 k k sin pk1 k k 1 pk pk cos pk ( k k k k pk k k sin pk k k 1 jk 1 k k pk1 sin pk1 j sin k dk ( kk p k k k k1 k k cos pk1 k k 1 k k pk sin pk ( k k k k pk k k cos pk pk1 dk k pk dk k 1

11 11 11 Modling o In-Plan Tim Domain Simulaion: olling Exnal inpus and consains, such as: Calculaion, ( H x x z b u A x z u sin ( cos ] [sin ] [cos ( g D D H g g b (1, ] [cos ] [sin ( cos ] [cos ] [sin n ons H D D M M M A olling spd involvd, n+1 unknown vaiabls Tim simulaion o ach ick: disi. ocs and domaions Lina quaion solving poblm Und din inpus: vlociy/acclaion, conac suac

12 Modling o In-Plan Tim Domain Simulaion: suls Convgnc o dynamic o sady-sa in im simulaion Dynamic spons 1 Mod Fq (Hz

13 Modling o Damping aio wih MPTM: A ypical soluion xampl o ough poblms Qusion: using viscous o sucual damping in modal hoy o y modls, spcially longiudinal dicion popis 13 Fo xampl: olling sisanc issu in low vlociis mx cx kx F 1 j mx k j x F Using sucual damping aio du o hyssis 13

14 Modling o Damping aio: Diiculis 14 Sucual damping aio bings mo poblms: no analyical ansin quaion How o g h sucual damping aio How o us and din i in sady-sa cas How o us and din i in ansin cas Th modl basd on MPTM will solv hs poblms 14

15 Modling o Damping aio Obain h sucual damping aio om viscous damping aio 15 H H visco suc 1 k j kk 1 j k k k 15 ω ω k ->β k =ξ k

16 Modling o Damping aio Sady-sa soluion wih sucual damping sady-sa spons in olling is qual o an hamonic inpu which has h hoical soluion 16 k m x x kx F cos ( F 1 k x cos( an ( 1/ [( k ( k ] k N x( i X cos( b V X 1 [( b ll ( ] 1/, an 1 ( b b k kv 16

17 Modling o Damping aio Dynamic ansin wih sucual damping Th valu o viscous damping usd in ansin should b changd wih vlociis Th viscous damping is obaind by compaing is sadysa sul wih sucual damping sul 17 d ji X k N k 1 X k cos( b jk jk k V ( k bk ( kkbk 1 k N x( i X cos( b V X [( b ll ( ] 1/, j kv bk λ k = an 1 ξ kω k b k ω k b k an 1 ( b b k kv ξ k ω k b k = β k ω k, ξ k = β kω k ωk 17

18 Modling o Damping aio: suls olling sisanc (N olling sisanc (N olling sisanc Dynamic ansin spons ov a cla Sucual damping aio Viscous damping aio 8 6 aio:. aio:.1 aio: Vlociy (km/h Vlociy (km/h 18

19 Conclusions MPTM is an civ y analyical modling mhod by using only sandad modal xpimns almos wihou quiing any oh xpimns. In-plan y saic and dynamic simulaions basd on MPTM shows h compl analyical pocss wih gomic moion, mchanics and modal hoy, xnal inpus, and calculaion pocdus. I can also b usd in viual poving gound simulaion and oh condiions. Modling o sucual damping aio shows good agmns in olling sisanc and oh calculaion suls. Mo impoanly, his is h is im h mhods o xacion and usag o sucual damping in y mchanics a poposd. MPTM as h analyical modl can b usd o sudy and calcula mo y mchanics popis in al nvionmns

20 Thank You o you anion!