PARAMETRIC SENSITIVITY ANALYSIS OF A HEAVY DUTY PASSENGER VEHICLE SUSPENSION SYSTEM

Transcription

1 VOL. 4, NO. 8, OCTOBER 009 ISSN ARPN Jounal of Engineeing and Alied Siene Aian Reeah Publihing Netwok ARPN. All ight eeved. PARAMETRIC SENSITIVITY ANALYSIS OF A HEAVY DUTY PASSENGER VEHICLE SUSPENSION SYSTEM T. Ram Mohan Rao and G. Venkata Rao Deatment of Mehanial Engineeing, Vaavi College of Engineeing, Hydeabad, India tmao@yahoo.om ABSTRACT Suenion tem deign la an imotant ole in imoving aenge omfot and oad holding aabilitie of an automobile. Thee i a omomie between the oad holding and ide omfot. While Ride omfot i dietly elated to the aeleation ened by aenge when taveling on a ough oad, oad holding ability i aoiated with the ontat foe of the tie and oad ufae. Suenion tavel o woking ae efe to the elative dilaement between the ung- ma and the un- ung mae of the vehile. The eent mathematial wok aim to detemine the diomfot, oad holding and woking ae in a aenge bu by olving the elevant obabiliti equation uing MATLAB though a quate a model. The vaiability in the aamete of ing tiffne and daming ae ued to evaluate the tandad deivation of the vetial vehile body aeleation, tie adial foe and elative dilaement between wheel and vetial body. The ational eletion of daming and uenion toke and an etimation of eed limit an be had fom thee tudie. Keywod: vehile, uenion tem, diomfot, oad holding, woking ae, quate a model.. INTRODUCTION The main tak of the aenge vehile uenion deigne i eduing both vehile body aeleation and the dynami tie load. Thi i to inue good ide omfot fo the aenge and edue the damage to the vehile tutue. Alo, the imovement of ide quality in a vehile an edue the aenge fatigue, theeby eulting in ineaed afety and omfot and vehile ontol fo a dive. It ha been obeved that movement of a vehile on andom oad ufae i one of the main eaon of geneating vibation in it omonent [, ]. Seveal otimization tehnique wee ued ealie to otimize aamete of uenion tem in whih diffeent objetive funtion wee ued. Otimal uenion aamete, atiulaly daming o-effiient wee geneated and by uing the otimized uenion aamete the vehile ide quality wa imoved. The uenion tem edue the tanmiion of oillation to the vehile body fom oad ufae ditubane. The hai hould be well iolated fom the oad ufae with the minimal uenion tavel, yet ovide good handling efomane [3]. Geneally a vehile uenion tem may be ategoized a eithe aive, emi ative and fully ative tem. Paive uenion tem inlude the onventional leaf ing and hok abobe ued in mot aenge heavy vehile. Paive tem doe not have any ontol element inooated in them and theefoe ae inexenive. The ing ae aumed to have almot linea haateiti while mot of the hok abobe exhibit nonlinea elationhi between foe and veloity. In a aive tem, thee element have fixed haateiti and hene have no mehanim fo feed bak ontol. In a vehile uenion tem thee ae a vaiety of efomane aamete, whih need to be otimized. Thee ae thee imotant aamete given below whih hould be aefully onideed in deigning a vehile uenion tem [4]. Ride omfot i dietly elated to the aeleation ened by aenge when taveling on a ough oad. Road holding ability i aoiated with the ontat foe of the tie and the oad ufae. Thee ontat foe ae aumed to deend linealy on the tie defletion. Woking ae efe to the elative dilaement between the ung and un ung mae. It hould be lee than the attle ae. In the eent ae, a mathematial eeentation fo ide omfot, oad holding and woking ae i made by onideing the tandad deviation of the thee uenion aamete. The thee uenion aamete ae vetial vehile body aeleation y&, tie adial foe vehile body F u y y. and dilaement between wheel and One of the ealy ae whih deibe the obabiliti anali of uenion tem i by Kong Huiguo [5], whee the methodology i deibed in detail. The method ha been ove the yea, efined and the eent book by Matinu Gobbi [6] deibe the S-PSD and S- PSD methodologie ued in thi ae.. Modeling of the aenge bu a a aive tem The two degee of feedom quate model hown in Figue- i the mot ommonly ued model in the deign tudie fo aive uenion tem. It onit of a ing and a dame onneting the body ung ma to a ingle wheel UN ung ma, whih in tun i onneted to the gound via the tie ing. 5

