An innovative geometric error compensation of the multi-axis CNC machine tools with non-rotary cutters to the accurate worm grinding of spur face gears

• The geometric errors to the machining with non-rotary cutters are compensated. • The cutter rotation angle is considered for the machining with non-rotary cutters. • The geometric errors are modeled by considering the cutter rotation angle. • The cutting point is chosen as the reference point in the compensation algorithm. As one of the main error sources, the geometric errors are compensated in this work for the accurate worm grinding of spur face gears. The previous methods of the geometric error compensation are usually applied to the machining with rotary cutters, of which the error of cutter rotation angle is not compensated since it does not affect the machining result. These methods are inappropriate to the worm grinding of face gears, because the worm is a non-rotary cutter and the machining result is sensitive to the error of cutter rotation angle. In this work, an innovative geometric error compensation method is proposed to the machining with non-rotary cutters based on two main points. First, the cutter rotation angle is considered to both the modeling and compensation of the geometric errors. Second, the instantaneous ideal contact point, which is calculated according to the generation process of the worm grinding of face gears, is chosen as the reference point to the compensation algorithm rather than the cutter tip point used in the previous method. The proposed method is validated by the example with both the theoretical calculation and practical machining.