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.