Modeling Mixed Lubrication in Point and Line Contact by Non-Normalized Discretization

Visco-elastohydrodynamic lubrication and wear model amended by deformation velocity

Surface topography plays an important role in mixed lubrication. However, the influence of the surface topography's morphological characteristics on lubrication performance is still not fully understood. In this article, we employ digital filtering and the Johnson transformation system, and we use a mixed plasto-elastohydrodynamic lubrication model to simulate the lubricated contact between rough spherical surfaces with different morphological characteristic parameters. The influence of skewness, kurtosis, and the wavelength factor, that is, the ratio between the autocorrelation lengths in the transversal and longitudinal directions, on contact pressure, film thickness, and von Mises (subsurface) stress, is examined with the mixed plasto-elastohydrodynamic lubrication model. The results confirm that plastic deformation leads to lower pressure distribution, distributed over a larger contact area than the pure elastohydrodynamic lubrication solution. Moreover, it is found that an increase in the kurtosis may improve the lubrication performance, while the opposite is true for the skewness and the wavelength factor. We believe that the insights obtained by means of the numerical simulations presented herein, would facilitate the design and manufacturing processes of the surfaces used for machine elements operating in the mixed plasto-elastohydrodynamic lubrication regime.

The effect of roughness is an important consideration in the lubrication analysis and surface geometric design of heavy-duty machine elements. Deterministic simulation techniques have been developed for the investigation of point-contact mixed-lubrication problems. Such approaches should also be extended to obtain deterministic mixed lubrication solutions for journal-bearing conformal-contact systems. However, journal-bearing mixed lubrication involves a much larger area of surface interaction as compared to that in point contact problems. It is difficult to use similar micro/nano scale meshes directly to journal bearings under the current computation capability. It is a great challenge to develop a new deterministic numerical model for the mixed lubrication of journal bearing systems with the consideration of the effect of surface geometry design. This paper presents a macro-micro scale finite-element local-enrichment model for the deterministic analysis of conformal-contact mixed lubrication, in which a coarse mesh is used to determine the elastic deformation of a journal bearing surface, whilst locally refined meshes are used for the analysis of the roughness effect. The results from investigating the performance of bearing surfaces with sinusoidal and dimple textures suggest that the minimum film thickness may be improved through an appropriate surface texture configuration.Copyright © 2006 by ASME

This paper is in two parts. In the first, a comparison is made between film thicknesses determined by point and by line contact. The two are shown to give identical results. In the second part, fourteen test fluids were chosen to provide a variety of molecular structures. Eight polymers were studied at several concentration. A considerable amount of viscosity loss was observed at both point and line contacts. The difference between the two was negligible. This is important a it shows that the polymer molecules were moving straight through the contact and not going round the point contact. This is useful experimentally as point contact devices are much easier to build and use than line contact devices. The viscosity loss under EHL conditions was found to be 10 to 20 percent larger than that observed in a capillary high-shear viscometer. This is thought to be due to the completely different stress pattern in the two. The entry viscosity of the polymer-thickened oil differs hardly at all from the straight oil so the resulting film thickness of polymer-thickened oil and straight oil is almost the same.

Pivot design and angular misalignment effects on tilting pad journal bearing characteristics: Four pads for load on pad configuration

The Reynolds equation has been widely applied in lubrication analyses, but the extent and limit of its application have not been fully explored. Great efforts have been made so that the solution convergence speed and accuracy are significantly improved. However, while the working conditions are severe, such as extremely heavy load, low speed, and low viscosity due to temperature increase, the lubricant film thickness becomes very thin and surface contact may occur. As a consequence, the lubrication solution becomes difficult. Contact and thin-film or mixed lubrication under severe conditions are of great importance, as many components operate in such regimes. This article investigates the solution evolution of the Reynolds equation as the entraining velocity decreases, using the unified mixed elastohydrodynamic lubrication (EHL) model presented by Hu and Zhu. By comparing the ultra-low speed solution of the Reynolds equation with that of dry contact analysis, it is found that the solution of the Reynolds equation finally converges to those of the corresponding dry contact under otherwise the same operating conditions. The results manifest that with the unified solution approach the Reynolds equation system can be used to handle the situation of dry contact and mixed lubrication, in which both hydrodynamic lubrication and surface contact coexist.

