Combined Effects of Thermal and Non-Newtonian Character of Lubricant on Pressure, Film Profile, Temperature Rise, and Shear Stress in E.H.L.

1987 ◽  
Vol 109 (4) ◽  
pp. 666-670 ◽  
Author(s):  
S. H. Wang ◽  
H. H. Zhang
Keyword(s):  
Temperature Rise ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Hydrodynamic Lubrication ◽  
Lubrication Equation ◽  
Minimum Film Thickness ◽  
The Coefficient Of Friction ◽  
Shape Equation ◽  
Rheological Character ◽  
Film Profile

A derivation of the lubrication equation suitable for nonlinear rheological model is presented. Full numerical solutions coupling the lubrication equation with film shape equation and energy equation are obtained to reveal the combined influence of thermal and non-Newtonian character of lubricant on elasto-hydrodynamic lubrication. Results show that the minimum film thickness is influenced only slightly in general. Nevertheless, the spikes of pressure and temperature rise, and the coefficient of friction are strongly affected by the rheological character of lubricant. It is concluded that both the temperature rise and non-Newtonian character of the oil film should be considered in E.H.L. analysis in order to obtain reliable results.

A Rapid Method of Numerical Calculation for Oil Film Temperature in Engine Bearings

2007 ◽  
Author(s):  
Katsuhiro Ashihara ◽  
Hiromu Hashimoto
Keyword(s):  
Numerical Calculation ◽  
Film Thickness ◽  
Rapid Method ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Hydrodynamic Lubrication ◽  
Dimensional Model ◽  
Calculation Time ◽  
Oil Film ◽  
3 Dimensional

In the design and analysis of engine bearings for automobiles, the elastic deformation of bearing surface due to high pressure and temperature of oil film affects significantly on the bearing characteristics. Thermo-elasto-hydrodynamic lubrication analysis (TEHL) is usually used to consider such effects, but a large amount of calculation time is needed to obtain the numerical solution of oil film temperature by solving the conventional type of 3-dimensional energy equation in TEHL. This paper describes a rapid method of numerical calculation of oil film temperature in engine bearings. In this modeling, it is assumed that the temperature distribution in the oil film thickness direction takes the parabolic form. Under such an assumption, averaging the 3-dimensional energy equation over the film thickness, the 2-dimensional energy equation is newly obtained. The numerical solutions of oil film temperature based on the 2-dimensional model are compared with the solutions based on the 3-dimensional model. It is confirmed that the calculation time is remarkably reduced to obtain the oil film temperature with an allowable accuracy. Moreover, the predicted oil film temperature by the 2-dimentional model is compared with measured data, and the good agreement is seen between them.

The Optimum Slider Bearing in Terms of Friction

1972 ◽  
Vol 94 (3) ◽  
pp. 275-279 ◽  
Author(s):  
S. M. Rohde
Keyword(s):  
Variational Method ◽  
Film Thickness ◽  
Variational Formulation ◽  
Slider Bearing ◽  
One Dimensional ◽  
First Case ◽  
Minimum Film Thickness ◽  
The Coefficient Of Friction ◽  
Constant Viscosity ◽  
Film Profile

The film profile which minimizes the coefficient of friction and the film profile which minimizes the total friction force for a given load for a one-dimensional slider bearing are determined using a variational method. The lubricant is assumed to be incompressible and of constant viscosity. The flow is assumed to be laminar, and the optimization in the first case is based upon an assumed minimum film thickness. It is shown by the use of the nonlocal variational formulation that these profiles do yield a minimum among all admissible profiles.

