An optimal method to clamping force determination based on the minimum norm principle

It is important to determine the clamping forces correctly in the fixture design task. Therefore, constraint conditions of the workpiece stability were systematically investigated. Simultaneously, the optimal algorithm of clamping forces was proposed. Firstly, the mathematical model of workpiece stability was established on the basis of the screw theory. Secondly, the optimization of clamping forces was formulated according to the minimum norm principle. Based on the linear approximation of the friction cone and non-negative variable transformation, the solution technology was proposed by slacking the optimization of clamping forces into the constrained linear programming problem. Finally, took example for the typical "3-2-1" locating scheme, the optimal design procedure of clamping forces was illustrated. The analytical results show that the minimum norm principle based algorithm to clamping force optimization is effective and feasible, and the experimental data are verified to be reliable. The proposed method not only changes the experiential approach to fixture design in the traditional process planning, but also enriches the basic theory of fixture design.