Wheel Dynamic Response to Rolling Excitation on Road Weiji Wang1, a*

Transcription

1 Secon International Conference on Mechanics, Materials an Structural Engineering (ICMMSE 7) Wheel Dynamic Response to Rolling Excitation on Roa Weiji Wang, a* Department of Engineering an Design, University of Sussex, Brighton B 9Q, Unite Kingom a w.j.wang@sussex.ac.uk Keywors: Wheel structural ynamics, oise reuction, Damping Abstract. In this paper, tyre wheel ynamic response to roa excitation uring rolling has been simulate using finite element moelling in a graphical programming environment. he actual contact is an area not a single line an the contact eges are subject to continuous impacts uring the rolling. he structural response to the impact generates structure borne noise as part of pollution to the environment. o reuce the wheel noise can be achieve by attenuating the intensity of structural vibration. he relationship between the noise generation energy of wheel an amping is investigate. It is propose to reuce the noise by increasing the amping in the tyre structure. he effectiveness has been emonstrate by the simulation result. Introuction A major part of noise of fast travelling vehicle on roa is generate from the tyre ue to impact between the tyre contact area an roa surface. he vehicle tyre noise has been rawn great attention as increasing number of vehicles is operating on the roa an eman on environment quality is rising in recent ecaes. One of the rubber tyre functions is to isolate the vibration excitation cause by the roa roughness for the rier. However, fast rolling wheel generates noise to all its surrounings through the air. Due to main target for tyre research an evelopment have been the roa gripping urability an safety, significant measures taken to reuce the noise has been limite so far. yre ynamic moelling for the behaviour an its interaction with roa surfaces have been mae significant efforts [-3]. he iea using amping material to absorb vibration an noise also have been propose for a long time [4-8]. A typical existing prouct example inclues that an acoustic amping sheet is formulate for maximum amping efficiency over a broa frequency an temperature range with easy peel an stick features. ests show that the absorption can be from 3 B to 4 B from frequency Hz to 5Hz. he higher the frequency, the more effective. herefore, to use amping material to reuce tyre rolling noise becomes a hope for roa noise solution. In this work, the tyre vibration reuce by amping material is simulate. It is shown that the more tyre vibrating energy can be issipate in the amping, the more structure borne noise can be reuce. Furthermore, as an option, the amping material can be combine with a certain type of piezoelectric material, an the vibrating energy can be recovere at least partially an transferre into electricity use by sensors or other power neee evices. his paper will be focuse on the simulation of vibrating wheel using finite element moel in graphical ynamics environment, an how the vibrating energy is issipate by increasing the amping in the tyre structure. For better unerstaning of tyre wheel ynamic behaviour, isplaying the ynamic characteristics is realise in MALAB SIMULIK environment as this graphically presents the real-time ynamic behaviour of a wheel. his novel methoology has combine the merit of real-time simulation an straightforwar finite element visual effect. he result is useful in wheel esign incluing the selection of structure geometry an amping materials. Copyright 7, the Authors. Publishe by Atlantis Press. his is an open access article uner the CC BY-C license ( 8

