A New Regularization of Coulomb Friction

[+] Author and Article Information
D. Dane Quinn

Department of Mechanical Engineering, The University of Akron, Akron, Ohio 44325-3903e-mail: quinn@uakron.edu

J. Vib. Acoust 126(3), 391-397 (Jul 30, 2004) (7 pages) doi:10.1115/1.1760564 History: Received July 01, 2002; Revised January 01, 2004; Online July 30, 2004
Copyright © 2004 by ASME
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Grahic Jump Location
Representation of Coulomb’s law of friction. The heavy line represents the friction force at zero velocity.
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Threshold contact velocity model as proposed by Karnopp 2, represented in terms of ẋ and feq
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Velocity-based regularization of the classical law of friction (see Martins and Oden 12)
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Modified friction law proposed in Eqs. (4)
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Numerical simulations of Eq. (5) (4th-order Runge-Kutta method, Δt=0.01). Each integration begins with the initial conditions (x(0),ẋ(0))=(2.75,0.00). Note the different scale used in Fig. 5(c).
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Force evolution for the proposed friction model (Eqs. (4)) near the point of sticking (cf. Fig. 5(c)). Note that 2.50≤t≤3.50. The dashed line represents x(t) while the solid line reflects f(t), the value of the frictional force as a function of time.
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Percent dissipation error per forcing cycle (μ=1). Dexact is the value calculated from the semi-analytical solution. The proposed friction law is marked with triangles and connected by solid lines, the classical definition of Coulomb friction is marked with squares and connected by long dashes, while the velocity-limited friction law is marked with pentagons and connected by short dashes. In panel b, the proposed and velocity-limited regularizations are almost coincident.
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n-dof discrete model. We consider uniform normal loads, with μNi=1.
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Friction-induced dissipation for the n-dof chain (n=32, α=0.25, ω=0.50) as the numerical step size Δt is varied. The proposed friction law is marked with triangles and connected by solid lines, the classical definition of Coulomb friction is marked with squares and connected by long dashes, while the velocity-limited friction law is marked with pentagons and connected by short dashes.
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Multiple frictional contacts. The lower block rests on a surface moving with velocity u̇(t).
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Stick-slip dynamics generated with multiple frictional contacts with κ=2, μ1=0.50,μ2=0.25,u(t)=sin(0.50t). In each panel the lower block (x1,ż1) is indicated by the solid line while the response of the upper block (x2,ż2) is dashed.



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