A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts. I. Direction of lubricant entrainment coincident with the major axis of the Hertzian contact ellipse

1985 ◽  
Vol 397 (1813) ◽  
pp. 245-269 ◽  
Keyword(s):  
Film Thickness ◽  
Flow Direction ◽  
Elastohydrodynamic Lubrication ◽  
Analytical Techniques ◽  
Major Axis ◽  
Minor Axis ◽  
Hertzian Contact ◽  
Limited Information ◽  
Wide Range ◽  
Contact Ellipse

Engineers have known since the last century that a substantial film of lubricant must be present at the contact between gear teeth. However, it is only in the last twenty-five years that analytical techniques have developed to the extent where theoretical predictions of film thickness are in accord with experience. This has come about through the in­ corporation in analysis of the effects of elastic distortion of the solids and the enhancement of lubricant viscosity due to pressure. Formulae for the prediction of both minimum and central film thickness in con­centrated contacts such as those occurring in gear sets, rolling element bearings and cam and follower arrangements are now available to designers. Elastohydrodynamic analyses have almost entirely been restricted to the case of pure rolling in which the direction of lubricant entrainment has coincided with the minor axis of the Hertzian contact ellipse. While such analyses are indeed satisfactory for a wide range of practical configurations, there are situations for which the effects of flow direction have not been adequately explored. For example, in the roller-rib contacts in cylindrical and taper roller bearings and in the conjunctions occurring in high conformity gearing, a more reasonable approximation to the geometric configuration would be to consider the lubricant entraining vector to be parallel to the major axis of the contact ellipse. More generally in helical, spiral bevel and hypoid gearing the lubricant entrainment may be at an angle to the minor axis of the Hertzian ellipse. Part I of the present paper presents a study of the case where lubricant entrainment coincides with the line of the major axis of the contact ellipse, while part II addresses the more general case of an arbitrary flow direction. Seventy-two new solutions to the problem of the elastohydrodynamic lubrication of concentrated contacts with rolling along a principal axis have been computed. In part I of the paper thirty-three of these solutions are presented for lubricant entrainment in the direction of the major axis of the contact ellipse. These latter solutions therefore extend the range of geometrical configurations considered previously by B. J. Hamrock and D. Dowson, whose design predictions are widely used at present. New expressions for the calculation of minimum and central film thickness are presented, which enable the prediction with confidence of these quantities for the case when the lubricant entraining vector coincides with the major axis of the Hertzian contact ellipse. Comparison of the very extensive data presented in the paper with the limited information available from previous relevant studies is undertaken. In addition the major features distinguishing the new solutions for those previously computed are identified. It is expected that the results of the study will enable the lubricant film thickness to be predicted with increased confidence for a wide range of machine elements.

A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts. II. General case, with lubricant entrainment along either principal axis of the Hertzian contact ellipse or at some intermediate angle

1985 ◽  
Vol 397 (1813) ◽  
pp. 271-294 ◽  
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Major Axis ◽  
Hertzian Contact ◽  
Analysis And Design ◽  
Principal Axes ◽  
Wide Range ◽  
Central Regions ◽  
Machine Elements ◽  
Initial Objective