2 Dynamic Moel an Impact Responses to Roa Excitation he noise reuction is to be achieve by reucing the intensity of structural vibration generate from continuous impact by the roa. A wheel with impact from roa surface can be shown Fig.. Due to weight of vehicle, the wheel surroune with a tyre is no longer roun, an the contact of a wheel to the groun is no longer at only point O but along a flat line A-O-B. B O Fig. Roa impact on rolling wheel. Fig. Finite Element Wheel Moel. During fast rolling (assume counter-clockwise), the velocity of contact A is significant, an the ege of contact receives an impact from the groun. his impact is continuously happening to the circumference of the tyre. In aition, the contact B receives an impact ue to suen release of previously compresse rubber. A finite element moel of a tyre wheel using beam elements is assemble shown in Fig.. he insie circle an raial beams represent the metal rim, an the outer circumference an raial beams represent the rubber tyre. With egrees of freeom, the ynamics of the moel is governe by the equation of motion [9, ]: [ m ]{ && z} + [ c]{ z& } + [ k]{ z} = { u(t) } where, [ m], [ c], [ k], { z}, { u( t) } are the mass matrix, amping matrix, stiffness matrix, isplacement vector an external force vector, respectively. For emonstrating the methoology only, the amping is assume to be linear an viscous. he structural isplacement response { z} is cause by the external force from the roa impact { u (t)}. For simulation, in the state space, the equation of motion Eq. () can be expresse as { x& } = [ A] { x} + [ B]{ u} { y} = [ C] { x} + [ D] { u} where, the coefficient matrices are z I { x} =, [ A] z& = m k m c, [ B] = m,[ C] = [ I ], [ D ] = [ ]. he external force{ u(t) } is the excitation from the roa, equivalent to a circular forces acting in raial irection continuously along the circumference. For builing the structural moel, beam elements have been chosen to escribe the wheel tyre an wheel metal rim with ifferent mass, stiffness an amping parameters as in Fig.. During the rolling, the vibrating kinetic energy an potential energy in the tyre structure E = { z& } [ m]{ z& } + { z} [ k]{ z} is to be ampe. he linear an = c z&. Using amping work viscous amping force is { } [ ]{ } W { f } { z} = { f } { z& } t { z& } [ c]{ z& } f = = t, in the case that the system is subject to the impulse at () 9 ()

3 t=, E ( ) = W. i.e., the initial energy of the response to the impulse will be totally issipate by the amping after a certain perio of time. he structural borne noise is relate to the total vibration I = z& z& t over one whole wheel revolution [4]. he higher the amping, the intensity { } { } quicker the amping absorbs, an the shorter there will be for generating noise by the vibrating structure. Simulation Moel for Dynamic Responses MALAB SIMULIK software is use for a real time graphical simulation for the wheel ynamics. he state space tyre wheel system is illustrate as in Fig. 3. he multiple inputs are the roa impulses applie on the finite element noes in the impact irection shown by the arrow in Fig.. Consiering the relative motion, assuming the roa is rotating relative to the wheel, the center of the wheel is regare fixe. Fig. 3 he SIMULIK moel for wheel ynamics. Fig. 4 he subsystem for applying impacts on wheel. he continuous impact on the wheel uring the rolling on roa is simulate as a series of impulses with sequential time elays applie along the wheel circumference noes as in Fig. 4. A MALAB function is use to control the geometrical irections of the applie impulses. he key coe of the function is as below: function U = fcn(u, u, u3, u4, u5, u6, u7, u8, u9, u, u, u, u3, u4, u5, u6, u7, u8, u9, u, u, u, u3, u4, u5, u6, u7, u8, u9, u3, u3, u3)

4 =length(u);u=zeros(95,);b=*pi/64-pi/; U(4)=u*cos(B);U(5)=u*sin(B); B=B+*pi/3; U(7)=u*cos(B);U(8)=u*sin(B); ; B=B+*pi/3; U()=u3*cos(B); U()=u3*sin(B); U=-U; Dynamic Responses A complete set of impulses are applie to the wheel tyre along the circumference noes. he first impulse an the subsequent ones over one revolution are shown in Fig. 5. he total structural vibration intensity I varying with the amping factor is shown in Fig. 6, which ecreases as amping increases. herefore, the structural borne noise can be to be reuce by increasing the amping in the structure. Fig. 7 an 8 shows it takes longer time for lower amping oscillation to ecay than higher amping. By increasing the amping, the isplacement intensity is reuce as illustrate in Fig. 9. Each isplacement curve is corresponing to a time instant. he isplacements at equally space time instants form a eformation clou. x -8 Structure Vib Intensity.5 u() Intensity u () t (sec) Fig. 5 Upper: first impulse. Lower: impulses along wheel circumference for one revolution amping factor Fig. 6 otal structural vibration intensity. 4 x -7 4 x isplacement - z (m) time (sec) Fig. 7 he wheel response at contact noe by single impact t (sec) Fig. 8 he wheel response at contact noe by single impact with higher amping. Fig. 9 Displacement instants on wheel from left to right: single impact response, one revolution responses an one revolution responses with higher amping.

