A Set-Valued Force Law for Spatial Coulomb-Contensou Friction

2003 ◽  
Author(s):  
Remco I. Leine ◽  
Christoph Glocker
Keyword(s):  
Coulomb Friction ◽  
Augmented Lagrangian ◽  
Rigid Bodies ◽  
Friction Torque ◽  
Sliding Velocity ◽  
Time Stepping ◽  
Extended Contact ◽  
Tippe Top ◽  
Augmented Lagrangian Approach ◽  
Pseudo Potential

The aim of this paper is to develop a contact law for combined spatial Coulomb friction and normal friction torque (drilling friction) as a function of sliding velocity and spin. We will call this extended contact law the Coulomb-Contensou friction law and derive it from a non-smooth velocity pseudo potential. A Runge-Kutta time-stepping method is briefly presented for the numerical simulation of rigid bodies with Coulomb-Contensou friction. The algebraic inclusion describing the contact problem is solved with an Augmented Lagrangian approach. The theory and numerical methods are applied to the Tippe-Top, which illustrates the importance of Coulomb-Contensou friction for the dynamics of systems with friction.

On the Implementation of Coulomb Friction in a Volumetric-Based Model for Contact Dynamics

2007 ◽  
Author(s):  
Yves Gonthier ◽  
John McPhee ◽  
Christian Lange
Keyword(s):  
Coulomb Friction ◽  
General Purpose ◽  
Friction Torque ◽  
Contact Dynamics ◽  
Contact Model ◽  
Elastic Behavior ◽  
Published Data ◽  
Winkler Elastic Foundation ◽  
Tippe Top ◽  
Object Shapes

A contact model based on volumetric properties is presented. The model properties are derived assuming the elastic behavior of the contacting objects can be approximated as a modified Winkler elastic foundation model, and that the contact surface between the objects is approximately flat. The resulting model includes friction and features a contact force proportional to the inter-penetration volume. The work shows that the Coulomb friction is affected by the relative motion. The contact model can be used as a general-purpose tool to model contact dynamics for a broad range of object shapes because the volumetric quantities that serve as input to the contact model can be determined for any object shape. A numerical simulation of a Tippe-Top is presented, and the results are shown to be consistent with published data, but with a higher spinning friction torque.

Modeling Contact Dynamics of Vanes With Adjustable Upstream Flow Angles

2012 ◽  
Author(s):  
Daniel Schurzig ◽  
Sebastian Tatzko ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Coulomb Friction ◽  
Nonlinear Behavior ◽  
Simulation Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Dynamics ◽  
Flow Angle ◽  
Complementarity Conditions ◽  
Time Stepping ◽  
Upstream Flow

In this paper, a simulation method is proposed for a sub-category of compressor vanes showing nonlinear behavior due to an adjustable upstream flow angle. The proposed algorithm computes the forced response of a single vane based on the New-mark time stepping scheme after reducing the structural matrices using the Craig-Bampton method. The contacts are modeled by Coulomb friction and Newton impact constraints. Contact forces are determined using linear complementarity conditions with decoupled orthogonal friction force directions. Different discretization methods for the cylindrical contact partners are proposed. Finally, numerical results are shown in order to validate the proposed algorithms.

Analysis and Computation of Two Body Impact in Three Dimensions

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Yan-Bin Jia ◽  
Feifei Wang
Keyword(s):  
Closed Form ◽  
Contact Point ◽  
Positive Definiteness ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Sliding Velocity ◽  
Form Analysis ◽  
Coulomb’S Friction ◽  
The Matrix ◽  
Single Contact Point

A formal impulse-based analysis is presented for the collision of two rigid bodies at single contact point under Coulomb's friction in three dimensions (3D). The tangential impulse at the contact is known to be linear in the sliding velocity whose trajectory, parametrized with the normal impulse and referred to as the hodograph, is governed by a generally nonintegrable ordinary differential equation (ODE). Evolution of the hodograph is bounded by rays in several invariant directions of sliding in the contact plane. Exact lower and upper bounds are derived for the number of such invariant directions, utilizing the established positive definiteness of the matrix defining the governing ODE. If the hodograph reaches the origin, it either terminates (i.e., the contact sticks) or continues in a new direction (i.e., the contact resumes sliding) whose existence and uniqueness, only assumed in the literature, are proven. Closed-form integration of the ODE becomes possible as soon as the sliding velocity turns zero or takes on an invariant direction. Assuming Stronge's energy-based restitution, a complete algorithm is described to combine fast numerical integration (NI) with a case-by-case closed-form analysis. A number of solved collision instances are presented. It remains open whether the modeled impact process will always terminate under Coulomb's friction and Stronge's (or Poisson's) restitution hypothesis.

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