Thermo-elastohydrodynamic Lubrication Research Articles

A Numerical Investigation of Mixed Thermal Elastohydrodynamic Lubrication in Tilting-Pad Journal Bearing

Abstract The tilting-pad journal bearing in the cooling system of the nuclear power plant is equipped below the ground and vertically positioned to accomplish its function for water transfer. Usually, the loading conditions are relatively stable since the required water volume almost remains the same level during the operation, but the loading direction cannot be known in advance. Furthermore, the bearing is designed with several separate pads, which allows the bearing to support the loading flexibly. The safety application of nuclear energy requires the bearing to have a reliable ability to maintain the rotating motion of gear sets. This study develops a numerical model to simulate the mixed thermo-elastohydrodynamic lubrication for the tilting-pad journal bearing in the nuclear plant. The elastic and thermal fields are properly determined, and the induced displacement is taken into account for an accurate description of film thickness. The asperity contact due to misaligned journal is well evaluated in the local area where the lubrication film cannot separate the surfaces. A parametric study is undertaken in detail to reveal the aspects that influence bearing lubrication. The conclusions potentially provide fundamentals for further lubrication optimization of the bearing system.

Comparative analysis of angular contact bearing stiffness calculated by Hertz contact and thermo-elastohydrodynamic lubrication

Stiffness is the key dynamic parameter of the angular contact ball bearing. This work established a dynamic bearing model based on Hertz theory and thermo-elastohydrodynamic lubrication (TEHL) and compared the contact angle, inner race position, and stiffness. In most cases, the stiffness calculated via Hertz was higher than when using TEHL. The axial stiffness values determined via the two theories were close, while the radial stiffness calculated via the Hertz theory was smaller than that determined by TEHL under light load and high speed. Considering the elastic deformation of the races and the initial contact angle, the results obtained by TEHL displayed a lower error rate in the experiment than Hertz.

Analysis and Optimization of Nanolubricated Journal Bearing under Thermoelasto-Hydrodynamic Lubrication Considering Cavitation Effect

This work deals with the effect of the cavitation and the elastic deformation on the steady-state thermal performance of plain journal bearing using CFD-FSI technique. As a case study, a bearing lubricated with SAE40W oil dispersed with TiO2 nanoparticles was extensively analyzed. The hydrodynamic pressure, oil film temperature, and the other bearing parameters have been calculated. The nanoparticles volume fractions, journal speeds, and eccentricity ratios have been considered. Krieger Dougherty model was implemented with the Vogel- Barus exponential viscosity to include the effects of the oil temperature and TiO2 nanoparticles volume fraction on the lubricant viscosity. The cavitation effect was implemented using Zwart-Gerber-Belamari model. The optimum journal position, the attitude angle, and the load have been obtained using Multi-Objective Genetic Algorithm. The mathematical model was successfully verified with the pressure and the total deformation published by Dhande with 4% and 2% deviation between the results respectively. The film temperature of the present work was compared to that obtained numerically by Li et al and experimentally by Ferron and Boncompain with 2% maximum deviation between the results. An enhancement in the load-carrying capacity of the bearing with a little growth in oil film temperature were obtained when using TiO2 nano lubricant.

Thermo-elastohydrodynamic lubrication performance study of step seal under transient condition

Purpose This paper aims to study the impact of transient velocity changes on sealing performance during reciprocating sealing processes. Design/methodology/approach Establish a model of transient mixed lubrication, solve the transient Reynolds equation, consider the effect of temperature rise at the seal interfaces, and determine the behavior of the seal interfaces, such as film thickness and fluid pressure. Evaluation with friction and leakage rate, calculate the variation of sealing performance with reciprocating velocity under different working conditions, and verify it through bench experiments. Findings Within a reciprocating stroke, the frictional force decreases with increasing velocity, and the frictional force of the outstroke is greater than that of the instroke; at the time of the stroke transition, the fluid pressure is smallest and the rough peak contact pressure is greatest. At present, the dynamic pressure effect of fluids is the largest, and the friction force also increases, which increases the risk of material wear and failure. Friction and leakage increase with increasing pressure and root mean square roughness. As temperature increases, friction increases and leakage decreases. In studying the performance variations of seal components through a reciprocating sealing experiment, it was found that the friction force decreases with increasing velocity, which is consistent with the calculated results and more similar to the calculated results considering the temperature rise. Originality/value This study provides a reference for the study of transient sealing performance.

