Topology Optimization of Fixture Clamping Locations for Machining Processes Integration internship

Abstract

This work addresses the optimization of fixture clamping locations to minimize workpiece de- formation under prescribed external machining forces. The approach employs finite element analysis (FEA), introducing bar elements on the exterior surface of a 3D tetrahedral workpiece mesh. The design variables are the densities of these bar elements, formulated using the SIMP homogenization method. A linear static analysis is used to evaluate the objective function. The algorithm, implemented in Python, includes finite element assembly and sensitivity analysis. Optimization is performed using a prewritten Python module that implements the Method of Moving Asymptotes (MMA). To improve computational efficiency, the Guyan-Irons method is successfully applied, reducing the system by keeping only relevant degrees of freedom (DOFs), thus significantly reducing computation time. The framework is demonstrated on two test cases: a simple academic example involving a cylindrical workpiece under point loading, and a more realistic turbine impeller subjected to a machining tool path. The effect of physical and numerical parameters on the optimal solution is investigated to reduce intermediate density values. Since tetrahedral elements are not ideal for high-accuracy simulations, this work is intended as a proof of concept.