Space Grant Consortium - University of Wisconsin - Green Bay

which involved dropping an increasing number of spheres modeled with rigid body frictional
contacts in a box using two different multibody dynamic engines. The ‘LCP’ column denotes the
program which exploits the improved formulation, while the ‘Penalty’ column uses the
inefficient penalty-based method (Madsen, Pechdimaljian et al. 2007).
The motivation for this research project stems from the fact that a majority of the virtual
prototyping software used by industry today relies on simple, brute force methods to solve rigidbody
frictional contact problems. This creates a limit on the number of frictional contacts that
can be simulated efficiently. High-fidelity models with many contacts, such as tracked vehicles
or vibration feeders, cannot be used in the design process because even small simulations can
take hours to days to complete on a state-of-the-art desktop computer. The primary goal of this
project is to be able to model and simulate real-life mechanisms by leveraging this new rigidbody
frictional contact formulation. Simulations are expected to take much less time, but
solution accuracy must be maintained if the new method is to be useful. The mechanism of
choice is a tracked sub-system of a hydraulic excavator similar to the model used in a previous
project (Madsen 2007). There are many rigid-body frictional contacts present in the model, and
short simulations using industry grade software took many hours to complete.
Table 1: Number of rigid spheres vs. CPU time using LCP and Penalty contact approaches
Number of Max Number of LCP CPU time (seconds) Penalty CPU time (seconds)
Spheres Mutual Contacts
1 1 0.7 0.41
2 3 0.73 3.3
4 14 0.73 7.75
8 44 0.76 25.36
16 152 0.82 102.78
32 560 1.32 644.4
The second goal of this research is to determine if the improved fixed-point iterative method will
yield tracked vehicle simulation results that are accurate when compared to those from
previously performed simulations. Concretely, the time evolution of the displacements,
velocities, and accelerations of all bodies should be similar to the values previously obtained.
This demonstrates that using the new fixed-point iterative method to solve the set of LCPs that
arise from modeling frictional contacts as a set of unilateral constraints yields accurate results
when compared to identical simulations carried out using proven methods. Because this new
method enforces contact constraints on the velocity-level, there can be a drift in these constraint
equations due to numerical errors (Studer and Glocker 2005). Also, the new formulation is not
proven to have unique solution, although it has been shown to converge to a single solution
under most circumstances (Anitescu 2006).
Procedure
The first step in the project was to select an appropriate model in which to apply the new
multibody dynamic formulation. A hydraulic excavator model similar to that described in
(Madsen 2007) was selected because the system contains many rigid-body frictional contacts.
The computational model is described, and then the modeling procedure using two different
multibody dynamic engines is discussed. The inefficient penalty based formulation for contact
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