Study on Non-Lnear Dynamc Characterstc of Vehcle Suspenson Rubber Component Zhan Wenzhang Ln Y Sh GuobaoJln Unversty of TechnologyChangchun, Chna Wang Lgong (MDI, Chna [Abstract] The dynamc characterstc of rubber component s one of mportant factors that nfluences the NVH performances of vehcle In common case, smulaton model bult on ADAMS software consders only the lnear characterstc But n some specal cases, rubber components nstalled n the vehcle suspenson always work n non-lnear condton Amed at the research dffculty of ths knd of non-lnear dynamc characterstc, a numercal ft method had been put forward based on energy analyss theory n ths paper To acheve the nonlnear dynamc characterstc of rubber component n the vehcle dynamcs smulaton model based on the ADAMS, a user wrtten subroutne has been compled, and a custom solver was created, hence the non-lnear analyss of vehcle dynamcs can be acheved Key words: Vehcle Suspenson Rubber Component ADAMS Software Non-lnear Dynamc Characterstc Energy Analyss INTRODUCTION Wth economy growng and traffc envronment mprovng n Chna, the performance of modern vehcle s requred more and more strctly In order to reduce the transference of vbraton and nose, and to mprove the comfortablty of vehcle, the rubber component s used wdely n vehcle structure, especally n some poston where connect and jon the parts of suspenson For example, Aud1 car has more than 1 rubber components nstalled n front suspenson, t s to utlze the far characterstc of rubber components to reduce vbraton and nose Snce many rubber components were used n vehcle, ther dynamc characterstc affect vehcle performance, especally on the dynamc characterstc of suspenson The dynamc characterstc of rubber components s mostly obtaned by testng In common case, the dynamc characterstc of rubber components consdered as lnear But n some specal places, for example n the jont of low control arm and lateral stablty-bar of Aud1, the dynamc characterstc of rubber component s often workng n non-lnear range Based on the energy analyss theory ntroduced n reference [1], ths paper uses dynamc tral data to deal wth the nonlnear dynamc characterstc of rubber components, and puts forward the numercal fttng method based on energy analyss, and realzes non-lnearzaton of vehcle dynamc smulaton LINEAR DYNAMIC CHARACTERISTIC OF RUBBER COMPONENT The dynamc characterstc of rubber components can be classed by lnear and non-lnear characterstc [2], and t s always descrbed by the relatonshp of force and deformaton In the process of vehcle dynamc smulaton, the dynamc model of rubber components serously affects the analyss precson The dynamc characterstc of rubber components n the lnear range, can de obtaned by analyss the force-deformaton curve of rubber component whch got by actng perodcal exctng force In the lnear range, the force-deformaton relatonshp of rubber component can be descrbed wth followng equatons Exctng dsplacement of rubber component can be descrbe as: Xt ( = X cos( ωt 1 Where: X ampltude of exctng dsplacement; ω exctng frequency Correspondng deformaton force of rubber component s: Ft ( = Fcos( ωt+ δ 2 2 Internatonal ADAMS User Conference Page 1 of 5
Where: F ampltude of deformaton force; δ phase dfference between deformaton force and exctng dsplacement In fact, the phase of deformaton force precedes to that of exctng dsplacement, and the phase dfference δ s δ < 9 Expandng the equaton of deformaton force as: F( t = Fk( t + Fc( t 3 Where: F Fk ( t = Fcosδ cos( ωt = cosδxcos( ωt X 4 Fc ( t = F snδ sn( ωt The frst equaton of (4 denotes the sprng force caused by the dynamc stffness of rubber F component, then the dynamc stffness K s cosδ X The second equaton of (4 denotes the dampng force caused by the dampng of rubber component, whch can be expressed as: F t = F C X t F = sn δ CX ( t ω X [ ] c ( snδ ωsn( ω ω X The phase dfference between the dampng force and exctng dsplacement s 9, and equvalent dampng F coeffcent C s snδ ω X Dynamc stffness K and equvalent dampng coeffcent C of rubber component can be obtaned after F X and δ be measured Commonly, X and δ are functons of exctng frequencyω So dynamc stffness K and equvalent dampng coeffcent C are also functons of exctng frequencyω [1] After removng the tems relatng wth tme from the equaton of exctng dsplacement and deformaton force, the curve of dynamc exctng dsplacement-deformaton force s: 2X 2 2 X 2 2 X F cosδ + F = sn δ 6 X X F F Ths equaton defnes an ellpse curve, seeng Fg1 Ths s the feature of the lnear dynamc characterstc of rubber component δ can be calculated wth the functon of exctng dsplacement and deformaton force or the coordnates of ABCD 5 Fg1 A typcal ellpse curve of lnear dynamc characterstc of rubber C D ANALYSIS OF NON-LINEAR DYNAMIC CHARACTERISTIC When the exctng force acted on the rubber component exceed a certan range, the curve of exctng dsplacement-deformaton force wll no longer be an ellpse, and that changes gradually to crescent, seeng Fg2 At ths tme, the dynamc characterstc of rubber component analyss method wth the lnear analyss assumpton appears obvous shortcomngs On the bass of B O Y A X 2F 2 Internatonal ADAMS User Conference Page 2 of 5
