Transmission system accuracy optimum allocation for multiaxis machine tools’ scheme design

Transmission components are the main mechanical elements in a machine system, the accuracy level of the transmission system is one of the major sources of the machining error of multiaxis machine tools. This article investigates motion error analysis, volumetric motion error model for transmission system and the accuracy allocation method for multiaxis machine tools during the early design stage. For this purpose, a transmission system volumetric motion error model, which is based on the motion error matrix and screw theory, is derived for mapping transmission components’ error parameters to the volumetric motion errors of machine tools. The volumetric motion error matrix combines motion errors along the machine tools’ kinematic chains. Subsequently, the volumetric motion error model is expressed as a volumetric motion error twist, which is formulated from the volumetric motion error matrix. Additionally, the transmission system volumetric motion error twist model is used as design criteria for accuracy optimum allocation, with constraints on the twist magnitude and design variable limits. Then, design optimization is performed by using a multiobjective nonlinear optimization technique to minimize the manufacturing cost and volumetric motion error twist pitch. To solve this multiple objective optimum problem, this study proposes an approach integrating Lagrange multiplier and gradient descent operator with non-dominated sorting genetic algorithm-II (NSGA-II). Modified non-dominated sorting genetic algorithm-II searches for an allocation scheme Pareto optimal front. Consequently, VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) determines the best compromise solution from the Pareto set. Finally, a numerical experiment for the optimal design of a numerical control machine tool is conducted, which highlights the advantages of the proposed methodology.