Elastohydrodynamic Lubrication Research Articles

Effect of Surface Roughness on the Friction Moment in a Lubricated Deep Groove Ball Bearing

Deep groove ball bearings (DGBBs) are extensively utilized in industrial machinery, mechanical systems, and household appliances due to their simple design, low maintenance, and ability to operate at high speeds. A critical issue in the performance of these bearings is the power loss by internal friction torque, which adversely affects system efficiency, longevity, and reliability, particularly in demanding applications such as aviation and marine systems. The friction torque in DGBBs is influenced by factors such as load, speed, surface roughness, and lubricant viscosity, making the precise understanding of these elements essential for optimizing system efficiency. Despite its significance, the effect of surface roughness on friction torque in DGBBs remains underexplored. This paper presents an analytical model to evaluate the frictional moments resulting from interactions between the ball–race and ball–cage in lubricated, low-speed DGBBs. This model employs a mixed elastohydrodynamic lubrication approach to determine the friction coefficient at the contact interfaces. This study explores how surface roughness and speed affect both ball–race and ball–cage friction torque, offering a comprehensive analysis of their influence on overall frictional torque. Additionally, the effect of surface roughness on ball–cage contact forces is investigated, enhancing the understanding of its contribution to friction torque. These insights aim to improve DGBB design and operation, maximizing performance and energy efficiency.

The Temperature Dependence of Divergence Pressure

The so-called controversy in elastohydrodynamic lubrication (EHL) regarding the nature of the shear dependence of viscosity, Eyring versus Carreau, is truly a controversy regarding the pressure and temperature dependence of low-shear viscosity. Roelands removed data that contradicted his claims of accuracy for his correlation. The Roelands hoax became acceptable in EHL because ignoring the universal previtreous piezoviscous response made the traction calculated with the Eyring assumption appear to be reasonable. Traction and minimum film thickness calculations sometimes require the description of viscosity at pressures up to the glass transition pressure. There have been few measurements of viscosity at pressures up to glass pressure. Therefore, a need exists for a piezoviscous model that extrapolates accurately, and the Hybrid model fills that need. Here, an improved relation for the temperature dependence of divergence pressure is offered and extrapolation is demonstrated for a polyalphaolefin and propylene carbonate. A linear dependence of divergence pressure with temperature is more useful than previous versions. An improvement in the capability of high-pressure viscometry is suggested based upon the fractional Stokes Einstein Debye relation and the relatively simple measurements of DC conductivity.

A Starved Lubrication Model: Applications to Evaluate Gear Mesh and Response Prediction of Material Plasticity

This study presents a model of starved mixed Elastohydrodynamic Lubrication (EHL) in point and line contact to investigate the lubrication performance and material response. In formulating the governing equations for the lubrication, the dimensional Reynolds equation is discretized to involve all possible regimes from the boundary lubrication to fully hydrodynamic lubrication, and an additional algorithm is provided to determine the fractional film content based on the profiles of pressure distribution and film thickness. Solutions of the point contact from the present model are compared with those reported by the previous studies and good consistency can be found. The three-dimensional line contact is used to predict the load carrying capabilities of the film thickness at the interface of mating spur gear teeth. A return mapping method is implemented to take the plastic revolution into account. The solution at the initial stage of a startup process with the lubricant entrainment velocities of ux = uy = 0 is compared with that from a dry contact to validate the elasto-plastic solutions. Sample cases are presented to reveal the effects of inlet oil supply condition and material plasticity on lubrication starvation.

Vibration properties of full ceramic bearing under elastohydrodynamic fluid lubrication based on the energy approach

As an important part of rotating machinery, heat generation due to friction is inevitable during the rotating process of bearings. A large amount of heat causes the temperature of lubricating oil to increase, viscosity of lubricating oil to decrease, and lubricating performance decreases. Addressing the issue of inadequate lubrication between the rolling element and raceway due to increased lubricating oil temperature, this study focuses on full-ceramic ball bearings. It examines the impact of temperature fluctuations on the bearing's lubrication condition and investigates the vibration characteristics of the full-ceramic bearing. The variation in the viscosity of lubricating oil with respect to temperature is measured via a rotary viscometer. A dynamic model of the silicon nitride full-ceramic ball bearing, which considers the effects of elastohydrodynamic lubrication, is established. The impacts of changes in lubricating oil viscosity due to different temperatures on oil film pressure, oil film thickness, and bearing vibration are analyzed and then compared with experimental data. It is observed that under conditions of constant load and speed, the film thickness of the lubricating oil decreases as the viscosity decreases. Additionally, the second peak value of oil film pressure is reduced with the declining viscosity of the lubricating oil. As the viscosity decreases, the vibration of the bearing increases. The amplitude discrepancy between the simulated vibration signal and experimental vibration signal of the full-ceramic bearing is found to be less than 10 %, verifying the validity of the dynamic model.

