Complete numerical solutions were obtained for the time-dependent thermal elastohydrodynamic lubrication (EHL) of line contacts under combined vertical and longitudinal vibrations. It was assumed that the contact was composed of two infinitely long steel rollers. These rollers were then simplified as an infinite plane and an equivalent roller. The lubricant was assumed to be a Ree-Eyring non-Newtonian fluid. The time-dependent numerical solutions were achieved instant after instant in each period of vibrations. The periodic error was checked at each end of the vibration period until the responses of pressure, film thickness and temperature were all periodic functions with the frequency of the roller's vibrations. At each instant, the pressure field was solved with a multi-grid method, the surface deformation was solved with a multi-level multi-integration technique, and the temperature field was solved with a finite difference scheme through a sweeping process. It was shown that the normal vibration dominated the EHL characteristics and could be either strengthened or weakened slightly depending on the phase of the tangential vibration. It was also found that the vibration of the roller could produce transient surface dimples within the contact conjunction.

The instability of the rotor dynamic system supported by oil journal bearing is encountered frequently, such as the half-speed whirl of the rotor, which is caused by oil film lubricant with nonlinearity. Currently, more attention is paid to the physical characteristics of oil film due to an oil-lubricated journal bearing being the important supporting component of the bearing-rotor systems and its nonlinear nature. In order to analyze the lubrication characteristics of journal bearings efficiently and save computational efforts, an approximate solution of nonlinear oil film forces of a finite length turbulent journal bearing with couple stress flow is proposed based on Sommerfeld and Ocvirk numbers. Reynolds equation in lubrication of a finite length turbulent journal bearing is solved based on multi-parametric principle. Load-carrying capacity of nonlinear oil film is obtained, and the results obtained by different methods are compared. The validation of the proposed method is verified, meanwhile, the relationships of load-carrying capacity versus eccentricity ratio and width-to-diameter ratio under turbulent and couple stress working conditions are analyzed. The numerical results show that both couple stress flow and eccentricity ratio have obvious influence on oil film pressure distribution, and the proposed method approximates the load-carrying capacity of turbulent journal bearings efficiently with various width-to-diameter ratios. This research proposes an approximate solution of oil film load-carrying capacity of turbulent journal bearings with different width-to-diameter ratios, which are suitable for high eccentricity ratios and heavy loads.

Viscoelastic damping material has been widely used in engineering machinery to absorb vibration and noise. Dynamic behavior of the viscoelastic damping material is mainly affected by temperature and frequency. Classical dynamic behavior equations of the viscoelastic damping material have complex structures with multiple and ambiguous parameters. So a novel variable-order fractional constitutive model (VOFC) is established based on the variable-order fractional operator. Then the viscoelastic dynamic equations are derived by Laplace transform of the VOFC model. The dynamic thermomechanical analysis tests by the three-point bending mode are carried out at variable temperatures and frequencies, and the frequency spectrum of the dynamic behavior, i.e. the loss modulus, storage modulus and loss factor are obtained. Against the test data, the VOFC model is compared with classical models such as the integer-order Maxwell model, constant fractional-order Kelvin-Voigt model, constant fractional-order Maxwell model and constant fractional-order standard linear solid model. The results show that the VOFC model can describe dynamic behavior of the viscoelastic damping material at different temperatures and frequencies more accurately. And the VOFC model has simpler structure and only two parameters with clearly physical meaning. Finally, a calculation software is designed and developed, which simplifies the process of predicting viscoelastic dynamic behavior in a wide frequency range.

This paper studies the effect of the dimple cross-sectional profile on the behavior of gas parallel slider bearings using the numerical method. The numerical method is performed in MATLAB software. The influence of geometrical parameters of dimples on the dimensionless average pressure is studied for different dimple cross-sectional profiles. The geometrical parameters of dimples include dimple depth, dimple area density, transversal textured ratio, and longitudinal textured ratio. It is found that the hydrodynamic lubrication of dimple-textured gas parallel slider bearings is controlled by the dimple depth, dimple area density, transversal textured ratio, longitudinal textured ratio, and dimple cross-sectional profile. Furthermore, the impact of sliding speed on the hydrodynamic lubrication is studied for different dimple cross-sectional profiles. The results indicate that the optimum sliding speed for maximizing the hydrodynamic pressure is controlled by the dimple cross-sectional profile.