The Elasto-Hydrodynamic Lubrication of Soft, Highly Deformed Contacts Under Conditions of Nonuniform Motion

1986 ◽  
Vol 108 (4) ◽  
pp. 545-550 ◽  
Author(s):  
C. J. Hooke
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Dynamic Analysis ◽  
Hydrodynamic Lubrication ◽  
Steady State Analysis ◽  
Entrainment Velocity ◽  
Sinusoidal Motion ◽  
Minimum Film Thickness ◽  
Rapid Reversal ◽  
Nonuniform Motion

A method is described for the calculation of the film thicknesses in soft, highly deformed contacts for situations where the entrainment velocity is not constant. Two particular results are presented. It is shown that, where there is a rapid reversal of motion, the steady state analysis remains acceptable. However, for a contact reciprocating with a sinusoidal motion, it does not, and here the minimum film thickness occurs at the end of the stroke. The minimum film thickness lies at the end of the contact furthermost from the area swept during the stroke and can only be determined by a dynamic analysis.

EHL Film Thickness Computations at Low Speeds: Risk of Artificial Trends as a Result of Poor Accuracy and Implications for Mixed Lubrication Modelling

2005 ◽  
Vol 219 (4) ◽  
pp. 285-290 ◽  
Author(s):  
C. H. Venner
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Mixed Lubrication ◽  
Validity Of Results ◽  
Erroneous Conclusion ◽  
Low Speeds ◽  
Lubrication Models ◽  
Circular Contact

When numerical and experimental results are compared to validate elasto-hydrodynamic lubrication (EHL) models, it is of utmost importance that grid-converged results are used. In particular at low speeds and high loads, solutions obtained using grids that are not sufficiently dense will exhibit an artificial trend that does not represent the behaviour of the continuous modelling equations. As it coincides with a trend observed in experiments this may lead to the erroneous conclusion that the theoretical model on which the numerical simulations are based is accurate. This risk is illustrated in detail. It is further shown that EHL models based on the Reynolds equation in a steady state circular contact predicts a positive film thickness as long as the grid used in the calculations is sufficiently dense. This has significant implications for the validity of results obtained using mixed lubrication models based on a Reynolds model and a film thickness threshold.

On the crucial role of ellipticity on elastohydrodynamic film thickness and friction

2016 ◽  
Vol 230 (12) ◽  
pp. 1503-1515 ◽  
Author(s):  
J-D Wheeler ◽  
N Fillot ◽  
P Vergne ◽  
D Philippon ◽  
GE Morales Espejel
Keyword(s):  
Film Thickness ◽  
Maximum Pressure ◽  
Fluid Viscosity ◽  
Point Contacts ◽  
Entrainment Velocity ◽  
Minimum Film Thickness ◽  
Elliptical Contact ◽  
Thickness Variations ◽  
Poiseuille Flows

The study reported here deals with elastohydrodynamic point contacts and it is focused on the influence of contact ellipticity. In five velocity–load reference cases, ellipticity was varied from slender to wide configurations, including the circular contact. For each case, Hertzian pressure, Hertzian area, load, and entrainment velocity were kept constant while the ellipticity was varied by changing the curvature radii. In this context, the maximum central film thickness did not occur for the infinitely wide contact, but for a slender configuration close to the circular case. Moreover, the minimum film thickness reached its optimum for a wide but finite elliptical contact. For low ellipticity ratios, specific film thickness features were obtained. In particular, very high central/minimum film thickness ratios are found. The cause of these behaviors was found in the change of the convergent shape. When the ellipticity was varied, the Poiseuille flows parallel and transverse to the entrainment direction were significantly modified and these modifications were quantitatively analyzed for the different cases. The competition between the Couette and the Poiseuille flows was totally different between the narrow and the wide elliptical contact, and this change was responsible for the film thickness variations with ellipticity. Ellipticity also had an effect on friction as it influenced the maximum pressure which in turn impacts the fluid viscosity.

The Minimum Film Thickness in Line Contacts During Reversal of Entrainment

1993 ◽  
Vol 115 (1) ◽  
pp. 191-199 ◽  
Author(s):  
C. J. Hooke
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Rate Of Change ◽  
Radius Of Curvature ◽  
Operating Cycle ◽  
Minimum Film Thickness ◽  
Line Contacts ◽  
Involute Gears ◽  
Shaft Seals ◽  
Steady State Predictions

In contacts, such as cams, non-involute gears and shaft seals, where the direction of entrainment reverses during the operating cycle, the minimum film thickness is typically found just after the reversal. This paper shows that this minimum film thickness is determined by the rate of change of the entraining velocity and by the fluid and surface properties. For line contacts, four regimes of lubrication are found—as for the steady-state situation—and expressions for the film thickness in each regime are developed. This enables an outline design chart for the minimum film thickness to be constructed. It is shown that this information, together with the steady-state predictions is sufficient to determine the variation of film thickness with time in most situations where load, radius of curvature, and entraining velocity vary.

