APPROXIMATION METHODS IN THE NONLINEAR-ANALYSIS OF PLANAR TRACKED VEHICLES

In many chain drives and tracked vehicle system applications, the shap e of a closed chain may not significantly change during the functional operation of the system. This paper presents certain approximation me thods which assume that the chain shape does not change. Because of th e high frequency contact and impact forces, using approximate numerica l schemes based solely on the kinematic descriptions of the closed cha in, may lead to erroneous results. Different procedures for the numeri cal solution of the dynamic equations of motion of the tracked vehicle s are presented. The tracked vehicles are modeled as two kinematically decoupled subsystems; the first is the chassis subsystem which consis ts of the chassis, rollers, idlers, and sprockets, and the second is t he track subsystem which consists of the track links, interconnected b y revolute joints. While there is dynamic force coupling between these two subsystems, there is no inertia coupling since the equations of t he two subsystems are not kinematically coupled. The objective of the procedures developed in this investigation is to examine the feasibili ty of improving computational efficiency by observing that the shape o f a track does not significantly change even though its links undergo significant displacements. In such cases the magnitudes of the nonline ar terms propagate along the diagonals of a velocity influence coeffic ient matrix which is the only source of nonlinearity in the generalize d inertia matrix of the track subsystem. Optimized numerical methods, based on coordinate permutations and reduction of the degrees of freed om of the track chain, are introduced and their effectiveness in the d ynamic modeling of tracked vehicles is examined. Numerical results obt ained using the two methods of coordinate prediction and coordinate re duction are presented and compared to the results obtained using the r ecursive kinematic equations in which all degrees of freedom of the tr ack chain are considered. The analysis procedure developed in this inv estigation is applied to only a planar tracked vehicle model.