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

Abstract

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.

Improving CNC Turning Machine Precision through Vibration Analysis for Clamping Error Detection Employing Principal Component Analysis

“…The two primary directions of future trends are incremental innovation, which focuses on incremental enhancements and long-term viability and disruptive innovation, which involves high-risk research for possible innovations in technology [71]. Figure 12 shown three main areas of investigation here discussed: modelling strategies before done by Chan et al [72] 74] have offered an evaluation of the operational abilities of a high-precision machine tool through analysis of its virtual counterpart built with CAD. Utilizing the ANSYS Workbench simulation software, comprehensive static and modal analyses were carried out in order to determine the tool's static bending and stiffness.…”

Design and Analysis of a 5-Axis Gantry CNC Machine Tool

“…14,117,354 pyramid mesh elements are employed with 2,538,140 nodes after Jacobian and skew ratio checks. The pure penalty algorithm (prone to assign higher contact stiffness values [13]) is employed with 0.2 relaxation tolerance on the contact interfaces.…”

“…These mode shapes are related with the Z column and gantry structures. The natural frequencies predicted by FE is expected to be lower after the 4 th mode due to contact parameters, since the related modes are related with linear guides and connection elements, however, the used contact algorithm is prone to assign higher contact stiffness values [13].…”

“…Another way to forecast and maintain the required stiffness values is employing FEM and structural optimization techniques [10], such as topology, shape or crossbeam optimizations [1,10,11]. Modelling of mechanical interfaces in FE analyses is critical during the simulation and structural optimization for even regular-sized machine tools [13]. Thus, massive component sizes and weights make contacts more critical for large-scaled machine tools.…”

Development of a vibration free machine structure for high-speed micro-milling center

“…Representing the contacts in machine tool is a challenging issue which is required for accurate prediction of machine tool behavior. For ease of computational issues, the contact forces have been directly mapped onto the FE model of machine tool topological optimization problem [24]. Mohammadi and Ahmadi [25] proposed a single degree of freedom model with nonlinear restoring force to determine the vibration response of a KUKA machining robot at tool center point.…”