Efficient Prediction of Cutting Force and Stability in Five-Axis Machining of Complex Surfaces Based on Dimensional Compression

With the rapid development of high-end equipment manufacturing, the number and size of complex surfaces continue to increase. Five-axis machining has become the dominant machining method. Effective prediction of cutting force and stability is of great significance for improving machining efficiency and quality. However, due to the complex and time-varying cutting geometry in five-axis machining of complex surfaces, low prediction efficiency has become a key issue restricting the research and engineering application of cutting force and stability. To address this issue, this study introduces the concept of dimensional compression and establishes an efficient prediction model for cutting force and stability. Each tool position along the tool path is discretized into inclined plane milling based on finite difference, thereby simplifying the research object. The tool twist angle and feed deflection angle are defined to describe the spatial relationship in five-axis machining. Using these two angles as new basis variables, a compressed space is constructed, and a mapping relationship between tool position and spatial point sets is established, further reducing the dimensionality of the research object. The cutting edge contact interval is determined using the spatial constraint method. Based on the full discretization method, the cutting force and stability of inclined plane milling are predicted, and the results are uniformly stored in the compressed space to form a sample point library. Consequently, the prediction process of complex surface five-axis machining is transformed into a process of sample point retrieval, significantly improving computational efficiency. Cutting force and vibration experiments in five-axis machining of complex surfaces are conducted. The results show that the predicted results are in good agreement with the experimental measurements, validating the accuracy of the proposed model and demonstrating its capability to guide practical machining.