Dynamic modeling method of the bolted joint with uneven distribution of joint surface pressure

Abstract

The dynamic characteristics of the bolted joints have a significant influence on the dynamic characteristics of the machine tool. Therefore, establishing a reasonable bolted joint dynamics model is helpful to improve the accuracy of machine tool dynamics model. Because the pressure distribution on the joint surface is uneven under the concentrated force of bolts, a dynamic modeling method based on the uneven pressure distribution of the joint surface is presented in this paper to improve the dynamic modeling accuracy of the machine tool. The analytic formulas between the normal, tangential stiffness per unit area and the surface pressure on the joint surface can be deduced based on the Hertz contact theory, and the pressure distribution on the joint surface can be obtained by the finite element software. Futhermore, the normal and tangential stiffness distribution on the joint surface can be obtained by the analytic formula and the pressure distribution on the joint surface, and assigning it into the finite element model of the joint. Qualitatively compared the theoretical mode shapes and the experimental mode shapes, as well as quantitatively compared the theoretical modal frequencies and the experimental modal frequencies. The comparison results show that the relative error between the first four-order theoretical modal frequencies and the first four-order experimental modal frequencies is 0.2% to 4.2%. Besides, the first four-order theoretical mode shapes and the first four-order experimental mode shapes are similar and one-to-one correspondence. Therefore, the validity of the theoretical model is verified. The dynamic modeling method proposed in this paper can provide a theoretical basis for the accurate dynamic modeling of the bolted joint in machine tools.