0
TECHNICAL PAPERS

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
Your Session has timed out. Please sign back in to continue.

References

Guran, A., Pfeiffer, F., and Popp, K., eds., 1996, Dynamics with Friction: Modeling, Analysis and Experiment, Vol. 7 of Series on Stability, Vibration and Control of Systems, World Scientific, Singapore.
Karnopp,  D., 1985, “Computer Simulation of Stick-Slip Friction in Mechanical Dynamic Systems,” ASME J. Dyn. Syst., Meas., Control, 107, pp. 100–103.
Oden,  J. T., and Pires,  E. B., 1983, “Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problems in Elasticity,” ASME J. Appl. Mech., 50, pp. 67–76.
Tariku,  F. A., and Rogers,  R. J., 2001, “Improved Dynamic Friction Models for Simulation of One-Dimensional and Two-Dimensional Stick-Slip Motion,” ASME J. Appl. Mech., 123, pp. 661–669.
Abadie, M., 2000, “Dynamic Simulation of Rigid Bodies: Modelling of Frictional Contact,” Impacts in Mechanical Systems, B. Brogliato, ed., Vol. 551 of Lecture Notes in Physics, Springer-Verlag, Berlin, pp. 61–144.
Pfeiffer,  F., 1991, “Dynamical Systems With Time-Varying or Unsteady Structure,” Z. Angew. Math. Mech.,71(4), pp. T6–T22.
Brogliato, B., 1999, Nonsmooth Mechanics: Models, Dynamics and Control, Springer-Verlag, London, 2nd ed.
Shaw,  S. W., 1986, “On The Dynamic Response of A System With Dry Friction,” J. Sound Vib., 108, pp. 305–325.
Berger,  E. J., Begley,  M. R., and Mahajani,  M., 2000, “Structural Dynamic Effects on Interface Response: Formulation and Simulation Under Partial Slipping Conditions,” ASME J. Appl. Mech., 67, pp. 785–792.
Tan,  X., and Rogers,  R. J., 1998, “Simulation of Friction in Multi-Degree-of-Freedom Vibration Systems,” ASME J. Dyn. Syst., Meas., Control, 120, pp. 144–146.
Leine,  R. I., Van Campen,  D. H., De Kraker,  A., and Van Den Steen,  L., 1998, “Stick-Slip Vibrations Induced by Alternate Friction Models,” Nonlinear Dyn., 16, pp. 41–54.
Martins,  J. A. C., and Oden,  J. T., 1983, “A Numerical Analysis of a Class of Problems in Elastodynamics With Friction,” Comput. Methods Appl. Mech. Eng., 40, pp. 327–360.
Oden,  J. T., and Martins,  J. A. C., 1985, “Models and Computational Methods for Dynamic Friction Phenomena,” Comput. Methods Appl. Mech. Eng., 52, pp. 527–634.
Song,  P., Kraus,  P., Kumar,  V., and Dupont,  P., 2001, “Analysis of Rigid-Body Dynamic Models for Simulation of Systems With Frictional Contacts,” ASME J. Appl. Mech., 68, pp. 118–128.
Ruina,  A. L., 1983, “Slip Instability and State Variable Friction Laws,” J. Geophys. Res., 88(B12), pp. 10359–10370.
Gu,  J.-C., Rice,  J. R., Ruina,  A. L., and Tse,  S. T., 1984, “Slip Motion and Stability of a Single Degree of Freedom Elastic System With Rate and State Dependent Friction,” J. Mech. Phys. Solids, 32(3), pp. 167–196.
Haessig,  D. A., and Friedland,  B., 1991, “On the Modeling and Simulation of Friction,” ASME J. Dyn. Syst., Meas., Control, 113, pp. 354–362.
Burridge,  R., and Knopoff,  L., 1967, “Model and Theoretical Seismicity,” Bull. Seismol. Soc. Am., 57, pp. 341–371.
Carlson,  J. M., and Langer,  J. S., 1989, “Mechanical Model of an Earthquake Fault,” Phys. Rev. A, 40(11), pp. 6470–6484.
Menq,  C.-H., Bielak,  J., and Griffin,  J. H., 1986, “The Influence of Microslip on Vibratory Response, Part I: A New Microslip Model,” J. Sound Vib., 107(2), pp. 279–293.
Quinn,  D. D., and Segalman,  D. J., 2003, “Using Series-Series Iwan-Type Models for Understanding Joing Dynamics,” ASME J. Appl. Mech., in press.
Pfeiffer, F., and Glocker, C., 1996, Dynamics of Rigid Body Systems with Unilaterial Constraints, Wiley Series in Nonlinear Science, John Wiley and Sons, New York.
Synnestvedt,  R. G., 1996, “An Effective Method for Modeling Stiction in Multibody Dynamic Systems,” ASME J. Dyn. Syst., Meas., Control, 118, pp. 172–176.
Rice,  J. R., and Ruina,  A. L., 1983, “Stability of Steady Frictional Slipping,” ASME J. Appl. Mech., 50, pp. 343–349.

Figures

Grahic Jump Location
Multiple frictional contacts. The lower block rests on a surface moving with velocity u̇(t).
Grahic Jump Location
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.
Grahic Jump Location
Representation of Coulomb’s law of friction. The heavy line represents the friction force at zero velocity.
Grahic Jump Location
Velocity-based regularization of the classical law of friction (see Martins and Oden 12)
Grahic Jump Location
Modified friction law proposed in Eqs. (4)
Grahic Jump Location
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).
Grahic Jump Location
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.
Grahic Jump Location
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.
Grahic Jump Location
n-dof discrete model. We consider uniform normal loads, with μNi=1.
Grahic Jump Location
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.
Grahic Jump Location
Threshold contact velocity model as proposed by Karnopp 2, represented in terms of ẋ and feq

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In