Influence of new surface micro-structures on the performance behaviours of fluid film tilting pad thrust bearings

2021 ◽  
pp. 095440622110309
Author(s):  
JC Atwal ◽  
RK Pandey
Keyword(s):  
Mass Conservation ◽  
Performance Parameters ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Thrust Bearings ◽  
Lubrication Equation ◽  
Tilting Pad ◽  
Minimum Film Thickness ◽  
Newton Raphson ◽  
Micro Structures

Performance parameters such as power loss, minimum film thickness, and maximum oil temperature of the sector-shaped tilting pad thrust bearings employing the new micro-structural geometries on pad surfaces have been investigated. The lubrication equation incorporating the mass-conservation issue is discretized using the finite element method and the solution of resulting algebraic equations is obtained employing a Newton-Schur method. The pad equilibrium in the analysis is established using the Newton-Raphson and Braydon methods. The influence of attributes of micro-structures such as depth, circumferential and radial positioning extents have been explored on the performance behaviours. It is found that with the new micro-structured pad surfaces, the performance parameters significantly improved in comparison to conventional plain and conventional rectangular pocketed pads.

Hydrodynamic Lubrication of Pocket Bearings and Effect of Contouring the Inner and Outer Regions, and Optimum Design Data

1989 ◽  
Author(s):  
C. Bagci ◽  
C. J. McClure ◽  
S. K. Rajavenkateswaran
Keyword(s):  
Optimum Design ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Load Flow ◽  
Temperature Dependent Viscosity ◽  
Design Data ◽  
Planar Surfaces ◽  
Friction Factors ◽  
The Coefficient Of Friction ◽  
Dependent Viscosity

Abstract The article investigates pocket bearings with contoured profiles of exponential forms on both surfaces inside and outside of the step boundary forming hydro-dynamic action surfaces, and develops optimum design data yielding efficient slider bearings with small pockets with higher load capacities than conventional pocket bearings. In the case of a pocket bearings, in addition to the Reynolds equation used for the regions inside and outside the pocket, the continuity equation along the pocket boundary is satisfied to form the complete model of the bearing. The optimum design data includes dimensionless load-, flow-, temperature rise-, power loss-, stiffness-, and the coefficient of friction factors. Incompressible lubricant with temperature dependent viscosity is considered. Detailed study of conventional pocket bearings with planar surfaces is included. Some optimum exponential pocket bearings yield up to 561 percent increase in load capacity as compared to the conventional tapered bearings.

An Averaging Technique for the Analysis of Rough Surface High Bearing Number Gas Flows

1999 ◽  
Vol 121 (2) ◽  
pp. 333-340 ◽  
Author(s):  
James W. White
Keyword(s):  
Surface Roughness ◽  
Rough Surface ◽  
Numerical Solutions ◽  
Scale Effects ◽  
Wavy Surface ◽  
Universal Property ◽  
Flying Height ◽  
Lubrication Equation ◽  
Product Term ◽  
Bearing Number

Earlier analytical solutions by White (1980, 1983, 1992, 1993) included Couette effects, transverse diffusion, and mass storage in a model lubrication equation for narrow width wavy surface high bearing number gas films. The model lubrication equation did not include longitudinal diffusion effects due to the high bearing number restriction. Crone et al. (1991), however, reported numerical solutions of the full Reynolds equation for a gimbal mounted slider subject to wavy surface roughness. The first objective of this work is to reconcile the differences observed between the reported results of White and those of Crone et al. for moving and stationary roughness. The second objective is to describe how to best apply what appears to be a universal property of a high bearing number gas film subjected to a rough surface. Each solution of the model lubrication equation by White (1980, 1983, 1992, 1993) produced a product term based on local gas pressure and clearance (Z = Ph) that is independent of roughness details but which is dependent on the statistical properties of the roughness. In the present work, this characteristic is treated as a universal property of all high bearing number rough surface gas films. The product variable Z = Ph is introduced into the generalized full lubrication equation, and the resulting lubrication equation is ensemble averaged before a solution is attempted. This removes the short length and time scale effects due to the surface roughness. Solution of the ensemble averaged equation for Z(x, y, t) then follows by standard analytical or numerical methods. The unaveraged pressure is then given by P(x, y, t) = Z(x, y, t)/h(x, y, t) and the ensemble averaged or mean pressure at a point is computed from Pm(x, y, t) = Z(x, y, t)E(1/h(x, y, t)), where E(1/h) represents the ensemble average of 1/h. Using this technique, numerical solutions of the full generalized lubrication equation based on kinetic theory were obtained for a low flying gimbal mounted slider. Results indicate that the nominal flying height increases and the minimum flying height decreases as surface roughness increases.

