Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

Influence of lubricant properties on elastohydrodynamic lubrication

In this paper, a recent solution on the thermal-elastohydrodynamic lubrication of rolling and sliding cylinders is extended to consider a more rigorous analysis of temperature by using a two-dimensional finite difference method. The effect of the local pressure-temperature dependent viscosity, the compressibility effect of the lubricant and the heat from compression of the lubricant are considered in the solution of the Reynolds and the energy equations. Two series of results were obtained. The first is a heavily loaded series intended to correlate with Crook's experimental results, and the second is a moderately loaded series intended to correlate with experimental data (15). These results show that temperature has a moderate influence upon the shape of the pressure and film profile, but very little effect upon the magnitude of the film thickness in the contact zone. The frictional force, however, is strongly influenced by the temperature rise in the film. Crook's experimental film thickness data and tho...

A Refined Solution to the Thermal-Elastohydrodynamic Lubrication of Rolling and Sliding Cylinders

The theory of partial elastohydrodynamic contacts

There is currently considerable debate concerning the most appropriate rheological model to describe the behaviour of lubricant films in rolling–sliding, elastohydrodynamic contacts. This is an important issue since an accurate model is required to predict friction in such contacts. This paper reviews the origins of this debate, which primarily concerns a divergence of views between researchers using high pressure, high shear rate viscometry and those concerned with the measurement and analysis of elastohydrodynamic friction; the former advocate a Carreau-based shear stress/strain rate model while the latter generally favour an Eyring-based one. The crucial importance of accounting for shear heating effects in analysing both viscometric and friction data is discussed. The main criticisms levied by advocates of a Carreau-based model against Eyring’s model are discussed in some detail. Finally, the ability of both types of rheological model to fit elastohydrodynamic friction measurements for a quite simple, well-defined base fluid is tested, using previously measured pressure–viscosity behaviour for the fluid. Both models appear to fit the experimental data over a wide temperature range quite well, though fit of the Eyring model appears slightly closer than that of the Carreau–Yasuda model. Friction data from a wider range of well-defined fluid types are needed to identify categorically the most appropriate model to describe elastohydrodynamic friction.

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History, Origins and Prediction of Elastohydrodynamic Friction

The Rheological Behavior of the Lubricant in the Contact Zone of a Rolling Contact System

Two methods have been evolved for finding pressure distributions in lubricating rolling contact. In the first method, the circumferential profile of the gap between rolling disks is found by using an X-ray technique, and the pressures are inferred from the observed deformations of the disks. Several profiles have been obtained for a range of loadings, temperatures, and rolling speeds by using steel disks with polyphenyl ether as the lubricant, and plausible (though not greatly detailed) pressure distributions were derived from some of them. The second method uses a strip of manganin coaling on a glass disk which is loaded into lubricated, rolling contact with a second glass disk. The change in electrical resistance of the manganin due to film pressures is measured. The data recorded by this technique also appear to be reasonably reproducible and consistent. Presented as an American Society of Lubrication Engineers paper at the Lubrication Conference held in Washington, D. C, October 13–16, 1964.

Methods for Determining Pressure Distributions in Lubricated Rolling Contact

The thickness of the film formed by each of five lubricants between a pair of disks in rolling contact has been measured by an X-ray technique for a range of loads (80,000 to 225,000 psi maximum Hertz stress), two temperatures (178 F and 250 F), and three speeds (4300 fpm to 9100 fpm). An empirical formula fitted to the X-ray data shows a much higher sensitivity of film thickness to load than is normally predicted. In order to judge whether the measurements themselves are at fault, the X-ray measuring process has been reexamined for accuracy, especially where load-dependent errors might arise. Some weaknesses are noted, such as in the amount of X-ray absorption, but these should not affect load sensitivity greatly. New experiments designed to find effects of imperfect collimation of X-rays indicate that reflection of X-rays may be significant, but these effects too do not seem to account for the anomalies of the film thickness measurements.

Interpretations of the Thickness of Lubricant Films in Rolling Contact. 1. Examination of Measurements Obtained by X-Rays

Ball bearing lubrication simulation by rolling disk apparatus, emphasizing surface slip and related thermal effects alterable by geometric expansion

J. C. Bell

Papers

The Rheological Behavior of the Lubricant in the Contact Zone of a Rolling Contact System

Methods for Determining Pressure Distributions in Lubricated Rolling Contact

Interpretations of the Thickness of Lubricant Films in Rolling Contact. 1. Examination of Measurements Obtained by X-Rays

Simulation of Ball-Bearing Lubrication With a Rolling-Disk Apparatus

Interpretations of the Thickness of Lubricant Films in Rolling Contact. 2. Influence of Possible Rheological Factors