Design of Trailing Arm Suspension

Transcription

1 International Jornal of Engineering Reearch & Technology (IJERT) Vol. 3 Ie 6, Jne Deign of Trailing Arm Spenion Santoh Ukamnal P G Scholar, Atomotive Engineering VIT Univerity, Vellore, India Sagar Olekar P G Scholar, Atomotive Engineering VIT Univerity, Vellore, India Kiran Chadhary P G Scholar, Atomotive Engineering VIT Univerity, Vellore, India P. Bakar Aitant Profeor, School of Mechanical and Bilding Science VIT Univerity, Vellore, India Abtract Spenion i a term given to the ytem of pring, damper and linkage that connect wheel to vehicle body which allow relative motion, maintain contact between wheel and road and alo damp ot road hock. Spenion ytem aim to improve the ride comfort, handling and afety. Now a day mot of the paenger car e independent penion ytem which allow wheel to relative to frame withot affecting other wheel. Mot commonly ed rear penion i trailing arm penion ytem. Thi paper deal with mathematical modelling of a qarter car trailing arm penion ytem. The qarter car model of two degree freedom ytem i olved in MATLAB and time repone i plotted. The parameter ch a pring tiffne, damping ratio of prng and n-prng mae of the qarter car model are optimized to get good comfort and vehicle handling. Deign of the penion geometry i carried ot in CAD oftware. The optimized vale of pring tiffne, damping coefficient of prng and n-prng mae are copled with the geometry deign and i analyzed in LOTUS SUSPENSION ANALYSER to get vario vale of the penion geometry. Keyword traling arm, matlab, lot penion analyi, qarter car. I. INTRODUCTION Atomobile chai i monted on the axle throgh a penion ytem. De to neven road profile and variable velocity, vehicle i bjected to random excitation. It affect comfort and road handling characteritic. The main objective of penion ytem i to afegard the paenger againt road hock which may be in the form of bonce, roll, pitch etc. Alo penion ha to limit the body diplacement to a minimm. Spenion ytem of a vehicle i bjected to a force de to vertical loading, rolling, braking, acceleration and cornering. Fnction of penion ytem are- To pport vehicle and paenger weight. To afegard the paenger againt road hock and provide riding comfort. To maintain teering and vehicle handling characteritic, which i achieved by mean of mechanical linkage and controlling relative motion between prng and nprng ma. To provide tability to vehicle dring pitching or rolling, while in motion. Spring and damper are mot widely ed element in vehicle. Spring redce the force tranmitted to the chai while travelling over bmp redce the acceleration of the chai while wheel fall on a depreion or pothole. Damper redce the tendency of the chai to bonce p and down after the ditrbance and alo prevent the exceive bilt p of amplitde of bonce when the excitation freqency i nearer to the natral freqency the ytem. Spenion ytem i claified into paive, active, emiactive ytem. Paive penion ytem atifie the reqirement only at certain operating condition. Hard pringing will increae acceleration force dring light loading and oft pringing will redce the body height when heavily loaded. Active penion control the vertical movement of wheel throgh an on-board ytem. Active penion ytem e eparate actator that exert an independent force on the penion to improve the riding characteritic. Semi-active ytem can only change the vico damping coefficient and do not impart any additional force to the penion ytem. In mot of paenger paive penion ytem i widely ed. In paive penion ytem, there i alway compromie between paenger comfort and handling. In paive penion ytem high tiffne pring give good handling bt poor comfort. Low tiffne pring give good comfort and le handling. The main advantage of paive penion ytem i that the deign i imple and alo economical. Alo maintenance cot i low. Trailing arm penion i motly ed for the rear penion of the paenger car. It i alo called a crank axle penion ytem. Control arm placed longitdinally along the driving direction and monted on penion b frame or body on both the ide. Control arm i bjected to high torional and bending tree. It allow the wheel to move p and down only. No change in camber and toe de to lateral and vertical force. Increaed n-prng ma of trailing arm redce the ride qality. In thi wok qarter car model i conidered for the analyi. In qarter car model, the vehicle i converted into pring and damper ytem which ha one forth ma of the vehicle. The eqation of motion are derived for the qarter model. 87

