Hydrodynamic Lubrication Conditions Research Articles

OPERATING CHARACTERISTICS OF POROUS FLOATING – RING JOURNAL BEARINGS OPERATING WITH AN IMPROVED BOUNDARY CONDITIONS

The static characteristics of porous floating ring journal bearing under hydrodynamic lubrication condition when operating with an improved boundary conditions are theoretically analyzed. An isothermal finite bearing theory was adopted during this analysis. The effect of different parameters, namely, permeability, geometrical dimensions of the ring and the bearing are considered. It was assumed that oil is supplied through the outside diameter of the bearing under low supply pressure. The angular extent of the oil – film formed in journal – ring and ring – bearing oil films was obtained by applying the integral momentum equation at the leading edge of the oil – film to define the beginning of the oil extent. While, the continuity of flow across the trailing edgewas used to define the end of the oil extent. Numerical results show that the bearing performance affected by different parameters namely, permeability, eccentricity ratios of inner and outer oil – film, the clearance ratios, and the radii ratios.

OPERATING CHARACTERISTICS OF POROUS FLOATING – RINGJOURNAL BEARINGS OPERATING WITH AN IMPROVEDBOUNDARY CONDITIONS

The static characteristics of porous floating ring journal bearing under hydrodynamic lubrication condition when operating with an improved boundary conditions are theoretically analyzed. An isothermal finite bearing theory was adopted during this analysis. The effect of different parameters, namely, permeability, geometrical dimensions of the ring and the bearing are considered. It was assumed that oil is supplied through the outside diameter of the bearing under low supply pressure. The angular extent of the oil – film formed in journal – ring and ring – bearing oil films was obtained by applying the integral momentum equation at the leading edge of the oil – film to define the beginning of the oil extent. While, the continuity of flow across the trailing edgewas used to define the end of the oil extent. Numerical results show that the bearing performance affected by different parameters namely, permeability, eccentricity ratios of inner and outer oil – film, the clearance ratios, and the radii ratios.

Friction reduction in low-load hydrodynamic lubrication with a hydrophobic surface

A novel tribometer capable of measuring low friction forces and low loads at high speeds has been employed to measure the friction coefficient in a pure sliding, ball-on-flat contact in hydrodynamic lubrication conditions. The tribometer was custom-built for measuring friction at low loads, to allow the authors to investigate the feasibility of using the liquid-slip phenomenon for the lubrication of high-sliding MEMS. The theory behind lubrication with liquid slip and its effect on friction is briefly discussed. Contacting surfaces were treated to create hydrophobic/hydrophilic or hydrophilic/hydrophilic pairs. Hydrophobic surfaces were made by coating mica with a self-assembled silane monolayer while the hydrophilic surfaces used were freshly cleaved mica and plasma-cleaned steel. Experiments were conducted at sliding speeds of up to 2 m/s and loads below 0.2 N. An aqueous glycerol solution was used as lubricant. Results obtained with hydrophilic/hydrophilic surfaces were in accord with hydrodynamic lubrication theory. Tests with hydrophobic/hydrophilic surfaces revealed a reduction in friction, which may be attributed to lubricant slip against the hydrophobic surface.

Surface roughness effect on finite journal bearings with flexible porous liners

The effects of surface roughness on the static characteristics of finite porous journal bearings under hydrodynamic lubrication conditions are investigated in this paper. The well-established Christensen stochastic theory of hydrodynamic lubrication of rough surfaces is used to incorporate the effects of surface roughness into the Reynolds equation. The analysis takes into account the flexibility of the porous liner by using a thin liner model. The effects of velocity slip at the surface of the porous medium are considered in the analysis by using the Beavers-Joseph criterion. The mathematical model is then solved numerically by finite-difference methods for mean hydrodynamic pressure, which in turn gives the hydrodynamic load. The effects of the surface roughness parameter, surface pattern, eccentricity ratio, length-to-diameter ratio, permeability parameter, and flexibility parameter on the hydrodynamic load-carrying capacity, attitude angle, and friction factor are discussed.

포토리소그라피를 이용한 마이크로 딤플의 밀도에 따른 마찰 특성

Surface texturing of tribological application is another attractive technology of friction reducing. Also, reduction of friction is therefore considered to be a necessary requirement for improved efficiency of machine. In this paper attempts to investigate the effect of density for micro-scale dimple pattern using photolithography on bearing steel flat mated with pin-on-disk. We demonstrated the lubrication mechanism for a Stribeck curve, which has a relationship between the friction coefficient and a dimensionless parameter for lubrication condition. It is found that friction coefficient is depended on the density of surface pattern. It was thus verified that micro-scale dimple could affect the friction reduction considerably under mixed and hydrodynamic lubrication conditions from based on friction map. Lubrication condition regime has an influence on the friction coefficient induced the density of micro dimple.

