Technical Brief

A Continuous Velocity-Based Friction Model for Dynamics and Control With Physically Meaningful Parameters

[+] Author and Article Information
Peter Brown

Systems Design Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: pm2brown@uwaterloo.ca

John McPhee

Fellow ASME
Systems Design Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: mcphee@uwaterloo.ca

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 27, 2015; final manuscript received May 11, 2016; published online June 2, 2016. Assoc. Editor: Dan Negrut.

J. Comput. Nonlinear Dynam 11(5), 054502 (Jun 02, 2016) (6 pages) Paper No: CND-15-1402; doi: 10.1115/1.4033658 History: Received November 27, 2015; Revised May 11, 2016

Friction is an important part of many dynamic systems, and, as a result, a good model of friction is necessary for simulating and controlling these systems. A new friction model, designed primarily for optimal control and real-time dynamic applications, is presented in this paper. This new model defines friction as a continuous function of velocity and captures the main velocity-dependent characteristics of friction: the Stribeck effect and viscous friction. Additional phenomena of friction such as microdisplacement and the time dependence of friction were not modeled due to the increased complexity of the model, leading to reduced performance of real-time simulations or optimizations. Unlike several current friction models, this model is C1 continuous and differentiable, which is desirable for optimal control applications, sensitivity analysis, and multibody dynamic analysis and simulation. To simplify parameter identification, the proposed model was designed to use a minimum number of parameters, all with physical meaning and readily visible on a force–velocity curve, rather than generic shape parameters. A simulation using the proposed model demonstrates that the model avoids any discontinuities in force at initial impact and the transition from slipping to sticking.

Copyright © 2016 by ASME
Topics: Friction , Simulation
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Fig. 1

Coulomb friction model

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Fig. 2

Velocity dependence of friction: Stribeck effect and viscous friction

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Fig. 3

Andersson friction model

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Fig. 4

Hollars friction model

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Fig. 5

Specker friction model

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Fig. 6

Choice of vd in Specker's model

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Fig. 7

Proposed new friction model showing the contribution of the three summands

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Fig. 8

Setup of the stick–slip (a) and impact experiments (b)

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Fig. 9

Mass velocity (top) and friction acting on mass (middle), with slip-to-stick transition enlarged (bottom)

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Fig. 10

Horizontal velocity compared with the rotational velocity times the radius (top) and friction forces (middle) for the impact simulation




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