Boundary lubrication of sliding concentrated steel contacts

This paper presents a unified mathematical model spanning the entire mixed lubrication for rolling-sliding line contacts. A load-sharing parameter is defined to divide the lubrication spectrum into three regions with increasing proportion of solid load sharing: light-mixed lubrication, significant-mixed lubrication and near-boundary lubrication. The main effort of the work is to develop a model for significant-mixed lubrication and integrate it with two previously developed governing-equation based models for light-mixed and near-boundary lubrication. A preliminary model is first developed by means of smooth, monotonically increasing interpolations of key contact variables obtained by the light-mixed and near-boundary lubrication models. The variables include surface temperature in the contact, friction coefficient, friction power intensity and proportion of solid contact area to the area of the line contact. The model is then refined by factoring in a potential transition of surface tribofilm breakdown which may take place in the second half of the region of significant-mixed lubrication. A basic parametric analysis is presented in the paper to show the sensibility of the model in analyzing the effects of operating conditions on contact stability. The model may be used to perform basic design and analysis calculations for line contacts with various degrees of mixed lubrication. It may also be implemented into a gear-meshing model to study the gear performance under various temperature and lubrication conditions.

The planetary gear system typically operates under mixed lubrication, where elevated temperatures can accelerate lubricant film breakdown and lead to thermal deformation and scuffing. This article proposes a finite element method (FEM)-based model that combines a mixed elastohydrodynamic lubrication (EHL) model with a structural thermal analysis model to investigate the thermal behavior of planetary gears. The lubrication of rough surfaces is simulated using a mixed EHL submodel that incorporates measured surface topographies into the film thickness calculation, whereby the friction coefficients are obtained and utilized for the calculation of frictional heat flux. The structural thermal analysis submodel incorporates thermal boundary conditions based on convective heat transfer coefficients to simulate the temperature field, and the effects of speed and torque on the temperature distribution are examined. The thermal deformation and stress of gears are calculated, and their distribution and underlying formation mechanisms are investigated. Finally, the scuffing safety factor is determined using the contact temperature and critical scuffing temperature to evaluate the scuffing risk within the planetary gear system. The conclusions may offer valuable insights for the design of planetary gear systems with enhanced resistance to thermal deformation and scuffing failure.

Purpose Crossed helical gears have point contact and their surfaces are subject to high surface stress. Contact stress and root tooth stress are the most common sources of failure in crossed helical gear. This paper aims to study the load-carrying capacity and performance of crossed helical gear teeth with different gear tooth profiles. To overcome defects and reduce the sensitivity to small shaft angle changes. The combined tooth profile is designed to reduce the bending stresses, contact stresses and tooth deflection, and prevent pinion failure in the gearbox. Design/methodology/approach The principle of the method is a line contact is introduced instead of a point contact between two teeth in mesh with each other. The tooth surface of the helical gear is designed and cut by a modified tool. Higher normal pressure angles like 25° and 35° are used. The modified involute is accomplished to eliminate interference between the teeth. Engineering software packages have been applied to generate all crossed helical gears gear profiles. The modification is compounding curves consisting of an epicycloid-involute-hypocycloid gear teeth profile generated by the cutter modified. Findings The stresses in the crossed helical gear teeth profile were reduced by increasing the normal pressure angle values. Using a 35° pressure angle the enhancement percentage in contact stress and teeth fillet region will be about 29.345% and 15.421%, respectively. The best enhancement in a gear’s resistance is the epicycloid-involute-hypocycloid gear teeth profile. The enhancement was 32.610% and 18.588%. The skew in line of action in skewed helical gear will be sensitive when the crossing angles are small. Their teeth surface tends to be easily worn out; however, the wearing process will be reduced by using a proposed gear teeth profile. Practical implications The gear teeth to be modified are cut by a shaper process. The modifying rack cutter of this study can be used as a reference for creating a different helical gears sample. The helical teeth surface is modified to become an envelope of the other. This makes an original point contact change into a line contact. The epicycloid-involute-hypocycloid gear teeth profile is preferred for a higher contact ratio and a large load capacity. This work explicitly introduces a new method of kinematic consideration to improve the load capacity of crossed helical gear. Originality/value This paper showed some novel results by the unique shape of the rack-cutter designed to generate different helical angles and different gear positions. In the future, it will make valuable contributions to the further development of the dynamic performance of a crossed helical gear system through the study in the field of using asymmetric teeth profiles of helical gears with tip relief as the manner to enhance the crossed helical gear performance. Investigation of crossed helical gear by applying a predesigned parabolic function of transmission error enables the absorption of linear discontinuous functions caused by misalignment.

