Modeling of rigid body contacts for dynamic simulation
The range of engineering problems in which it is necessary to analyze the dynamics of intermittent frictional contacts is extensive. For example, in many manufacturing processes several nominally rigid bodies undergo multiple, concurrent, dynamic frictional contacts. In order to successfully design and optimize such processes, a method for modeling and simulating mechanical systems with frictional contacts is necessary. While rigid body methods are often employed, it is well established that use of load dependent friction can introduce mathematical inconsistencies and ambiguities. In these situations, we argue that compliant contact models, while increasing the length of the state vector, can successfully resolve existence and uniqueness issues (and are more realistic). The simplicity and efficiency of rigid body models, however, provide strong motivation for their use during those portions of a simulation when the compliant contact model indicates a unique and stable solution. Singular perturbation theory is used with linear complementarity theory to establish conditions for the validity of the rigid body model with rolling and sliding unilateral contacts.
In a similar context, modeling of unilateral constraint activation has traditionally relied on rigid body impact models. To date there remains no settled approach to modeling simple collision between two rigid bodies (many existing models suffer from possible energetic inconsistencies and/or inability to predict observed experimental results). Available rigid body models are evaluated based on their ability to generate allowable impulses. Additionally, the inverse problem of determining necessary impulses to produce desired post-impact motion is investigated. The differential and algebraic approaches to rigid body collision are extended to the multiple contact case through development of an LCP-based solution procedure, and issues of existence/uniqueness and solution sensitivity and stability are examined. We present algorithms for using lumped compliance in resolution of multiple contact-impact. Results from sliding and drop impact experiments involving 1 (simple collision) and 2 (impact with active unilateral constraint) contacts are presented. Comparison of pre- and post-impact states reveals functional relationships for prediction of collision outcome and permits assessment of existing models. Finally, applications of developed multiple contact-impact algorithms are demonstrated through simulation for planning of assembly and part feeding operations.