Machine tool vibrations play a significant role in hindering productivity during machining. The growing vibrations accelerate tool wear and chipping, cause a poor wave surface finish, and may damage the spindle bearing. Some research showed that tribological properties such as friction factors can have obvious influences on the topography of rough surfaces and the nonlinear dynamic characteristics of machine tool systems. Therefore, studying the vibration friction dynamic characteristics on the normal contact stiffness (NCS) of joints of CNC machine tools is absolutely necessary for improving the machining accuracy and precision of the whole system. The study results of NCS of joints of the CNC and the friction coefficient are discussed in this paper. The model of NCS based on fractal parameters was obtained. The models of deformations of the rough surfaces and contact surfaces were deduced. The results showed that the NCS based on the calculation method considering the elastic–plastic deformation of the asperity is much higher in precision than the methods considering only elastic or plastic deformation separately. The observations this paper described suggest that in the CNC machine tools system, higher D and G and higher friction coefficients lead to higher normal contact stresses (NCSs).