METHODS FOR THE CALCULUS OF THE ROAD WHEEL VERTICAL LOAD

Transcription

1 The 3rd International Conference on Computational Mechanic and Virtual Engineering COMEC OCTOBER 29, Braov, Romania METHODS FOR THE CALCULUS OF THE ROAD WHEEL VERTICAL LOAD Profeor Ticuşor CIOBOTARU, PhD, MSc, Aoc. profeor Valentin VÎNTURIŞ, PhD Military Technical Academy, Bucharet, ROMANIA, cticuor2@yahoo.com Abtract - The tatic vertical load of the wheel road play a key role in the optimization of the upenion. The input criteria for et up the upenion include the clearance of the vehicle, the longitudinal inclination of the vehicle a well a the tiffne of the upenion reulted from ride comfort optimization. Additional calculu difficultie occur for vehicle with more than 3 road wheel on each ide. The paper preent an analytical model for calculu of the vertical load of the road wheel applied to a tracked vehicle with 7 independent torion bar upenion on each ide. For a imilar vehicle, the vertical load are etimated uing multi-body baed oftware, uch a Recurdyn. Neglecting the influence of the track, the method may be extended for wheeled platform with independent upenion. Key word: tracked vehicle, road arm, torion bar upenion, tatic load 1. INTRODUCTION The upenion of the tracked vehicle play an eential role in the tabilization of the hull, providing ride comfort and firing accuracy. Due to the large ma of the vehicle, the optimization of the upenion rie difficultie in balancing the oftne required by the ride comfort incentive with the rigidity required by a the firm poition of the hull and by the rapid diipation of the hull ocillation. A key tep in deign of the military tracked vehicle upenion i the evaluation of the vertical load of the road wheel. The vertical load of the road wheel mut balance the total weight of the vehicle and ha to provide a horizontal poition of the hull. The mobility of military vehicle croing terrain with oft oil i limited by the power needed to overcome the rolling reitance and by the thrut of oil. Both limitation depend on the vertical preure exerted by the track on the deformable oil. A reult of the preure of the track, the oil beneath the track change it mechanical characteritic, influencing accordingly the traction. The exiting model dealing with the interaction between track and oft oil can be grouped into two large categorie. On one ide there are analytical model baed on Bekker equation for decribing the relationhip between the inkage and preure []: 1 n p z=. (1) kc b+ k φ The friction modulu, coheion modulu and the exponent of oil deformation are determined by experiment uing a pecial device, the bevameter. A relatively narrow lit of value for preure inkage parameter exit for conideration in mobility aement [[6]], depite the fact thi lit wa implemented in multi-body pecialied oftware a RecurDyn. The relation (1) prove the importance of the etimation of the road wheel vertical load. 2. THE STATICS OF THE INDIVIDUAL SUSPENSION The large majority of the military tracked vehicle ue torion bar independent upenion. The running gear of uch type of vehicle i chematized in Figure 1 and offer a fat view of the exiting interaction between the upenion and the track. 139

2 Figure 1 Schematic repreentation of the tracked vehicle running gear Figure 2 Torion bar individual upenion The individual torion bar upenion i repreented in Figure 2. The initial angle of the road arm, noted β repreent the deign element which determine the value of the road wheel vertical load for the tatic ituation of the vehicle. The actual poition of the road arm, correponding to the tatic poition of the vehicle, i defined by the value of the angle of the road arm meaured to the horizontal, noted β. The aim of the individual upenion tatic i to determine the relation between the vertical load of the road wheel and the deign parameter of the upenion. The chematization of the road arm i preented in Figure 3. Figure 3 The chematization of the road arm Finally, the following relation reult for the tiffne of the individual upenion: π G d ( β β) c= 2 32 L b (coβ+ f in β)(inβ in β) a (2) 1

3 where: G tranveral elaticity modulu, d diameter of the torion bar, L a length of the torion bar, f rolling reitance coefficient of the road wheel on the track, b road arm length. The relation (2) indicate a non-linear dependence of the tiffne veru the actual poition of the road arm expreed by the angle β. Meanwhile, becaue the initial poition of the road arm differ, the tiffne characteritic of the road arm differ too. If the road wheel rolling reitance i neglected, the relation (2) become: π G d ( β β) c= 2 32 L b (inβ in β) coβ. (3) a The tiffne of the individual upenion, calculated for the tatic poition reult by impoing ( ) π G d β β 2 a b β=β : c = () 32 L (inβ in β ) coβ The tifne for the actual poition may be expreed taking into conideration the relation (3) and () a follow: c ( β β ) (inβ in β ) coβ =. (5) c β β (in β in β ) co β ( ) c c Figure Variation of the rated tiffene of the individual upenion The graphical variation of the ratio given by (5) i given in Figure. An important variation i oberved around the tatic poition of the road arm, for which the plotted ratio become equal to 1. The main concluion of the tudy regarding the tatic of the individual upenion i that i mandatory to take into conideration the variation of the tiffne with repect to the poition of the road arm in order to calculate the vertical load of the road wheel. 3. THE STATICS OF THE SUSPENSION ASSEMBLY Taking into conideration the whole upenion coniting of 7 individual upenion on each ide, the balance of the force and moment acting on the hull which i alope with the angle ϕ, the following ytem of imultaneou equation reult: N Gπd ( βi βi ) G = i= 1 32La bco( βi ϕ) N Gπd ( βi βi ) l co ϕ+ ( H g hi )inϕ = (6) 1 32 a co( ) i i= L b βi ϕ H = li in ϕ H g (1 co ϕ ) + hi coϕ+ bin( βi ϕ) i= 1,..., N 11

