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.

Effect of Rolling Velocity and Maximum Hertzian Pressure on Fluid Film in Steady State EHL Line Contact with Rough Surface and Linear Piezoviscosity

2014 ◽  
Vol 592-594 ◽  
pp. 1371-1375
Author(s):  
Nitesh Talekar ◽  
Punit Kumar
Keyword(s):  
Surface Roughness ◽  
Steady State ◽  
Film Thickness ◽  
Rough Surface ◽  
Computer Code ◽  
Fluid Film ◽  
Line Contact ◽  
Rolling Velocity ◽  
Load Carrying ◽  
Lubricated Contact

Consideration of surface roughness in steady state EHL line contact is the first step towards understanding the lubrication of rough surface problem. Current paper investigates the use of sinusoidal waviness in the contact; more precisely it gives performance of real fluid in EHL line contact. The effect of various parameters like rolling velocity (U) and maximum Hertzian pressure (ph) on surface roughness by using properties of linear and exponential piezo-viscosity is taken into consideration to evaluate behavior of pressure distribution of load carrying fluid film and film thickness. Full isothermal, Newtonian simulation of EHL problem gives described effects. Spiking or fluctuation of pressure and film thickness curves is expected to show presence of irregularities on the surface chosen and amount of fluctuation depends on certain parameters and intensity of irregularities present. Rolling side domain of-4.5 ≤ X ≤ 1.5 with grid size ∆X=0.01375 is selected. A computer code is developed to solve Reynolds equation, which governs the generation of pressure in the lubricated contact zone is discritized and solved along with load balance equation using Newton-Raphson technique.

Film Thickness and Friction Investigations in a Fluid Film Thrust Bearing Employing A New Conceived Micro-Texture on Pads

2020 ◽  
Vol 143 (6) ◽  
Author(s):  
J. C. Atwal ◽  
R. K. Pandey
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Mass Conservation ◽  
Fluid Film ◽  
Element Formulation ◽  
Algebraic Equations ◽  
Pocket Depth ◽  
Lubricating Film ◽  
Minimum Film Thickness ◽  
Radial Length

Abstract This paper presents the performance behaviors (coefficient of friction, minimum film thickness, and pressure distributions) of a fluid film thrust bearing using a newly conceived micro-texture on pads. In the numerical investigation, the Reynolds equation has been discretized using the finite element formulation followed by the solution of algebraic equations employing the Fischer-Burmeister-Newton-Schur (FBNS) algorithm, which satisfies the mass-conservation phenomenon arising due to the commencement of cavitation in the lubricating film. The effects of parameters (micro-texture/pocket depth, circumferential/radial length of micro-texture and pocket, etc.) of new texture on the performance behaviors of the thrust bearing have been explored and presented herein for the range of input data. It has been found that the minimum film thickness has increased up to 48%, and the friction coefficient reduced up to 24% in comparison to conventional plain pad case.

Study on curved surface design of sliding pair based on stepped topography model

2019 ◽  
Vol 72 (1) ◽  
pp. 86-92 ◽  
Author(s):  
Zhenpeng Wu ◽  
Vanliem Nguyen ◽  
Zhihong Zhang ◽  
Liangcai Zeng
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Liquid Film ◽  
Bearing Capacity ◽  
Fluid Film ◽  
Curved Surface ◽  
Surface Model ◽  
Content Type ◽  
Lubrication Performance ◽  
Minimum Film Thickness

Purpose The stepped topography of the friction pairs mainly causes the fluid film thickness to change in the direction of motion. In this region, there have very few topographical design methods for continuous or non-linear distribution of the fluid film. The purpose of this study is to analyze the effect of the curved surface on the performance of the liquid film. Design/methodology/approach First, a numerical simulation is used to solve the optimal bearing capacity and friction coefficient of the liquid film under the condition of the minimum film thickness. Then, the curved surface described by the sinusoidal curve equation is applied in the transitional region of maximum and minimum film thickness. The bearing capacity and the friction coefficient of the liquid film are respectively simulated and compared in the same condition of the minimum film thickness. Findings The research results show that the liquid film using the curved surface transition model, the optimal bearing capacity is significantly increased by 32 per cent while the optimal friction coefficient is clearly reduced by 38 per cent in comparison with using stepped surface model. Originality/value The friction pair with curved transition enables better lubrication performance of the liquid film and better adaptability under unstable conditions.

