scholarly journals Effect of Geometry on Hydrodynamic Film Thickness

1979 ◽  
Vol 101 (2) ◽  
pp. 231-237 ◽  
Author(s):  
D. E. Brewe ◽  
B. J. Hamrock ◽  
C. M. Taylor
Keyword(s):  
Film Thickness ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Exact Expression ◽  
Geometry Effect ◽  
Load Dependence ◽  
Viscosity Effects ◽  
Minimum Film Thickness ◽  
Contour Plots

The influence of geometry on the isothermal hydrodynamic film separating two rigid solids was investigated. Pressure-viscosity effects were not considered. The minimum film thickness is derived for fully flooded conjunctions by using the Reynolds boundary conditions. It was found that the minimum film thickness had the same speed, viscosity, and load dependence as Kapitza’s classical solution. However, the incorporation of Reynolds boundary conditions resulted in an additional geometry effect. Solutions using the parabolic film approximation are compared with those using the exact expression for the film in the analysis. Contour plots are shown that indicate in detail the pressure developed between the solids.

scholarly journals Elastohydrodynamic Film Thickness Model for Heavily Loaded Contacts

1974 ◽  
Vol 96 (3) ◽  
pp. 472-479 ◽  
Author(s):  
S. H. Loewenthal ◽  
R. J. Parker ◽  
E. V. Zaretsky
Keyword(s):  
Film Thickness ◽  
Measured Data ◽  
Type Ii ◽  
X Ray ◽  
Polyphenyl Ether ◽  
Load Dependence ◽  
Test Conditions ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Thickness Measurements

An empirical elastohydrodynamic (EHD) film thickness formula for predicting the minimum film thickness occurring within heavily loaded contacts (maximum Hertz stresses above 1.04 × 109 N/m2 (150,000 psi)) was developed. The formula was based upon X-ray film thickness measurements made with synthetic paraffinic, fluorocarbon, Type II ester and polyphenyl ether fluids covering a wide range of test conditions. Comparisons were made between predictions from an isothermal EHD theory and the test data. The deduced relationship was found to adequately reflect the high-load dependence exhibited by the measured data. The effects of contact geometry, material and lubricant properties on the form of the empirical model are also discussed.

Film Thickness, Friction, and Scuffing Failure of Rib/Roller End Contacts in Cylindrical Roller Bearings

1992 ◽  
Vol 114 (2) ◽  
pp. 311-316 ◽  
Author(s):  
H. Aramaki ◽  
H. S. Cheng ◽  
D. Zhu
Keyword(s):  
Film Thickness ◽  
Critical Load ◽  
Strongly Correlated ◽  
Wear Process ◽  
Load Dependence ◽  
Roller Bearings ◽  
High Speeds ◽  
Lubrication Performance ◽  
Minimum Film Thickness ◽  
Cylindrical Roller

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.

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.

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.

Boundary Conditions of a Viscous Flow Between Surfaces With Rolling and Sliding Motion

1968 ◽  
Vol 90 (1) ◽  
pp. 254-261 ◽  
Author(s):  
N. Tipei
Keyword(s):  
Film Thickness ◽  
Boundary Conditions ◽  
Fluid Motion ◽  
Fluid Film ◽  
Radius Of Curvature ◽  
Physical Conditions ◽  
Sliding Motion ◽  
Load Carrying ◽  
Minimum Film Thickness ◽  
Whole Space

The fluid motion between surfaces with different radii of curvature and velocities is studied, assuming that the viscous fluid is carried by the solid surfaces but does not fill up the whole space. The boundary conditions at the inlet are examined in connection with those at the outlet of the fluid film. It is shown that only a part of the fluid carried by the surfaces, depending on the velocities and the initial rates of flow ratio, penetrates into the contact zone. Thus an interpretation of the flow field is proposed, differering from the usually assumed shape of the streamlines, by assuming the existence of a counterflow at the inlet. By using some physical conditions in various representative situations, as well as an equilibrium condition for the vortex flow, the real quantity of fluid and the entry and exit points are determined. Thereafter, the film extent, pressure distribution, load-carrying capacity, and minimum film thickness are obtained. Tables are given with the characteristic angles of the fluid film as functions of the minimum film thickness-radius of curvature ratio. The calculated values are in a satisfactory agreement with the experiments of other authors, especially when using the Prandtl-Hopkins conditions at the outlet.

