MODAL ANALYSIS OF THREE-WHEELER AUTOCHASSIS USING ANSYS

Transcription

1 Iteratioal Joural of Mechaical Egieerig ad Techolog (IJMET) Volume, Issue, Februar 9, pp;76-75, rticle ID: IJMET 74 vailable olie at ISSN Prit: ad ISSN Olie: IEME Publicatio Scopus Idexed MODL NLYSIS OF THREE-WHEELER UTOCHSSIS USING NSYS N.S.Prasaa Rao Professor, Dept of Mechaical Egieerig, shoka Istitute of Egieerig ad Techolg, Hderabad - Telegaa State, Idia. P. Suil Kumar ssistat Professor, Departmet of Mechaical Egieerig, shoka Istitute of Egieerig ad Techolg, Hderabad BSTRCT The reasos for maufacturers ivest their time ad moe i order to improve the Performace of damic characteristics. I modal aalsis, Damic behavior of the vehicle ca be observed. it is essetial to estimate atural frequecies to avoid the resoace coditios. For proper Ride comfort ad safet i the preset research atural frequecies are determied uder pa load ad without paload coditios of the chassis i roll mode, pitch mode, tramp mode. Kewords: Modal aalsis,three wheel chassis,mode shapes. Cite this rticle N.S.Prasaa Rao ad P. Suil Kumar,Performace Modal alsis Of Three-Wheeler utochassis Usig ss. Iteratioal Joural of Mechaical Egieerig ad Techolog ()(), pp;76-75, THREE-WHEELED UTO CHSSIS MODEL DESCRIPTION Baa Rear egie (Diesel) is selected for aalsis purpose. The overall legth of the chassis is 65mm ad the wheelbase is mm. The specificatios of the vehicle are show i Table editor@iaeme.com

2 Modal alsis of Three-Wheeler utochassis Usig ss Table. Model discriptio summar Compoets Egie Tpe Power Dimesios Weights: Specificatio Sigle clider 4-stroke Diesel Egie 3 rpm Legth: 65 mm Width: 3 mm Height: 7 mm Wheel base: mm Groud clearace: 7 mm Kerb weight: 353 kg Gross Vehicle Weight: 68 kg Max. paload: 33 kg. NSYS MODEL FOR THREE WHEELED CHSSIS The model cosists of chassis elemets, suspesio ad tres ad the specificatios values are listed i the Table. Descriptio Table. Stiffess ad Dampig values Stiffess (K)(N/m) Dampig Coefficiet (C)(N-s/m) Frot Suspesio 3,7 3,5 Rear Right Suspesio 49,8,7.5 Rear Left Suspesio 5,4,7.5 Frot Tre,38,6 557 Rear Right Tre,5, Rear Left Tre,5, MTHEMTICL BCKGROUND. MODL NLYSIS I modal aalsis there will be o excitatio forces actig o the sstem. I the preset work the u-damped case is cosidered. Therefore assume, F ; [C] () B substitutig equatios (5.) i geeral equatio of motio (5.9) it ca be modified as, as, [M] Q + [K] Q () as the displacemets i pricipal modes are siusoidal, the displacemet ca be assumed B differetiatig twice, we get, Substitutig these i equatio () we get Q U si t Q - U max si t - [M]U max si t+[k] U max si t 77 editor@iaeme.com

3 Rearragig the above equatio ields, N.S.Prasaa Rao ad P. Suil Kumar [K] U max [M] U max Pre-multiplig with [K] ad rearragig it become, Let us cosider [][K ][M] ad Thus, the above equatio become, [K] [M] U max U max []U max U max (3) This equatio represets a stadard Eige value problem. Satisfig these equatios there will be values of ad for each value the above equatios will have a solutio for U. The values kow as Eige vectors, which idicate the odal amplitude of vibratio. The eigevalue problem ca be solved usig differet umerical methods. Oe of the quicker ad accurate methods is laczo s optio ad the solutio procedure was described below. I the solutio procedure, the laczo s algorithm reduces matrix [] tri-diagoal form based o a iterative process. Startig with a trial vector, the method geerates a sequece of mutuall orthogoal vectors. Let us cosider a orthogoal matrix [P] such that, [ P ] U U max Substitutig for U max i equatio () it become, T Pre-multiplig with[ P], [ ][ P] U [ P] U [ P] T [][P]U U [ [ P] T [ P] I] Let P P T (4) Where [] is required tri-diagoal matrix. Thus, above equatio become, [ ] U U (5) This trasformatio from [] to [] is kow as orthogoal similarit trasformatio ad equatio (5.4) has same solutios as that of equatio (5.). B pre-multiplig equatio (5.3) with [P]it become, Cosider each obtai, [ ][ P] [ P][ ] (6) th i colum of [P] as a vector i ad substitutig [] i variables, is 78 editor@iaeme.com

4 Modal alsis of Three-Wheeler utochassis Usig ss ],...,, [ ],...,, ][ [ Which ca be expaded to give, ] [ + (7) ) ] [ (8) ] [ + (9) Now choosig value such that T, ad pre-multiplig equatio (5.6.) with we get, ] [ T as, T Now cosider a vector Z such that, Z () Z is a kow vector i terms of [], ad also T from equatio (5.7)? Z Z ; Z Z T ; Z geeralizig, T T z z z V Z V V, ] [ + () The equatios (5. ca be used repeatedl to covert to. fter this coversio QR methods was used for extractio of Eige values ad vector of matrix the ame QR iterative process derived from otatios used i algorithm. The matrix ca be expressed as, [ ][ Q ] [R] () Where [Q] is orthogoal matrix ad [R] is upper triagular matrix ad we ca express, [R][Q ][Q ] T [ ][Q ] (3)