2 International Jornal of Engineering Reearch & Technology (IJERT) Vol. 3 Ie 6, Jne The work on the penion ytem how the comparion between active, emi active and paive penion ytem. It i alo tated that comfort can be increaed by ing low tiffne pring [1]. Another tdy how the effect of vehicle velocity and wheel bae on RMSAR vale i.e. Root Mean Sqare Acceleration Repone. In that it i fond that RMSAR i proportional to vehicle velocity and inverely proportional to wheel bae. The two degree of freedom half car model i conidered and tdied for the random road inpt vale [2]. The improvement in paive penion ytem i done by ing controller to change the pring tiffne and damping. Proportional Integral Derivative (PID) controller i deigned for qarter car model of paenger car to improve ride comfort and handling characteritic. The prng ma diplacement and acceleration ha been redced by ing active penion ytem [3]. II. OBJECTIVE The objective of the preent work are a follow: A. Mathematical Modeling The phyical penion ytem of a vehicle i converted to qarter car model with pring ma and damper ytem, where in vibration repone i analyzed. B. Arriving at Optimm Vale of Spring and Damper Coefficient To get the good comfort and handling characteritic. C. Static Geometry for Trailing Arm To get the leat amont of deviation in the penion geometry at bmp and rebond. D. Kinematic Analyi of Trailing Arm Spenion Change in roll center and wheel bae change can by analyzed in LOTUS Spenion Analyi [6]. Repone time of the deigned qarter car model i plotted in SIMULINK. III. METHODOLOGY To tdy any penion ytem, it i important to derive the eqation of motion related to the ytem and then olving them by appropriate mathematical tool. Generally for analyi of vehicle penion ytem vario type of penion model are ed. The mot commonly ed model are qarter car model, half car model and fll car model. In the preent work the qarter car model i conidered for the tdy. The advantage of the qarter car model i that it i imple and eay to analyze. In thi particlar model, only one forth of the vehicle i taken into conideration to develop a vehicle penion. Thi model i two dimenional model becae only vertical movement i taken into conideration. It i baically conit of a ingle wheel which i repreented in the form of a pring. However in ome cae the wheel can be conidered a eqivalent to a parallel combination of pring and a damper. The actal hock aborber i amed to pport only one forth of the weight of the total car body ma inclding paenger weight. The qarter car model conidered in thi work i hown in fig 1. Fig. 1. Qarter car model The eqation derived from the qarter car model are a follow: m x k m x k Where, m m k k c c x x x x c x x 0 x y k x x c x y c x x 0 = Sprng Ma (Kg) = Unprng Ma (Kg) = Spenion Spring Stiffne (N/m) = Tire Stiffne (K/m) = Damping Coefficient (N/m) = Tire Damping Coefficient (N/m) = Sprng Ma Diplacement (m) = Unprng Ma Diplacement (m) Spenion parameter are taken from the literatre rvey. TABLE I. SUSPENSION PARAMETERS m Sprng Ma 250 Kg m Unprng Ma 50 Kg k Spring Stiffne N/m k Tire Stiffne N/m c Damping Coefficient 1000 N/m b Wheel track 1.7m a Wheel bae 2.7m Tyre ize 255/35 ZR19 In order to approach for the deign of trailing arm penion, the parameter involved mt be tdied. The trailing arm act a a rocker member of the penion where in it i monted to the chai by pivot point. The pring and damper are attached to the arm by pivot point, to get reqired relative motion dring moment of the arm. The parameter involved are [5]: Length of trailing arm Angle of trailing arm. Ride height. Inclination of the pring and damper. The pivot point of the trailing arm i bjected to force like; thrt force, braking force and cornering force. 88

3 International Jornal of Engineering Reearch & Technology (IJERT) Vol. 3 Ie 6, Jne Conidering all thee force, the pivot point of the trailing arm i divided into two point, to hare the load effectively. Initial approximation of the geometry i conidered for pecified wheel track and bae, and the effect of each parameter on the penion geometry i determined by varying ingle parameter and keeping all other parameter contant. By thi way, optimm vale of the parameter are obtained. The CAD model of the trailing arm i prepared by the optimm vale of the penion geometry and i hown in the figre 2-4. TABLE III. SUSPENSION CO-ORDINATES Component X (mm) Y (mm) Z (mm) Trailing pivot point to the frame Damper lower trailing arm end Damper body end Wheel pindle point Wheel centre point The derived eqation of motion are olved by ing SIMULINK programming. The parameter hown in table I are ed in the programming to get the prng ma diplacement, prng ma acceleration. The bae excitation given i the ine profile with amplitde of 0.1m and freqency of π rad/ec. The SIMULINK program ed to olve the eqation i hown in the fig. 5. Fig. 2. Iometric view of the trailing arm penion Fig. 5. Simlink model Fig. 3. Side view of the inclined trailing arm penion IV. RESULTS AND DISCUSSION After olving the eqation by ing the SIMULINK program following relt are obtained. Fig. 4. Top view of the trailing arm penion The aembled tatic geometry model i imported in the LOTUS penion analyzer by getting the co-ordinate of the pivot point of the entire aembly. TABLE II. Parameter Camber Angle Toe Angle Roll Centre Height STATIC TRAILING ARM PARAMETERS Vale 0 deg 0 deg mm Fig. 6. Repone of ytem for ine bmp inpt in SIMULINK The above repone plot how the prng ma deflection, nprng ma deflection and penion working pace with repect to time for the ine bmp road inpt. From the repone plot maximm prng ma diplacement and acceleration are 89