In this work, new approaches for the dimensional synthesis of both tooth and operating basic surfaces for hyperbolic gear transmissions are presented. Both traditional worm-gearing hyperbolic transmissions (point contact) and non-traditional ones (line contact) are considered regarding constraints as the manufacturing method, the standardized tool modules and the limit normal of contact. For point contact, the location of the pitch point is done by chosen the parameters of the operating basic surfaces (the cone angle of the worm) and of the teeth basic surfaces (axial module and helix angle of the worm). For line contact, the given parameters of the operating basic surfaces are the cone angle and the worm radius at “zero plane”, and the axial module of the teeth basic surfaces. A comparative study of optimal synthesis, considering different solutions of traditional (point contact) hyperbolic transmissions and non-traditional (line contact) ones, is also included. The objective functions were the sliding velocity and the efficiency, and constrictions above were considered.

ABSTRACTThermoelastohydrodynamic lubrication (TEHL) analysis of line or point contacts is usually done by simultaneously and numerically solving the Reynolds equation, the Boussinesq equation of an elastic semi-infinite body, the energy conservation equation, and the load balance equation. Although a number of publications are available in this field, there is still a lack of general-purpose and widely used TEHL software for engineering applications. On the other hand, commercial software for both the solid structure and fluid flow analyses have become easy design tools. To expand the application of the commercial software to TEHL simulation, coupling of structure and fluid analyses is required. This study gives some demonstrations of the 3D finite element method (FEM) simulations of line contact TEHL problems using ANSYS version 13.0. The equilibrium equations of momentum and continuity and the energy conservation equation of lubricating fluids are solved with CFX. The elastic deformation of solids is calculated with the ANSYS Structure module. Through the fluid–solid coupling interfaces, the fluid pressure, solid deformation, and thermal flow are transferred between the fluid and solid domains. The computational fluid domain is enlarged, enclosing the contact zone, in the 3D model. Further, the 3D model can treat the realistic constraint conditions of solid deformation, whereas conventional TEHL analysis uses the assumption of semi-infinite body. The simulation results for pressure, lubricant film thickness, and temperature distributions are compared with the traditional Reynolds approach, and reasonable agreement for pressure and film thickness distributions has been obtained.

Fluid lubrication and mixed lubrication can both be phenomena in the study of the lubrication of rough surfaces. In this paper, we take the surface as random process and, by studying the contact of surfaces which present roughness, we can put forward a method which defines the transition from fluid lubrication to mixed lubrication, by looking for the first contact point between the two surfaces. This study suggests that the transition between fluid and mixed lubrication relates to the number of asperities on the contacting surfaces, an advance on former methods. We also apply this method to piston ring/cylinder lubrication research. The results show that the transition changes with time.

General Elastohydrodynamic Lubrication Code (GEHLC) is a FORTRAN code for calculating the lubrication performance of line and point contacts used in machine elements such as gears, rolling bearings, cam and follower systems, and traction drives, etc. It adopts the most recent results published by Chittenden and Dowson et al. (1), to evaluate isothermal film thickness of point contacts, and uses the thermal reduction factor (2) to account for the inlet heating effects on the film thickness. By using Bair and Winer's analysis (3), a viscoelastic fluid model has been employed in this program to calculate shear stress in the film with bisection technique and In predict the coefficient of friction. Using this program one can also obtain flash temperature distribution on the two solid surfaces from a simplified heat conduction analysis based on work by Bolt (4), Jaeger (5), and Archard (6), et al. Typical results are presented for elliptical contacts used in rolling bearings. Presented at the 42nd Annual Meetin...

It is well known that the inclusion of surface tension in the linear water-wave problem introduces an additional term in the free-surface boundary condition. Furthermore, if the fluid contains one or more partially immersed bodies, edge conditions describing the motion of the fluid at each contact line need to be applied. In this paper, an inverse procedure is used to construct examples of two-dimensional, surface-piercing trapping structures for non-zero values of surface tension. The problem is considered with two separate edge conditions that are appropriate for investigations involving trapped modes. The first edge condition fixes each contact line and the procedure used forces the bodies to be horizontal at the contact points; it is shown that results can be found for all values of surface tension. The second condition forces the free-surface slope to be zero at the contact points, and results are obtained for a restricted range of surface tension values.