4 Solving by ucceive iteration the imultaneou equation (6) in order to obtain the horizontal poition of the hull ( ϕ= ), the value of the tatic angle reult. The iteration are generated by adjuting the initial angle β i. Conequently, the road wheel vertical load are calculated uing the following relation: G π d ( i i Q ) mi = β β. (7) 32La b coβi Table 1 preent the reult of the experimental data compared with calculated data. Table 1 Vertical load of the road wheel experimental veru calculated data Experimental data Road Arm Q left [N] Q right [N] Q average [N] Qcalc [N] Total It i mentioned that thi model i directly applicable for upenion uing only the torion bar a elatic element. The pread of hydroga upenion require an epecially dedicated model with repect to the non-linear characteritic of the individual upenion. Depite the high accuracy of the calculated value, the main diadvantage of thi analytical model cannot be ignored.. VERTICAL LOADS OF THE ROAD WHEEL FOR HYBRID SUSPENSIONS The individual hybrid upenion conit of a road arm acted by both the torion bar and the hydroga element. The tudy of thi type of upenion i convenient to be done uing the multibody ytem approach. Thu, the pecialied oftware Recurdyn (derived from ADAMS by the addition of everal toolbox with pre-defined element of the tracked vehicle running gear) repreent a valuable option. The chematization of the hybrid upenion performed under Recurdyn i preented in Figure 5. Road wheel Hydroga element Torion bar Road arm Figure 5 Individual upenion of the virtual model (right and left road wheel) The imulation include the tudy of the tatic poition of the vehicle on a flat urface. The data obtained through imulation were compared with the data obtained by experiment. 5. MEASUREMENTS OF THE ROAD WHEELS LOAD AND THE PRESSURE DISTRIBUTION The experiment were performed on a heavy tracked vehicle with 6 road wheel and double pin track. The method conited of replacing a track pad with the device preented in Figure 6. 12

5 Figure 6 General view of the intrumented track pad The geometry of the track pad wa reproduced by the two pin, marked 1, interconnected through the train gauge tenion enor, noted 2. Thi enor allow the meaurement of the longitudinal tenion of the track. The beam train gauge enor, marked 3, allow the meaurement of the vertical force acting on the platform. If the weighting platform i placed upide, the vertical load of the road wheel i meaured. In the ituation for which the platform i placed downide, in direct contact with the oil, the preure exerted by track on oil i meaured. Additionally, the platform (not repreented in Figure 6) wa equipped with two train gauge diaphragm preure enor for direct meaurement of the preure. Figure 7 View of the intrumented pad interted into the vehicle track The intrumented pad wa intercalated into the track (Figure 7) uing the regular link; conequently, the longitudinal tenion of the track wa etup accordingly. The ignal collected from the tain gage enor were recorded uing a data acquiition ytem aited by a portable computer. The reult are ummarized in Figure 8, emphaiing a good correlation of the meaured data with data obtained through imulation. A narrow difference exit between the experimental data and the reult obtained by uing multibody approach. 13

6 5 315 LEFT AVG RIGHT Calculated Figure 8 The vertical load of the road wheel - comparion of the meaured data with the reult of the imulation A reult of the above preented tudie, the vertical load of the road wheel may be accurately calculated uing adequate approache. 6. CONCLUSIONS The approach baed on the multybody theory offer the bet etimation of the vertical load of the road wheel. The uage of thi method i facilitated by the releae of everal commercial pecialied program which allow enough flexibility in etting up the deign parameter. Meanwhile, thee program are very ueful in taking into conideration the tructure of the modern upenion. REFERENCES [1] Bekker, M. G., Introduction to Terrain-Vehicle ytem, The Univerity of Michigan Pre, Ann Arbor, 1969 [2] Ma Z.D. and. Perkin N.C., Modelling Of Track-Wheel-Terrain Interaction For Dynamic Simulation Of Tracked Vehicle Sytem, DETC99/VIB-82, Proceeding of the 1999 ASME Deign Engineering Technical Conference September 12-15, 1999, La Vega, Nevada [3] Rowland D., Tracked vehicle ground preure and it effect on oft ground performance, Proceeding of the fourth international conference of the ISTVS, Stockholm; 1972 [] Rowland D., A review of vehicle deign for oft ground operation, Proceeding of the fifth international conference of the ISTVS,Detroit; 1975 [5] Vînturiş. V., Ciobotaru T., Grigore L., The modeling and imulation of the military tracked vehicle upenion load, International Conference OffRoad Vehicle, Bucharet, September, 28 [6] Wong, J.Y.: Theory of Ground Vehicle (2nd), John Willey & Son, ISBN , New York,