The Linear Programming Approach to Clamping Forces Determination with the Frictional Consideration

In machining process, the workpiece is subject to cutting forces and torques. To resist these external loads, a fixture can supply clamping forces to completely restrain the workpiece. However, insufficient clamping forces cannot prevent the workpiece from translation and rotations, whereas excessive clamping forces may cause strongly the improper workpiece-fixture system deformations. Therefore, how to effectively determine the optimum clamping forces is the main objective of this paper. Firstly, a mechanistic model is proposed to measure the stability of clamping forces against these external loads. Secondly, a relaxation method is further established to true obtain the optimum clamping forces by solving the proposed model. The presented approach is conceptually simple and computationally efficient. It is particularly useful in the early stages of fixture design and process planning.