Active Suspensions For Tracked Vehicles
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1 Active Suspensions For Tracked Vehicles Y.G.Srinivasa, P. V. Manivannan 1, Rajesh K 2 and Sanjay goyal 2 Precision Engineering and Instrumentation Lab Indian Institute of Technology Madras Chennai 1 PEIL 2 PEIL Lab Indian Institute of Technology Madras Indian Institute of Technology Madras Chennai Chennai Contact ygs@iitm.ac.in ABSTRACT The aim of this paper is to study the ride dynamic performance of a high-speed tracked vehicle with active suspensions, and to compare it with that of a tracked vehicle having passive suspensions. To achieve the above mentioned purpose, a non-linear, inplane ride dynamic model which evaluates the driver s seat acceleration, ride height and hull angular acceleration of a typical high-speed tracked vehicle has been developed, and its motion has been simulated. The ride dynamic behavior of a typical high-speed tracked vehicle negotiating a round bump is studied using a non-linear, in-plane ride dynamics simulation model. The dynamic track load and track-terrain interaction is taken into account in the simulation. The wheel/track-terrain interaction is modeled with an equivalent damper and continuous radial spring. The dynamic track load is modeled considering the track belt stretching and the initial track tension. The influence of each of the parameters initial track tension, stiffness of torsion bar, longitudinal stiffness of track belt and damping rate of the suspension unit on the ride dynamics of the vehicle is studied through the computer simulation. 1. INTRODUCTION Active suspension system move each wheel up and down to control body motion in response to road abnormalities. The system responds to inputs from the road and the driver. With an active suspension, a vehicle can simultaneously provide the smooth ride of a soft suspension along with superior handling associated with a firm suspension. The driver safety and comfort of a tracked vehicle traversing off-road terrains depends on the ride vibrations. An off-road vehicle is subjected to a ride vibration of low 1
2 frequency and large amplitude, which causes body discomfort to the operator, and limits the mobility and performance of the vehicle. Computer simulation using an analytical model is an efficacious method for evaluating the ride characteristics of vehicles without turning to time-consuming and expensive process of repeated testing. In this paper, a non-linear, in-plane ride dynamics simulation model of a typical high-speed tracked vehicle is developed considering the dynamic track load and wheel/track-terrain interaction, and a parametric sensitivity analysis is performed. The influence of each of the parameters initial track tension, stiffness of torsion bar, longitudinal stiffness of track belt and damping rate of the suspension unit on the ride dynamics of the vehicle is studied. 2. LITERATURE SURVEY The ride dynamics of off-road vehicles has drawn extensive research and development efforts in improving suspension systems to achieve safety and comfort of vehicle operator and improved mobility performance. But only a few similar studies on the ride dynamics of tracked vehicles have been reported in the literature. A brief literature survey of previous investigations has been presented below. Wong [7] presents a brief review of the state of the art of the tracked vehicle dynamics including mobility over soft terrain, ride dynamics over rough surfaces and maneuverability. Le [8] shows that the slip of the track over the terrain can be identified from the trajectory data using an extended Kalman Filter. The use of a suitable soil model can then allow key soil parameters to be estimated as the vehicle passes over the soil. Dhir [1] presents a non-linear in-plane computer model of a typical high mobility tracked vehicle for suspension dynamic analysis and ride quality assessment. A parametric sensitivity analysis was carried out using the validated computer model in order to assess the influence of conventional suspension parameters on the ride performance of the test vehicle. Rakheja [9] studied the ride dynamics of a military armored personal carrier where the road wheel was modeled to have point contact with the terrain. [2], [3] and [4] discuss various active and semi-active suspension systems and their characteristics for various frequencies. 3. DEVELOPMENT OF RIDE DYNAMIC OF MODEL The various forces, which act on the wheel, are: 1. Compression force resulting from the interaction of wheel with terrain. 2. Force acting on each of the wheels due to track tension. Note that the track tension is dynamic in nature Since the track will be stretched while the vehicle moves on the terrain. Figures 1 and 2 show how the road wheel and the hull wheels have been modeled in order to evaluate the forces acting on them. 2
