Effect of Micro-Dimples on Hydrodynamic Lubrication of Textured Sinusoidal Roughness Surfaces

Surface texturing has been applied to improving the tribological performance of mechanical components for many years. Currently, the researches simulate the film pressure distribution of textured rough surfaces on the basis of the average flow model, and however the influence of roughness on the film pressure distribution could not be precisely expressed. Therefore, in order to study the hydrodynamic lubrication of the rough textured surfaces, sinusoidal waves are employed to characterize untextured surfaces. A deterministic model for hydrodynamic lubrication of microdimple textured rough surfaces is developed to predict the distribution of hydrodynamic pressure. By supplementing with the JFO cavitation boundary, the load carrying capacity of the film produced by micro-dimples and roughness is obtained. And the geometric parameters of textured rough surface are optimized to obtain the maximum hydrodynamic lubrication by specifying an optimization goal of the load carrying capacity. The effect of roughness on the hydrodynamic pressure of surface texture is significant and the load carrying capacity decreases with the increase of the roughness ratio because the roughness greatly suppresses the hydrodynamic effect of dimples. It shows that the roughness ratio of surface may be as small as possible to suppress the effect of hydrodynamic lubrication. Additionally,there are the optimum values of the micro-dimple depth and area density to maximize the load carrying capacity for any given value of the roughness ratio. The proposed approach is capable of accurately reflects the influence of roughness on the hydrodynamic pressure, and developed a deterministic model to investigate the hydrodynamic lubrication of textured surfaces.

Solitary Wave Solutions of a Generalized Derivative Nonlinear Schrdinger Equation

With the aid of a class of nonlinear ordinary differential equation （ODE） and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Sehrodinger equation （GDNLSE） have been found out, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of GDNLSE satisfy certain constraint conditions. For more general GDNLSE, the similar results are also given.

Simulation of pavement roughness based on time domain model

In order to describe pavement roughness more intuitively and effectively, a method of pavement roughness simulation, i.e., the stochastic sinusoidal wave, is introduced. The method is based on the primary idea that pavement roughness is denoted as the sum of numerous sines or cosines with stochastic phases, and uses the discrete spectrum to approach the target stochastic process. It is a discrete numerical method used to simulate pavement roughness. According to a given pavement power spectral density （PSD） coefficient, under the condition that the character of displacement frequency based on the time domain model is in accordance with the given pavement surface spectrum, the pavement roughness is optimized to stochastic equivalent vibrations by computer simulation, and the curves that describe pavement roughness under each grade are obtained. The results show that the stochastic sinusoidal wave is suitable for simulation of measured pavement surface spectra based on the time domain model. The method of the stochastic sinusoidal wave is important to the research on vehicle ride comfort due to its rigorous mathematical derivation, extensive application range and intuitive simulation curve. Finally, a roughness index defined as the nominal roughness index （NRI） is introduced, and it has correlation with the PSD coefficient.