Multigrid, An Alternative Method for Calculating Film Thickness and Pressure Profiles in Elastohydrodynamically Lubricated Line Contacts

1986 ◽  
Vol 108 (4) ◽  
pp. 551-556 ◽  
Author(s):  
A. A. Lubrecht ◽  
W. E. ten Napel ◽  
R. Bosma
Keyword(s):  
Film Thickness ◽  
Multigrid Method ◽  
Computing Time ◽  
Alternative Method ◽  
Pressure Profiles ◽  
Minimum Film Thickness ◽  
Line Contacts ◽  
Pressure Spike ◽  
Order Of Magnitude

Film thickness and pressure profiles have been calculated for line contacts at moderate and high loads, using a Multigrid method. Influence of the compressibility of the lubricant on the minimum film thickness and on the pressure spike has been examined. The required computing time is an order of magnitude less than when using the previous methods.

Multigrid, an Alternative Method of Solution for Two-Dimensional Elastohydrodynamically Lubricated Point Contact Calculations

1987 ◽  
Vol 109 (3) ◽  
pp. 437-443 ◽  
Author(s):  
A. A. Lubrecht ◽  
W. E. ten Napel ◽  
R. Bosma
Keyword(s):  
Film Thickness ◽  
Iterative Methods ◽  
Multigrid Method ◽  
Computing Time ◽  
Point Contact ◽  
Two Dimensional ◽  
Point Contacts ◽  
Pressure Profiles ◽  
Minimum Film Thickness ◽  
Method Of Solution

Detailed and accurate film thickness and pressure profiles have been calculated for point contacts at moderate and high loads, using a multigrid method. The influence of the compressibility of the lubricant and of the number of nodal points on the calculated minimum film thickness and maximum spike pressure have been examined. The required computing time is two orders of magnitude less, compared with the calculations using “classical” iterative methods.

Thermal Non-Newtonian Elastohydrodynamic Lubrication of Rolling Line Contacts

1991 ◽  
Vol 113 (3) ◽  
pp. 481-491 ◽  
Author(s):  
H. Salehizadeh ◽  
N. Saka
Keyword(s):  
Film Thickness ◽  
Contact Region ◽  
Elastohydrodynamic Lubrication ◽  
Pressure Profile ◽  
Shear Stresses ◽  
Hertz Contact ◽  
Minimum Film Thickness ◽  
Line Contacts ◽  
Pressure Spike ◽  
Heavy Loads

The two-dimensional thermal elastohydrodynamic equations were numerically solved for a Ree-Eyring type lubricant under pure rolling conditions. Profiles of lubricant pressure, film thickness, and temperature were obtained for medium to heavy loads and moderate to high rolling speeds. The pressure results generally show a small secondary peak near the outlet, but at the highest load considered no pressure spike is obtained and the pressure profile is almost Hertzian. The film thickness results show an increase in minimum film thickness with increasing rolling speeds, but at a lesser rate than those predicted for a Newtonian fluid under isothermal conditions. It is found that unless the lubricant becomes non-Newtonian in the inlet region, the reduction in minimum film thickness at high rolling speeds is completely due to thermal effect. The lubricant temperature profile and the amount of heat generated and dissipated in the contact region were also calculated. The lubricant temperature reaches a maximum just before the entrance to the Hertz contact region. Both shear and compression heating are found to be important in raising the lubricant temperature in the inlet. As the lubricant enters the Hertz contact zone, the temperature first drops rapidly, because of the rapid heat conduction to the rollers, and then remains almost constant for most of the Hertz contact. Near the exit where the pressure gradients are large, the lubricant temperature drops rapidly below the ambient because of lubricant expansion. The lubricant then heats up rapidly before leaving the contact area as a result of heat generated by shear stresses.

Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part III—Fully Flooded Results

1977 ◽  
Vol 99 (2) ◽  
pp. 264-275 ◽  
Author(s):  
B. J. Hamrock ◽  
D. Dowson
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Load Parameter ◽  
Mineral Oils ◽  
Minimum Film Thickness ◽  
Pressure Spike ◽  
Contour Plots ◽  
Order Of Magnitude ◽  
Speed Parameter ◽  
Ellipticity Parameter

Utilizing the theory developed by the authors in an earlier publication, the influence of the ellipticity parameter, the dimensionless speed, load, and material parameters on minimum film thickness was investigated. The ellipticity parameter was varied from one (a ball on a plate configuration) to eight (a configuration approaching a line contact). The dimensionless speed parameter was varied over a range of nearly two orders of magnitude. The dimensionless load parameter was varied over a range of one order of magnitude. Conditions corresponding to the use of solid materials of bronze, steel, and silicon nitride and lubricants of paraffinic and naphthenic mineral oils were considered in obtaining the exponent in the dimensionless material parameter. Thirty-four different cases were used in obtaining the minimum film thickness formula given below as H¯min=3.63U0.68G0.49W−0.073(1−e−0.68k) A simplified expression for the ellipticity parameter was found where k=1.03RyRx0.64 Contour plots were also shown which indicate in detail the pressure spike and two side lobes in which the minimum film thickness occurs. These theoretical solutions of film thickness have all the essential features of the previously reported experimental observations based upon optical interferometry.