3 Fig. 1 Schematic representation of a multi-wheeled tracked vehicle. At any point of time, the points of intersection with the terrain of the hull wheels and the road wheels are calculated and then use is made of angle alpha and gamma as shown in the figure to evaluate the net footprint force according to the formula given below. F wn =2K rw R w [Sin(α w /2)-( α w /2)Cos(α w /2)] (1) In order to evaluate the dynamic track load, the length of the track at any instant is evaluated and the following formula is made use of in order to calculate the tension force. Fig. 2: Resultant horizontal and vertical forces. Fig. 3: Determination of track deflection T tr = K tr (L tr L tr0 ) + T tr0 ; if L tr > L tr0 (2a) T tr = T tr0 ; if L tr < L tr0 (2b) The net vertical force acting on the hull wheel as well as the road wheel F wny = F wn Cos(γ) + T tr [Sin(ε1) + Sin(ε2)] (3a) F wny = F wn Sin(γ) + T tr [Cos(ε1) + Cos(ε2)] (3b) The total track length is expressed as 3
4 L tr = α w R w + α h R h + L h + L j. (4) The following equations of motion are made use of to evaluate hull vertical as well as angular acceleration. Bounce motion of road wheel: A w (i)={f wny (i)- [f s (i) + f d (i)]}/ M w g (5a) r(i) = y(i)- Y h + a(i)sin(θ) (5b) v r (i) = v(i) - v h + a(i)ωcos(θ) (5c) Evaluation of spring and damping forces: f s (i) = K s r(i) (6) f d (i)= C s v r (i) (7) Evaluation of hull CG acceleration and hull angular acceleration: A h ={ [f s (i)+ f d (i)]+ F hyk }/M h g (8a) F hyk is found out in a manner similar to that adopted for road wheel. Here f s (i) and f d (i) are forces evaluated at the previous time step. Ang h ={ ([f s (i) + f d (i)] [a(i) Cos(θ) - a(i) Sin(θ)] + b w (i) F wx (i)) + (a hk [F hy *Cos (θ) - F hx Sin(θ)]+ b hk [F hx Cos(θ)+F hy Sin(θ)]}/ I h (8b) After obtaining the hull acceleration as well as the angular acceleration new hull velocity, new hull displacement as well as hull angular velocity and angular position are found out as follows: ω(j) = ω(j-1) + Ang h t (9a) θ(j)= θ(j-1)+ ω(j-1) t + Ang h t 2 /2 (9b) v h (j)= v h (j-1)+ A h t (10a) y h (j) = y h (j-1) + v h (j-1) t + A h t 2 /2 (10b) Acceleration of driver s seat is calculated as A d = A h + a 0 [Ang h Cos(θ) ω 2 Sin(θ)] (11) The tracked vehicle is displaced horizontally by a distance equal to horizontal velocity times the time-step. New footprint forces and the dynamic track load are found out. Accelerations, velocities and displacements from the ground level of road wheels as well as the hull wheels are found out. The procedure is repeated again from the beginning until the simulation time is over. 4. RESULTS AND DISCUSSIONS Using the above formulae, a program was written and the results were obtained for the following data: Table 1. Parameters used in the simulation of tracked vehicle model. 1 R w Radius of the road wheels m. 4
5 2 T tr0 Initial track tension KN 3 L tr0 Initial track length m 4 K tr Longitudinal stiffness of the track N/m 5 M w Mass of a road wheel Kg 6 K s Spring constant of the suspension unit (for N/m. each wheel). 7 M h Sprung mass Kg 8 I h Hull Pitch Moment of inertia Kg.m^2. 9 Y cg Height of CG above ground level initially m 10 a 0 (Refer to the schematic diagram) 1 m 11 b 0 (Refer to the schematic diagram) 0 m 12 a h1= a h2 (Refer to the schematic diagram) m 13 b h1= b h2 (Refer to the schematic diagram).48 m 14 a 1= a 6 (Refer to the schematic diagram) m 15 a 2= a 5 (Refer to the schematic diagram) m 16 a 3= a 4 (Refer to the schematic diagram) m 17 b 1 to b 6 (Refer to the schematic diagram) 0.3 m Assumptions: 1. The driver s seat is assumed to be rigidly attached to the hull. 2. The CG of the hull is assumed to be at its geometric center. 4a. Comparison of performance of active and passive suspension systems The active suspension systems having a feed back controller built in them respond to the road inputs in a better way and compensate the disturbance form the road by applying appropriate control force to the hull to reduce the seat vertical acceleration. The results of the simulations done on the tracks for the given vehicle model clearly shows the reduction in the seat vertical acceleration and angular acceleration levels in case of the active suspension systems as compared to the passive systems and hence resulting in better ride comfort for the driver. 4b. Comparison of Driver seat vertical acceleration levels As can be seen in the following graphs the net seat vertical acceleration levels has shown a reduction of the order of 10 factor on the use of the active suspension systems as compared to the passive ones. 5