The half-wetted bearing. Part 1: Extended Reynolds equation

Recent research has shown that, when a liquid is partially wetting or non-wetting against a very smooth solid surface, the conventional no-slip boundary condition can break down. Under such circumstances, the Reynolds equation is no longer applicable. In the current paper, the Reynolds equation is extended to consider the sliding, hydrodynamic lubrication condition where the lubricant has a no-slip boundary condition against the moving solid surface but can slip at a critical shear stress against the stationary surface. It is shown that such a ‘half-wetted’ bearing is able to combine good load support resulting from fluid entrainment with very low friction due to very low or zero Couette friction.

Ball toroidal CVT: a feasibility study based on topology, kinematics, statics and lubrication

In this paper, a feasibility study of a special kind of toroidal CVT is presented based on different standpoints. The mechanism is briefly described and its kinematic structure is analysed. Its corresponding graph, which turns out to be not planar, is detected by means of a new method for classifying the nonholonomic pairs. The degrees of freedom are so evaluated and the independent circuits are identified. The kinematic analysis leads to a symbolic expression of the global transmission ratio and a simple relation between the two control angles is found to be necessary to theoretically avoid sliding at the contact points. The static force analysis is also carried out in order to ascertain the best method for applying the static pre-load needed to operate the transmission by friction in automotive applications. Finally, the two spherical pairs, which are embodied in the system, are made subject to a feasibility check by analysing the hydrodynamic lubrication conditions and by obtaining through a numerical approach, the oil film thickness and the pressure field over all the spherical domain. Results are provided which show how the two pairs work better if a component of hydrostatic lubrication is adopted.

Numerical Analysis of Static Characteristics at Start of Operation in Porous Journal Bearings With Sealed Ends

Static characteristics at the start of the operation are theoretically investigated in a porous journal bearing with sealed ends lubricated only by the oil initially provided within its pores. This is a preliminary study for estimating the variation of these characteristics with running time. A simple analytical model of the mixed lubrication regime is proposed on the basis of the assumption that the external forces acting on the journal, i.e., the applied static load, the oil-film force and the force at the boundary friction part, are balanced. Numerical results show that air penetrates into the porous matrix at the oil-film rupture zone due to negative pressure in the porous matrix; this causes the reduction of oil content within the porous matrix and contributes to formation of the oil film in the bearing clearance. The oil leakage from the porous matrix induced by the air penetration suggests that, even if hydrodynamic lubrication conditions are possible at the start of operation, the lubrication mode will become mixed or boundary lubrication conditions with running time. The numerical data on the static characteristics are presented in graphical form, illustrating the effects of the Sommerfeld number in the hydrodynamic and mixed lubrication regimes.

Analysis of Oil-Film Pressure Distribution in Porous Journal Bearings Under Hydrodynamic Lubrication Conditions Using an Improved Boundary Condition

Pressure distributions in the oil film of a porous journal bearing are investigated theoretically and experimentally under hydrodynamic lubrication conditions. The circumferential boundary condition for the oil-film pressure is obtained by applying an integral momentum equation to the oil-film region in the bearing clearance. The oil-film pressure distributions are numerically solved using this momentum equation and taking into consideration the balance between oil fed into the clearance and that lost from it. The present analysis shows the occurrence of a negative film pressure before the trailing end of the oil-film region. The experimental results confirm the existence of this negative film pressure. Furthermore, the angular position of the trailing end of the oil-film region obtained in the present analysis moves toward the downstream region, yielding better agreement with the measured and calculated film regions than was found in our previous analysis based on the quasi-Reynolds boundary condition.

Heating Effects in the Drawing of Wire and Strip Under Hydrodynamic Lubrication Conditions

The use of high metal processing speeds to meet the demands for increased productivity has focused attention on the pronounced heating of tooling and workpiece which occurs under these conditions. In the present study, heating under hydrodynamic conditions in wire and strip drawing is addressed by considering a two-dimensional representation of the tool-lubricant-workpiece interface. An analytical formulation is presented for prediction of the resultant temperatures. The model considers deformation heating in the strip, lubricant viscosity to be a function of temperature and pressure, and matches the heat flux at the strip-lubricant boundary. Convection of heat in the lubricant film is considered. The model is constructed in terms of the governing non-dimensional parameters and solved by a Crank-Nicolson finite difference technique. By comparison with solutions which do not consider convection, it is found that convection only begins to play a role in the resulting temperatures when the Graetz number U0h02/αLl is greater than 0.4. For the high speed drawing of aluminum with mineral oil used as a lubricant, the model predicts a monotonic increase in mean lubricant temperatures from 366 K to 404 K over a range of initial strip velocities of 20.3 m/s to 50.8 m/s. The maximum strip surface temperature is predicted to monotonically decrease from 345 K to 335 K over this range of strip velocities. The ratio (kLρLcpL/ksρscpS)1/2 is shown to be important in determining the relative temperatures of lubricant and strip. Results are compared to those metalworking analyses which do not consider the role of the lubricant film.

