Thermo-elastohydrodynamic Lubrication Research Articles

A fast thermoelastohydrodynamic model for dynamically loaded journal bearings behaviour analysis

An efficient method for thermoelastohydrodynamic (TEHD) journal bearings lubrication analysis is presented. Lubrication film temperature is treated as a time-dependent two-dimensional variable and is averaged over the film thickness. In order to compute the film and solids temperature, a new heat flux conservation algorithm, based on both Finite Element (FEM) - Finite Volume (FVM) methods, is proposed. A key point in this analysis is the consideration of different heat transfer coefficients at film - solids and solids - surroundings boundaries. The Reynolds equation in the film is solved using the FEM discretization. A mass-conserving cavitation algorithm is applied and the effect of viscosity variation with the temperature is taken into account.

Transient thermoelastohydrodynamic lubrication analysis of an involute spur gear

A meshing of a gear is a typical example where non-stationary condition exists. Load, velocity, curvature of meshing point vary along the line of action at any time. A complete numerical solution to the transient thermoelastohydrodynamic lubrication (EHL) problem of an involute spur gear is obtained by using simplified multigrid method. A Newtonian fluid model is assumed and the surface roughness of gear teeth is ignored. The gear teeth are assumed to be rigid. The load is first assumed to be carried by either two pairs of gear teeth or by only one pair. This transition from two to one pair and vice versa is modelled as a trapezoidal variation of the load by simplifying the experimental load spectrum. The results show that thermal effects can strongly influence the approach and recess point film thickness. It also reveals that, the maximum pressure, the maximum friction coefficient and the highest film temperature all occur in the vicinity of pitch point. The minimum film thickness usually occurs at the approach point except reduction ratio equals to one. The effects of slip ratio, velocity and load on the film temperature and friction coefficient are discussed in the paper.

Thermal validation of a misaligned grease-lubricated journal bearing model

Bearing temperatures predicted by a misaligned grease-lubricated journal bearing simulation were compared with experimental data. The numerical simulation combines a steady state mixed thermo-elastohydrodynamic lubrication model with a semiempirical soap-thickened grease rheology model. Circumferential temperature profiles were measured using a test fixture and journal test specimens of 5.1 cm diameter and 1.9cm wide over a range of bearing loads (3.8–30kN) and angular misalignments (from −0.08° to 0.05°) at 166r/min rotational speed. The results show that the maximum temperatures in the numerical and experimental profile agree within 5 per cent over the range of loads and misalignments studied.

Thermoelastohydrodynamic lubrication for the connecting rod big-end bearing under dynamic loading

This paper discusses an experimental device used to investigate thermoelasto-hydrodynamic behaviour of connecting rod big-end bearing models. Theoretical results for this device are obtained by calculation with a two-dimensional thermoelastohydrodynamic model. A brief description of both theoretical development and experimental device is presented. After the presentation of measurement results, a comparison with theoretical results is discussed.

Transient thermo‐elastohydrodynamic lubrication of gear teeth

AbstractDuring a gear mesh cycle, load, rolling and sliding velocities, curvature, and temperature change rapidly. In this paper, a transient, thermo‐elastohydrodynamic lubrication model is presented that has been used to study the lubrication parameters at 250 contact points along the path of a contact. The working flanks were assumed to be smooth. The line load was calculated at every contact point, using the finite‐element method. Dynamic loading was not considered. The steady‐state temperature field of the working flanks was used to obtain the surface temperature at the inlet of each contact point, determined by an experimental‐analytical method presented previously. In this model, the lubricant is considered to follow the Ree‐Eyring constitutive equation. The influences of both pressure and temperature on density, thermal conductivity, and specific heat of the lubricant are also taken into account. Results are presented for an FZG type A gear pair lubricated with an FVA No. 4 reference oil; these include film shape, pressure and temperature distributions, as well as friction coefficient.