Lubrication Prediction of Sphere‐Gradient Coated Half Space Interfaces

ABSTRACTFunctionally graded coating (FGC) has played a pivotal role in numerous engineering applications owing to its exceptional properties. This work proposes a novel elastohydrodynamic lubrication (EHL) model with FGC, in which the elastic deformation and stress are computed using influence coefficients (ICs) and discrete convolution‐fast Fourier transform (DC‐FFT) algorithm. Comparisons are made with homogeneous EHL solutions and finite element analysis (FEA) to validate its accuracy. The study systematically explores how coating elastic modulus, coating thickness and substrate elastic modulus influence contact and lubrication behaviours. The developed model is expected to establish a theoretical framework for FGC material design, enhancing the performance of friction pairs.

A Simplified Non‐Hertzian Wheel‐Rail Adhesion Model Under Interfacial Contaminations Considering Surface Roughness

ABSTRACTThe accuracy and efficiency of the wheel‐rail adhesion model are important to the wheel‐rail rolling contact issues. The purpose of this study is to develop a simplified non‐Hertzian wheel‐rail adhesion model under interfacial contaminations to predict the wheel‐rail adhesion coefficient. Firstly, a non‐Hertzian full elasto‐hydrodynamic lubrication (EHL) model was developed and applied to determine the wheel‐rail contact pressure and film thickness under interfacial contaminations. Then, the empirical formula of central film thickness available to non‐Hertzian wheel‐rail normal contact relating to train speeds, axle loads and material parameters were proposed based on a large number of non‐Hertzian full EHL simulation for smooth surface under interfacial contaminations using linear regression. The empirical non‐Hertzian central film thickness formula and minimum film thickness formula for wheel‐rail contact obtained in this paper show certain differences from the formulas based on Hertzian contact. Using the proposed non‐Hertzian central film thickness formula, a simplified non‐Hertzian wheel‐rail contact adhesion model was developed, and the adhesion coefficient was obtained at different speeds and compared with the field test data. The numerical results showed good agreement with field test data.

Physics-Informed Neural Networks for the Reynolds Equation with Transient Cavitation Modeling

Gaining insight into tribological systems is crucial for optimizing efficiency and prolonging operational lifespans in technical systems. Experimental investigations are time-consuming and costly, especially for reciprocating seals in fluid power systems. Elastohydrodynamic lubrication (EHL) simulations offer an alternative but demand significant computational resources. Physics-informed neural networks (PINNs) provide a promising solution using physics-based approaches to solve partial differential equations. While PINNs have successfully modeled hydrodynamics with stationary cavitation, they have yet to address transient cavitation with dynamic geometry changes. This contribution applies a PINN framework to predict pressure build-up and transient cavitation in sealing contacts with dynamic geometry changes. The results demonstrate the potential of PINNs for modeling tribological systems and highlight their significance in enhancing computational efficiency.

Transient mixed thermal elastohydrodynamic lubrication analysis of aero ball bearing under non-steady state conditions

A transient mixed thermal elastohydrodynamic lubrication model of bearing considering the thermal effect and the changes in velocity, load, and contact geometry is proposed. Based on the bearing dynamic and lubrication analysis, the effects of bearing rotational speed and start-stop conditions on the dynamic behavior and lubrication performance are studied. Results show that when the bearing rotational speed exceeds a certain critical value, the increasing speed will reduce the film thickness, especially the outer raceway. The increasing bearing acceleration can cause a higher slide-roll ratio and film temperature at the initial start-up process. Compared with the start-up process, the lubrication change in the shut-down process has a similar opposite trend, but the overall lubrication performance is better.

Dynamic Modeling of Angular Contact Ball Bearing with Local Defects under EHL Considering Impact Force

In order to analyze the operating status of angular contact ball bearings(ACBBs) with local defects in more detail, a dynamic model of ACBB with local defects considering impact force under elastohydrodynamic lubrication conditions is proposed. Firstly, an elastohydrodynamic lubrication model for defective bearings considering spin is established, the film thickness and film stiffness of the defective bearings are calculated, and then time-varying displacement excitation model and time-varying stiffness model for local defects in angular contact ball bearings is presented. Based on this, an instantaneous impact force function related to defect size and bearing speed is established. Secondly, based on Hertz contact theory and impact force function, a dynamic calculation method for ACBBs with local defects on the outer ring is proposed. Finally, the vibration characteristics of ball bearings with faults are investigated, and the influence of different parameters on the dynamic response of the bearings is analyzed. The calculation results show that under lubrication conditions, the impact force on the vibration of the bearing is significantly weakened. With the increase of defect size and load, the frequency of bearing fault characteristics remain unchanged, but its amplitude increases. As the bearing speed increases, the characteristic frequency and amplitude of bearing faults increase.

Wedge-loading planetary traction drive: Modeling and performance analysis

The continuous development of motors with high speed and high power density has significantly increased the demand for high-speed reducers. Traction drive has emerged as a new option for high-speed reducers due to its high transmission efficiency and accuracy in high-speed transmission. In the previous theoretical studies on traction drive, the traction coefficient was set as a fixed value, and the influence of elastohydrodynamic lubrication (EHL) on the traction coefficient was ignored. Therefore, this paper investigated the wedge-loading planetary traction drive (WL-PTD) and established a theoretical model combining the macroscopic and microscopic traction mechanisms of the traction drive based on Hertzian contact and mixed elastohydrodynamic lubrication (mixed EHL). The loading principle and transmission performance of WL-PTD were studied through numerical computations, and the effects of different design parameters on transmission performance were discussed. When the input speed of WL-PTD was 10,000 rpm, the peak value of the global sliding coefficient was approximately 1.27×10−5, and the maximum transmission efficiency reached 97.41%, indicating an excellent transmission performance of the WL-PTD. The findings of this study can provide theoretical guidance for subsequent optimization design.