Simple Formulas for Performance Parameters Used in Elastohydrodynamically Lubricated Line Contacts

1989 ◽  
Vol 111 (2) ◽  
pp. 246-251 ◽  
Author(s):  
Ping Pan ◽  
B. J. Hamrock
Keyword(s):  
Film Thickness ◽  
Curve Fitting ◽  
Center Of Pressure ◽  
Operating Parameters ◽  
Performance Parameters ◽  
Practical Applications ◽  
Line Contacts ◽  
Pressure Spike

The film thickness and pressure in elastohydrodynamically lubricated conjunctions have been evaluated numerically for a rather complete range of operating parameters (dimensionless load, speed, and materials parameters) normally experienced in practical applications. From the film thickness and pressure throughout the conjunction a number of performance parameters were evaluated. By curve fitting the data, formulas were obtained that allow easy evaluation of the amplitude and location of the pressure spike, the minimum and central film thicknesses, the value of ρeHe, and the center of pressure.

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.

Thermal Elastohydrodynamic Lubrication of Axially Crowned Rollers

2021 ◽  
pp. 1-21
Author(s):  
Wassim Habchi
Keyword(s):  
Film Thickness ◽  
Design Parameter ◽  
Numerical Study ◽  
Elastohydrodynamic Lubrication ◽  
Negative Influence ◽  
Reference Case ◽  
Critical Design ◽  
Lubrication Performance ◽  
Minimum Film Thickness ◽  
Line Contacts

Abstract This work presents a comprehensive numerical study of thermal elastohydrodynamic lubrication performance in axially crowned rollers, based on a full-system finite element approach. Axial crowning has always been introduced to finite line contacts, as a mean for improving film thickness. Its influence on friction has often been overlooked though. The current work reveals that axial crowning has a negative influence on friction, increasing it significantly with respect to the reference case of straight rollers. It is shown that, with increased crowning height (or reduced crowning radius), minimum film thickness is increased, but so is friction. Therefore, film thickness enhancement comes at the expense of a deterioration in friction. Besides, achieving sufficient enhancements in minimum film thickness would require using relatively low crowning radii, which would lead to a substantial increase in friction. The frictional increase is traced back to an overall increase in contact pressures and effective contact area within the lubricating conjunction. It is also shown that, when film thickness is the most critical design parameter, the best compromise between enhanced film thickness and deteriorated friction would be to combine axial crowning with roller-end profiling. However, when friction is the most critical design parameter, a simple roller-end profiling would offer the best compromise.

An Efficient Algorithm for Thermal Elastohydrodynamic Lubrication Under Rolling/Sliding Line Contacts

1994 ◽  
Vol 116 (4) ◽  
pp. 762-769 ◽  
Author(s):  
Chao-Ho Hsu ◽  
Rong-Tsong Lee
Keyword(s):  
Film Thickness ◽  
Thermal Loading ◽  
Reduction Factor ◽  
Difference Approximation ◽  
Central Difference ◽  
Integration Algorithm ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Line Contacts ◽  
Thermal Ehl

One of the most time-consuming routines in thermal EHL problem is the calculation of the surface temperature integral. Combining the multigrid technique and the Newton-Raphson method, a modified multilevel, multi-integration algorithm for this integral is developed that can reduce the computational complexity from O (n2) to O (n ln n) for the thermal EHL problem of rolling/sliding line contacts. The employed standard central difference approximation to the coupled Reynolds and energy equations can yield the maximum difference of mass flow flux within one percent. Effects of dimensionless load, dimensionless materials parameter, slip ratio, and thermal loading parameter on the minimum film thickness are investigated. Correlation formula of thermal reduction factor for the minimum film thickness is derived for a wide range of slip ratios, loads, thermal loading parameters, and materials parameters.

New equations for enhanced film thickness in line contacts under pressurized ambient conditions

2016 ◽  
Vol 231 (5) ◽  
pp. 616-622 ◽  
Author(s):  
Niraj Kumar ◽  
Punit Kumar
Keyword(s):  
Film Thickness ◽  
Ambient Pressure ◽  
Elastohydrodynamic Lubrication ◽  
Viscosity Coefficient ◽  
Ambient Conditions ◽  
Alternative Approach ◽  
Film Forming ◽  
Highly Sensitive ◽  
Minimum Film Thickness ◽  
Line Contacts

An elastohydrodynamic lubrication model is proposed for line contacts under pressurized ambient conditions often encountered in hydraulic pumps, submarine machinery and many other submerged systems. It has been demonstrated that the film forming behavior under such conditions is essentially different from that in conventional elastohydrodynamic lubrication contacts. The numerical simulation results are regressed to develop new central and minimum film thickness equations for Newtonian fluids as functions of ambient pressure, speed, load, and material parameters. An alternative approach is also discussed which involves the use of existing film thickness formulas with ambient viscosity and pressure–viscosity coefficient pertaining to the desired pressure range. A film thickness enhancement of more than 100% over conventional elastohydrodynamic lubrication case is observed. This enhancement is shown to be highly sensitive to the pressure–viscosity coefficient. Besides, the effect of shear-thinning behavior is also investigated and it is found to lower the film thickness enhancement, especially at high ambient pressures.

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