The initial objective of the work reported in this paper was the development of generalized representations of film thickness results for elastohydrodynamic conjunctions in which lubricant entrainment coincided with one of the principal axes of the Hertzian conjunction. Some 106 solutions have been considered, including 33 presented in part I for entrainment along the major axis, four further solutions of a similar kind, the 34 solutions presented by Hamrock & Dowson ( J. lubr. Technol . 98, 264-276 (1977)) for entrainment along the minor axis and 35 new solutions for similar geometries. It has been shown that normalization of the principal parameters in terms of the curvature in the direction of lubricant entrainment, 1/ R e , permits the display of both central and minimum film thickness values as functions of the ratio of the radii of the solids normal to, and in the direction of, lubricant entrainment. These continuous curves enable film thickness to be predicted over a very wide range of geometrical configurations, but valid empirical expressions for both central and minimum dimensionless film thickness have also been developed. The second major feature of the study was to develop elastohydrodynamic solutions for the non-symmetrical conditions encountered when the lubricant entraining vector did not coincide with either of the principal axes of the conjunction. Such solutions are more representative of the conditions encountered in certain machine elements than the symmetrical solutions already reported. Examples of the resulting nonsymmetrical pressure distributions, elastic deformations and film shapes are presented. It is shown that normalization in terms of the curvature in the direction of lubricant entrainment, and the use of a simple trigonometric function, enables both the central and minimum film thicknesses to be predicted for any entrainment angle. It is demonstrated that this comprehensive and generalized presentation of new and previous solutions to the elastohydrodynamic lubrication problem for elliptical conjunctions yields film thickness predictions that compare very well indeed with specific solutions reported earlier. It is further shown that the central film thickness is little affected by the orientation of the lubricant entraining vector for many ellipsoidal solids, but that the minimum film thicknesses encountered cover a much wider range of values. In many cases the minimum film thicknesses occur in side-lobes located near the lateral boundaries of the Hertzian conjunction, which perform a sealing role and thus permit the generation of near-Hertzian hydrodynamic pressures in the central regions of the conjunction. The results are expected to provide a basis for the analysis and design of a wide range of machine elements operating in the elastohydrodynamic régime of lubrication.

Elastohydrodynamic Film Thickness in Concentrated Contacts: Part 1: Experimental Investigation for Lubricant Entrainment Aligned with the Major Axis of the Contact Ellipse

1986 ◽  
Vol 200 (3) ◽  
pp. 207-217 ◽  
Author(s):  
R J Chittenden ◽  
D Dowson ◽  
C M Taylor
Keyword(s):  
Experimental Investigation ◽  
Film Thickness ◽  
Major Axis ◽  
Lubricant Film ◽  
Capacitance Measurement ◽  
Experimental Investigations ◽  
Lubricant Film Thickness ◽  
Wide Range ◽  
Experimental Apparatus ◽  
Contact Ellipse

Experimental investigations of the lubricant film thickness generated in elastohydrodynamic elliptical contacts have been undertaken since the early 1960s. The majority of these studies has been concerned with circular or near circular contact situations, although a wide range of geometries in which lubricant entrainment was directed along the minor axis of the contact ellipse has also been considered. The information available on lubricant film thickness in geometrical conditions where lubricant entrainment was aligned with the major axis of the contact ellipse has, however, been severely limited. The experimental investigation described in this paper is therefore concerned with the measurement of lubricant film thickness in the unusual geometrical conditions recently analysed theoretically by the authors (1, 2). The measurements were made with the aid of a twin disc machine for geometries ranging from a radius ratio of unity down to a value of 0.112. The experimental apparatus is described and details are given of the special test discs which were manufactured to produce such geometries. The capacitance measurement technique adopted is detailed along with the numerical model developed to allow the measured values of inter-disc capacitance to be interpreted in terms of the lubricant film thickness. The lubricant film thickness developed in four geometrical situations was investigated at four rotational speeds and five loads. This allowed a comparison to be made with the film thickness values predicted by recent elastohydrodynamic theory for changes in both speed and load. The film thickness deduced from the capacitance measurements was considered to be representative of that found at the centre of contact, and good agreement was found between experiment and all aspects of the theoretical predictions.

