Spatial Expression of Assembly Geometric Errors for Multi-axis Machine Tool Based on Kinematic Jacobian-Torsor Model

Assembly geometric error as a part of the machine tool system errors has a significant influence on the machining accuracy of the multi-axis machine tool. And it cannot be eliminated due to the error propagation of components in the assembly process, which is generally non-uniformly distributed in the whole working space. A comprehensive expression model for assembly geometric error is greatly helpful for machining quality control of machine tools to meet the demand for machining accuracy in practice. However, the expression ranges based on the standard quasi-static expression model for assembly geometric errors are far less than those needed in the whole working space of the multi-axis machine tool. To address this issue, a modeling methodology based on the Jacobian-Torsor model is proposed to describe the spatially distributed geometric errors. Firstly, an improved kinematic Jacobian-Torsor model is developed to describe the relative movements such as translation and rotation motion between assembly bodies, respectively. Furthermore, based on the proposed kinematic Jacobian-Torsor model, a spatial expression of geometric errors for the multi-axis machine tool is given. And simulation and experimental verification are taken with the investigation of the spatial distribution of geometric errors on five four-axis machine tools. The results validate the effectiveness of the proposed kinematic Jacobian-Torsor model in dealing with the spatial expression of assembly geometric errors.