Abstract This paper proposes a novel approach to analyze the inverse problems of elastohydrodynamic lubrication (EHL). First, a finite-difference method is employed to discretize the elastic deformation and the force balance equations. The discretizing equations can be rearranged into a matrix form. The pressure distribution can be expressed in an appropriate function and then substituting it into the matrix form. The least-squares error method is adopted to find the undetermined coefficients, which generates a smooth pressure distribution based upon a small number of measuring points on the film thickness map and overcomes the problems of pressure fluctuations obtained from the traditional methods. The apparent viscosity can be solved from the Reynolds equations by using the least-squares method to predict the optimum value of the pressure-viscosity index ( ). The proposed method is applied to analyze four kinds of the inverse problems, namely, EHL of line contacts, EHL of point contacts, pure squeeze EHL motion of circular contacts, and elastohydrodynamic thin film lubrication (EHTFL). This paper discusses the effects of the implemented errors on the predicted value of apparent viscosity. The errors are implemented at the film thickness, the load, the effective elastic modulus, the viscosity at ambient pressure, and the mean velocity. Results show that the implemented errors in load and effective elastic modulus have a significant influence on the accuracy of the results, but the errors in average velocity and in the viscosity at ambient pressure do not have a significant effect. In these implemented errors, the resolution of the film thickness measurement plays the most important role in determining the accuracy of the apparent viscosity. Even when errors in the film thickness measurements are deliberately introduced, the inverse approach still provides a satisfactory value of the pressure-viscosity index. The resulting apparent viscosity errors are much smaller than those generated when using the traditional inverse method. The inverse approach can allow higher measurement error than traditional inverse method, and the allowable resolution range can be increased to about 3-10 times. Base on the viscous adsorption theory, the modified Reynolds equation is derived for EHTFL. In this theory, the film thickness between lubricated surfaces is simplified as three fixed layers across the film, and the viscosity and the density of lubricant vary with pressure in each layer. The difference between classical EHL and EHTFL is investigated to find the important parameters of EHTFL. Results show that the proposed model can reasonably calculate the film thickness and the viscosity under EHTFL. Adsorbent layer thickness and viscosity significantly influence the lubrication characteristics of the contact conjunction. The inverse approach is developed to evaluate the pressure of contact region, pressure-viscosity index ( ) of oil film, and the film thickness and viscosity of adsorbent layer under EHTFL. This paper also uses a self-development EHL tester with the optical interferometry equipment to observe the EHL film thickness map of circular contacts under the steady state and the pure squeeze motion. The inverse approach can be used to estimate the pressure distribution on a film thickness map obtained from optical EHL tester. By using this pressure distribution, the estimated pressure-viscosity index can be obtained. Result shows that the inverse approach predicts a larger value of the pressure-viscosity index than the actual value. The error between the actual and the estimated values of is less than 7 percent. When the minimum film thickness is less than 30 nm, the inverse approach based on EHTFL theory can reduce the error between the actual and the estimated values of .

¡@¡@An integrated device, which can be used to detect the ferrous particle concentration and the viscosity of the lubricating oils, is designed and manufactured. These two measurement units are conducted through the theoretical analysis of the design model, and the design drawing, the manufacturing, and the assembly of the components, respectively. Finally, the experiments are conducted to detect the performance of this integrated device. ¡@¡@In the measurement unit of the ferrous particle concentration, the geometry for the poles of the magnet and the air-gap flux density are designed using the Ohm¡¦s law and the magnetic hysteresis law, so that the ferrous particles in the lubricating oils is captured by the magnetic attraction at the air gap between the poles of the magnet. The pile of ferrous particles is connected with the Hall-effect sensors into a magnetic circuit. Results show that the sensitivity of the ferrous concentration measured using the magnetic circuit in series is about 600 times that using the magnetic circuit in parallel. The error is less than 0.3 ppm under the eight repeat tests. ¡@¡@In the measurement unit of the viscosity of the lubricating oils, the piston is squeezed into the oil to measure the viscosity. Since the container is easy to clean, the precision and the repeatability can be promoted. The error is less than 5% under the eight repeat tests. ¡@¡@When these two units are integrated into a measuring device, it is found that the interference between them can be neglected, and only one analysis procedure of sample oil can measure the ferrous particle concentration and the viscosity of the lubricating oils. Hence, the user can detect the lubricating oils used in many machines using this device to understand the abnormal wear and the deterioration of the oil.

Thesis (Ph. D.)--University of Chicago, Department of Mathematics, June 2001. / Includes bibliographical references. Also available on the Internet.

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Viscoelastic surfactant (VES) fluids are preferred for many applications in the oil industry. Their viscoelastic behavior is due to the overlap and entanglement of very long wormlike micelles. The growth of these wormlike micelles depends on the charge of the head group, salt concentration, temperature, and the presence of other interacting components. The problem with these fluids is that they are expensive and used at temperatures less than 200°F. The viscoelasticity of nanoparticle-networked VES fluid systems were analyzed in an HP/HT viscometer. A series of rheology experiments have been performed by using 2-4 vol% amidoamine oxide surfactant in 13 to 14.2 ppg CaBr2 brines and 10.8 to 11.6 ppg CaCl2 brines at different temperatures up to 275°F and a shear rate of 10 s-1. The nanoparticles evaluated were MgO and ZnO at 6 pptg concentration. In addition, the effect of different nanoparticle concentrations (0.5 to 8 pptg) and micron size particles on the viscosity of VES fluid was investigated. The oscillatory shear rate sweep (100 to 1 s-1) was performed from 100 to 250°F. The effect of fish oil as an internal breaker on the viscosity of VES micelles was examined. This study showed that the addition of nanoparticles improved the thermal stability of VES micellar structures in CaBr2 and CaCl2 brines up to 275°F and showed an improved viscosity yield at different shear rates. Micro- and nanoparticles have potential to improve the viscosity of VES fluids. Lab tests show that for VES micellar systems without nanoparticles, the dominant factor is the storage modulus but when nanoparticles are added to the system at 275°F the loss modulus becomes the dominant factor. These positive effects of nanoparticles on VES fluid characteristics suggest that these particles can reduce treatment cost and will exceed temperature range to 275°F. With this work, we hope to have better understanding of nanoparticle/viscoelastic surfactant interaction.

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