Mathematical approach for optimal machining fixture layout and clamping forces

Abstract

Machining fixtures are used to locate and constrain a workpiece during machining operation. An ideal fixture design exhibits minimal moment while machining. The purpose of this work is to design an optimum fixture layout in order to reduce the maximum elastic deformation of the workpiece by reducing the moment caused by the clamping and machining forces acting on the workpiece while machining. This can be achieved by selecting the optimal locations of fixturing elements such as locators and clamps. The objective equations are formed based on equilibrium conditions and are solved for minimum value of clamping force condition for various fixture layouts. The required equations are formulated based on the equilibrium conditions of forces, moments and stick/slip conditions. Then these equations are solved for several fixture layouts and the corresponding clamping force sets are found. Thus the clamping forces satisfying constraints, along with its respective layout are solved for deformation values using ANSYS software. Layout providing minimum deformation value is selected as the optimal one.