Stiffness Model of Bolted Joint of Machine Tool Based on Multi-scale Theory

Computer numerical controlled (CNC) machine tools are comprised of numerous parts mainly connected by bolts. Accurate modeling of the contact stiffness of bolted joints is therefore a crucial element in predicting the dynamic performance of CNC machine tools. This paper presents a contact stiffness model of a bolted joint based on multi-scale theory. The model uses a series of stacked three-dimensional sine waves to describe the multi-scale roughness of the contact surface, and each frequency level is considered to be a single layer of asperities, which are stacked on top of each other. A relationship between the contact area ratio and frequency level can be deduced. Moreover, the contact stiffness at each frequency level can be represented within the model as a spring in series, therefore, the total stiffness is obtained by summing the contact stiffness at each frequency level. An experimental setup consisting of a box-shaped specimen was used to validate the numerical model of the bolted joint for the case of equal bolt pre-tightening forces and relative errors between the multi-scale natural frequencies and experimental frequencies were found to be less than 5.91%. This suggests the multi-scale model can be used to effectively predict the dynamic characteristics of CNC machine tools.