5 Conclusion A finite element moel is combine into the graphical ynamic simulation for visualizing vehicle wheel s response to roa excitation. Real time ynamic behaviour of the wheel to continuous impacts from the roa uring rolling is isplaye. he calculation result has inicate that the vibration which generates noise can be attenuate by increasing the amping in the wheel structure. herefore, the structure borne noise can be reuce in favour of the passengers in the vehicle an resients close to highways. his author propose moelling an simulation have improve the unerstaning of wheel ynamics an can be use for environment frienly wheel esign an evelopment. References []. Sakata, H. Morimura, Effects of ire Cavity Resonance on Vehicle Roa oise, ire Sci. ech. SCA 8() (99) [] E. J. i, D. S. Snyer, et al, Raiate oise from ire/wheel Vibration, ire Sci. ech. SCA 5() (997) 9-4. [3] M. V. Blunell, he moelling an simulation of vehicle hanling Part 3: tyre moelling. IMechE. Proceeings: Part K: J. Multi-boy Dyn. 4 () -3. [4] K. Larrson, W. Kropp, A high-frequency three-imensional tyre moel base on two couple elastic layers. J. Soun Vibr. 53(4) () [5] W. Kropp, K. Larsson, F. Wullens, P. Anersson, F. X. Becot, he generation of tyre/roa noise mechanisms an moels, ICSV, Stockholm, 3. [6] Y. J. Kim, J. S. Bolton, Effects of rotation on the ynamics of a circular cylinrical shell with application to tire vibration, J. Soun Vibr. 75 (4) [7] L. G. Hartleip,. J. Roggenkamp, Case stuy - Experimental etermination of airborne an structureborne roa noise spectral content on passenger vehicles, SAE oise an Vibration Conference 5, raverse City, USA, paper [8] H. B. Pacejka, yre An Vehicle Dynamics, n Eition, ELSEVIER 6. [9] M. V. Blunell, D. Harty, Intermeiate tyre moel for vehicle hanling simulation. IMechE. Proceeings: Part K: J. Multi-boy Dyn. (K) (6) 4-6. [] B. S. Kim, G. J. Kim,. K. Lee, he ientification of tyre inuce vehicle interior noise, Appl. Acoust. 68() (7) [] P. Kint, P. Sas, W. Desmet, hree-imensional Ring Moel for the Preiction of the yre Structural Dynamic Behaviour, Proc. ISMA8, [] Y.. Wei, C. Oertel, Moelling Vibration an Impacting Behaviour of ire by Absolute Finite Element Metho, ire echnology EXPO, Cologn February. [3] H. Olsson, ire force an moment moelling using FEA results, ire echnology EXPO, Cologn February. [4] M. P. orton, Funamentals of oise an Vibration Analysis for Engineers, Cambrige University Press, 989, ISB: [5] C. F. Bears, Structural Vibration Analysis an Damping, AROLD, 996, ISB: [6] E. I. Rivin, Stiffness an Damping in Mechanical Design, Marcel Dekker, Inc. 999, ISB:

6 [7] C. W. De Silva, Vibration Damping, Control, an Design, CRC Press, 7. ISB: [8] D. horby, Structural Dynamics an Vibration in Practice - An Engineering Hanbook, ELSEVIER, 8, ISB: [9] P. I. Kattan, Matlab Guie to Finite Elements An Interactive Approach, Springer. [] A. J. M. Ferreira, MALAB Coes for Finite Element Analysis- Solis an Structures, Springer 9. ISB