The predictive modeling of diagonal errors in precision machine tools based on multi-body system theory

The overall spatial accuracy of a precision machine tool directly influences its machining quality. As a representative form of spatial motion realized through multiaxis linkage, the diagonal error of the spatial body effectively reflects the linkage error characteristics. To improve the prediction of machine tool accuracy, this paper presents a modeling and prediction approach centered on the spatial body diagonal error. First, the structure of a five-axis machine tool is analyzed, and the mathematical relationship between tolerance and geometric errors is established using the Fourier series. Subsequently, an error transmission model grounded in multi-body system theory is developed to quantitatively predict diagonal errors. The proposed model is validated through both simulation and experimental analysis. Results indicate that the maximum deviation between predicted and measured values is 2.4 μm, demonstrating the accuracy and practical applicability. This method offers valuable insights into the evolution of tolerance and diagonal error, providing theoretical support for precision design and optimization of machine tools.