Analysis of lubricating characteristics of high-pressure radial piston pump with thermo-elastohydrodynamic coupling

The behavior of piston-cylinder interfaces takes important influences on lubricating characteristics of the high-pressure piston pump. For the sake of revealing the lubricating characteristics of radial piston pumps, a transient thermo-elastohydrodynamic lubrication model to analyze the interface between piston and cylinder is established with considering the effects of the bushing elastic deformation, viscosity-temperature-pressure, heat conduction and piston tilting, on the basis of coupling the finite element method and finite difference method. Furthermore, the influences of design parameters (camshaft speed, inlet pressure and average clearance) on the load carrying capacity, leakage, viscous friction, and temperature rise of the friction-pair interfaces are analyzed. The results indicate that the average clearance has the most significant influence on the lubrication performance. Increasing the average clearance from 2 to 6 μm resulted in a substantial decrease in load carrying capacity by approximately 50% and friction force by approximately 65%. The temperature rise showed a significant reduction of 55%, while the leakage increased by approximately 3-fold.

A New Thermal Elasto-Hydrodynamic Lubrication Solver Implementation in OpenFOAM

Designing effective thermal management systems within transmission systems requires simulations to consider the contributions from phenomena such as hydrodynamic lubrication regions. Computational fluid dynamics (CFD) remains computationally expensive for practical cases of hydrodynamic lubrication while the thermo elasto-hydrodynamic lubrication (TEHL) theory has demonstrated good accuracy at a lower computational cost. To account for the effects of hydrodynamic lubrication in high-power transmission systems requires integrating TEHL into a CFD framework such that these methodologies can be interfaced. This study takes an initial step by developing a TEHL solver within OpenFOAM such that the program is prepared to be interfaced with a CFD module in future versions. The OpenFOAM solver includes the Elrod–Adams cavitation model, thermal effects, and elastic deformation of the surfaces, and considers mixing between the recirculating flow and oil feed by applying energy and mass continuity. A sensitivity study of the film mesh is presented to show the solution variation with refinement along the circumferential, axial and radial directions. A validation case is presented of an experimental single axial groove journal bearing which shows good agreement in the pressure and temperature results. The peak pressure in the film is predicted within 12% and the peak temperature in the bush is predicted within 5% when comparing the centerline profiles.

Study on lubrication characteristics of rotary combination seals under stress relaxation

Temperatures in the drilling environment can reach 150 °C and pressures up to 30 MPa, all of which can cause oil film rupture and even seal failure. In addition, under high pressure, viscosity changes can lead to stress relaxation, which may eventually cause seal failure as well. In order to study the influence of high temperature and high pressure conditions on seal performance during stress relaxation, the pressure permeation loading method on both sides is used in the finite element model to simulate the fluid pressure on both sides of the seal interface, and the TEHL (thermo-elastohydrodynamic lubrication) model of the rotary combination seal is also established. On this basis, the TEHL characteristics of the rotary combination seal under different working conditions were analyzed. The results show that: Firstly, the contact pressure and von Mises stress of the seal tend to increase at high temperature, and the higher the temperature, the faster the growth rate, while the increase of the seal area temperature leads to the thinning of the oil film thickness and the high oil film pressure. Secondly, at high fluid pressure, the contact pressure of the rotary combination seal gradually increases, and its peak is close to the peak oil-side contact pressure. Thirdly, with the increase of the linear speed (or rotational speed), the oil film pressure and thickness increase. Fourthly, the larger the rotational speed, the larger the volume leakage and friction, and the larger the compression ratio, the larger the contact pressure.

Sensitivity of TEHL Simulations to the Use of Different Models for the Constitutive Behaviour of Lubricants

This study compares the film thickness, lubricant temperature, and traction curves of two groups of commonly used constitutive models for lubricants in thermo-elastohydrodynamic lubrication (TEHL) modelling. The first group consists of the Tait equation of state, the Doolittle Newtonian viscosity model, and the Carreau shear thinning model. The second group includes the Dowson equation of state, the Roelands–Houpert Newtonian viscosity model, and the Eyring shear thinning model. The simulations were conducted using a Computational Fluid Dynamic and Fluid-Structure Interaction (CFD-FSI) approach, which employs a homogeneous equilibrium model for the flow simulation along with a linear elastic solver to describe the deformation of the solid materials. The simulations were conducted under a load range of 100 kN/m to 200 kN/m and a slide-to-roll-ratio (SRR) range between 0 and 2 using Squalane lubricant. The results show up to a 10% deviation in central film thickness, a 31% deviation in coefficient of friction (CoF), and a 38% deviation in maximum lubricant temperature when using the different constitutive models. This study highlights the sensitivity of TEHL simulation results to the choice of constitutive models for lubricants and the importance of carefully selecting the appropriate models for specific applications.