Study on Mechanism of Lubrication in Porous Journal Bearings. Pressure Distributions in Oil Film under Hydrodynamic Lubrication Conditions.

Pressure distributions in the oil film of a porous journal bearing are investigated theoretically and experimentally under hydrodynamic lubrication conditions. The circumferential boundary condition for the oil-film pressure is obtained by applying an integral momentum equation to the oil-film region in the bearing clearance. The oil-film pressure distributions are numerically solved using this momentum equation and taking into consideration the balance between oil fed into the clearance and that lost from it. The present analysis shows the occurrence of a negative film pressure before the trailing end of the oil-film region. The experimental results confirm the existence of this negative film pressure. Furthermore, the angular position of the end of the oil-film region obtained in the present analysis moves toward the downstream region, yielding better agreement of the measured and calculated film regions than those found in our previous analysis using the quasi-Reynolds condition.

Microstructure of roughened surface in metal rolling

Flat rolled aluminum products have a $25 billion market worldwide annually. The topography of the rolled surface is a key measure of surface quality. A dull surface finish can be generated by non-homogeneous surface deformation when the sheet is rolled under conditions of hydrodynamic lubrication. This is undesirable for some applications where high reflectivity is required, though it improves paintability. Wilson and Schmid have investigated the influence of lubrication conditions on roughening. Although the texture evolution during the hot and cold rolling of aluminum has been studied, the basic mechanisms of the roughening process are not fully understood. The purpose of the present research is to explore the microstructural changes associated with the evolution of surface roughness and to use this information to develop mathematical models which can accurstely describe the surface roughening evolution process.A TEM study of cross-sectional microstructure evolution of aluminum alloy Al 5052-0 material during cold rolling in the presents of a thick lubricant film has been conducted. Commercial aluminum alloy AL 5052-0 as-received was used in the experiments.

A Study of the Mechanism of Lubrication in Porous Journal Bearings: Effects of Dimensionless Oil-Feed Pressure on Frictional Characteristics

The frictional characteristics of a porous bronze bearing are investigated experimentally under hydrodynamic and mixed lubrication conditions. The results show that under the same value of dimensionless oil-feed pressure pˆs, the relationship between the coefficient of friction μ and the Sommerfeld number S can be represented by a single friction curve extending from the hydrodynamic regime to the mixed regime. With decreasing S, μ decreases in the hydrodynamic regime and then steeply increases in the initial stage of the mixed regime. However, at lower values of S, μ becomes steady and its value remains almost the same for various pˆs. The value of S at the transition point from the hydrodynamic regime to the mixed regime is significantly affected by pˆs, becoming smaller for higher pˆs. To estimate μ in the mixed regime, a simple frictional model is proposed on the basis of the assumption that the load supported by the fluid film and the coefficient of fluid friction in the mixed regime are determined by the oil film extent and that they are the same as those at the transition point. The calculated values of μ based on the model are found to approximately agree with the experimental results.

A Study of the Mechanism of Lubrication in Porous Journal Bearings: Effects of Dimensionless Oil-Feed Pressure on Static Characteristics Under Hydrodynamic Lubrication Conditions

The static characteristics of porous journal bearings under hydrodynamic lubrication conditions are theoretically investigated assuming that the oil is fed through their outside diameters under a small pressure. The angular extent of the oil film formed in the bearing clearance is numerically solved on the basis of the following postulate: when the oil film extent reaches steady state, the inflow of oil into the bearing clearance through the porous matrix due to the oil-feed pressure must make up for the oil leakage from the ends through the clearance gap and that into the porous matrix due to the hydrodynamic pressure in the film. Numerical results show that the dimensionless oil-feed pressure significantly influences the static characteristics. Experiments are also conducted for confirmation after the theoretical examination.

Mixed lubrication model for microbearings containing microasperities of defined geometry

For applications involving small-size bearings, the hydrodynamic lubrication conditions are not fulfilled and a mixed lubrication model, involving geometrical characteristics of the microasperities which are responsible for abrasion, is presented. In micromechanical systems, the mixed lubrication condition is assumed to be a steady-state regime. Abrasion is considered as the dominant phenomenon and its dependence on the geometry of microasperities is studied. It is assumed that the lubricant properties do not significantly influence the lubrication conditions in this model. The degree of lubrication is averaged by a modifier. Conical, pyramidal and spherical shapes of microasperities are assumed. It is found that for conical and pyramidal microasperity shapes, the friction coefficient depends only on the tip, angle of the protrusions. For a spherical shape, the friction coefficient depends also on the depth of the wear plough. Experiments done with macroscopic samples for dry and mixed lubrication show no detectable correlation between the macroshape of the test sample and the friction coefficient. Assuming in turn, for the same samples, uniform and regular shapes of the microasperities, geometric characteristics of these regular shapes can be determined. Reciprocal, for a certain configuration of the microasperities, the friction coefficient can be anticipated. This model provides a quantitative guide to the proper design of surface topography in order to get a minimal friction coefficient during the mixed lubrication regime.