5 N.S.Prasaa Rao ad P. Suil Kumar B calculatig [R][Q] we carr out trasformatio of diagoal form. Now the matrix [ ] ca be reduced ito upper triagular form usig acobi rotatio matrix R ca be expressed as, [R][P] [P] T, [P] T T ( ) ( 3,) P ](, ) [ (4) Where rotatio matrix [P] T (, i) is to reduce elemet (, i) to zero. But from equatio () we have. [ Q ][P] (,) [P] ( 3,) [P] (, ) The QR iterative algorithm cosists of repeatig the process give i equatio () ad (5.) for K th iteratio ad it ca be represeted i geeralized form of equatio as. [ ] k [Q ] k [R] k ad[ ] k + [ Q ] k [R] k The ask,[ ] ad [Q ] [Q ] [Q ] k [Q ] k U Where values ad U are the required results. The boudar coditios applied for modal aalses are, the groud odes of the tres are arrested completel. Usig FEM ver large umber of atural frequecies are obtaied. 3. RESULTS ND DISCUSSION The list of the atural frequecies ad modes shapes of the model are give i the Table 3. as these mode shapes idicate, the phsical behavior at each frequec. Table 3. Mode Frequecies (Lade d Ulade Model) S.No Mode Frequec (Hz) LDEN UNLDEN Bouce mode.98.7 Roll mode Pitch mode Twist mode Frot hop mode Rear tramp mode The bouce mode i ulade ad lade coditios is show i Fig 6. ad Fig 6.3, the frequec for this mode is.7hz for without pa load (ulade) coditio ad.98hz for lade coditio, durig this mode the maximum displacemets are.7m ad.5m respectivel at the rear portio (ode 7) of the chassis. B usig simple oe degree of freedom rigid bod model of the chassis, the frequec of bouce mode is calculated for both lade ad ulade coditios ad foud that aroud.4hz ad.85hz respectivel. These values are close compariso with results obtaied through FEM, which proves the cosistec of model. The deformatios of chassis i the roll mode as show i the Fig 3.4 ad Fig 3.5 for both ulade ad lade coditios ad the frequec of this modes is 4.6Hz ad 3.Hz respectivel. Maximum displacemets are.m ad.7m obtaied at extremes eds of the left portio of the passeger seatig locatio (ode 6). I pitch mode the deformatio of chassis are show i the Fig 3.6 ad Fig 3.7 for ulade ad lade coditios ad the frequec of this mode is 7.68Hz ad 5.3Hz respectivel. Durig this mode the maximum displacemet 7 editor@iaeme.com

6 Modal alsis of Three-Wheeler utochassis Usig ss occurred at driver seat locatio for both lade ad ulade cases ad the values are.m ad.7m respectivel. The deformatios of chassis i the twist mode as show i the Fig 3.8 ad Fig 3.9 for both ulade ad lade coditios ad the frequec of these modes are 6.6Hz ad.7hz respectivel ad the displacemets are.7 ad.mm. Fig 3. ad Fig 3. depicts the frot hop mode shape of the chassis ad frequecies are.3hz ad 9.7Hz, displacemets are. ad.6 for both ulade ad lade coditios. Fig 3. ad Fig 3.3 shows the rear wheels tramp mode for both lade ad ulade coditio of the three-wheeler chassis. The correspodig frequecies are 7. Hz ad 6.89Hz, displacemets are.3m ad.7m respectivel. The three sigificat modes bouce, roll ad pitch are depedet o the suspesio sstem ad this statemet is proposed b the V.Balamuruga [7]. From Table 3. it is observed that frequecies of the lade chassis less tha that of ulade chassis this ma be because as of the load of the chassis icreases frequecies are decreases. Figure 3. Bouce mode of chassis without paload Figure 3.3 Bouce mode of chassis with paload 7 editor@iaeme.com

7 N.S.Prasaa Rao ad P. Suil Kumar Figure 3.4 Roll mode of chassis without paload Figure 3.5 Roll mode of chassis with paload Figure 3.6 Pitch mode of chassis without paload 7 editor@iaeme.com

8 Modal alsis of Three-Wheeler utochassis Usig ss Figure 3.7 Pitch mode of chassis with paload Figure 3.8 Twist mode of the chassis without paload Figure 3.9 Twist mode of the chassis with 73

9 N.S.Prasaa Rao ad P. Suil Kumar Figure 3. Frot hop mode without paload Figure 3. Frot hop mode with paload Figure 3. Rear tramp mode without paload 74

10 Modal alsis of Three-Wheeler utochassis Usig ss Figure 3.3 Rear tramp mode with paload REFERENCES [] K. Sata Rao, G. Musalaiah ad K. Mohaa Krisha Chowdar FiiteElemetalsisofaFour Wheeler utomobile CarCHSSIS INDIN Joural of Sciece ad Techolog, Vol 9(), DOI:.7485/ist/6/v9i/83339, Jauar 6 [] Satosh Hiremath, Naresh Kumar, Nagaredd.G, Lakha Rathod Modal alsis of Two- Wheeler Chasis Iteratioal Joural of Egieerig Scieces & Research Echolog [3] rchit Tomar & Dheer Sigh Modellig ad alsis of a Chassis Frame b Usig Carbo Fiber ad E-Glass Epox as Composite Material: Comparative Stud Iteratioal Research Joural of Egieerig ad Techolog 3(4), 6, 7-76 [4] K.shok redd, p.suil kumar Desig ad alsis of Harmoic alsis of Three wheel uto chasis usig ss 75 editor@iaeme.com