This paper addresses the contact problem associated with the filament/workpart interaction that arises during brushing processes. A discretized model of a filament within the brushing tool is developed by employing Lagrange’s equations in conjunction with special constraint equations that are appropriate for the impact and impending large displacement of a flexible fiber whose tip traverses a flat, rigid surface. This formulation leads to the identification of five nondimensional parameters which fully characterize the filament/workpart contact problem. A damping mechanism is also included which can be used for modeling complex filament interactions that arise during the actual brushing operation. Special consideration is given to examining the initial filament/workpart impact and the subsequent forces that are generated along the contact region. Initial velocity of the filament is determined by employing an inelastic impact mechanics analysis. Time-varying transient response of the filament is then obtained by employing a predictor-corrector technique in conjunction with a finite difference method. Overall brush force is computed by a superposition of filament contact forces exerted onto the workpart surface. Numerical results are reported and compared with experimentally obtained data for an actual brush/workpart system.

1.
Gear
C. W.
,
Leimkuhler
B. J.
, and
Gupta
G. K.
,
1985
, “
Automatic Integration of Euler-Lagrange Equations with Constraints
,”
Journal of Computational Applied Mathematics
, Vols.
12 & 13
, pp
77
90
.
2.
Goldsmith, W., 1960, Impact, Edward Arnold Ltd., London.
3.
Heinrich
S. M.
,
Stango
R. J.
, and
Shia
C. Y.
,
1991
, “
Effect of Workpart Curvature on the Stiffness Properties of Circular Filamentary Brushes
,”
ASME Journal of Engineering for Industry
, Vol.
113
, No.
3
, pp.
276
282
.
4.
Rosenberg, R. M., 1977, Analytical Dynamics of Discrete Systems, Plenum Press, New York.
5.
Shia
C. Y.
, and
Stango
R. J.
,
1994
, “
On the Frictional Response of Circular Filamentary Brush in Contact with Planar Workpart
,”
International Journal of Machine Tools and Manufacture
, Pergammon Press, Vol.
34
, No.
3
, pp.
308
315
.
6.
Shia, C. Y., Stango, R. J., and Heinrich, S. M., 1993, “Analysis of Contact Mechanics for Circular Filamentary Brush/Workpart System—Part I: Modeling and Formulation and Part II: Solution Method and Numerical Studies,” Proceedings of the ASME Symposium on Contact Problem and Surface Interactions in Manufacturing and Tribological Systems, New Orleans, LA, PED-Vol. 67, TRIB Vol. 4, pp. 171–190.
7.
Stango, R. J., 1992, “Rational Approach for Design and Development of Advanced Brushing Tools,” Proceedings of the 18th Annual NSF Grantees Conference on Design and Manufacturing Systems Research, Atlanta, GA, pp. 1105–1108.
8.
Stango
R. J.
,
Cariapa
V.
,
Prasad
A.
, and
Liang
S. K.
,
1991
, “
Measurement and Analysis of Brushing Tool Performance Characteristics—Part I: Stiffness Response and Part II: Contact Zone Geometry
,”
ASME Journal of Engineering for Industry
, Vol.
113
, No.
3
, pp.
283
296
.
9.
Stango
R. J.
,
Fournelle
R. A.
, and
Chada
V.
,
1995
, “
Morphology of Surfaces Generated by Circular Wire Brushes
,”
ASME Journal of Engineering for Industry
, Vol.
117
, No.
1
, pp.
9
15
.
10.
Stango
R. J.
,
Heinrich
S. M.
, and
Shia
C. Y.
,
1989
, “
Analysis of Constrained Filament Deformation and Stiffness Properties of Brushes
,”
ASME Journal of Engineering for Industry
, Vol.
111
, pp.
238
243
.
11.
Thomson, T., 1981, Theory of Vibration With Applications, 2nd ed., Prentice-Hall, New Jersey.
12.
Zhang, B., Bagchi, A., and Paul, F. W., 1992, “Surface Roughness Analysis in Wheel Brush Polishing,” Proceedings of the ASME Symposium on Engineering Surfaces, Anaheim, CA, PED-Vol. 62, pp. 179.
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