scholarly journals Hydrodynamic Lubrication of Rigid Nonconformal Contacts in Combined Rolling and Normal Motion

1985 ◽  
Vol 107 (1) ◽  
pp. 97-103 ◽  
Author(s):  
M. K. Ghosh ◽  
J. Hamrock ◽  
D. Brewe
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Carrying Capacity ◽  
Hydrodynamic Lubrication ◽  
Normal Velocity ◽  
Load Carrying Capacity ◽  
Velocity Parameter ◽  
Load Carrying ◽  
Geometry Parameter ◽  
Net Load

A numerical solution to the problem of hydrodynamic lubrication of rigid point contacts with an isoviscous, incompressible lubricant has been obtained. The hydrodynamic load-carrying capacity under unsteady (or dynamic) conditions arising from the combined effects of squeeze motion superposed upon the entraining motion has been determined for both normal approach and separation. Superposed normal motion considerably increases net load-carrying capacity during normal approach and substantially reduces net load-carrying capacity during separation. Geometry has also been found to have a significant influence on the dynamic load-carrying capacity. The ratio of dynamic to steady state load-carrying capacity increases with increasing geometry parameter for normal approach and decreases during separation. The cavitation (film rupture) boundary is also influenced significantly by the normal motion, moving downstream during approach and upstream during separation. For sufficiently high normal separation velocity the rupture boundary may even move upstream of the minimum-film-thickness position. Sixty-three cases were used to derive a functional relationship for the ratio of the dynamic to steady state load-carrying capacity β in terms of the dimensionless normal velocity parameter q (incorporating normal velocity, entraining velocity, and film thickness) and the geometry parameter α. The result is expressed in the form β={α−0.028sech(1.68q)}1/q The ratio of the dynamic to steady state peak pressures in the contact ξ increases considerably with increasing normal velocity parameter during normal approach, with a similar decrease during separation. The ratio is expressed as a function of q and α by ξ={α−0.032sech(2q)}1/q

Profile Design for Misaligned Journal Bearings Subjected to Transient Mixed Lubrication

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Thomas Gu ◽  
Q. Jane Wang ◽  
Shangwu Xiong ◽  
Zhong Liu ◽  
Arup Gangopadhyay ◽  
...  
Keyword(s):  
Film Thickness ◽  
Performance Metrics ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
Industrial Applications ◽  
Mixed Lubrication ◽  
Asperity Contact ◽  
Minimum Film Thickness ◽  
Profile Design

Misalignment between the shaft and the bearing of a journal bearing set may be inevitable and can negatively impact journal bearing performance metrics in many industrial applications. This work proposes a convex profile design of the journal surface to help counteract the negative effects caused by such a misalignment. A transient mass-conserving hydrodynamic Reynolds equation model with the Patir–Cheng flow factors and the Greenwood–Tripp pressure–gap relationship is developed to conduct the design and analysis. The results reveal that under transient impulse loading, a properly designed journal profile can help enhance the minimum film thickness, reduce mean and peak bearing frictions, and increase bearing durability by reducing the asperity-related wear load. The mechanism for the minimum film thickness improvement due to the profile design is traced to the more even distribution of the hydrodynamic pressure toward the axial center of the bearing. The reason for the reductions of the friction and wear load is identified to be the decreased asperity contact by changing the lubrication regime from mixed lubrication to nearly hydrodynamic lubrication. Parametric studies and a case study are reported to highlight the key points of the profile design and recommendations for profile height selection are made according to misalignment parameters.

scholarly journals Analysis of Starvation Effects on Hydrodynamic Lubrication in Nonconforming Contacts

1982 ◽  
Vol 104 (3) ◽  
pp. 410-417 ◽  
Author(s):  
D. E. Brewe ◽  
B. J. Hamrock
Keyword(s):  
Film Thickness ◽  
Hydrodynamic Lubrication ◽  
Three Dimensional ◽  
Point Contact ◽  
Sharp Decrease ◽  
Reduction Factor ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Contour Plots ◽  
Starvation Effects

Numerical methods were used to determine the effects of lubricant starvation on the minimum film thickness under conditions of a hydrodynamic point contact. Starvation was effected by varying the fluid inlet level. The Reynolds boundary conditions were applied at the cavitation boundary and zero pressure was stipulated at the meniscus or inlet boundary. The analysis is considered valid for a range of speeds and loads for which thermal, piezoviscous, and deformation effects are negligible. It is applied to a wide range of geometries (i.e., from a ball-on-plate configuration to a ball in a conforming groove). Seventy-four cases were used to numerically determine a minimum-film-thickness equation as a function of the ratio of dimensionless load to dimensionless speed for varying degrees of starvation. From this, a film reduction factor was determined as a function of the fluid inlet level. Further, a starved fully flooded boundary was defined and an expression determining the onset of starvation was derived. As the degree of starvation was increased, the minimum film thickness decreased gradually until the fluid inlet level became critical. Reducing the fluid inlet level still further led to a sharp decrease in the minimum film thickness. An expression determining the critically starved fluid inlet level was derived. The changes in the inlet pressure buildup due to changing the available lubricant supply are presented in the form of three-dimensional isometric plots and also in the form of contour plots.

