Geometric error sensitivity analysis for a 6-axis welding equipment based on Lie theory

The influence of geometric errors on the accuracy of machine tools tends to attract more attention to the increasing demand for high-precision machining. In this paper, geometric error modeling and sensitivity analysis are employed to quantify the importance of geometric error for a new efficient and automatic 6-axis welding equipment. The geometric error model of the 6-axis welding equipment with 36 geometric error components is established based on Lie theory. Based on the geometric error model, the new sensitivity analysis method, in which the deviation of the welding torch pose is treated as a distance metric in SE(3), is proposed to evaluate the influences of geometric errors on the accuracy of the welding torch. And the sensitivity coefficient of each geometric error is derived by considering the basic value of geometric errors. Numerical simulations of a typical welding trajectory for intersecting pipes are conducted to analyze the sensitivity of geometric errors by the new method. The simulation results verified the validity of the sensitivity analysis method and the dominant geometric errors affecting the accuracy of the welding equipment were identified. Compared with the previous sensitivity analysis method, the proposed sensitivity analysis method considers the orientation error and position error of the welding torch simultaneously, which is more convenient and effective, and can also be applied in precision design and geometric error compensation of machine tools.