In order to enable off-road vehicle dynamics analysis simulations when traveling on soft soil, a deformable Vehicle Terrain Interface (VTI) model that interfaces with existing vehicle and tire dynamics models was developed. It is modularized to be interfaced to a multibody dynamics vehicle that supports the Standard Tire Interface (STI). Any tire model can be used that supports the STI as well; currently, both rigid and flexible tire models are supported.
Geometry associated with the terrain profile is a combination of low-fidelity terrain height measurements, with superimposed NURBS for high-frequency content. The terrain model can efficiently query the current height by locally defining the surface as an equidistantly spaced x-y grid, and using bi-linear interpolation of the nearest four points. Points on the surface also contain information on the state of deformation of the soil, notably the undisturbed terrain height, the type of terrain, and the energy and power involved in the soil deformation. The terrain takes a set of tire-terrain interface forces from the tire model, applies it to the surface of the terrain, evaluates the terramechanics problem, and updates the soil states and deformed surface profile for the subsequent time step.
In the context of off-road vehicle simulations, terrain models fall into three categories of increasing complexity: rigid terrain where the main focus is an accurate surface profile, use of empirical relationships to find pressure and sinkage directly under the tire, or finite/discrete element approaches. Any off-road vehicle dynamics simulation where the soil deforms considerably requires a terrain model that accurately reflects the deformation and response of the soil to all possible inputs of the tire in order to correctly simulate the response of the vehicle.
In this approach, fast simulations are possible due to the inherent parallel nature of the subsoil stress calculations, which are the major computational bottlenecks. Parallel CPU and GPU hardware is utilized to accelerate these computations. The model will be exercised using a rigid tire with and without lugs to demonstrate the ability to handle complicated tire geometry.
The Vehicle-Terrain Interaction model involves three main components: (1) a surface loading mechanism due to 3D tire geometry contact with the terrain, (2) stress propagation of the load through the subsoil, and (3) rigorous vertical soil stress/strain relationship.
At the beginning of a time step, the vehicle passes the tire wheel spindle state data, which includes the position and velocity of the Center of Mass (CM) in the reference frame indicated by the Standard Tire Interface. The tire passes an updated geometry profile to the terrain in the form of a height map query, and the terrain database returns the collision information. Forces at the tire/terrain interface are found at each time step by using a combination of normal and slip forces, in conjunction with soft-soil tire boundary forces. These forces are passed from the tire to the terrain model, where the terrain model applies Boussinesq and Cerruti soil mechanics equations to determine the pressure distribution in the volume of affected material. The model treats a column of soil as a system of discretized soil volumes, and each volume element is modeled using viscoelastoplastic compressibility relationships that relate subsoil pressures to a change in bulk density of the soil, which in turn produces soil displacements and changes to other soil state variables. The outputs of the terrain model include tire-terrain pressure distribution, terrain surface deformation, updated soil states, and power/energy required to deform the soil.
In order to determine the effect the subsoil stress equations have when they are applied to the discretized soil volume, a simplified tire that is assumed to be rigid applies a normal force on the surface of the terrain according to the tire-terrain interaction model. A compression/rebound soil response is caused by an applied vertical displacement of 7" to the tire over 1 second, followed by a horizontal wheel displacement at a constant velocity to demonstrate the rigid wheel’s effects on the terrain while traveling at a steady state velocity of 1.5 MPH. A rotational displacement is applied to result in a minimal value of slip.
The second simulation example is run, which is similar to the first, except that the rotational displacement is applied to give the tire a slip rate of approximately 15%. The total displacement of the soil in the vertical direction at the end of the simulation is concentrated about the loading area, and is strongly influenced by the choice of Frolich parameter value. There are slightly larger force vectors when compared to the low-slip simulation (mainly elongated in the direction of travel), indicating that the shear displacement- shear stress relations properly account for the tractive forces induced by wheel slip.
Example numerical results verify that the terrain database can handle tire geometry that is complex and non-uniform. The terrain model leverages parallel computing using both CPUs and GPUs and is shown to scale well, which will enable real-time deformable terrain to be simulated.
This work was done by Alexander Reid of US Army TARDEC. For more information, download the Technical Support Package (free white paper) at www.aerodefensetech.com/tsp under the Information Technology category. ARL-0159.