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Anisotropic force ellipsoid based multi-axis motion optimization of machine tools

The existing research of the motion optimization of multi-axis machine tools is mainly based on geometric and kinematic constraints, which aim at obtaining minimum-time trajectories and finding obstacle-free paths. In motion optimization, the stiffness characteristics of the whole machining system, including machine tool and cutter, are not considered. The paper presents a new method to establish a general stiffness model of multi-axis machining system. An analytical stiffness model is established by Jacobi and point transformation matrix method. Based on the stiffness model, feed-direction stiffness index is calculated by the intersection of force ellipsoid and the cutting feed direction at the cutter tip. The stiffness index can help analyze the stiffness performance of the whole machining system in the available workspace. Based on the analysis of the stiffness performance, multi-axis motion optimization along tool paths is accomplished by mixed programming using Matlab and Visual C++. The effectiveness of the motion optimization method is verified by the experimental research about the machining performance of a 7-axis 5-linkage machine tool. The proposed research showed that machining stability and production efficiency can be improved by multi-axis motion optimization based on the anisotropic force ellipsoid of the whole machining system.