Abstract:

Accurate modeling of the contact stiffness of bolted joints is therefore crucial to predict 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 multiple scales of roughness of the contact surface, and each frequency level is considered a layer of asperities, stacked iteratively on top of each other. The relationship between the contact area ratio and frequency level can be deduced. Moreover, the contact stiffness at each frequency level can be regarded as a spring in series in the model, therefore, the total stiffness can be obtained by summing the contact stiffness at each frequency level. The influences of contact load, material characteristic parameters and multi-scale parameters on the contact stiffness model are analyzed by mathematical simulation. An experimental setup consisting of the section beam specimen was used to validate the numerical model of the bolted joint for the case of equal pre-tightening forces. The relative error between the multi-scale natural frequencies and experimental frequencies was less than 9.94%, suggesting the multi-scale model can be effectively used in predicting the dynamic characteristics of CNC machine tools.

Key words: mechanical design, dynamic performance, bolted joint, multi?scale theory, stiffness model