Thermal effects in cylindrical journal bearings of high‐speed gearboxes

AbstractThe high rotational speeds and loads of gears operating in acceleration gearboxes causes problems related to the correct choice and design of journal or rolling bearings. In the case of journal bearings, these problems are connected with thermoelastohydrodynamic lubrication theory and the dynamics of the bearing system. However, of major importance is the problem of thermal effects in journal bearings. This has been considered for bearings used in a double‐helical gearbox with the pinion and output shaft operating in cylindrical journal bearings. The oil film pressure, temperature, viscosity distributions, and maximum and mean oil film temperatures have been determined. In calculations, laminar adiabatic and turbulent adiabatic models of oil films have been applied. The results of the calculations can be used in the design of cylindrical or other types of journal bearing in rotating machinery, including acceleration or reduction gearboxes.

Thermoelastohydrodynamic analysis of the static performance of tilting-pad journal bearings with the Newton–Raphson method

Thermoelastohydrodynamic lubrication (TEHD) analysis is presented to investigate the static performance of tilting-pad journal bearings. A completely numerical solution is obtained. The Newton–Raphson method is employed to predict the bearing characteristics of the hydrodynamic pressure, the eccentricity and the pad attitude angles simultaneously. For the temperature calculation, three-dimensional (3D) energy equations for the fluid under each pad and 3D heat transfer equations for the pads are solved using a sequential sweeping method. The elastic deformation and thermal expansion of each pad are calculated with the 20-node isoparametric finite element method. It is found that the Newton–Raphson method is a smart and efficient method. The results show that the elastic deformation due to the hydrodynamic pressure and the influence of the temperature elevation play an important role in the calculated bearing system.

Studies on the Effect of Spin Motion on Oil Film Thickness in Elastohydrodynamic Point Contacts.

Spin on the contact surfaces between two elements occurs in such diverse machine elements as angular contact ball bearings or continuously variable transmissions adapting traction drives. We experimentally and analytically studied the effect of spin on lubricating oil film thickness on angular contact ball and disk. Oil film thickness was measured under different spin angular velocities for constant rolling velocity and different contact loads using optical interference method. We clarified the effect of spin on minimum and central thickness of oil film and film shape and analyzed thermo-elastohydrodynamic lubrication (TEHL) considering spin under experimental conditions. Analytical and experimental results agreed well.

Thermo-Elastohydrodynamic Analysis of Connecting Rod Bearing in Internal Combustion Engine

A comprehensive method of thermo-elastohydrodynamic lubrication analysis for connecting rod bearings is proposed, which includes thermal distortion as well as elastic deformation of the bearing surface. Lubrication film temperature is treated as a time-dependent, two-dimensional variable which is averaged over the film thickness, while the bearing temperature is assumed to be time-independent and three-dimensional. It is assumed that a portion of the heat generated by viscous dissipation in the lubrication film is absorbed by the film itself, and the remainder flows into the bearing structure. Mass-conserving cavitation algorithm is applied, and the effect of variable viscosity is included in the Reynolds equation. Simulation results of the connecting rod bearing of an internal combustion engine are presented. It is shown that the predicted level of the thermal distortion is as large as that of the elastic deformation and the bearing clearance, and that the thermal distortion has remarkable effects on the bearing performance. Therefore, the thermo-elastohydrodynamic lubrication analysis is strongly recommended to predict the performance of connecting rod bearings in internal combustion engines.

The analysis of performance on spring-supported thrust pads inclusive of one-dimensional pressure build-up

In the paper, a solution of one dimensional fore-region pressure build-up is put forward. The performance of spring-supported thrust bearing is carried out with 3-dimensional thermo-elasto hydrodynamic (TEHD) lubrication theory inclusive of inlet pressure build-up, thermal-elastic distortion of pad and thermal effect. The effects of fore-region pressure build-up and the variation of some operating conditions on the performance of the pad are studied.

Thrust Bearings In the 2-D Thermal Elastohydrodynamic Lubrication: On the Slider Velocity Corresponding to the Maximum Load

The thermo-elastohydrodynamic lubrication is considered for Newtonian and power-law fluids. A numerical method available in the literature is utilized in obtaining solutions, for a given set of parameters, leading to establishing the maximum carrying load in terms of the slider velocity. Comparison is made with the classical lubrication theory. It is shown that there exists a threshold of the slider velocities for which increase of the slider velocity is detrimental to the ability to support loads.