Elastohydrodynamic Lubrication of Elliptical Contacts for Materials of Low Elastic Modulus: II—Starved Conjunction

1979 ◽  
Vol 101 (1) ◽  
pp. 92-98 ◽  
Author(s):  
B. J. Hamrock ◽  
D. Dowson
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Rolling Direction ◽  
Numerical Procedure ◽  
Elastohydrodynamic Lubrication ◽  
Radius Of Curvature ◽  
Low Elastic Modulus ◽  
Minimum Film Thickness ◽  
Contour Plots ◽  
Lubrication Conditions

By using the theory and numerical procedure developed by the authors in earlier publications, the influence of lubricant starvation upon minimum film thickness in starved elliptical elastohydrodynamic conjunctions for low-elastic-modulus materials has been investigated. Lubricant starvation was studied simply by moving the inlet boundary closer to the center of the conjunction. The results show that the location of the dimensionless inlet boundary m* between the fully flooded and starved conditions can be expressed simply as m* = 1 + 1.07 [(Rx/b)2Hmin,F]0.16, where Rx is the effective radius of curvature in the rolling direction, b is the semiminor axis of the contact ellipse, and Hmin,F is the dimensionless mimimum film thickness for the fully flooded condition. That is, for a dimension-less inlet distance m less than m*, starvation occurs; and for m ≥ m*, a fully flooded condition exists. Furthermore, it has been possible to express the minimum film thickness for a starved condition as Hmin,S = Hmin,F [(m − 1)/(m* − 1)]0.22. Contour plots of the pressure and film thickness in and around the contact are presented for both the fully flooded and starved lubrication conditions. It is evident from the contour plots that the inlet pressure contours become less circular and that the film thickness decreases substantially as the severity of starvation increases. The results presented in this report, when combined with the findings previously reported, enable the essential features of starved, elliptical, elastohydrodynamic conjunctions for materials of low elastic modulus to be ascertained.

Elastohydrodynamic Lubrication of Elliptical Contacts for Materials of Low Elastic Modulus I—Fully Flooded Conjunction

1978 ◽  
Vol 100 (2) ◽  
pp. 236-245 ◽  
Author(s):  
Bernard J. Hamrock ◽  
Duncan Dowson
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Pressure Distribution ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Low Elastic Modulus ◽  
Minimum Film Thickness ◽  
Contour Plots ◽  
Order Of Magnitude ◽  
Ellipticity Parameter

Our earlier studies of elastohydrodynamic lubrication of conjunctions of elliptical form are applied to the particular and interesting situation exhibited by materials of low elastic modulus. By modifying the procedures we outlined in an earlier publication, the influence of the ellipticity parameter k and the dimensionless speed U, load W, and material G parameters on minimum film thickness for these materials has been investigated. The ellipticity parameter was varied from 1 (a ball-on-plate configuration) to 12 (a configuration approaching a line contact). The dimensionless speed and load parameters were varied by 1 order of magnitude. Seventeen different cases were used to generate the following minimum- and central-film-thickness relations: H˜min=7.43(1−0.85e−0.31k)U0.65W−0.21H˜c=7.32(1−0.72e−0.28k)U0.64W−0.22 Contour plots are presented that illustrate in detail the pressure distribution and film thickness in the conjunction.

Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part IV—Starvation Results

1977 ◽  
Vol 99 (1) ◽  
pp. 15-23 ◽  
Author(s):  
B. J. Hamrock ◽  
D. Dowson
Keyword(s):  
Film Thickness ◽  
Numerical Procedure ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
Contact Center ◽  
Minimum Film Thickness ◽  
Pressure Spike ◽  
Contour Plots

Utilizing the theory and numerical procedure developed by the authors in an earlier publication the influence of lubricant starvation on minimum film thickness was investigated. This study of lubricant starvation was performed simply by moving the inlet boundary closer to the contact center. From the results it was found that for the range of conditions considered the value of dimensionless inlet distance at the boundary between fully flooded and starved conditions (m*) can be expressed simply as m*=1+3.06Rxb2Hc,F0.58 or m*=1+3.34Rxb2Hmin,F0.56 that is, for a dimensionless inlet distance (m) less than m*, starvation occurs, and for m ≥ m*, a fully flooded condition exists. Furthermore, it has been possible to express the central and minimum film thickness for a starved condition as Hc,S=Hc,Fm−1m*−10.29Hmin,S=Hmin,Fm−1m*−10.25 Contour plots of the pressure and film thickness in and around the contact are shown for the fully flooded and starved lubricant condition. From these contour plots it was observed that the pressure spike becomes suppressed and the film thickness decreases substantially as starvation increases.

Predictive tool for frictional performance of piston ring-pack/liner conjunction

2019 ◽  
Vol 13 (3) ◽  
pp. 5513-5527
Author(s):  
J. W. Tee ◽  
S. H. Hamdan ◽  
W. W. F. Chong
Keyword(s):  
Film Thickness ◽  
Mathematical Models ◽  
Piston Ring ◽  
Published Data ◽  
Predictive Tool ◽  
Frictional Losses ◽  
Fundamental Understanding ◽  
Minimum Film Thickness ◽  
Piston Ring Pack ◽  
Ring Pack

Fundamental understanding of piston ring-pack lubrication is essential in reducing engine friction. This is because a substantial portion of engine frictional losses come from piston-ring assembly. Hence, this study investigates the tribological impact of different piston ring profiles towards engine in-cylinder friction. Mathematical models are derived from Reynolds equation by using Reynolds’ boundary conditions to generate the contact pressure distribution along the complete piston ring-pack/liner conjunction. The predicted minimum film thickness is then used to predict the friction generated between the piston ring-pack and the engine cylinder liner. The engine in-cylinder friction is predicted using Greenwood and Williamson’s rough surface contact model. The model considers both the boundary friction and the viscous friction components. These mathematical models are integrated to simulate the total engine in-cylinder friction originating from the studied piston ring-pack for a complete engine cycle. The predicted minimum film thickness and frictional properties from the current models are shown to correlate reasonably with the published data. Hence, the proposed mathematical approach prepares a simplistic platform in predicting frictional losses of piston ring-pack/liner conjunction, allowing for an improved fundamental understanding of the parasitic losses in an internal combustion engine.

Sinusoidal Three-Lobe Bearings—Optimization and Stability Charts

1980 ◽  
Vol 102 (4) ◽  
pp. 416-424 ◽  
Author(s):  
W. E. ten Napel ◽  
R. Bosma
Keyword(s):  
Film Thickness ◽  
Stability Parameters ◽  
Stability Regions ◽  
Damping Coefficients ◽  
Optimum Position ◽  
Minimum Film Thickness ◽  
Stiffness And Damping

In contradistinction to the commonly used segmented three-lobe bearing, another type of bearing, i.e., the sinusoidal three-lobe bearing has been investigated in this paper. The main advantage of this bearing is that it can very easily be manufactured. Special attention has been paid to problems of optimization with regard to minimum film thickness and friction, respectively. Stiffness and damping coefficients have been calculated as well as stability regions and stability parameters. Additionally, the optimum position of the oil grooves has been investigated.

Sign in / Sign up

Export Citation Format

Share Document