On the Surface Dimple Phenomena in Elliptical TEHL Contacts With Arbitrary Entrainment

2002 ◽  
Vol 125 (1) ◽  
pp. 102-109 ◽  
Author(s):  
Jing Wang ◽  
Peiran Yang ◽  
Motohiro Kaneta ◽  
Hiroshi Nishikawa
Keyword(s):  
Temperature Distribution ◽  
Theoretical Analysis ◽  
Film Thickness ◽  
Frictional Coefficient ◽  
Elastohydrodynamic Lubrication ◽  
Minor Axis ◽  
Hertzian Contact ◽  
Intermediate Angle ◽  
Minimum Film Thickness ◽  
Good Agreement

Theoretical analysis and optical interferometry experiments are performed to investigate the dimple phenomena in thermal elastohydrodynamic lubrication (TEHL) of elliptical contacts under pure sliding conditions. The lubricant entrainment is along the major and minor axes of the Hertzian contact ellipse or at some intermediate angle. Good agreement is achieved between theoretical and experimental results and the surface dimple phenomena occurring in glass-steel conjunctions are explained by the temperature-viscosity wedge mechanism. The influence of the angle between the minor axis and the entrainment vector on the position and shape of the dimple, the central and minimum film thickness, the temperature distribution and the frictional coefficient is discussed.

A Starved Mixed Elastohydrodynamic Lubrication Model for the Prediction of Lubrication Performance, Friction and Flash Temperature With Arbitrary Entrainment Angle

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Wei Pu ◽  
Dong Zhu ◽  
Jiaxu Wang
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Industrial Applications ◽  
Operating Conditions ◽  
Flash Temperature ◽  
Machined Surface ◽  
Lubrication Performance ◽  
Wide Range ◽  
Starved Lubrication

In this study, a modified mixed lubrication model is developed with consideration of machined surface roughness, arbitrary entraining velocity angle, starvation, and cavitation. Model validation is executed by means of comparison between the obtained numerical results and the available starved elastohydrodynamic lubrication (EHL) data found from some previous studies. A comprehensive analysis for the effect of inlet oil supply condition on starvation and cavitation, mixed EHL characteristics, friction and flash temperature in elliptical contacts is conducted in a wide range of operating conditions. In addition, the influence of roughness orientation on film thickness and friction is discussed under different starved lubrication conditions. Obtained results reveal that inlet starvation leads to an obvious reduction of average film thickness and an increase in interasperity cavitation area due to surface roughness, which results in significant increment of asperity contacts, friction, and flash temperature. Besides, the effect of entrainment angle on film thickness will be weakened if the two surfaces operate under starved lubrication condition. Furthermore, the results show that the transverse roughness may yield thicker EHL films and lower friction than the isotropic and longitudinal if starvation is taken into account. Therefore, the starved mixed EHL model can be considered as a useful engineering tool for industrial applications.

Analysis of EHL Circular Contact Shut Down

2002 ◽  
Vol 125 (1) ◽  
pp. 76-90 ◽  
Author(s):  
Jiaxin Zhao ◽  
Farshid Sadeghi
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Contact Area ◽  
Elastohydrodynamic Lubrication ◽  
Hertzian Contact ◽  
Analytical Prediction ◽  
Transient Pressure ◽  
Mean Velocity ◽  
Thickness Change ◽  
Contact Width

In this paper, an isothermal study of the shut down process of elastohydrodynamic lubrication under a constant load is performed. The surface mean velocity is decreased linearly from the initial steady state value to zero. The details of the pressure and film thickness distributions in the contact area are discussed for the two stages of shut down process, namely the deceleration stage and the subsequent pure squeeze motion stage with zero entraining velocity. The nature of the balance between the pressure, the wedge and the squeeze terms in Reynolds equation enables an analytical prediction of the film thickness change on the symmetry line of the contact in the deceleration period, provided that the steady state central film thickness relationship with velocity is known. The results indicate that for a fixed deceleration rate, if the initial steady state surface mean velocity is large enough, the transient pressure and film thickness distributions in the deceleration period solely depend on the transient velocity. The pressure and film thickness at the end of the deceleration period are then the same and do not depend on the initial steady state velocity. From the same initial steady state velocity, larger deceleration rates provide higher central pressure increase, but also preserve a higher film thickness in the contact area at the end of the deceleration period. Later in the second stage when the axisymmetric pressure and film thickness patterns typical of pure squeeze motion form, the pressure distribution in the contact area resembles a Hertzian contact pressure profile with a higher maximum Hertzian pressure and a smaller Hertzian half contact width. As a result, the film thickness is close to a parabolic distribution in the contact area. The volume of the lubricant trapped in the contact area is then estimated using this parabolic film thickness profile.