2 VOL. 4, NO. 8, OCTOBER 009 ISSN ARPN Jounal of Engineeing and Alied Siene Aian Reeah Publihing Netwok ARPN. All ight eeved. Figue-. Quate a model. Aoding to Newton eond law, the um of foe ating on a ma equal to the ma time it aeleation. In thi ae, the foe ating on ung ma m i the ing foe due to K and dame foe due to C exeted on the ung ma. The foe ating on the UN ung ma m i the ing k, K and dame foe C. The linea equation of motion etaining to the tem model ae m & yu C y& y& u k + k yu ξ = 0 & & & m + C + k = 0 Whee m - ma of the wheel lu at of the ma of the uenion am i.e. un ung ma m - ¼ of the body ma i.e., ung ma k - tie adial tiffne ξ - Road iegulaity inuoidal oad ufae ofile C - uenion daming K - uenion tiffne y - Vetial dilaement of ung ma y u - vetial dilaement of un ung ma The eone of the vehile model ae eetively, the vetial vehile body aeleation, the foe alied between oad and wheel F, the elative dilaement between wheel and vehile body y u. The diomfot i evaluated by omuting the tandad deviation of the vetial vehile body aeleation. The highe the tandad deviation, the y& highe i the diomfot. The oad holding i evaluated by omuting the tandad deviation of the tie adial foe F.The vaiation of tye adial foe an lead to a lo of ontat with the gound and oo handling ability. The woking ae i evaluated by omuting the tandad deviation of the elative dilaement between wheel and vehile body y u y& i.e., the woking ae i elated to deign and aking ontaint, a well a to wheel lateal vibation. Road holding and woking ae i titly elated to ative afety. Diomfot, oad holding F and woking ae y& y u ae the objetive funtion.. TRANSFER FUNCTIONS OF THE PROPOSED MODEL The atio of the Lalae tanfom of the out ut vaiable to the inut vaiable i.e. the tanfe funtion, unde the aumtion that all initial ondition ae zeo, an be witten a follow: The tanfe funtion between dilaement ξ and i given by y u k k + j m yu j = 3 D j D j 3 4 = k k + jk km + km + km + j m + m + mm 4 The tanfe funtion between the imoed dilaement ξ and ead y k k + j j = 5 D j The tanfe funtion between ξ and y& S i H j = Y j 6 The tanfe funtion between ξ and F i H j = k y j 7 The tanfe funtion between ξ and y -y u i H j = y j y j 8 3 u The dilaement ξ oad iegulaity may be eeented by a andom vaiable defined by a tationay and egodi tohati oe with zeo mean value. The owe etal denity PSD of the oe may be detemined on the bai of exeimental meauement whih ae olleted fom liteatue [4].. Powe etal denity of the oe In the eent wok, two eeentation fo Powe etal denitie ae onideed. PSD ξ Ab v = 9 6

3 VOL. 4, NO. 8, OCTOBER 009 ISSN ARPN Jounal of Engineeing and Alied Siene Aian Reeah Publihing Netwok ARPN. All ight eeved. ξ = + A v PSD 0 Whee A b, A v ae the oad oughne aamete. and = a v. The value of the oeffiient ad/m deend on the hae of the oad iegulaity etum and eed v m/e. In a log log aled lot, Equation 9 take the hae of a one-loed owe etal denity, whih an be indiated a S-PSD. A bette oelation with meaued eta an be obtained by eoting to moe omlex eta a uggeted by diffeent eeahe. In a log-log aled lot of the equation 0, owe eta denity take the hae of a two-loe whih an be indiated a S-PSD. An idea of owe etal denity fo diffeent load ondition an be had fom Figue- and table a fomulated by ISO [7]. Figue-. Road oughne laifiation by ISO. Table-. Road oughne value laified by ISO. Degee of oughne SΩ x 0-6 Road la Range Geometi mean A vey good < 8 4 B Good C aveage D oo E vey oo F G H > 3768 a. Deivation of tandad deviation in analytial fom The vaiane of a andom vaiable deibed by a tationay and egodi tohati oe i + l Π P SDl = d Analytial olution fo l fo PSDl an be witten a N k j N k j PSDl = D j D j D k k Whee k a olynomial of degee K, and Nk- i a olynomial of a degee k-. 3. FORMULAE REFERRING TO THE S-PSD The analytial fomulae giving the diomfot, oad holding and woking ae ae obtained by olving analytially the equation. Vaiane of the vehile body aeleation y& quae of, y& = / A y bv & & y 3 m + m k = + & y k m 4 Vaiane of the foe ating between oad and wheel F quae of F F = / A b v F 5 = m m 6 P F + m + m k kkm k m k P = + + m m m + m m + m m Vaiane of the elative dilaement between wheel and vehile body y -y u quae of / A b v y y u y u = 7 m 8 m + = 3. Anali fo the aenge bu uing S-PSD Table- give efeene value fo the diffeent vaiable fo the aenge bu unde invetigation. Alo hown ae the lowe and ue bound value, whih ae the limit to whih the efeene value an vay. By olving equation 3 to 8 uing MATLAB, along with the efeene vehile aamete, aeleation, oad holding and woking ae ae omuted. 7