dynamc testng of rubber component, a numercal fttng method descrbed the non-lnear dynamc characterstc of rubber component whch base on the energy analyss s put forward n ths paper Obvously, the curve of loadng and unloadng s closed The area enclosed by the curves denotes the energy consumed by the dampng of rubber component that provded by external exctng dsplacement Xt ( = X cos( ωt The energy consumed by dampng of rubber component n a crcle s: W = F( t dx( t 2π = F X sn( ωtcos( ωt+ δ d( ωt 7 = πfx snδ Loadng-unloadng curve of rubber component s also a closed curve n the non-lnear dynamc characterstc testng So we can assume: Loadng curve: Fa( x = ax + b x ( x, x t Unloadng curve: Fr( x = cx + d x ( x, x t Where: s nteger and dependent by the precson of vehcle dynamc analyss Now the energy consumed by dampng of rubber component n the non-lnear dynamc characterstc testng s: xt xt W= F( xdx F( xdx x ( x, x t a x x r 8 For ce St f f ness Damp ng Load ng Fg2 Fttng prncple of non-lnear characterstc of rubber component O If the stffness of rubber component s represented wth the mean value of loadng and unloadng curve (seeng Fg2, the non-lnear dynamc characterstc of rubber component can be denoted as: d( [ Fa( x + Fr( x ]/2 K = dx x ( x, x t 9 1 = ( a + c x The functon of dampng relatve to exctng dsplacement can also be obtaned: dw C = = Fa( x Fr( x dx = a c x + b d ( ( Unl oad ng Def or mat on 1 2 Internatonal ADAMS User Conference Page 3 of 5
Force (KN Fg3 Dynamc testng result Deformaton (mm Fg4 Fttng result of dynamc test Deformaton (mm TEST DATA PROCESS AND EXAMPLE ANALYSIS Accordng to the method educed above, a numercal fttng works for the dynamc testng of suspenson rubber bushng of a domestc car s carred out The fttng result s presented by Fg 3~Fg6 Fg3 s the curve of non-lnear exctng dsplacement-deformaton force of rubber component under external exctng, the frequency of external exctng s 11 Hz Fg4 s the curve of dynamc characterstc after fttng It s clear that the fttng result agrees wth the testng result consstently Force (KN Force (KN Force (KN Fg5 Dynamc stffness characterstc Frequency (Hz Deformaton (mm Fg6 Dynamc dampng characterstc Frequency (Hz Deformaton (mm The 3D-surface of exctng frequencydeformaton and dynamc stffness are showng on Fg5 whle the exctng frequency changed from 1 Hz to 2 Hz, t s obtaned by fttng the testng result of rubber component Fg6 shows the 3D-surface of exctng frequencydeformaton and dampng A parameter table of non-lnear dynamc characterstc of rubber component can be bult wthn the frequency range when the external exctng frequency changed By means of judgng the exctng frequency of model, the non-lnear dynamc characterstc of rubber component can be obtaned by the nterpolaton method based on the table As a result, the effect of lnear and non-lnear dynamc characterstc of rubber component to vehcle can be consdered n the process of vehcle dynamc analyss 2 Internatonal ADAMS User Conference Page 4 of 5
Fg7 Analyss result of lnear system Fg8 Analyss result of non-lnear system Accordng to ths method, an ADAMS user subroutne was compled and an ADAMS custom solver was created, and a free vbraton system that conssts of a part supported by a rubber component s analyzed wth the solver The stffness of rubber component s usng the dynamc stffness whle the exctng frequency s 11Hz Accordng to the lnearzaton assume, The stffness of rubber component s 14KN/mm, the dampng rato s 2, and mass of the part s 245Kg The calculaton result s shown n Fg7 Meanwhle, Fg8 shows the analyss result when the nonlnear dynamc characterstc of rubber component was taken nto account In the Fg7 and Fg8, the top drawng s the dsplacement-force curve, the bottom drawng s the vbraton frequencyampltude curve The calculaton result ndcates that the system wll vbrate wth nherent frequency about 11 Hz, and t s a typcal lnear and one degree of freedom vbraton system Consderng the non-lnear stffness characterstc of rubber component, the response frequency s abundance, whch shows the typcal characterstc of non-lnear and one degree of freedom vbraton system, and manfests the effect of non-lnear stffness characterstc of rubber component to system vbraton CONCLUTION The method of energy analyss s smple and practcal, whch can be appled to study the nonlnear dynamc characterstc of rubber component of vehcle suspenson The analyss result of one degree of freedom vbraton system ndcates that the method of dealng wth the non-lnear dynamc characterstc of rubber component of vehcle suspenson put forward n ths paper can be used reasonably to the dynamc analyss of vehcle The study method makes up the shortage of lnearzaton assume of rubber component of vehcle suspenson, and provdes a feasble method for the smulaton of non-lnear dynamc of vehcle REFERENCE 1 Guo Konghu, Influence of tre dynamc sde-slp characterstc on vehcle shmmy, Automoble Technology, 19954 2 [Japan]Hu Yuan Chun Yan, Mu Chuanwen Translate, Antvbraton Rubber and Its Applcaton, Chna Ralway Publshng Company,1982 3 Ca Yanchun, L Chengde, The Transent Response and Analyss of Automoble Non-lnear System, Chanchun Automoble Research Insttute, 1989511 4 Wen Qang, Yu Zhuopng, Zhang Ljun, Zhang Janqang, Wu Langshou, Testng Research of Rubber Bearng of Suspenson and Its Statc and Dynamc Stffness Characterstc Shangha Automoble, 19988 2 Internatonal ADAMS User Conference Page 5 of 5