Modified Jacobian-Torsor Based Error Modeling and Quantitative Sensitivity Analysis for Single Axis Assembly of Machine Tool

The influence of component errors on the final error is a key aspect of error modeling of CNC machine tool. Nevertheless, the mechanism by which the errors in mechanical parts accumulate to result in the component errors and then impact the final error of CNC machine, has not been identified; the identification of this mechanism is highly relevant to precision design of CNC machine. In this study, error modeling based on the Jacobian-torsor theory is founded to determine the mechanism by which fundamental errors in mechanical parts influence the comprehensive error of single-axis assembly. Firstly, the constraints of small displacement torsors (SDTs) for typical features and the statistical solution are proposed to perfect the modified Jacobian-torsor model theoretically. Next, the modified Jacobian-torsor model is applied to the error modeling of a single-axis assembly in a three-axis machine center. Furthermore, the comprehensive errors of the single-axis assembly are evaluated by Monte Carlo simulation based on the synthesized error model. The accuracy and efficiency of the modified Jacobian-torsor model are verified through a comparison between the simulation results and the measured data from a batch of similar vertical machine centers. Based on the modified Jacobian-torsor model, the application of quantitative sensitivity analysis of single-axis assembly is investigated, along with an analysis of the analysis of key error sources to the synthetical error ranges of the single-axis assembly. This model is providing a comprehensive method for the better understanding of the key error source of the machine tool and has the potential to enable error allocation and precision improvement of the assembly and the whole machine tool in future.