4 VOL. 4, NO. 8, OCTOBER 009 ISSN ARPN Jounal of Engineeing and Alied Siene Aian Reeah Publihing Netwok ARPN. All ight eeved. Table-. Data of the efeene oad vehile fo anali. Deign vaiable Refeene value Lowe and ue bound m kg m m kg m k N/m k k N/m k N/m Note: ubit indiate efeene value Table-3. Data of the oad oughne fo anali. Paamete Refeene value A b m.4 E 5 a = / v ad / m 0.4 A v m 3.5E 5 Figue-4. Road holding a a funtion of vehile eed S-PSD and S-PSD model. Figue-3. Diomfot a a funtion of vehile eed S- PSD and S-PSD model. Figue-5. Woking ae a a funtion of vehile eed S-PSD and S-PSD model. Figue 3, 4 and 5 how, eetively the, oad holding tandad deviation fo diomfot y& F and woking ae y y u a funtion of the 8

5 VOL. 4, NO. 8, OCTOBER 009 ISSN ARPN Jounal of Engineeing and Alied Siene Aian Reeah Publihing Netwok ARPN. All ight eeved. v vehile eed onideing the efeene vehile while uing S-PSD model. 3. Fomulae efeing to the S PSD The analytial fomulae giving the diomfot, oad holding and woking ae ae obtained by olving analytially equation Vaiane of the vehile body aeleation of y& y& quae k k + + m + k k m + m k + + mm & z = v 9 m D Whee D = k 3 4 k + k + k m + m + km + m + m + mm = av = / A av v v Vaiane of the foe ating between oad and wheel Fz quae of A + B + C D S S S F = v 0 k m S Whee A = k B C m + m k m m + m + m k Fz + + m 4 S = k k m + m k m + k + m + m + m m 3 S 4 S = k mm kk + k + km + k m + m Vaiane of the elative dilaement between wheel and vehile body y = k k m + k m m + m + m + m m 3 y y quae of u y y u v D The main diffeene between the fomulae efeing to the S PSD equation 3 8 and thoe efeing to S PSD 9 i that in the fit et of fomulae, the unning ondition aamete A b and v ae alwa not mixed with tem model aamete m,m,k,k,. The ooite ou fo S PSD fomulae in whih unning ondition aamete, ae mixed with model aamete m, m, k, K,. Thi imlie that fo S PSD exitation, the minima of &, a funtion of the y, F uenion aamete do not deend on unning ondition A b, v. 3.3 Anali of aenge bu uing S-PSD The eult fo the aenge bu uing S-PSD ae given in Figue 3, 4 and 5 along with thoe fos- PSD model. It an be een that the eult vay ubtantially, eeially at high eed. Thu, the S-PSD model ovide a moe ealiti anali of the uenion aamete. v 4. PARAMETER SENSITIVITY ANALYSIS The dynami eone of the oad vehile tem model in Figue- i analyzed on the bai of Equation 3-. By onideing now the ue and lowe bound fo diffeent aamete. The fomulae deived ealie have a geneal meaning and an be ued fo imulating the omfot, oad holding and woking ae of evey oad vehile that ould be modeled a in Figue-. Fo evey new deign, thi oedue need to be eeated. An examination of equation 3, 5 and 7 fo IS-PSD model how that the non-dimenional tandad deviation do not deend on vehile eed. The ooite ou fo the non-dimenional tandad deviation deived fom equation 9- given by S- PSD model. Fo thi eaon thee non-dimenional tandad deviation ae analyzed at two diffeent vehile eed, low eed 30m/ and high eed 60 m/. The eult of the vaiou anale ae lotted a a funtion of aamete atio like k /k i.e., eent tiffne of ing to the efeene vehile ing tiffne. Similaly othe atio fo whih the eone i lotted ae k /k, m /m, m /m and /. The aamete ae vaied within wide ange. The data ae eented in non-dimenional fom, i.e., the 9

6 VOL. 4, NO. 8, OCTOBER 009 ISSN ARPN Jounal of Engineeing and Alied Siene Aian Reeah Publihing Netwok ARPN. All ight eeved. tandad deviation of inteet j i divided by the oeonding one omuted by onideing the j aamete at thei efeene value eoted in Table, i.e., = m, m, k, k m, m, k, k, & & y F F, = The eult of the aamete enitivity anali ae hown in Figue 6 to 0. Figue-7. / v. dimenionle atio k /k. & & Figue-8. / v. dimenionle atio m /m. & & Figue-6. / v. dimenionle atio k /k. & & Figue-9. / v. dimenionle atio m /m. & & 0

