In this paper, a mechanics formulation is outlined and used for evaluating the steady-state, large deflection of a slender member subjected to displacement-dependent centrifugal load. The problem is examined within the context of rotating filamentary cup brushes that are used in surface finishing operations. Several parameters which are closely related to the machining performance and service life of cup brushes are identified and reported, including filament tip spatial distribution and orientation, filament stress, and the steady-state configuration of the working surface of the cup brush during free rotation. Numerical results indicate that filament inertia forces can lead to significant fiber displacement and stress and thus, must be included as an integral part of the design of rotary cup brushes.

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