Research on influence mechanism of geometric error sources on tooth surface error of VH-CATT gear special machine tool

The variable hyperbolic circular arc tooth trace cylindrical (VH-CATT) gear is a new type of gear that can be efficiently processed with special machine tools. However, geometric errors can affect the machining accuracy of these special machines, leading to a reduction in gear surface quality and potential failure during application. To address this issue, this paper establishes a machine tool coordinate system based on the gear forming principle and derives a motion transfer matrix between components using the Huston lower numbered body array method. An error model for the tooth surface, which includes 40 sources of machine tool error, is established, and the equation for the tooth surface with error terms is derived. A second-order approximation is used to represent the characteristics of the gear error surface, and the impact of individual error sources is analyzed through simulation. Then, comprehensive simulation of all error sources is conducted, and gear machining experiments and data inspection are performed to obtain gear surface error data for comparison. By comparing the measured gear surface error data with the comprehensive error simulation, it is shown that the actual error trend is consistent with the simulation, confirming the correctness of the geometric error model of the special machine tool. This model demonstrates the influence of machine tool error sources on gear tooth surface accuracy, and provides theoretical support for error compensation.