7 VOL. 4, NO. 8, OCTOBER 009 ISSN ARPN Jounal of Engineeing and Alied Siene Aian Reeah Publihing Netwok ARPN. All ight eeved. Figue-0. / v. dimenionle atio /. & & Figue-. v. dimenionle atio k /k. / F F Figue 6 to 0 give the eult of tandad deviation of the diomfot i.e., / a funtion of model aamete. Eah diagam ha been obtained by vaying one ingle aamete, the othe one being ontant and equal to thoe of the efeene vehile. & & Figue-3. / F F v. dimenionle atio m /m. Figue-. v. dimenionle atio k /k. / F F

8 VOL. 4, NO. 8, OCTOBER 009 ISSN ARPN Jounal of Engineeing and Alied Siene Aian Reeah Publihing Netwok ARPN. All ight eeved. Figue-4. v. dimenionle atio m /m. / F F Figue-6. / v. dimenionle atio y k /k. Figue-5. v. dimenionle atio /. / F F Figue to 5 give the eult of tandad deviation of the oad holding i.e., / F F a a funtion of model aamete. Eah diagam ha been obtained by vaying one ingle aamete, the othe one being ontant and equal to thoe of the efeene vehile. Figue-7. / v. dimenionle atio y k /k.

9 VOL. 4, NO. 8, OCTOBER 009 ISSN ARPN Jounal of Engineeing and Alied Siene Aian Reeah Publihing Netwok ARPN. All ight eeved. Figue-8. / v. dimenionle atio m /m. Figue-0. / v. dimenionle atio y /. Figue-9. / v. dimenionle atio m /m. Figue 6 to 0 give the eult of tandad deviation of the woking ae i.e., / a funtion of y model aamete. Eah diagam ha been obtained by vaying one ingle aamete, the othe one being ontant and equal to thoe of the efeene vehile. 5. CONCLUSIONS The atial ignifiane of the above deibed anali an be aeiated if one onide the deteioation / vaiation of tiffne and daming due to wea and tea of omonent and eene of dut and mud olleted. It i obeved fom Figue 6 to 0 that: The tye adial tiffne k influene ignifiantly the influene i tonge at high eed onideing the S- PSD y& y& m y& Ineae with the uenion tiffne k Doe not deend ignifiantly on the wheel ma Deend tongly on the vehile body ma m the uenion daming ha influene on the tandad deviation Fom the Figue to 5, it i obeved that: Deend linealy on the tye tiffne k F Ineae with the uenion tiffne k almot the ooite ou at high eed onideing the S- PSD Ineae with the wheel ma m F F 3

10 VOL. 4, NO. 8, OCTOBER 009 ISSN ARPN Jounal of Engineeing and Alied Siene Aian Reeah Publihing Netwok ARPN. All ight eeved. F Doe not deend ignifiantly on the vehile body ma m The uenion daming ha ignifiant influene on the tandad deviation F It i alo obeved that the woking ae y -y u i uh that fom the Figue, 6-0. y I not influened by k and k fo the S-PSD exitation y y The influene of m on u i le imotant at high eed fo the S-PSD exitation y i tongly influened by the uenion daming A emaked by many ealie autho, the quate a model ha been a good aid fo the eliminay deign of vehile uenion tem. The quate a when analyzed ouled with the aamete venialitie an yield eult whih ae ubtantially bette fo efomane imovement. REFERNECES [] Dokaimih M.A. and El-Madany M.H Random eone of tato-emi taile tem Vehile tem dynami. 9: 87-. [] Paddan G.S. and Gilfin M.J. 00. Evaluation of whole- body vibation in vehile. Jounal of ound and vibation. 53: [3] Rill. G Vehile dynami. Letue note, Univeity of alied iene, Regenbug. [4] Rovat D.H. and Hubbad.M. 98. Otimal vehile uenion minimizing Rm Rattle ae ing-ma aeleation and jek. Tanation of the ASME. 03: [5] Kong Huiguo. Statitial anali of vehile vibation and dynami load, and eletion of uenion deign aamete. UM-MEAM-8-5. [6] Matinu G., Gobbi M, Miano C Otimal deign of omlex mehanial tem- with aliation to vehile engineeing. Singe. [7] zadeh E and Taghiad H.D Ative vehile uenion with otimal tate feedbak ontol. Jounal of Mehanial Siene. 4