Determination of minimum clamping forces for dynamically stable fixturing

This paper presents a model-based framework for determining the minimum required clamping forces that ensure the dynamic stability of a fixtured workpiece during machining. The framework consists of a dynamic model for simulating the vibratory behavior of the fixtured workpiece subjected to time- and space-varying machining loads, a geometric model for capturing the continuously changing geometry and inertia of the fixture-workpiece system during machining, a static model for determining the localized fixture-workpiece contact deformations due to clamping, a model for checking the dynamic stability of the fixtured workpiece, and a model for determining the optimal set of clamping forces that satisfies the stability criteria for a given machining operation. The clamping force optimization problem is formulated as a bilevel nonlinear programming problem and solved using the Particle Swarm Optimization (PSO) technique featuring computational intelligence. A simulation example solved using the developed approach reveals that the minimum required clamping forces for dynamically stable fixturing are significantly affected by the fixture-workpiece system dynamics and its continuous change during machining due to the material removal effect. (C) 2005 Published by Elsevier Ltd.