ABSTRACT A continuous model of Coulomb friction is used with a tangent space formulation of differential algebraic equations of motion for simulation of multibody dynamic model problems. Characteristics of the model problems studied are similar to those encountered in broad classes of multibody systems, without the associated geometric and analytical complexities. An implicit trapezoidal numerical solution algorithm is used to simulate dynamic response that includes the onset of stiction, its progression, and its termination, avoiding stiff behavior that is reported in the literature when index 3 formulations are used. Analytical criteria for stiction are derived for a three mass Coulomb friction model problem that defines the onset of and departure from stiction events with redundant equations of constraint. The tangent space formulation with implicit trapezoidal integration is applied to this analytical model to compute dynamic response, determine ranges of constraint forces that may occur during periods of stiction, and demonstrate that dynamic response is a discontinuous function of model parameters when stiction occurs. Accuracy of the continuous model of Coulomb friction is established, through comparison of results with those of the analytical model. Cartesian coordinate models of higher dimension are presented for three and four mass model problems that encounter a higher degree of redundancy in constraints during periods of stiction. Simulation of the Cartesian coordinate models, which have characteristics similar to more general multibody systems, yields accurate solutions, without any indication of stiffness in the tangent space equations of motion. Methods successfully demonstrated in model problems provide a foundation for simulation of spatial multibody dynamic systems with friction.
[1]
Bernard Brogliato,et al.
The contact problem in Lagrangian systems subject to bilateral and unilateral constraints, with or without sliding Coulomb’s friction: a tutorial
,
2016,
Multibody System Dynamics.
[2]
Uri M. Ascher,et al.
Computer methods for ordinary differential equations and differential-algebraic equations
,
1998
.
[3]
Marek Wojtyra,et al.
Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems
,
2017
.
[4]
Le Xuan Anh,et al.
Dynamics of Mechanical Systems with Coulomb Friction
,
2003
.
[5]
Edward J. Berger,et al.
Friction modeling for dynamic system simulation
,
2002
.
[6]
Olof Friberg,et al.
Computer aided kinematics and dynamics of mechanical systems, by E. J. Haug, Allyn and Bacon, Boston, 1989. No. of pages: 511. Price: £47.10 (hardback), ISBN 0-205-11669-8; £18.95 (international student edition), ISBN 0-205-12097-0
,
1990
.
[7]
E. Haug,et al.
Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion—I theory
,
1986
.
[8]
Ettore Pennestrì,et al.
Review and comparison of dry friction force models
,
2016
.
[9]
Edward J. Haug,et al.
An index 0 Differential-Algebraic equation formulation for multibody dynamics: Holonomic constraints
,
2017
.
[10]
Filipe Marques,et al.
A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems
,
2016
.
[11]
John McPhee,et al.
A Continuous Velocity-Based Friction Model for Dynamics and Control With Physically Meaningful Parameters
,
2016
.