The machine tools are consisted of many parts and most of them are connected by the bolts. Accurate modeling of contact stiffness and damping for bolted joint is crucial in predicting the dynamic performance of machine tools. This paper presents a modified three-dimensional fractal contact model to obtain the stiffness and damping of bolted joint. Topography of the contact surface of bolted joint is fractal featured and determined by fractal parameters. Asperities in microscale are considered as elastic, elastic–plastic, and full plastic deformation. The expand coefficient ψ is introduced to the size-distribution function of asperities. The real contact area, contact stiffness, and damping of the contact surface can be calculated by integrating the microasperities. The relationship of contact stiffness, damping, fractal dimension D, and fractal roughness parameter G can be obtained. Experiments are conducted to verify the efficiency of the proposed model. The results show that the theoretical mode shapes are in good agreement with the experimental mode shapes. The relative errors between the theoretical and experimental natural frequencies are less than 3.33%, which is less than those of the W-K model and L-L model. The presented model can be used to accurately predict the dynamic characteristic of bolted assembly in the machine tools.

The nonuniform cantilever beam and Hertzian contact model have been widely used to derive the mesh stiffness of spur gear assuming that the contact surface is absolutely frictionless. However, studies have confirmed that machined surfaces are rough in microscale and can be simulated by the Weierstrass–Mandelbort function. In order to get a reasonable and precise mesh stiffness model, the M-B contact model and finite element method are combined to express the local contact stiffness K_h. Through the simulation and comparison, the analytical finite element method is proved to be consistent with the traditional models and introduces the roughness parameters of machined tooth surface into the meshing process. Furthermore, the results also show that it is advantageous to improve the total mesh stiffness by increasing the fractal dimension D and input torque T as well as decreasing the roughness parameter G. In this paper, a relationship is built between the total mesh stiffness of gear sets with tooth surface characters and input torque, which can be a guidance in the design of the tooth surface parameters and the choice of the processing method in the future.

The thermal contact conductance is an important problem in the field of heat transfer. In this research, a three-dimensional fractal theory based on the thermal contact conductance model is presented. The topography of the contact surfaces was fractal featured and determined by fractal parameters. The asperities in the microscale were considered as elastic, elastic-plastic, or plastic deformations. The real contact area of the asperities could be obtained based on the Hertz contact theory. It was assumed that the rough contact surface was composed of numerous discrete and parallel microcontact cylinders. Consequently, the thermal contact conductance of the surface roughness was composed of the thermal constriction conductance of microcontacts and the air medium thermal conductance of microgaps. The thermal contact conductance of rough surfaces could be calculated by the microasperities integration. An experimental set-up with annular interface was designed to verify the presented thermal contact conductance model. Three materials were used for the thermal contact conductance analysis with different fractal dimensions D and fractal roughness parameters G. The numerical results demonstrated that the thermal contact conductance could be affected by the elastic-plastic deformation of the asperities and the gap thermal conductance should not be ignored under the lower contact load. The presented model would provide a theoretical basis for thermal transfer engineering application.