An Analytical Solution for the Normal Load Carrying Capacity of Lightly Loaded Cylinders in Combined Rolling, Sliding and Normal Motion

1981 ◽  
Vol 103 (3) ◽  
pp. 467-468 ◽  
Author(s):  
T. F. Conry
Keyword(s):  
Analytical Solution ◽  
Film Thickness ◽  
Exponential Function ◽  
Carrying Capacity ◽  
Normal Load ◽  
Load Capacity ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Minimum Film Thickness

The analytical solution for the normal load carrying capacity of lightly loaded cylinders in combined rolling, sliding and normal motion is obtained. It is shown that the load capacity is inversely proportional to the dimensionless minimum film thickness. The results are presented graphically and approximated in the form of an exponential function.

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.

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.

Increase of Operational Safety of Tilting-Pad Journal Bearings by Extraction of Hot Oil at the Trailing Edge

2015 ◽  
Author(s):  
Sebastian Kukla ◽  
Nico Buchhorn ◽  
Beate Bender
Keyword(s):  
Film Thickness ◽  
Carrying Capacity ◽  
Maximum Temperature ◽  
Load Carrying Capacity ◽  
Trailing Edge ◽  
Tilting Pad ◽  
Load Carrying ◽  
Operational Safety ◽  
Minimum Film Thickness ◽  
Safety Parameters

A theoretical study is presented with the main objective on the operational safety parameters (minimum film thickness and maximum pad temperature) and thermomechanical deformations of a ø500 mm rocker pad tilting-pad journal bearing (TPJB) for application in large turbo machinery. It can be described by the following specifications: Five pads, 0.23 nominal preload, 60% offset, 56° pad arc angle, 350 mm pad length and 1.28‰ relative bearing clearance. Theoretical investigations are carried out for circumferential speeds up to 78 m/s and static loads up to 3.60 MPa. The simulation tool simultaneously solves both Reynolds and energy equations for the oil film (3D temperature distribution) on the one hand and computes thermomechanical deformations of the pad on the other hand. The simulations are conducted for a single pad and are supported by boundary conditions taken from experiments. The results with regard to static bearing characteristics and pad deformation show good agreement with experiments. The impact of axial pad arching on operational safety parameters and load-carrying capacity are shown and compared to experimental results. It is shown that the axial deviation in film thickness Δh can be even higher than the minimum film thickness hmin. This leads to reduced hydrodynamic pressure build-up towards the axial edges and therefore significantly decreased safety parameters or load-carrying capacity. In order to reduce pad crowning, radial bores through the pad body are modelled to simulate the extraction of hot oil from the trailing edge. In the simulation, the hot oil is used to heat up the back of the pad for a decrease of radial temperature gradients and thus pad arching. It is shown that by extracting 0.4 l/s of hot oil, a decrease in axial pad crowning from Δh = 47μm to Δh = 26μm can be achieved and that this leads to a decrease of 7.8 K in maximum temperature and an increase of 5 μm in minimum film thickness respectively a gain of load-carrying capacity of 0.4–0.6 MPa.

