Fourier transform based dynamic error modeling method for ultra-precision machine tool

In some industrial fields, the workpiece surface need to meet not only the demand of surface roughness, but the strict requirement of multi-scale frequency domain errors. Ultra-precision machine tool is the most important carrier for the ultra-precision machining of the parts, whose errors is the key factor to influence the multi-scale frequency domain errors of the machined surface. The volumetric error modeling is the important bridge to link the relationship between the machine error and machined surface error. However, the available error modeling method from the previous research is hard to use to analyze the relationship between the dynamic errors of the machine motion components and multi-scale frequency domain errors of the machined surface, which plays the important reference role in the design and accuracy improvement of the ultra-precision machine tool. In this paper, a fourier transform based dynamic error modeling method is presented, which is also on the theoretical basis of rigid body kinematics and homogeneous transformation matrix. A case study is carried out, which shows the proposed method can successfully realize the identical and regular numerical description of the machine dynamic errors and the volumetric errors. The proposed method has strong potential for the prediction of the frequency domain errors on the machined surface, extracting of the information of multi-scale frequency domain errors, and analysis of the relationship between the machine motion components and frequency domain errors of the machined surface.