An integrated finite element method, response surface methodology, and evolutionary techniques for modeling and optimization of machining fixture layout for 3D hollow workpiece geometry

Abstract

Machining fixtures play inevitable role in manufacturing to ensure the machining accuracy and workpiece quality. The layout of fixture elements, clamping forces, and machining forces significantly affect the workpiece elastic deformation during machining. The clamping and machining forces are necessary to immobilize and machine the workpiece, respectively. Finding the appropriate layout of fixture elements is the other possible way to reduce the workpiece deformation, which in turn improves the machining accuracy. The finite element method interfaced with evolutionary techniques is normally used for fixture layout optimization. In the finite element method, the workpiece is discretized into a number of small elements and fixture elements are placed only on the nodes. Hence, evolutionary techniques are capable of searching the optimal fixture layout from those discrete nodal points than from the entire area on the locating and clamping face. To overcome these limitations, in this research paper, response surface methodology is employed to establish a quadratic model between the position of fixture elements and maximum workpiece deformation. This enables the optimization techniques to search for the optimal solution in the continuous domain of the solution space. Then, the real-coded genetic algorithm based discrete optimization, continuous optimization based on binary-coded genetic algorithm and particle swarm optimization are employed to optimize the developed quadratic model and their performances are compared. The result clearly shows that the integration of finite element method, response surface methodology with particle swarm optimization is better than the integration with genetic algorithm to optimize the machining fixture layout and also reduces the computational complexity and time to a greater extent.