A Demonstrably Optimum One Dimensional Journal Bearing

1972 ◽  
Vol 94 (2) ◽  
pp. 188-192 ◽  
Author(s):  
S. M. Rohde
Keyword(s):  
Film Thickness ◽  
Carrying Capacity ◽  
Journal Bearing ◽  
Infinite Length ◽  
Load Carrying Capacity ◽  
One Dimensional ◽  
Load Carrying ◽  
Minimum Film Thickness ◽  
Constant Viscosity ◽  
Nonlocal Formulation

By the use of a new variational technique, the bearing profile which maximizes the load carrying capacity of an infinite length journal bearing is obtained. The lubricant is assumed to be incompressible and of constant viscosity. The flow is assumed to be laminar and the optimization is based upon a minimum film thickness. The solution obtained is a concentric step bearing with a film thickness ratio of 1.812 and a ridge to pad ratio of 0.328. It is mathematically shown by the use of the “nonlocal” formulation that this step profile does yield a maximum among all profiles sufficiently “close.”

The Minimum Film Thickness in Lubricated Line Contacts during a Reversal of Entrainment—General Solution and the Development of a Design Chart

1994 ◽  
Vol 208 (1) ◽  
pp. 53-64 ◽  
Author(s):  
C J Hooke
Keyword(s):  
Film Thickness ◽  
Rate Of Change ◽  
Operating Conditions ◽  
Radius Of Curvature ◽  
Velocity Change ◽  
Surface Separation ◽  
Residual Film ◽  
Minimum Film Thickness ◽  
Line Contacts ◽  
Interpolation Procedure

In most line contacts the load, effective radius of curvature and entraining velocity change with time. Generally this is ignored when calculating the film thickness and a quasi-steady solution is obtained. Under most conditions the errors introduced by this are either small or are not critical. However, when the entraining velocity reverses, as, for example, in some designs of cams, the quasi-steady approach predicts that the film thickness will be zero. In practice a residual film persists and can provide adequate surface separation. Previous papers by the author have shown that the minimum film thickness at entrainment reversal depends on the rate of change of the entraining velocity. Expressions for the film thickness in the four regimes of lubrication—rigid isoviscous, rigid piezoviscous, elastic isoviscous and elastic piezoviscous—were obtained and the variations of the film thickness in the transitions between adjacent regimes examined. The present paper examines the region where more than two regimes overlap. The values of film thickness obtained are then used to develop an interpolation procedure for the accurate calculation of the minimumfilm thickness under all operating conditions.

Improvement of lubrication performance of water lubricated polymer bearing via enlarged axial end bearing diameter

2019 ◽  
Vol 71 (4) ◽  
pp. 564-572
Author(s):  
Fangrui Lv ◽  
Donglin Zou ◽  
Na Ta ◽  
Zhu-Shi Rao
Keyword(s):  
Film Thickness ◽  
Carrying Capacity ◽  
Load Carrying Capacity ◽  
Content Type ◽  
Lubrication Performance ◽  
Load Carrying ◽  
Minimum Film Thickness ◽  
The Impact ◽  
Polymer Bearing ◽  
Practical Implications

Purpose The purpose of this paper is to improve the lubrication performance of a water-lubricated polymer bearing with axial grooves, especially enlarge the minimum film thickness. Design/methodology/approach The bearing diameter is enlarged near the axial ends of the journal, with axial openings of a trumpet shape. A numerical model is developed which considers the proposed trumpet-shaped openings, bush deformation and grooves. The generatrix of the trumpet-shaped opening is assumed to be a paraboloid. Three different variations are covered, and the influences of the trumpet-shaped openings’ parameters on the bearing performance are analyzed. Findings The appropriate trumpet-shaped openings at the axial ends effectively increase the minimum film thickness, and the impact of trumpet-shaped openings on load carrying capacity is very small or even negligible. For the water-lubricated polymer bearing with axial grooves analyzed in this paper, the appropriate trumpet-shaped openings increase the minimum film thickness from 0.53 to 11.14 µm and decrease the load carrying capacity by 2.48 per cent. Practical implications The results of this study can be applied to marine propeller shaft systems and other systems with polymer bearings. Originality/value This paper has presented an approach for significantly increasing the minimum film thickness of a water-lubricated polymer bearing. A study on the performance improvement of water-lubricated polymer bearings with axial grooves is of significant interest to the research community.

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