The proximate analytic results of fractal dimension and fractal roughness were derived. Some solutions associated with normal contact stiffness in joint interface were modified. A general Matlab program was compiled to solve the domain extension factor. The analytic expression for the tangential contact stiffness was deduced about joint interface. A joint interface selected as an example in XHK5140 automatic tool-changing CNC vertical boring and milling machine tool in terms of the experimental results about test specimen, the theoretical expressions for normal and tangential contact stiffness were validated via the correlation of similar vibration shape and quantitative comparison tenet of natural frequencies. The theoretical vibration shapes were in good line with the experimental ones. The relative error between the theoretical natural frequencies and the experimental results distributed from -16.8% to 16.8%. 