A Synchronous Optimization of Magnitude and Placement of Multiple Clamping Forces for Fixture Design

Abstract

In order to resist external loads, multiple clamping forces will be produced to a workpiece so that its correct position can be immobilized during the entire machining operation. However, insufficient clamping forces cannot prevent the workpiece from motions whereas excessive clamping forces may cause the improper deformations of workpiece-fixture system. Therefore, a novel approach to clamping force determination is proposed for fixture design. Firstly, the measure method of magnitudes and placements of clamping forces is established from the various measure spaces to the uniform measure space for the first time. Secondly, a synchronous optimal model of magnitudes and placements of clamping forces is formulated as nonlinear constrained equations according to the minimum total complementary energy principle. By solving the resulting nonlinear equations, all contact forces including clamping forces and their application placements can accurately predicted in the frictional workpiecefixture system. This method is illustrated with example cases. The method presented here may also have an application to other passive, indeterminate problems such as power grasps in robotics.