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RESEARCH PAPERS

Efficient Simulation of a Dynamic System with LuGre Friction

[+] Author and Article Information
Nguyen B. Do, Aldo A. Ferri

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405

Olivier A. Bauchau

School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-015

J. Comput. Nonlinear Dynam 2(4), 281-289 (Mar 18, 2007) (9 pages) doi:10.1115/1.2754304 History: Received September 01, 2005; Revised March 18, 2007

Friction is a difficult phenomenon to model and simulate. One promising friction model is the LuGre model, which captures key frictional behavior from experiments and from other friction models. While displaying many modeling advantages, the LuGre model of friction can result in numerically stiff system dynamics. In particular, the LuGre friction model exhibits very slow dynamics during periods of sticking and very fast dynamics during periods of slip. This paper investigates the best simulation strategies for application to dynamic systems with LuGre friction. Several simulation strategies are applied including the explicit Runge–Kutta, implicit Trapezoidal, and implicit Radau-IIA schemes. It was found that both the Runge–Kutta and Radau-IIA methods performed well in simulating the system. The Runge–Kutta method had better accuracy, but the Radau-IIA method required less integration steps.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Normalized friction force versus slip velocity: (a) Coulomb; (b) Sticktion; and (c) Stribeck friction laws

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Figure 2

Saturation approximation of signum nonlinearity

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Figure 3

Smooth approximation of signum nonlinearity

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Figure 4

Delayed switching time

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Figure 5

Description of the frictional interface in the LuGre model

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Figure 6

Stick-slip system. The parameters are M=1kg, K=2N∕m, and U increases at the constant rate of 0.1m∕s; i.e., U=0.1tm.

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Figure 7

LuGre function g versus y2 using values in Table 1

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Figure 8

Maximum magnitude eigenvalue versus y2

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Figure 9

y1 versus τ using ode45 with RelTol=1×10−4 and AbsTol=1×10−6

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Figure 10

y2 versus τ using ode45 with RelTol=1×10−4 and AbsTol=1×10−6

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Figure 11

y3 versus τ using ode45 with RelTol=1×10−4 and AbsTol=1×10−6

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Figure 12

fL versus τ using ode45 with RelTol=1×10−4 and AbsTol=1×10−6

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Figure 13

λmax(J) versus τ; from ode45 with RelTol=1×10−7 and AbsTol=1×10−7

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Figure 14

(a) Maximum eigenvalue during the transition from microslip to macroslip; and (b) maximum eigenvalue during the transition from macroslip to microslip

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Figure 15

Closeup of y3 versus τ; ode45 with RelTol=1×10−4 and AbsTol=1×10−6

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