Lundberg형 프로파일의 원통형 로울러의 탄성유체윤활 해석

In this article, the problem of predicting the film thickness in so-called narrow or slender elliptic contacts is revisited. In particular, the variation of the minimum film and central film thickness and their ratio with load and ellipticity are studied. It is shown that the minimum film tends to decrease linearly with increasing ellipticity. The central film thickness, until a certain threshold, decreases very slowly, and then decreases linearly too, with a slope independent of the Hertzian pressure. The ratio central to minimum film thickness is not a constant and varies strongly with ellipticity and load conditions. In this article, it is shown that the ratio of central to minimum film thickness is a linear function of a single nondimensional parameter which has the physical meaning of the ratio of the length of the inlet pressure sweep to the relative width of the contact. Results for narrow contacts published in the engineering literature when represented as a function of this parameter exhibit the same trend. The behaviour is the consequence of the same unifying mechanism that, in the last decade, was discovered to determine aspects of behaviour in elasto-hydrodynamically lubricated (EHL) contacts under time varying conditions, such as surface waviness deformation. For these problems, the single parameter dependence facilitated the development of simple engineering tools (e.g. to predict the roughness deformation). The observation in this article that the ratio central to minimum film thickness is also governed by this parameter opens new perspectives to develop a simple computational engineering tool to predict central and minimum film thickness in EHL contacts.

Recently developed colorimetric interferometry technique was used for the study of both minimum and central film thicknesses for a wide range of operating parameters. Over 300 film thickness maps were obtained for the combination of four values of the materials parameter G, five values of the load parameter W and many values of the speed parameter U. The use of a spacer layer extended the range of film thickness measurement down to 5 nm. An excellent agreement was found between experimental values and data obtained from numerical solution presented by Venner and ten Napel, especially for thin lubrication films. An increase in a speed exponent with increasing material parameter G was observed for both central and minimum film thicknesses. The minimum film thickness and, thereby, the ratio between central and minimum film thickness was confirmed to be of a stronger dependence on material and load dimensionless parameters than Hamrock and Dowson equations predict. Presented at the 54th Annual Meeting Las Vegas, Nevada May 23–27, 1999

Numerical analysis is performed to study the transient behavior of EHL finite line contact of a cylindrical roller and flat plane under load impulse. In the present work, effect of pressure on the density and viscosity of lubricant is considered. Finite difference method is used to discretize the governing equations. Multilevel Multi-integration method is used to calculate the elastic deformation. Moreover, Multigrid method is implemented to accelerate the convergence process. Uniqueness of this finite line contact analysis is that it provides an ability to determine the transient behavior of lubricated contact even at the edges of roller. Results show that the load impulse causes squeezing and separation movement within the contact that develops film dimple and pressure ripples at the inlet region, which propagate towards the exit region due to the entrainment motion. It is noticed that the time taken by oil film [Formula: see text] to travel the Hertzian contact width and the time period [Formula: see text] of load impulse decides the behavior of lubricated contacts. Firstly, under a relatively heavy load when the contact width is large enough so that [Formula: see text], then a significant rise in central film thickness (CFT), central minimum film thickness (CMFT) and minimum film thickness (MFT) occurs after the execution of load impulse. Further, under the light load generating a relatively small contact width such that [Formula: see text], then comparatively a small rise in CFT occurs right during the load impulse. Lastly, for a given load if the time period of impulse [Formula: see text] is large enough satisfying the condition [Formula: see text], then a considerable reduction in CFT, CMFT and MFT takes place during the application of load impulse. Moreover, as compare to other cases, for [Formula: see text] the steady state condition is reestablished after a relatively more number of time cycles. It is observed that the maximum pressure and MFT occurs at the contact edges of roller which can be controlled by a proper choice of the radius of end profile [Formula: see text].

Minimum, central and average film thicknesses have been calculated for the isothermal E.H.L. point contact case, for a variety of load, rolling speed, and material parameters. The equations governing this problem were solved using a Multigrid method. This technique offers the possibility to work with a very fine grid, obtaining detailed and accurate solutions, at the cost of moderate cpu times and storage requirements, on medium size computers. Computations for low loads, requiring a large inlet zone, have been carried out using local grid refinements. The fluid in these calculations is assumed to be compressible and its viscosity-pressure behavior is described by either the Roelands equation, or the Barus equation. The ratio between the calculated minimum film thickness and the central value varied with the parameters governing the problem, but for low loads, a value of 3/4 was obtained. The film thickness behavior at these low loads can be accurately described in terms of the minimum film thickness. For higher loads, however, a description based on a film thickness, averaged over the Hertzian contact, is more appropriate to be compared with the asymptotic solution (Ertel, Grubin).