scholarly journals Theoretical and Experimental Investigations on Transient Run-Up Procedures of Journal Bearings Including Mixed Friction Conditions

Lubricants ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 105 ◽  
Author(s):  
Maximilian Prölß ◽  
Hubert Schwarze ◽  
Thomas Hagemann ◽  
Philipp Zemella ◽  
Philipp Winking
Keyword(s):  
Experimental Data ◽  
Energy Equation ◽  
Hydrodynamic Lubrication ◽  
Frictional Coefficient ◽  
Journal Bearings ◽  
Numerical Code ◽  
Experimental Investigations ◽  
Lubrication Regime ◽  
Mixed Friction ◽  
Run Up

This paper focuses on the operating behavior of journal bearings for industrial machinery application during run-ups. For this purpose, a numerical simulation code that is based on a two-dimensional extended and generalized Reynolds equation and a full three-dimensional energy equation, was advanced by a theoretical model considering the effects of mixed friction and warming of journal components during start-up. The mixed friction routine contained the elastic half-spaces model proposed by Boussinesq, which considers the influence of rough surfaces by implementing flow factors and calculates additional stiffness and dissipation in areas with solid interactions. Furthermore, a transient term was added in the energy equation to consider the thermal inertia of journal, and bearing to ensure a realistic heating during run-ups. Results of the prediction were compared to experimental data taken from a special test rig built up for validation procedures. Besides the conventional sensors for temperature, oil flow, and relative motion between shaft and stator, a contact voltage measurement was installed to determine the intensity of mixed friction. The evaluation of experimental data by Stribeck curves, based on a shaft torsion measurement, indicated a significant influence of run-up time on frictional moment. The friction coefficient of the rotor bearing system was strongly influenced by the run-up time. A short run-up time reduced the frictional coefficient in the mixed lubrication regime while the opposite behavior was observed in the hydrodynamic lubrication regime. The numerical code predicted these tendencies in good agreement with experimental data, however, only if the transient energy model was applied.

Analysis of Heat Conduction in a Heterogeneous Material by a Multiple-Scale Averaging Method

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
James White
Keyword(s):  
Heat Conduction ◽  
Thermal Energy ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Scale Effects ◽  
Three Dimensional ◽  
Heterogeneous Material ◽  
Multiple Scale ◽  
Computational Effort ◽  
Short Scale

In order to better manage computational requirements in the study of thermal conduction with short-scale heterogeneous materials, one is motivated to arrange the thermal energy equation into an accurate and efficient form with averaged properties. This should then allow an averaged temperature solution to be determined with a moderate computational effort. That is the topic of this paper as it describes the development using multiple-scale analysis of an averaged thermal energy equation based on Fourier heat conduction for a heterogeneous material with isotropic properties. The averaged energy equation to be reported is appropriate for a stationary or moving solid and three-dimensional heat flow. Restrictions are that the solid must display its heterogeneous properties over short spatial and time scales that allow averages of its properties to be determined. One distinction of the approach taken is that all short-scale effects, both moving and stationary, are combined into a single function during the analytical development. The result is a self-contained form of the averaged energy equation. By eliminating the need for coupling the averaged energy equation with external local problem solutions, numerical solutions are simplified and made more efficient. Also, as a result of the approach taken, nine effective averaged thermal conductivity terms are identified for three-dimensional conduction (and four effective terms for two-dimensional conduction). These conductivity terms are defined with two types of averaging for the component material conductivities over the short-scales and in terms of the relative proportions of the short-scales. Numerical results are included and discussed.

