The kinematic accuracy reliability analysis of a special machine tool for variable hyperbolic circular-arc-tooth-trace cylindrical gears

Kinematic reliability is an important evaluation index for measuring the dynamic kinematic accuracy of mechanisms, which can more essentially reflect the kinematic performance of the mechanisms. Based on the traditional theory of mechanism kinematic reliability design, this study conducts an in-depth exploration of the kinematic accuracy of a special machine tool for variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gears. To address the principle errors and low processing accuracy in machining VH-CATT cylindrical gears, this research innovatively applies advanced reliability assessment methodologies to this specific machine tool, providing a novel theoretical reference for its precision design. By considering drive error as the key factor, systematic error analysis of the machine tool was conducted. An error calculation model for the machine tool was established using homogeneous coordinate transformation and multi-body system theory. The advanced first-order second-moment (AFOSM) was adopted to accurately calculate the kinematic reliability of the machine tool in the x , y , and z directions, as well as the combined direction and reliability sensitivity. To ensure the accuracy of the calculation results, the Monte Carlo method was further used for verification. The results indicated that the values obtained by the two methods were highly consistent, fully validating the effectiveness and applicability of the AFOSM in calculating the kinematic reliability and reliability sensitivity of this machine tool. This research provided a novel theoretical framework for the kinematic accuracy reliability analysis of dedicated machine tools, offering significant insights for precision design and error compensation.