In this research, a rigid ball impacting on an elastic half-space with lubricant in between is modeled by using the transient modified Reynolds equation, which considers the coupled effects of Navier-slip and flow rheology, the ball motion equation, and the deformation equations. In the impact-plasto-elastohydrodynamic lubrication (PEHL) point contact problems, the deformation mechanism consists of the elastic deformation based on linear elasticity, and the plastic deformation based on the flow rule and hardening model, as the von Mises stress is greater than the yield strength. The elastic-perfectly plastic (EPP) model is used first for basic studies, and the linear hardening model is used for further discussion. The impact-elastohydrodynamic lubrication (impact-EHL) model overestimates the central pressure, impact load, and minimum film thickness, while underestimating central film thickness and the position of minimum film thickness occurrence as compared to the present results from the impact-plasto-elastohydrodynamic lubrication (PEHL) model. As the slip length increases or the flow index decreases, the central film thickness decreases. For shear-thickening fluid (n > 1), the effects of slip weaken the shear-thickening effects, and make the central film thickness closer to that of a Newtonian fluid without slip. The effects of slip on the pressure distributions seem insignificant due to the force balance, and thus the central pressure and the elastic/plastic deformation. Moreover, the strain-hardening effect shows the inhomogeneous yield strength after one impact.

Tapered roller bearings are widely used in high axial-load and radial-load applications. In this study, a numerical analysis is performed to study a finite line contacts EHL problem between a tapered roller and raceway in tapered roller bearings. Converged solutions are obtained for moderate load and material parameters using a finite difference method with non-uniform grids and the Newton-Raphson method. The contours and sectional plots of pressure distribution and film shape are compared. The pressure distribution and film shapes near both ends of the roller are very different from those in the central part and are transversely asymmetric. The maximum pressure and absolute minimum film thickness always occur at the small end of the roller.

Recent numerical results have indicated that the relationship between the film thickness and the speed may not always follow the simple power law, especially under severe conditions. This paper is aimed at obtaining experimental results at high contact stresses and low speeds to study the thin film behavior. Ultrathin lubricant films were observed at maximum Hertz pressures of 0.52, 1.01, and 1.54 GPa by using an optical test rig. Central and minimum film thickness values were obtained with thin film colorimetric interferometry from chromatic interferograms. The nonlinear behavior of both central and minimum film thicknesses in log-log coordinates was observed as rolling speed and thereby film thickness decreased. This tendency became more obvious at higher contact pressures.

This part is a complimentary work to a previously published work on EHD lubrication behavior under pure sliding and combined rolling and sliding situations. In order to cover all aspects of EHD lubrication, the experimental work has been herein extended to present the results attained when two disks describe a pure rolling motion. A wide range of loads and speeds has been applied to the contacting disks under EHD regimes. The recorded pressure values and distribution confirm the existence of a second peak (spike) near the exit of the contact zone also under pure rolling situation. The spike has a value higher than maximum Hertzian pressure. A local constriction of oil film profile to identify the minimum EHD film thickness at trailing (exit) end of the film is observed to be nearby the location of the pressure spike. The results, compared to theoretical predictions, concluded that under pure rolling conditions, any increase in the applied load results in a corresponding increase in the developed pressure while a noticeable reduction in the minimum film thickness is recorded with decreasing rolling speeds.

Comparison of Exact and Sommerfeld Solution for the Pressure of a Journal Bearing

Experimental study of central and minimum film thickness in elastohydrodynamic elliptic contacts

Analysis of the thermal elastohydrodynamic lubrication of a finite line contact

The lubrication performance of rib/roller end contacts of cylindrical roller bearings was studied both theoretically and experimentally for end-crowned rollers and inclined ribs. A partial EHL program was used to calculate the film thickness and the friction in the rib/roller end contact. Calculated minimum film thickness shows a strong load dependence although the central film thickness is still a weak function of the load. The influence of the contact position on the film thickness was also investigated for roller skewness and design tolerance. It was found that the contact location affects the minimum film thickness strongly in spite of a weak influence on the central film thickness. Friction and scuffing experiments were conducted on a special rig, which can achieve arbitrary slide/roll ratio to simulate the rib/roller end contacts. Good agreements were found between measured and calculated friction based on the assumption that the lubricant was Newtonian. In scuffing experiments, scuffing propagation was observed on the rib contact surface. The critical load for scuffing is strongly correlated with the sliding velocity. The critical load at high speeds is lower than that at low speeds although the friction at high speeds is lower. These data imply the importance of the contact location and the wear process for film breakdown.

Elastohydrodynamic lubrication of line contacts

Hydrodynamics of liquid-liquid two-phase flow accounting for the coupling of dean vortices and Poiseuille flow

The capacitance technique was used to measure the minimum oil film thickness in engine bearing and the central oil film thickness between cam and tappet. This method is based on the measurement of total capacitance of oil film. For the measurement of the oil film thickness between cam and tappet, two surfaces were assumed to be flat and parallel within the Hertzian region and all the measured capacitance originated from this region. Shear rates from the measured minimum oil film thickness are over 10$^{6}$ sec$^{-1}$ in the greater part in both two cases. The minimum oil film thickness in engine bearing is larger than the surface roughness. Between cam and tappet it is mostly smaller than the surface roughness. In spite of the awkward restriction of the reliability of measured oil film thickness, it was known that the capacitance technique makes it possible to measure the oil film thickness in elastohydrodynamic and mixed lubrication regimes as well as in hydrodynamic regime. Therefore, it is also possible to classify the lubrication regimes based on the oil film thickness.