Surface contact stress-based nonlinear virtual material method for dynamic analysis of bolted joint of machine tool

The components of machine tools are mainly fixed and connected by bolts. The performance of the assembly can be affected by the dynamic characteristics of the bolted joints. This paper presents a nonlinear virtual material method based on surface contact stress to describe the bolted joint for accurate dynamic performance analysis of the bolted assembly. Fractal geometry theory is used to describe the surface topography. The elastic modulus and shear modulus of one micro-contact are derived based on fractal contact theory. The equivalent elastic modulus, Poisson ratio, and density of the bolted joint can be obtained through the weighted mean method. In order to obtain the stress distribution, the contact surface is assumed flat in the macro-scale, and the uneven distribution of contact stress can be obtained by the finite element method (FEM). The contact surface can be divided into several sections, and the parameters of a virtual material layer can be determined based on the mean contact stress. Both theoretical and experimental results for a bolted joint are obtained for a box-shaped specimen under equal pre-tightening force and bending moment effect. The results show that the theoretical mode shapes are in good agreement with the experimental mode shapes. The relative errors between the theoretical and experimental natural frequencies are less than 4.41%, which indicates that the present nonlinear virtual material method is appropriate for the bolted joint in modeling CNC machine tools.