Hsiao-Ming Chu

Effects of Couple Stresses on Pure Squeeze EHL Motion of Circular Contacts

A method for investigating the pure squeeze action in an isothermal elastohydrodynamically lubrication (EHL) problem, i.e., circular contacts lubricated with couple stress fluid, was developed. A constant load condition was used in the calculations. The initial conditions such as pressure profiles, normal squeeze velocities, and film shapes were obtained from the classical hydrodynamic lubrication theory at a specified large central film thickness. The coupled transient modified Reynolds, elasticity deformation, and load equilibrium equations are solved simultaneously. The simulation results reveal that the effect of the couple stress is equivalent to enhancing the lubricant viscosity, thus enlarging the film thickness. The effect of couple stress in thin film lubrication varies with film size. That is, the thinner the lubricating film is, the more obvious the effect of couple stress is. For larger characteristic length, materials parameter, and load, the central pressure, central film thickness, and rigid separation are larger than those of smaller characteristic length under the same load. The time needed to achieve maximum central pressure and the Hertzian pressure increases with increasing characteristic length.

Effects of Couple Stress on Elastohydrodynamic Lubrication at Impact Loading

In this paper, pure squeeze elastohydrodynamic lubrication motion of circular contacts with couple stress lubricant is explored at impact loading. On the basis of microcontinuum theory, the transient modified Reynolds equation is derived. Then it is solved simultaneously with the elasticity deformation equation and ball motion equation, thus obtaining the transient pressure profiles, film shapes, normal squeeze velocities, and accelerations. The simulation results reveal that the effect of the couple stress is equivalent to enhancing the lubricant viscosity, which would also enlarge the damper effect. Therefore, as the characteristic length of the couple stress fluid increases, the pressure spike and the dimple form earlier, the maximum pressure and the film thickness increase, and the diameter of the dimple, the rebounding velocity, the maximum value of the relative impact force, and the acceleration decrease. Furthermore, the fact that the contact central pressure for a ball impacting and rebounding from a lubricated surface reached two peaks during the total impact period is proved numerically in this analysis. As the effect of couple stress increases, the first and second peaks form earlier; as the total impact time decreases, the pressure of the first peak increases and that of the second peak decreases. Moreover, the phase shift between the time of the peak value of the squeeze acceleration and the zero value of the squeeze velocity increases with increasing the characteristic length of the couple stress fluid.

Rheological Characteristics for Thin Film Elastohydrodynamic Lubrication

This paper uses three lubrication models to explore the differential phenomenon in the status of thin film lubrication (TFL). According to the viscous adsorption theory, the modified Reynolds equation for thin film elastohydrodynamic lubrication (TFEHL) is derived. In this theory, the film thickness between lubricated surfaces is simplified as three fixed layers across the film, and the viscosity and density of the lubricant vary with pressure in each layer. Under certain conditions, such as a rough or concentrated contact of a nominally flat surface, films may be of nanometer scale. The thin film elastohydrodynamic lubrication (EHL) analysis is performed on a surface forces (SF) model which includes van der waals and solvation forces. The results show that the proposed TFEHL model can reasonably calculate the film thickness and the average relative viscosity under thin film EHL. The adsorption layer thickness and the viscosity influence significantly the lubrication characteristics of the contact conjunction. The differences in pressure distribution and film shape between surface forces model and classical EHL model were obvious, especially in the Hertzian contact area. The solvation force has the greatest influence on pressure distribution.

Inverse approach for estimating pressure and viscosity in the elastohydrodynamic lubrication of circular contacts

Abstract The film thickness under steady state conditions can be measured by using an optical interferometer. An inverse approach is proposed for estimating the pressure distribution on the basis of film thickness measurement in elastohydrodynamic lubrication (EHL) circular contacts. This approach is constructed from the approximated model of elastic deformation and force balance equations. To obtain an accurate pressure, it is necessary to divide the domain into a few regions on account of the singularity at the pressure spike. The principle of measuring point selection is proposed, and the problem of pressure fluctuation is overcome. On the basis of the smoothed pressure distribution, the apparent viscosity of the film can be obtained from the Reynolds equation. The least-squares method is used to compute the optimum value of the pressure-viscosity index. Results show that the best region for estimating the pressure-viscosity index is along the x axis because the Poiseuille term becomes zero in the Reynolds equation on account of the symmetry. In this region, the estimated pressure-viscosity index shows very good agreement with the exact value when measurement errors are neglected. When measurement errors are taken into account, the close agreement shows the potential of the proposed approach in estimating accurate values of the pressure-viscosity index. Generally, the error in estimating the pressure-viscosity index increases with increasing standard deviation of the measurement error, load, speed, material parameter and absolute error of the measured film thickness. The inverse approach can also be used to estimate the pressure distribution on a film thickness map obtained from an optical EHL tester. Moreover, the agreement between the actual and the estimated values of z is quite good.

Injection Molding Simulation of 3D Stacked-Chip Assembly Packaging with Different Entrances

This paper adopts a three-dimensional (3D) finite element method to simulate the injection molding of organic 3D stacked-chip assemblies. The geometry model of the assembly is simplified to a five-layered structure of stacked-chips with no solder bumps. The injection molding process incorporates 3D stacked-chip packaging and encapsulation techniques, and comprises primarily of multi-layer cavity-filling and reactive-thermosetting curing processes. The current investigation considers the effects of specifying different entrances on the resultant flow fronts, air-traps, and weld-lines. In general, the present results confirm the value of performing numerical simulations of the 3D stacked-chip packaging process to support the injection molding CAE approaches which are commonly applied nowadays to improve the packaging assembly design and to facilitate the rapid set up of mass-production conditions. The simulation results indicate that the best packaging results are obtained when the melt is introduced either at the center of the periphery side of the stacked-chip modulus or at its corner.