An Accurate Modeling Approach of Contact Stiffness in Milling Tool-holder Interface Using Fractal Theory

Abstract The contact stiffness of the tool-holder assembly interface affects the overall dynamic performance of the milling system. Currently, the contact parameters are primarily established by minimizing the frequency response in modal tests and through dynamic simulation results. However, alterations in the structure or material of the tool-holder system necessitate multiple modal tests, thereby increasing computational costs. This study aims to streamline the process of determining contact stiffness and enhance accuracy by developing an analytical model that considers tool-holder contact properties. Initially, the microstructure of the contact surface is characterized via fractal theory to determine its fractal parameters. Then the contact coefficient is introduced to precisely depict the area distribution function of the microcontact. Building upon this, a contact stiffness model is established which is verified by the modal tests. The test results indicate that utilizing this model can reduce the structural modal frequency calculation error to 0.56%. Finally, the Monte Carlo algorithm is employed to investigate the sensitivity of fractal parameters and radial interference on contact characteristics. The findings demonstrate that the fractal dimension has the greatest influence on the dynamic behavior of the tool-holder structure. This study proposes a milling tool-holder contact stiffness modeling method from a microscopic perspective, which offers sufficient computational accuracy to provide a theoretical basis for the selection of milling tool-holder structures in practical machining.