The Prediction of Stability in the Time-Delayed Milling Process of Spiral Bevel Gears Based on an Improved Full-Discretization Method

Spiral bevel gear drives are widely used in mechanical transmission devices due to their compact structure, smooth transmission, and cost-effectiveness. With the continuous improvement in mechanical product quality, higher and higher requirements are set for the precision, smoothness, and power density of gear transmission devices. Chatter can lead to poor workpiece surface finish on spiral bevel gears, excessive tool wear, and even damage to machine tools. Therefore, the effective prediction of milling chatter during the processing of spiral bevel gears is essential. Regenerative chatter is one of the most fundamental types of vibration in machining processes. This paper presents an improved fully discrete algorithm for predicting the stability of time-delayed cutting in the milling process of spiral bevel gears. The method is validated using single- and double-degree-of-freedom models, demonstrating its accuracy and computational efficiency. The results show that the proposed method improves computational efficiency while ensuring accuracy.