Effect of joint interfacial contact stiffness on structural dynamics of ultra-precision machine tool

The contact stiffness of the joint interface significantly affects the dynamic characteristics of a machine tool structure. Herein, an improved theoretical model is proposed to calculate the joint interfacial contact stiffness. This model is established based on fractal theory. To mitigate the plastic and elastic contact problems, the Stronge contact model is adopted to express the contact force in the plastic regime innovatively, whereas the elastic contact force is interpreted using Hertz theory; the domain extension factor is compensated to revise the microcontact size distribution. Furthermore, the rotational contact stiffness is first derived, which renders the contact model more comprehensive. A representative test structure is designed, and the contact model is validated by comparing the simulated contact stiffness with experimental results. The transfer matrix method for multibody systems is incorporated with fractal contact model to establish a dynamic model of an ultra-precision machine tool; this ensures that the dynamic characteristics of the machine tool can be predicted more precisely. Experiments involving a vibration response test and a modal test demonstrate the feasibility of the fractal contact and dynamic models. Based on these two models, the effect of the interfacial contact stiffness on the structural dynamics is investigated. As the preloads at two joints loosen by 15%, the maximum vibration displacements increase by 1.74% and 2.90%, respectively, indicating that the joint interface between the column and lathe bed is more sensitive. The procedure presented herein will facilitate the design and optimization of the complex structures.