Influence of Hydrodynamic Fluid Pressure and Shoe Tread Depth on Available Coefficient of Friction

2012 ◽  
Author(s):  
Gurjeet Singh ◽  
Kurt Beschorner
Keyword(s):  
Coefficient Of Friction ◽  
Hydrodynamic Lubrication ◽  
Fluid Pressure ◽  
Hydrodynamic Pressure ◽  
High Viscosity ◽  
Health Concern ◽  
Fluid Viscosity ◽  
Low Viscosity ◽  
The Coefficient Of Friction ◽  
Lubrication Mechanisms

Slip and fall accidents are a major occupational health concern. Identifying the lubrication mechanisms affecting shoe-floor-contaminant friction under biofidelic (testing conditions that mimic human slipping) conditions is critical to identifying unsafe surfaces and designing a slip-resistant work environment. The purpose of this study is to measure the effects of varying tread design, tread depth and fluid viscosity on underfoot hydrodynamic pressure, the load supported by the fluid (i.e. load carrying capacity), and the coefficient of friction (COF) during a simulated slip. A single vinyl floor material and two shoe types (work shoe and sportswear shoe) with three different tread depths (no tread, half tread and full tread) were tested under two lubrication conditions: 1) 90% glycerol and 10% water (219 cP) and 2) 1.5% Detergent-98.5% (1.8cP) water solutions. Hydrodynamic pressures were measured with a fluid pressure sensor embedded in the floor and a forceplate was used to measure the friction and normal forces used to calculate coefficient of friction. The study showed that hydrodynamic pressure developed when high viscosity fluids were combined with no tread and resulted in a major reduction of COF (0.005). Peak hydrodynamic pressures (and load supported by the fluid) for the no tread-high viscous conditions were 234 kPa (200.5 N) and 87.63 kPa (113.3 N) for the work and sportswear shoe, respectively. Hydrodynamic pressures were negligible when at least half the tread was present or when a low viscosity fluid was used despite the fact that many of these conditions also resulted in dangerously low COF values. The study suggests that hydrodynamic lubrication is only relevant when high viscous fluids are combined with little or no tread and that other lubrication mechanisms besides hydrodynamic effects are relevant to slipping like boundary lubrication.

An Experimental Investigation of Lubrication in Hydrostatic Extrusion Using Wax as a Model Material

1972 ◽  
Vol 94 (3) ◽  
pp. 913-919 ◽  
Author(s):  
A. Wuerscher ◽  
W. B. Rice
Keyword(s):  
Thin Film ◽  
Castor Oil ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Pressure Fluctuations ◽  
Model Material ◽  
Hydrostatic Extrusion ◽  
Strain Rates ◽  
The Coefficient Of Friction ◽  
Bearing Friction

This paper describes hydrostatic extrusion experiments in which paraffin wax was extruded, undertaken to test the validity of a theory proposed by Iyengar and Rice concerning the conditions necessary for hydrodynamic lubrication. Three fluids were used: castor oil, and two silicone fluids. Stress-strain curves obtained at several strain rates revealed that the particular wax behaves like many metals in that Y = Aεm. Strain-rates in the die are assessed, and corresponding values of Y are incorporated in the Hoffman and Sachs analysis of extrusion, which is then used to estimate the coefficient of friction from observed values of extrusion pressure. Analogy with journal bearing friction phenomena leads to the conclusion that at higher speeds hydrodynamic lubrication was attained with all three fluids, but that it was “thin-film” rather than “thick-film” predicted for similar billet speeds. Violent pressure fluctuations observed at higher speeds with castor oil, but not with the silicone fluids are attributed to smaller compressibility and viscosity of the castor oil.

Heat Transfer From a Circular Cylinder at Low Reynolds Numbers

1998 ◽  
Vol 120 (1) ◽  
pp. 72-75 ◽  
Author(s):  
V. N. Kurdyumov ◽  
E. Ferna´ndez
Keyword(s):  
Circular Cylinder ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Order Unity ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
High Degree

A correlation formula, Nu = W0(Re)Pr1/3 + W1(Re), that is valid in a wide range of Reynolds and Prandtl numbers has been developed based on the asymptotic expansion for Pr → ∞ for the forced heat convection from a circular cylinder. For large Prandtl numbers, the boundary layer theory for the energy equation is applied and compared with the numerical solutions of the full Navier Stokes equations for the flow field and energy equation. It is shown that the two-terms asymptotic approximation can be used to calculate the Nusselt number even for Prandtl numbers of order unity to a high degree of accuracy. The formulas for coefficients W0 and W1, are provided.

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