A quantitative analysis of double-sided surface waviness on TEHL line contacts

In this paper, the effects of double-sided surface waviness on Thermo-Elastohydrodynamic Lubrication (TEHL) in line contacts are investigated deterministically through numerical simulations. The effects of surface amplitude, wavelength, relative position, and slide-to-roll ratio have been studied. The classic approach, which consists of an equivalent deformable body with superimposed surface waviness, is critically evaluated and compared to results from full two-body simulations. Under the investigated conditions, the equivalent and two-body approaches show about 17%, 21%, and 26% deviations in maximum pressure, temperature, and friction, respectively. It is demonstrated that the fundamental cause of the observed deviations, which results in a phase shift that cannot be described by the equivalent geometry, is the tangential elastic deformation of surface asperities.

Machine learning based surrogate modelling for the prediction of maximum contact temperature in EHL line contacts

The present study aims at predicting the maximum temperature in line contacts depending on operating conditions. For this purpose, a thermo-elastohydrodynamic lubrication (TEHL) simulation model of a line contact is used to calculate the maximum temperature for a wide range of parameters. Subsequently, a neural networks (NN) approach is used to develop a surrogate model that is able to predict the maximum temperature on the basis of the operational parameters. The influence of different NN architectures and transfer functions on the accuracy is shown. A good agreement with a correlation coefficient (R) greater than 0.997 is achieved for a NN with two hidden layers. Furthermore, the impact of feature engineering on the prediction accuracy with limited data sets is presented.

A Design for High-Speed Journal Bearings with Reduced Pad Size and Improved Efficiency

Improving efficiency is a general task in the design process of high-speed journal bearings. A specific fixed-pad bearing geometry featuring reduced pad length and additional design measures with the intention of reducing frictional power loss is investigated, experimentally and theoretically, for a journal diameter of 500 mm up to surface speeds of 94 m/s and unit loads of 5.0 MPa. To model fluid flow in the bearing outside the lubricant gap, an extension to Elrod’s cavitation algorithm based on assuming the inertia of fluid flow is proposed. Validation of the extended thermo-elasto-hydrodynamic lubrication (TEHL) model shows good agreement between measurement and prediction in wide operating ranges, however, with systematic tendencies of the remaining deviations. Furthermore, measured local pressure and film thickness distributions indicate a complex formation of cavitation with an influence of axial flow that is not covered by pure Couette-flow in the cavitation region. Measured as well as predicted data prove increased bearing efficiency for high rotor speeds. To provide understanding on the impact of the applied design measures improving efficiency, their combination is separated into the individual ones. Reduced axial and peripheral pad length both contribute almost equally to the reduction in power loss and improve its value by 37% compared to the standard design. Finally, further steps to deeper identify the behavior of the bearing are comprehensively discussed.

Simulation sudden oil supply in starved high-speed angular contact ball bearing

Many high-speed angular contact ball bearings work without sufficient lubrication in the contact area. A dynamic model including starved thermo-elastohydrodynamic lubrication (TEHL) was proposed to investigate starved ball bearings. For the bearings subjected to axial and radial loads, the inlet film thickness suddenly increases, the friction coefficient drops rapidly, and the ball skids severely as it passes through the low load region. When the location of the change occurs in the low load region, the degree of skidding is significantly reduced. Furthermore, the outer contact zone mainly determines whether or not to skid. Therefore starved high-speed bearings need to avoid a sudden increase in the inlet film thickness in the outer contact zone.

