Dynamics of inertial pair coupled via frictional interface

TL;DR

This paper develops a comprehensive model for the dynamics of two inertial bodies coupled via a friction interface, incorporating Coulomb friction and discontinuities, and demonstrates trajectory convergence in a free system.

Contribution

It introduces a generalized modeling framework for friction-coupled inertial systems with discontinuous dynamics, including a closed-form ODE formulation with sign operators.

Findings

Global convergence of trajectories in a free system without external forces

Successful modeling of a harmonic oscillator with frictional coupling

Illustration of the framework's main features through a case study

Abstract

Understanding the dynamics of two inertial bodies coupled via a friction interface is essential for a wide range of systems and motion control applications. Coupling terms within the dynamics of an inertial pair connected via a passive frictional contact are non-trivial and have long remained understudied in system communities. This problem is particularly challenging from a point of view of modeling the interaction forces and motion state variables. This paper deals with a generalized motion problem in systems with a free (of additional constraints) friction interface, assuming the classical Coulomb friction with discontinuity at the velocity zero crossing. We formulate the dynamics of motion as the closed-form ordinary differential equations containing the sign operator for mapping both, the Coulomb friction and the switching conditions, and discuss the validity of the model in the generalized force and motion coordinates. The system has one active degree of freedom (the driving body) and one passive degree of freedom (the driven body). We demonstrate the global convergence of trajectories for a free system with no external excitation forces. Then, an illustrative case study is presented for a harmonic oscillator with a frictionally coupled second mass that is not grounded or connected to a fixed frame. This simplified example illustrates a realization and main features of the proposed (general) modeling framework. Some future development and related challenges are discussed at the end of the paper.