Mechanics analysis of constrained filament deformation and dynamic response of brushing tools
Abstract
Brushing tools are widely used in numerous surface finishing applications such as deburring, polishing and surface cleaning operations. Previous research has examined the filament forces, stresses and deformation which are associated with slowly-rotating circular brushes (i.e., quasi-static brushing conditions). In order to develop an improved understanding of the actual machining force generated during the brushing process, dynamic properties of the filament must be examined. In this research, an idealized discrete system is utilized to model dynamic properties of the filament. Governing equations of the system are formulated on the basis of an Euler-Lagrange approach in conjunction with the appropriate geometric constraints. This formulation is shown to automatically yield Differential-Algebraic Equations (DAE) of index-three, and such system of equations generally require sophisticated solution strategies. Initial velocity of the filament after sudden impact/contact with a flat, rigid workpart is computed by employing an inelastic impact mechanics analysis. A modified constraint method is proposed in order to transform the relationship between workpart forces into a constraint equation, leading to a matrix with banded-symmetric form. The index-three system of equations is reduced to an index-two system which is ultimately solved by employing a predictor-corrector iteration with constant step-size Backward Difference Formula (BDF). Overall brush response is calculated by a superposition of the response of all filaments which are in contact with the workpart surface. Numerical results are compared with existing solutions of (1) large deformation of a cantilever beam, (2) damped and undamped free vibration of a cantilever beam, and (3) quasi-static brush/workpart contact problem. A thorough parametric study is reported in order to reveal the effects of both design and operational parameters on the filament and overall brush responses. In addition, numerical results are compared with experimentally obtained data for an actual brush.
This paper has been withdrawn.