Modeling and adaptive compensation of tooth surface contour error for internal gearing power honing

The machining of high precision gears requires a strict and accurate co-movement relationship controlled by the electronic gearbox between the moving axes of the gear machine tools. This article proposes a tooth surface contour error modeling method and an adaptive electronic gearbox cross-coupling controller for internal gearing power honing. First, the electronic gearbox model is structured according to the generative machining principle of internal gearing power honing and the tooth surface contour error is established by means of homogeneous coordinate transformation and meshing principle. Then, the adaptive electronic gearbox cross-coupling controller is designed, which comprises the electronic gearbox cross-coupling controller and the fuzzy proportional–integral–derivative controllers whose universes of membership functions in fuzzy rules are optimized by particle swarm optimization to improve the adaptability and robustness to disturbance fluctuation and model uncertainty of the system. Finally, experiments are carried out on a self-developed gear numerical control system. The results have demonstrated that the estimated tooth surface contour error using the proposed method is very close to the actual one, and the proposed adaptive electronic gearbox cross-coupling controller can effectively reduce the tracking error and the tooth surface contour error when compared to the electronic gearbox cross-coupling controller and non–electronic gearbox cross-coupling controller (electronic gearbox controller without cross-coupling and adaptive compensation).