Effects of Differential Scheme and Mesh Density on EHL Film Thickness in Point Contacts

2006 ◽  
Vol 128 (3) ◽  
pp. 641-653 ◽  
Author(s):  
Yuchuan Liu ◽  
Q. Jane Wang ◽  
Wenzhong Wang ◽  
Yuanzhong Hu ◽  
Dong Zhu
Keyword(s):  
Film Thickness ◽  
Numerical Solution ◽  
System Approach ◽  
Elastohydrodynamic Lubrication ◽  
Mesh Size ◽  
Point Contacts ◽  
Wide Range ◽  
Mesh Density ◽  
Differential Scheme

This paper investigates the effects of differential scheme and mesh density on elastohydrodynamic lubrication (EHL) film thickness based on a full numerical solution with a semi-system approach. The solution variation with different schemes and mesh sizes is revealed based on a set of numerical cases in a wide range of central film thickness from several hundred nanometers down to a few nanometers. It is observed that when the film is thick, the effects of differential schemes and mesh density are not significant. However, if the film becomes ultra-thin, e.g., below 10–20 nanometers, the influence of mesh density and differential schemes becomes more significant, and a proper dense mesh and differential scheme may be highly desirable. The present study also indicates that the solutions from the 1st-order backward scheme give the largest film thickness among all the solutions from different schemes at the same mesh size.

The Elastohydrodynamic Lubrication of Elliptical Point Contacts Operating in the Isoviscous Region

1995 ◽  
Vol 209 (4) ◽  
pp. 225-234 ◽  
Author(s):  
C J Hooke
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Radius Ratio ◽  
Point Contacts ◽  
Reasonable Estimate ◽  
Wide Range ◽  
Minimum Film Thickness

The elastohydrodynamic lubrication of point contacts is examined and results for the minimum film thickness are presented for a wide range of radius ratios and operating conditions. The results are compared with the predictions of the appropriate regime formulae. Although these formulae give a reasonable estimate of the contact's behaviour, the actual clearances are often substantially different, particularly close to the regime boundaries. Interpolation equations for seven values of radius ratio are given and these should be sufficient to allow the minimum clearance to be estimated for most isoviscous point contacts.

Effects of Surface Roughness and Surface Force on the Thin Film Elastohydrodynamic Lubrication of Circular Contacts

2012 ◽  
Vol 67 (6-7) ◽  
pp. 412-418
Author(s):  
Li-Ming Chu ◽  
Jaw-Ren Lin ◽  
Jiann-Lin Chen
Keyword(s):  
Thin Film ◽  
Surface Roughness ◽  
Film Thickness ◽  
Contact Region ◽  
Load Condition ◽  
Elastohydrodynamic Lubrication ◽  
Surface Force ◽  
Surface Forces ◽  
Hertzian Contact ◽  
Deformation Equation

The effects of surface roughness and surface force on thin film elastohydrodynamic lubrication (TFEHL) circular contact problems are analyzed and discussed under constant load condition. The multi-level multi-integration (MLMI) algorithm and the Gauss-Seidel iterative method are used to simultaneously solve the average Reynolds type equation, surface force equations, the load balance equation, the rheology equations, and the elastic deformation equation. The simulation results reveal that the difference between the TFEHL model and the traditional EHL model increase with decreasing film thickness. The effects of surface forces become significant as the film thickness becomes thinner. The surface forces have obvious effects in the Hertzian contact region. The oscillation phenomena in pressure and film thickness come mainly from the action of solvation forces