Analysis of Thermoelastohydrodynamic Lubrication of Journal Bearing including the Effect of Surface Roughness and Cavitation

Analysis of Thermoelastohydrodynamic Lubrication of Journal Bearing including the Effect of Surface Roughness and Cavitation

TEHL analysis of VH-CATT cylindrical gear transmission in elliptical contact considering time-varying parameters

The lubrication characteristics of a cylindrical gear transmission with a variable hyperbolic circular-arc-tooth-trace (VH-CATT) are important theoretical bases for the tribology design of the gear and its fatigue life prediction. Existing lubrication characteristics studies of it are based on simplified linear contact models, which are limited to one specific meshing position only. Therefore, the mathematical models for tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) are established to calculate most time-varying parameters in a meshing period, such as the kinematic parameters, spatial geometric parameters, and contact parameters, are calculated. Accordingly, a thermo-elastohydrodynamic lubrication (TEHL) model of an elliptical contact of this gear transmission is presented. Using all the proposed mathematical models, the TEHL results with smooth and rough tooth surfaces in a meshing period are analyzed. The obtained results reveal that these models can be used to predict the distribution of the film thickness, pressure, and temperature rise on the smooth and rough tooth surfaces of VH-CATT cylindrical gear transmission in each contact area of a meshing period. And it shows that the time-varying parameters have great influences on lubrication performance. Furthermore, the lubrication mechanism in a meshing period is investigated systematically in VH-CATT cylindrical gear transmission.

Simulation of the load reduction process of high-speed angular contact ball bearing with coupling model of dynamics and thermo-elastohydrodynamic lubrication

The transient process can be accurately simulated using a dynamic ball bearing model. This paper proposed a dynamic model including thermo-elastohydrodynamic lubrication (TEHL) to investigate high-speed angular contact ball bearings. In this model, TEHL considering the spinning and the non-Newtonian effect was used to calculate the contact force and the friction force. The results showed that the gyroscopic moment of the ball increased in conjunction with a higher load when the axial load remained constant. Furthermore, the sliding speed and film temperature increased significantly in conjunction with a sudden decrease in the axial load from 800 N to 400 N in 3 ms due to an abrupt decline in the friction moment, while the gyroscopic moment was delayed.

Thermoelastohydrodynamic Characteristics of Low-Temperature Helium Gas T-Groove Face Seals.

Thermoelastohydrodynamic lubrication behaviors of helium gas T-groove face seals are numerically simulated under conditions of low temperature and high pressure, with the consideration of real-gas properties including compressibility coefficient, viscosity, and heat capacity. It is found that helium gas T-groove face seal presents a sharp divergent deformation at low temperature and high pressure, which makes the opening performance weaken and the leakage rate increase. This result is obviously different from the case of high-temperature gas face seals. As the sealing temperature drops from 300 K to 150 K, the leakage rate increases about 17% and the opening force decreases about 15%. Moreover, with the growth of rotational speed, both the outlet film pressure and the sealing performance present a non-monotonic trend. Specifically, while the rotating speed of moving ring raises from 3000 to 30,000 r·min−1, the leakage rate changes more than 30%, and the opening force is reduced about 10%.

Ultra-high-speed TEHL characteristics of T-groove face seal under supercritical CO2 condition

Purpose The purpose of this paper is to acquire sealing properties of supercritical CO2 (S-CO2) T-groove seal under ultra-high-speed conditions by thermo-elastohydrodynamic lubrication (TEHL) analysis. Design/methodology/approach Considering the choked flow effect, the finite difference method is applied to solve the gas state equation, Reynolds equation and energy equation. The temperature, pressure and viscosity distributions of the lubricating film are analyzed, and sealing characteristics is also obtained. Findings The face distortions induced by increasing rotational speed leads to the convergent face seal gap. When the linear velocity of rotation exceeds 400 m/s, the maximum temperature difference of the sealing film is approximately 140 K, and the viscosity of CO2 is altered by 17.80%. Near the critical temperature point of CO2, while the seal temperature increases by 50 K, the opening force of the T-groove non-contact seal enhances by 20% and the leakage rate declines by 80%. Originality/value The TEHL characteristics of the T-groove non-contact seal are numerically analyzed under ultra-high-speed, considering the real gas effect and choked flow effect. In the supercritical conditions, the influence of rotational speed, seal temperature, seal pressure and film thickness on sealing performance and face distortions is analyzed.

