An improved algorithm for the normal contact stiffness and damping of a mechanical joint surface

The contact stiffness and damping play an important role in determining the dynamic characteristics at various mechanical joint surfaces in an assembly body. In this article, a bi-fractal model is proposed to overcome the drawbacks of the G-W and M-B models, which only considered the contacts that have the same fractal parameters for the joint surfaces. A surface impact coefficient is also introduced to calculate the real contact area from the microscopic and macroscopic perspectives, which can be used to obtain the contact stiffness and damping of rough surfaces by applying the contact formula between rough planes. In addition, the contact body is approximated to a number of asperities stacked on a base, similar to a series structure of two springs. The series structure can reasonably account for the limitations of the contact stiffness and damping at joint surfaces. With these improvements, this study establishes a more precise joint surface model determining the stiffness-load and damping-load relationships. An experiment is performed to compare the contact stiffness and damping determined from this theory with the experiment results. The theoretical values correspond well with the experimental values. The contact stiffness increases non-linearly with the load; the increase is initially quick and then slows down and stabilises. A value of D = 1.42 is obtained as an estimated critical value which determined the contact damping increase or decrease with load. The model can predict the trend in the contact stiffness and damping based on the loading to better prepare for a dynamic assembly analysis.