Elastohydrodynamic Film Thickness in Concentrated Contacts: Part 2: Correlation of Experimental Results with Elastohydrodynamic Theory

1986 ◽  
Vol 200 (3) ◽  
pp. 219-226 ◽  
Author(s):  
R J Chittenden ◽  
D Dowson ◽  
C M Taylor
Keyword(s):  
Film Thickness ◽  
Experimental Studies ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Experimental Results ◽  
Experimental Techniques ◽  
Dimensionless Parameters ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Computational Procedures

The existence of a coherent film of lubricant between highly loaded machine elements has been recognized for many years. Over this period of time measurements of film thickness have gone hand in hand with theoretical analyses in the field now known as elastohydrodynamic lubrication. The experimental techniques of capacitance, electrical resistance and X-ray measurement have been supplemented by the use of optical interferometry while the analytical expressions obtained with the use of elegant simplifications have been superseded by those developed from extensive and comprehensive computational procedures. These developments in experimental techniques have yielded a substantial number of measurements of both minimum and central film thickness. Likewise, the advent of the digital computer has allowed the derivation of a large number of solutions to the problem of elastohydrodynamic lubrication of concentrated contacts. All these results, covering a wide range of geometrical conditions, are to be found in the literature, yet little attempt appears to have been made to assemble a representative set of experimental data to permit a detailed evaluation of the theoretical formulae for elliptical contacts. The second part of this paper therefore considers the correlation between a number of experimental studies covering a wide range of operating conditions and geometries, and the predictions of recent elastohydrodynamic theory. Some of the important aspects of each set of experimental results are then considered and examples are provided which illustrate the following points: 1. Good estimates of lubricant film thickness may be obtained from the theoretical expressions recently derived, even when the dimensionless parameters involved are outside the ranges considered in the derivation of the formulae. 2. The discrepancies which exist between theoretical predictions and some of the measured film thicknesses are nevertheless quite large, even when the dimensionless parameters are within their usual limits. On the whole there is good agreement between experiment and theory, while the general trend of the results indicates that theoretical predictions may underestimate the minimum film thickness by about 10 per cent and the central film thickness by about 25 per cent. This measure of agreement is quite remarkable when the extreme difficulty of interpreting the magnitudes of effective and very thin mean film thicknesses between machined components in various forms of experimental equipment is considered.

Elastohydrodynamic Lubrication Analysis of Conjugate Meshing Face Gear Pairs

2012 ◽  
Vol 57 (3) ◽  
pp. 1-10 ◽  
Author(s):  
Zihni B. Saribay ◽  
Robert C. Bill ◽  
Edward C. Smith ◽  
Suren B. Rao
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Gear Tooth ◽  
Elastohydrodynamic Lubrication ◽  
Transmission Efficiency ◽  
Hertzian Contact ◽  
Maximum Efficiency ◽  
Gear Pair ◽  
Face Gear ◽  
Fixed Axis

This paper investigates the nominal elastohydrodynamic lubrication (EHL) characteristics of the conjugate meshing face gears and predicts the mesh efficiency of the pericyclic transmission system. The meshing face-gear tooth geometries and meshing kinematics are modeled. Hertzian contact and the isothermal non-Newtonian lubricant film characteristics of the meshing face-gear pair are investigated. The friction coefficient is calculated with the effects of lubricant behavior and mesh kinematics. Finally, the pericyclic transmission efficiency is calculated as a function of friction coefficient, mesh loads, and mesh kinematics. The Hertzian contact behavior, film thickness, and friction coefficient values are simulated for an example fixed axis face-gear pair rotating at 1000 rpm with 3.4 kN-m torque. The EHL film thickness ranges from 0.1 to 0.25 μm in this example. The average friction coefficient is predicted as 0.05. The efficiencies of three different 24:1 reduction ratio 760 HP pericyclic transmission designs are investigated. The minimum and maximum efficiency in the given design space are 97% and 98.7%, respectively.

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