A real-time simulation model for tracked vehicles.

Abstract

There is a critical need for a model for high mobility tracked vehicles that can be used in real-time simulators and controller environments (hardware-in-the-loop). Such a model is essential for predicting the dynamic response (in real-time) of a tracked vehicle to driver inputs including steering, braking, and acceleration. The objective of this research is to provide this new modeling capability. A real-time model for tracked vehicles is developed by simplifying the equations of motion for critical track and suspension components. To this end, the entire track circuit is decomposed into a lower track circuit model and an upper track circuit model due to the physics that distinguish these two subsystems. For the lower track circuit, a track element model is developed for contact on a general terrain profile that captures the physics of contact with the terrain, sinkage and terrain mechanics, and track bridging. A connectivity algorithm is used to properly couple the track segments occurs road wheels. Upon discretization, this approach results in a tri-diagonal system of linear equations for efficient solution of track geometry, tension and sinkage, For the upper track circuit, an element model adopted from [Scholar, 1999] is used to capture the coupled longitudinal and transverse track vibration and track sag. This element model is then coupled across supporting rollers, idler and rive sprocket to form an entire upper track circuit as in [Scholar, 1999]. Results show that this approach captures the vibration of the upper track circuit using only a few (modal) degrees of freedom. To achieve real-time it is critical to improve the computational methods as much as the model itself. A new strategy for unsymmetric sparse matrix solvers is developed to eliminate operation counts. The strategy is benchmarked against existing software packages including SuperLU, UMFPACK, SPOOLS, and WSMP specialized for solving unsymmetric linear sparse matrix systems. The new strategy improves the calculation speed by 70 times when compared to UMFPACK. Likewise, efficient integrators for ordinary differential equations are essential for real-time computation. Herein, an integrator is selected in order to minimize the function evaluations per time step with acceptable accuracy, and it is tested for efficiency, accuracy, stability, and the ability to achieve real-time. As a first example, we evaluate a simplified tracked vehicle model composed of only two road wheels, and single upper and lower track spans. This model is used to validate the approximate wheel-track-terrain interaction model by comparing predictions with a higher-fidelity finite element model (FEM). Results for vehicles traversing flat and sinusoidal terrain show good agreement with FEM results. A second example consists of a full tracked vehicle model composed of seven road wheels (e.g. M1A1), and the associated entire track circuit. The dynamic response of this vehicle is studied while traversing both flat and rough terrain profiles, and real-time speeds are achieved. In order to evaluate accuracy, the full vehicle model is benchmarked against an existing high-fidelity model developed using the multi-body dynamics code DADS. The comparison demonstrates that the tracked vehicle model developed achieves real-time and is also ten times faster than the high-fidelity model (DADS).