A Hybrid Contact Implementation Framework for Finite Element Analysis and Topology Optimization of Machine Tools

Machine tool contacts must be represented accurately for reliable prediction of machine behavior. In structural optimization problems, contact constraints are represented as an additional minimization problem based on computational contact mechanics theory. An accurate contact constraint representation is challenging for structural optimization problems: (i) "No penetration" rule dictated by Hertz-Signorini-Moreau (HSM) conditions at contacts is satisfied by varying the contact stiffness during a finite element (FE) solution without control of a user which causes increased contact stiffness "erroneously" to avoid penetration of contacting node pairs in an FE solution; and (ii) the reliability of solutions varies according to the chosen computational contact method. This paper is devoted to the topology optimization of machine tools with contact constraints. A hybrid approach is followed that combines the computational contact problem framework and an obtained stable contact stiffness function (analytically or experimentally). According to the proposed method, the existing optimization problem in FE literature is restated in a reliable form for machine tool applications. To avoid the existing computational challenges and reliability problems, contact forces are directly mapped onto an FE model used in the restated topology optimization problem with the help of proposed method. In this study, the existing and the proposed methods for contact are investigated by means of the solid isotropic material with penalization model (SIMP) algorithm for topology optimization. The effectiveness of the proposed method is demonstrated by comparing the experimental measurements on a prototype machine tool manufactured according to the optimization solutions of the proposed method and those of a conventional machine tool