On the Maximum Allowable Loads in the Thermo-Elastohydrodynamic Lubrication

Thermo-elastohydrodynamic lubrication is considered. A numerical procedure for obtaining the maximum allowable load is presented. The maximum allowable load is defined as the load which, for a given set of parameters, when exceeded will cause either change of the lubrication character, or collapse of the fluid film if the film thickness was large relative to the surface roughness. The procedure is illustrated by applying it to the infinitely wide thrust bearings lubricated by the Newtonian or power-law fluid.

On the Numerical Analysis to the Thermoelastohydrodynamic Lubrication of a Tilting Pad Inclusive of Side Leakage

Numerical solutions are obtained for the thermoelastohydrodynamic lubrication of a tilting pad based on the three-dimensional flow of lubricant. For elastic deformation, the pad is idealized as a uniform plate with free boundaries so that a displacement coefficient matrix can be established by the conventional finite difference method. For pressure distribution, a fast Newton-Raphson's approach is used in solving the generalized Reynolds equation, film thickness equation, inlet pressure buildup equation, and the force balance and moment balance equations of the pad, simultaneously. For temperature distribution, the finite difference method is carried out with the help of a sweeping scheme.

Time-dependent TEHL solution to centrally supported tilting pad bearings subjected to harmonic vibration

The bearing performance of a centrally supported tilting square pad, subjected to harmonic vibration, is analysed numerically. Thermo-elastohydrodynamic lubrication analysis considers simultaneously the heat transfer, elastic deformation of the pad's working surface, side leakage, and the inlet pressure build-up effect. Governing equations with their boundary conditions are transformed into non-dimensional forms so that the problem's non-dimensional parameters are obtained. An efficient procedure is developed to solve the problem numerically. By idealizing the pad as a uniform plate, a compliancy coefficient matrix is established to calculate the pad's surface deformation due to various pressure distributions. At each time step the pressure is obtained by a fast Newton-Raphson method, whereas the temperature is determined by an efficient finite difference approach. A dynamic parameter is introduced to describe the effect of the pad's periodic motion, which is found to be as important as the wedge effect when the dynamic parameter approaches unity.

On the TEHL Theory. Part I: Dimensionless Problem Formulation

Since the thermoelastohydrodynamic and elastohydrodynamic lubrication (TEHL and EHL) problems are predominantly heat transfer (HT) and/or fluid mechanics (FM) problems, it is proposed that the pertinent dimensionless quantities defined, in some instances tabulated, and commonly used in these branches of engineering science (HT and FM) should be used consistently and uniformly throughout for TEHL and EHL studies. In support of this, it is shown by some mathematical considerations that the published dimensionless quantities (in the TEHL and the EHL problems) can be converted into HT and FM parameters—such as the Reynolds number, Euler number, Eckert number, Prandtl number or Fourier modulus. It is indicated that such parameters have an immediately recognizable physical meaning.

On the TEHL Theory, Part II: Ellipsoidal Profile Application

A simplified solution is obtained to the thermoelastohydrodynamic lubrication problem involving ellipsoidal contacts subjected to heavy loads. The results are plotted and discussed in terms of the pertinent dimensionless parameters. A set of formulas is proposed for the maximum temperature increases in the fluid film and of the bounding surfaces. A comparison is made with experimental data obtained elsewhere.

Analysis of maximum temperature for thermo-elastohydrodynamic lubrication in point contacts

A simplified solution to point contact thermo-elastohydrodynamic lubrication is presented in this paper. By simultaneously solving the energy equation and the surface temperature equation, three-dimensional temperature distributions in the contacts are obtained based on pressure and film thickness determined in calculations of isothermal elastohydrodynamic lubrication. A group of formulae for the maximum temperature rises of film and surfaces is proposed. Values predicted with the formulae are compared with experimental results of temperature measurement with an IR technique.

Thermo-elastohydrodynamic lubrication of an involute gear

This paper analyses the thermo-elastohydrodynamic lubrication on an involute spur gear tooth surface and the influence of the inlet temperature of the lubricant. The oil film temperature distribution shows a minimum near the point where the pressure distribution is a maximum and the energy loss a minimum. Then the temperature increases slightly in the outlet region. Calculated results show a decrease of a few percent in the maximum pressure distribution compared with an oil film on a rigid surface. Based on oil film thickness and gear tooth deflection, the load sharing coefficient and the relative transmitting errors are calculated. The behaviour of the oil film due to the variation of the normal tooth load at the transition point of the meshing is investigated also