Experimental Study on Mechanism of Lubrication in Porous Journal Bearings : Oil Film Formed in Bearing Clearance

An oil film formed in a bearing clearance is experimentally investigated to explicate the mechanism of lubrication in porous journal bearings. To visualize the oil film, a porous bronze bearing impregnated with a fluorescent-dyed oil is used for the test bearing, and the oil film is rendered visible by a pair of ultraviolet lamps. It is observed that the oil film is formed in the loaded part of the bearing and, in particular, it extends over a wide range for the relatively small static load and high oil-feed pressure. However, even under hydrodynamic lubrication conditions, the angular extent of the oil film for the porous journal bearing is significantly small as compared to that for the solid journal bearing. This suggests that the previous postulate for the solid journal bearings, i. e., the half-film condition known as the Gumbel or half-Sommerfeld condition, is not applicable to the theoretical analysis of the porous journal bearings, unless an unlimited amount of oil is supplied to the bearing gap through the oil-feed hole.

A Study on the Mechanism of Lubrication in Porous Journal Bearings. Theoretical Investigation of Oil Film Extent in Bearing Clearance under Hydrodynamic Lubrication Conditions.

The experimental results in a previous paper indicated that the angular extent of the oil film for porous journal bearings with no oil-feed hole, which is used as a small element of the feed port for nonporous bearings, is significantly smaller than half of the bearing circumference. In the present paper, the oil film extent under hydrodynamic lubrication conditions is theoretically analyzed on the basis of the following postulate : when the oil film extent reaches steady state, the inflow of oil into the bearing clearance through the porous matrix due to the oil-feed pressure must make up for the oil leakage from the clearance to both ends and to the porous matrix due to the hydrodynamic pressure generated in the oil film. The results show that the oil film region extends over a wide range for the higher dimensionless oil-feed pressure and smaller Sommerfeld number, which can be explained by the balance between the inflow and outflow across the oil film region. The data on the oil film extent are confirmed to be in agreement with the experimental results.

Experimental Study on Mechanism of Lubrication in Porous Journal Bearings. 2nd Report. Oil Film Formed in Bearing Clearance.

To visualize the oil film formed in the bearing clearance, a porous bronze bearing impregnated with a fluorescent dyed oil is used for the test bearing, and the oil film is rendered visible by a pair of ultraviolet lamps. The photographs are taken by a camera attached to an endoscope inserted into a hollow glass shaft. It is observed that the oil film is formed in the loaded part of the bearing. In particular, it extends over a wide range in the circumferential direction for the relatively small static load and high oil-feed pressure. However, even if under hydrodynamic lubrication conditions, the angular extent of the oil film for the porous journal bearing is significantly small as compared to that for the solid journal bearing. This suggests the previous postulate that the pressure-generating part of the oil film occupies half of the bearing circumference is not applicable to the theoretical analysis of the porous journal bearings, unless unlimited oil is supplied to the bearing gap through the oil-feed hole.

Experimental Investigation of Mechanism of Lubrication in Porous Journal Bearings: Part 1—Observation of Oil Flow in Porous Matrix

The oil flow in the porous matrix is experimentally investigated to explicate the mechanism of lubrication in the porous journal bearings. To visualize the flow in the porous matrix, a simplified model is used for the test bearing, whose matrix is composed of packed glass spheres having small uniform diameter. A dye-injection method is used for visualization. It is observed that there exists a circulation of oil through the porous matrix and this flow contributes to the lubrication in the porous bearings. The flow pattern is dependent on the lubrication conditions. Under hydrodynamic lubrication conditions, the oil in the porous matrix flows away from the position of the load line towards the unloaded region. However under boundary lubrication conditions, when the oil feed pressure is negligibly small, most of the oil in the porous matrix flows toward the region where the oil film pressure would take the minimum.

Short Bearing Theory Prediction of Inertial Turbulent Journal Orbits

The proposed method enables a straightforward solution of the nonlinear equations of the cylindrical motion of rotors on journal bearings in conditions of unsteady nonlaminar hydrodynamic lubrication taking into account the inertia forces of the fluid particles. The analysis is restricted to the case of rigid supports and rigid symmetrical rotor adopting the short bearing theory. Some meaningful examples of predicted journal orbits are reported for balanced and unbalanced rotors.