6 Fig. 4: Seat Vertical acceleration for Fig. 5: Seat Vertical acceleration for passive suspension system active suspension system 4c. Comparison of hull angular acceleration levels As can be seen in the following graphs the net seat angular acceleration levels has shown a reduction of the order of 8 factor on the use of the active suspension systems as compared to the passive ones. Fig. 6: Hull angular acceleration for a vehicle Fig. 7: Hull angular acceleration for with passive suspension system a vehicle with active suspension system 4d. Comparison of ride height levels The over all ride height increase of the vehicle has been reduced due to the use of an active suspension system as compared to a passive system. 6
7 Fig.8: The Hull CG variation with a passive suspension system 5. CONCLUSIONS Fig.9: The Hull CG variation with an active suspension system A time-domain computer simulation model is developed for the study of the ride dynamics of a tracked vehicle. The model is then made use of to perform a parametric sensitivity analysis. Based on the observations, the following conclusions can be drawn: 1. Increasing the stiffness of the suspension unit increases the acceleration levels of the driver s seat, whereas, a soft spring lowers them. 2. If the damping is not sufficient, crossing a bump at high velocity can cause the hull wheels to hit the ground after crossing the bump, which would result in very high accelerations. 3. Increasing the damping can prevent the occurrence of the large peak. But, as the damping increases, the acceleration levels are higher. Hence, optimal value of damping coefficient needs to be chosen. 4. The peak vertical acceleration increases as the initial track tension is increased. But the effect of track tension is not substantial as compared to that of other parameters. 5. The effect of change in stiffness and damping coefficient on the acceleration levels is quite small. Hence, to reduce the accelerations by a substantial amount, better suspensions need to be used. Future work includes extension of the model to replace the existing passive suspension by active suspension system and optimization of the power consumed. REFERENCES 1. A.Dhir and S.Sankar, Ride dynamics of high-speed track vehicles: Simulation with field validation, Vehicle system dynamics PP D.J.Purdy and D.N.Bulman, An experimental and theoretical investigation in to the design of an active suspension system for a racing car, Proceedings of IME, vol.211, Part D. 3. A.Hac, I.Youn and HH Chen, Control of suspensions for vehicles with flexible bodies Semi-Active suspensions, ASME Transactions, vol.118, Sept A.Hac, I.Youn and HH Chen, Control of suspensions for vehicles with flexible bodies Active suspensions, ASME Transactions, vol.118, Sept J.Y.Wong, Application of the computer simulation model NTVPM-86 to the development of a new version of the infantry-fighting vehicle ASCOD, Journal of Terramechanics.. 6. J.Y.Wong, Dynamics of track vehicles, Vehicle system dynamics, 28(1997), pp
8 7. A.T.Le, D.C.Rye and H.F.D.Whyte, Estimation of Track-soil interactions for autonomous tracked vehicles, Proceedings of the IEEE 1997 International Conference on Robotics and Automation. 8. S.Rakheja, M.F.R.Afonso and S.Sankar, Dynamic analysis of tracked vehicles with trailing arm suspension and assessment of ride vibrations, International Journal of Vehicle Design, vol.13, no.1, S.Rakheja, Y.Afework and S.Sankar, An analytic and experimental investigation of the driver-seat-suspension system, Vehicle Systems Dynamics, 23(1994), pp Wheeler P, Tracked vehicle ride dynamics computer program, SAE paper no , NOMENCLATURE 1. F wn = net footprint force acting at ith road wheel. 2. K rw = radial spring constant for the road wheels. 3. R w = radius of the road wheels. 4. R h = Radius of a hull wheel. 5. M h = Sprung mass. 6. I h = Hull Pitch Moment of 17. y(i) = relative displacement of ith wheel. 18. y h = relative displacement of hull wheel. 19. v r(i) = relative velocity across the suspension unit of ith wheel. 20. v(i) = vertical velocity of the ith wheel. inertia. 21. K s = spring constant of the 7. T tr0 = initial track tension. suspension unit. 8. L tr0 = initial track length. 22. C s = damping constant of the 9. L tr = track length at any time. suspension unit. 10. K tr = longitudinal stiffness of 23. F hy = vertical force acting on the track. 11. L j = length of the track between two successive wheels. 12. L h = Length of the track resting over the hull wheels. 13. f s = spring force of suspension unit. 14. f d = damping force of suspension unit. 15. M w = mass of a road wheel. 16. r(i) = relative displacement across suspension unit. the hull wheel 24. A h = acceleration of the hull CG 25. A d = acceleration of the driver s seat. 26. Ang h = hull pitch angular acceleration. 27. A w(i)= Acceleration of i th wheel. 28. ω= hull pitch angular velocity. 29. θ= hull pitch angular displacement 8
9 30. a 0 = Horizontal distance of diver s seat from hull CG. 9
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