On the Effect of Supplied Flow Rate to the Performance of a Tilting-Pad Journal Bearing—Static Load and Dynamic Force Measurements

Abstract Rotating machinery relies on engineered tilting-pad journal bearings (TPJB) to provide static load support with minimal drag power losses, safe pad temperatures, and ensuring a rotor-dynamic stable rotor operation. End users focus on reducing the supplied oil flow rate into a bearing to both lower operational costs and to increase drive power efficiency. This paper presents measurements of the steady-state and dynamic forced performance of a TPJB whilst focusing on the influence of supplied oil flow rate, below and above a nominal condition (50% and 150%). The test bearing has five pads, slenderness ratio L/D = 0.4, spherical pivots with pad offset = 50%, and a preload –0.40, with a clearance to radius ratio (Cr/R) ≈ 0.001 at room temperature. The bearing is installed under a load-between-pads (LBP) orientation and has a flooded housing with end seals. The test conditions include operation at various shaft surface speeds (32 m/s–85 m/s) and specific static loads from 0.17 MPa to 2.1 MPa. A turbine oil lubricates the bearing with a speed-dependent flow rate delivered at a constant supply temperature. Measurements obtained at a steady thermal equilibrium include the journal static eccentricity and attitude angle, the oil exit temperature rise, and the pads' subsurface temperatures at various locations, circumferential and axial. The rig includes measurement of the drive torque and shaft speed to produce the bearing drag power loss. Dynamic force coefficients include stiffness, damping, and virtual-mass coefficients. As expected, the drag power and the lubricant temperature rise depend mainly on shaft speed rather than on applied load. A reduction in oil flow rate to 50% of its nominal magnitude causes a modest increase in journal eccentricity, a 15% reduction in drag power loss, a moderate raise (6 °C) in pads' subsurface temperatures, a slight increase (up to 6%) in the direct stiffnesses, and a decrease (up to 7%) in direct damping coefficients. Conversely, a 1.5 times increase in oil flow rate causes a slight increase (up to 9%) in drag power loss, a moderate reduction of pads' temperatures (up to 3 °C), a maximum 5% reduction in direct stiffnesses, and a maximum 10% increase in direct damping. The paper also presents comparisons of the test results against predictions from a thermo-elastohydrodynamic (TEHD) lubrication model. In conclusion, a 50% reduced oil flow rate only causes a slight degradation in the test bearing static and dynamic force performance and does not make the bearing operation unsafe for tests with surface speed up to 74 m/s. As an important corollary, the measured bearing drag power differs from the conventional estimate derived from the product of the supplied flow rate, the lubricant-specific heat, and the oil exit temperature rise.

Thermo-elastohydrodynamic lubrication simulation of reciprocating rod seals under transient condition

A thermo-elastohydrodynamic lubrication transient simulation model for reciprocating rod seals was developed. In the model, the viscoelastic response of rubber materials under transient operating conditions was considered, and the transient Reynolds equation was solved. The stiffness matrix method, which is more stable and effective than the traditional influence coefficient method, was used to solve the problem of fluid - solid coupling in reciprocating sealing. The transient temperature distribution of the sealing system was calculated, and the viscosity of the fluid film was corrected according to the calculation result.

Temperature Variation at Solid-Fluid Interface of Thin Film Lubricated Contact Problems

Many calculating methods have been already developed for solving contact problems of parts such as gears, cams, and followers under fluid film lubrication conditions considering the temperature and pressure dependence. Similarly, the determination of the elasto-hydrodynamic pressure distribution the processes taking place in the lubricant and the contacting bodies, as well as in their environment, have to be dealt with simultaneously for the determination of the temperature field. A system of equation for the modelling of thermo-elastohydrodynamic lubrication between two contacting bodies containing hydrodynamic, thermodynamic, and strength problems is a highly non-linear system which becomes even more so if the temperature and pressure dependence of the material properties are considered. To solve this system, scientists started to use the finite element formulation in the 1960s and it was found to be a promising and reliable method. Earlier, the lubrication analysts used only the h-version finite element method (h-FEM) till 1991, when the first usage of the p-version finite element method (p-FEM) was published in the literature. In order to reduce the problem, in case of point or line contact, the contact bodies can be handled as semi-infinite ones. Following this simplification that had been successfully applied for the gap size determination, a substructure model was defined using analytical solution of the moving heat source. Instead of an iterative way between the solid and fluid problem, in this paper we present an efficient solution when thermal model for lubricant and surfaces were coupled and solved by a direct numerical method in one step.