4 International Jornal of Engineering Reearch & Technology (IJERT) Vol. 3 Ie 6, Jne calclated with contant vale of damping. By varying the vale of Kt/K, the diplacement and acceleration obtained and are plotted in the following graph. Fig. 10. Acceleration v Damping Fig. 7. Diplacement v Kt/K The above graph are plotted for the damping vale from 500N/m to 1200N/m. From the graph it i oberved that a damping increae deflection decreae. Bt in the acceleration, p to 800N/m damping vale it decreae and beyond 800N/m it vale tart increaing. So 800 N/m i elected a the optimm damping vale. Therefore, from the SIMULINK program the optimm vale obtained for thi penion ytem are Kt/K = 23 and damping coefficient i 800 N/m. Fig. 8. Acceleration v Kt/K From the above two graph optimm vale of Kt/K i determined. When Kt/K i 23, the prng ma diplacement and acceleration obtained are minimm o Kt/K vale i taken a 23. The lit of optimized parameter obtained from the mathematical modeling are hown in table IV. To obtain the optimm vale for damping coefficient, Kt/K i taken a 23 and by changing the damping vale prng ma deflection and acceleration are obtained. The graph for deflection and acceleration at contant Kt/K vale are hown below. TABLE IV. OPTIMUM PARAMETERS Optimm Parameter Sprng Ma (Kg) 250 Unprng Ma (Kg) 50 Kt/K 23 Tire Stiffne (N/m) Damping Coefficeint (N/m) 800 The obtained vale of the damping coefficient and pring tiffne from the mathematical modelling i copled with the tatic geometry deign of the trailing arm penion and i analyzed in LOTUS penion analyzer. Figre 11-13, how the model in generated in Lot penion Analyzer. Fig. 11. Front view of the geometry in Lot analyzer Fig. 9. Deflection v Damping 90

5 International Jornal of Engineering Reearch & Technology (IJERT) Vol. 3 Ie 6, Jne Camber Angle change: 0 deg. Toe angle change: 0 deg. Fig. 12. Side view of the geometry in Lot analyzer V. CONCLUSION In the preent work optimm vale for the penion tiffne and damping are obtained for good comfort and handling condition. From relt it i oberved that oft pring give good comfort i.e. le prng ma diplacement and acceleration. Very le and very high damping vale give more acceleration. So optimm vale i elected which give minimm prng ma acceleration. All the obtained penion parameter are checked by the LOTUS penion analyzer for kinematic analyi. For the calclated vale and it i oberved that there i no change in the camber and toe angle vale, and even change in wheel bae i alo within the deired limit. REFERENCES Fig. 13. Top view of the geometry in the Lot analyzer The generated model wa rn in LOUTS with the inpt parameter and the following relt were obtained. TABLE V. INCREMENTAL SUSPENSION PARAMETER VALUES Bmp Travel (mm) Roll Center Height (mm) Wheel bae Change (mm) [1] R. S. Sharp, and D. A. Crolla, Road Vehicle Spenion Sytem Deign- a Review, Vehicle Sytem Dynamic: International Jornal of Vehicle Mechanic and Mobility, 16 (1987), pp [2] J. A. Tamboli, and S. G. Johi, Optimm deign of a paive penion ytem of a vehicle bjected to actal random road excitation, Jornal of Sond and Vibration (1999) 219(2), pp [3] Moleewaran Senthil kmar, Development of Active Spenion Sytem for Atomobile ing PID Controller, Proceeding of the World Congre on Engineering 2008 Vol II WCE 2008, Jly 2 4, 2008, London, U.K. ISBN: [4] S.S.Rao Mechanical vibration ISBN [5] John C. Dixon, Spenion Geometry and Comptation, Wiley Pblication, 2009 pp [6] M. J. Brge, N. P. Fleming M. Wootton and S. J. William, A Tool for Rapid Vehicle Spenion Deign, SAE Internationl, SAE Technical Paper Serie, ISSN ,