Space Grant Consortium - University of Wisconsin - Green Bay

Validation of Novel Rigid Body Frictional Contact Algorithms using Tracked Vehicle
Simulation: a Stepping Stone for Billion Body Dynamics
Abstract
Justin Madsen 1
Simulation Based Engineering Laboratory
Department of Mechanical Engineering
University of Wisconsin – Madison
Computer modeling and simulation of mechanical systems with many rigid body frictional contacts is currently
limited due to inefficient formulation. A time-stepping method which describes frictional impacts and contacts as
unilateral constraints and solves the resulting linear complementarity problem on the velocity-impulse level with a
novel fixed-point iteration process has recently been introduced. Research has shown that this new method is
computationally efficient and converges to a solution under most circumstances.
This project applies the new methodology to a real engineering system, the tracked subsystem of a hydraulic
excavator. A nearly identical computational model is formulated and simulated using both the new method and
using industry-grade multibody dynamics software. The formulation of the models and simulation results are then
compared. Differences and problems using the new methodology are addressed, and conclusions allude to the need
for automatic decomposition of complex geometry.
Introduction
Over the last decade, simulation-based engineering in the form of virtual prototyping has been
increasingly utilized by engineers in the design process of mechanical systems. This is due to
economic factors such as cutting physical prototype costs and reduced time to market. In the case
of space exploration, testing a prototype under actual conditions can be cost prohibitive or even
impossible. As engineers apply virtual prototyping to increasingly complex systems, new
numerical and computational methods must be leveraged to sustain or, preferably, increase the
complexity of models that can be simulated.
Systems with large numbers of rigid-body frictional contacts are a group of models which would
greatly benefit from research into new mathematical and computational methods. Examples of
such systems include automobiles and lunar landing craft driving on terrain such as gravel or
sand. Pebble bed nuclear reactors or pharmaceutical drug packing processes could be accurately
simulated as well. However, these types of models have yet to be effectively simulated because
most multibody dynamics solvers handle rigid body frictional contacts in an inefficient manner,
exploiting simplex or penalty-based methods which result in a quadratic worst-case time
complexity (Tasora 2006). As the number of colliding bodies reaches well into the millions, an
algorithm with exponential complexity makes the task practically impossible even on
supercomputers. A time-stepping method which describes frictional impacts and contacts as
unilateral constraints and solves the resulting linear complementarity problem (LCP) on the
velocity-impulse level with a novel fixed-point iteration process has recently been proposed
(Anitescu and Potra 1997; Anitescu, Potra et al. 1999; Anitescu 2006). The interest in this new
method stems from the fact that it has been shown to have linear worst-case time complexity
(Tasora 2006). The table below shows the CPU time taken to complete of two sets of simulations
1 The author would like to thank the Wisconsin Space Grant Consortium for financial support
of this work through a Graduate Fellowship Grant.
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