On Transient EHL of a Skew Roller Subjected to a Load Impact in Rolling Bearings

2017 ◽  
Vol 739 ◽  
pp. 108-119
Author(s):  
Xiao Ling Liu ◽  
Da Tong Song ◽  
Pei Ran Yang
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Transient Condition ◽  
Skew Angle ◽  
Transient Effect ◽  
Outer Race ◽  
Minimum Film Thickness ◽  
Finite Line ◽  
Load Impact

Based on the non-steady state operating condition in machine elements, numerical analysis of a transient elastohydrodynamic lubrication (EHL) finite line contact between a skewed roller and an outer race in cylindrical roller bearings was carried out, and a complete numerical solution of skewed roller pairs EHL under the transient condition was obtained. The effects of the load impact, together with the skewing angle impulses on the lubricating performance of skew roller pairs were discussed. Results show that, different from the steady state, the transient effect of the skew roller lubrication is mainly governed by the skew angle impulse, and the load impact. The film dimple is generated during the load impact, or the skewing angle impulse due to the normal approach velocity of the film. Compared to that of the ideal roller, the minimum film thickness decreases due to the roller skew when the transient load happens. Variation in the skewing angle leads to contrary distribution of the film thickness at the two half parts of the roller. Meanwhile, it can decrease the minimum film thickness and be harmful to the lubrication compared to the steady state. Consequently, the transient effect in the process of lubrication of skew roller pairs should not be neglected.

scholarly journals Analysis of vibration characteristic for helical gear under hydrodynamic conditions

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668796 ◽  
Author(s):  
Fuhao Liu ◽  
Hanjun Jiang ◽  
Liang Zhang ◽  
Li Chen
Keyword(s):  
Film Thickness ◽  
Hydrodynamic Lubrication ◽  
Hysteresis Loops ◽  
Vibration Characteristic ◽  
Nonlinear Dynamic Model ◽  
Helical Gears ◽  
Root Cause ◽  
Minimum Film Thickness ◽  
Hydrodynamic Lubrication Theory ◽  
Driving Torque

Based on the elasto-hydrodynamic lubrication theory, a 2-degree-of-freedom nonlinear dynamic model of helical gears with double-sided film is proposed, in which the minimum film thickness behaves as a function of load parameters, lubricant parameters, and the geometry of the contact. Then, the comparison of the hysteresis loops in different gear models shows the soundness of the presented model. Using numerical method, the time evolution of lubricant normal force, minimum film thickness, and lubricant stiffness is obtained in order to demonstrate the influence of the driving torque and pinion’s velocity. The results obtained in this article can contribute to the root cause for the gear vibration and show that the hydrodynamic flank friction has almost no influence on the gear system.

Information Revelation in Markets with Pairwise Meetings: Complete Revelation in Dynamic Analysis

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Tanguy Isaac
Keyword(s):  
Steady State ◽  
Dynamic Analysis ◽  
Flow Model ◽  
Steady States ◽  
Information Revelation ◽  
Steady State Analysis ◽  
Entry Model ◽  
The One ◽  
State Analysis

We study information revelation in markets with pairwise meetings. We focus on the one-sided case and perform a dynamic analysis of a constant entry flow model. The same question has been studied in an identical framework in Serrano and Yosha (1993) but they limit their analysis to the stationary steady states. Blouin and Serrano (2001) study information revelation in a one-time entry model and obtain different results from the ones of Serrano and Yosha (1993). We establish that the main difference is not due to the steady state analysis but to the differences concerning the entry assumption.

Numerical investigation on single dent in EHL point contacts

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Qiancheng Qin ◽  
Xue-Feng Wang ◽  
Rufu Hu ◽  
Xiaomin Cheng
Keyword(s):  
Film Thickness ◽  
Maximum Pressure ◽  
Point Contacts ◽  
Governing Equations ◽  
Content Type ◽  
Entrainment Velocity ◽  
Minimum Film Thickness ◽  
Input Parameters ◽  
Pressure Peak ◽  
Lubricating Properties

Purpose This study aims to investigate the effects of single dent on the film thickness and pressure in elastohydrodynamically lubricated (EHL) point contacts by numerical analysis. Design/methodology/approach The governing equations of single dent were established and then the variations of the film thickness and pressure induced by the applied load, the entrainment velocity and the ball radius were investigated. Meanwhile, the film thickness and pressure under smooth and dented surfaces were compared with each other. Findings The dent enhances both the maximum pressure and the second pressure peak. The minimum film thickness arises before the dent under certain conditions. In the meantime, the pressure decreases at the inside of the dent and the film thickness is just the reverse. The entrainment velocity remarkably affects the overall film thickness, whereas the rest of the input parameters mainly decides the details of the film curve. All input parameters remarkably affect the overall pressure, especially the maximum pressure. Originality/value This work is helpful to understanding the effect of the single dent on the lubricating properties of EHL point contacts.

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