Modeling Friction in Smooth Multibody Systems in Absolute Coordinates

EasyChair Preprint 13336

Abstract

Popular formulations for multibody systems rely on unit-quaternions (Euler-parameters) for tracking orientations of rigid bodies. Consequently, numerical integration on quaternions also carries the normalization constraint on quaternions. Recent developments in multibody dynamics have demonstrated efficient solution methods for differential algebraic equations of frictionless constrained motion in absolute coordinates.  The state-of-the-art methods propose Lie-integration directly on the orientation matrix, thus circumventing the need to carry normalization constraint on quaternions. However, extracting accurate and unique orientation histories from the rotation matrix either requires numerically solving a set of nonlinear equations, or finding eigenvalues of the rotation matrix. Both of these processes incur additional computing cost. The presented study proposes a rotation-preserving exponential integration scheme that operates directly on quaternions. Further, we propose modifications in state-of-the-art differential variational inequality (DVI) framework for modeling friction in smooth systems using absolute coordinates. While DVI formalism is usually adopted for systems with contacts, simulating smooth systems with ideal joints with friction makes DVI method a universal formalism for rigid-body systems. The proposed method poses the general problem as an optimization problem with equality constraints, and emphasizes on resolution of the constraint forces into contact forces, to then evaluate the friction forces. The derived formulations are demonstrated through numerical simulations on three fundamental mechanical joints. Further, the simulation results of the proposed integration scheme are compared with those of state-of-the-art Lie-integration on rotation matrices. The successful implementation of the described approach further highlights the versatility of the DVI approach.

Keyphrases: Friction modeling, Lie integration, dynamic equilibrium, multibody systems

@booklet{EasyChair:13336,
  author    = {Ekansh Chaturvedi and Corina Sandu and Adrian Sandu},
  title     = {Modeling Friction in Smooth Multibody Systems in Absolute Coordinates},
  howpublished = {EasyChair Preprint 13336},
  year      = {EasyChair, 2024}}