TVMS calculation model for gear tooth tip chipping failure with EHL

This paper proposes a calculation method for Time-Varying Mesh Stiffness (TVMS) in the presence of tooth tip chipping defects under elastohydrodynamic lubrication (EHL). A contact stiffness model for tooth tip chipping defects under EHL is established, and an analytical equation for the TVMS of chipping defects under EHL is derived. The torsional stiffness at the chipping defect under EHL is introduced, considering the influence of roughness at the chipping defect on the characteristics of the oil film and its stiffness. The effects of chipping defect size, torsional stiffness of the chipping defect under EHL, roughness, and oil film stiffness on TVMS are analyzed, providing methodological support for improving the calculation accuracy of gear TVMS.

Thermal–Elastohydrodynamic Lubrication Characteristics of the Flow Distribution Pair of Balanced Double-Row Axial Piston Pumps

A theoretical model for the calculation of thermal elastohydrodynamic lubrication performance of the flow distribution pair of piston pumps is established, which is composed of the oil film pressure governing equation and energy equation, and solved by means of numerical solution and simulation. We carry out quantitative analysis of the influence of various parameters on the thermal elastohydrodynamic lubrication characteristics of the flow distribution pair. The results indicate that both the oil film thickness and the cylinder tilt angle of the flow distribution pair vary in a periodic manner. The increase in the rotational speed of the cylinder block will increase the film thickness of the oil film and reduce the fluctuation, and the inclination angle of the cylinder block and its fluctuation amplitude will decrease. An increase in working pressure will lead to a decrease in the average oil film thickness, an increase in fluctuations, and an elevation in both the tilt angle of the cylinder block and its fluctuation amplitude. The increase in the rotational speed of the cylinder block and the increase in the working pressure will lead to the increase in the viscous friction dissipation of the flow distribution pair, the increase in the oil film temperature and the increase in the leakage. The reduction in the sealing belt will lead to the reduction in oil film friction torque and leakage.

The investigations of asperity peaks and surface roughness on transient squeeze elastohydrodynamic lubrication

Abstract The effects of asperity peak contact pressure and surface roughness (SRN) on pure squeeze elastohydrodynamic lubrication (EHL) motion of circular contacts are investigated for fixed load by using Gauss-Seidel iteration method (GSIM) and finite difference method (FDM). The transient pressure, asperity peak contact pressure, elastic deformation, and film thickness during the pure squeeze process under distinct operating conditions in EHL regime are studied. The results indicate that the differences of the pressure and film thickness between SRNEHL model and EHL model are apparent in final stage due to elastic asperity peak contact. The asperity peak contact pressure will affect hydrodynamic pressure for fixed load, so the hydrodynamic pressure with roughness surface is smaller than that without roughness surface especially around the Hertzian contact (X=1) edge. These phenomena result in different changes in total pressure in different areas. For the contact region, the film thickness of smooth type (ST) is greater than those of circular roughness type (CRT), but this phenomenon reverses near X=1. The larger the C value, the earlier the asperity peak contact effect. Therefore, the greater the C values, the greater the asperity peak contact pressure, and the smaller the hydrodynamic pressure. The asperity peak contact effect significant changes many phenomena at contact region in squeezing final stage.

Measurement of slip length and friction reduction: An experimental study about boundary slip using omniphobic and 2D coatings

There is an intrinsic link between boundary slip and superlubricity. However, due to limitations in experimental techniques, the slip length cannot be precisely measured, leaving the mechanism of boundary slip controversial. This paper aims to accurately measure the slip length at the solid-liquid interface under oil-lubricated elastohydrodynamic lubrication (EHL) conditions using experimental methods, and to explore the friction reduction due to boundary slip. The study reveals that both omniphobic (lotus leaf essence) coatings and two-dimensional (2D) material (MoS2) coatings facilitate boundary slip. The slip length measurement method proposed in this study builds a bridge between oil film thickness and slip length, successfully addressing a key issue in boundary slip research. The findings confirm the significant friction reduction due to boundary slip, representing a major advancement in reducing friction in oil-lubricated EHL contacts through boundary slip. Future research should focus on searching for coating materials with a slip length on the micrometer scale so that superlubricity could be achieved.

A novel time-varying mesh stiffness model for orthogonal face gear drives considering EHL

PurposeThis study aims to research the time-varying mesh stiffness (TVMS) model for orthogonal face gear drives considering elastohydrodynamic lubrication (EHL) and provide a theoretical basis for understanding the dynamic characteristics of face gear drives.Design/methodology/approachConsidering EHL, a novel model is proposed to calculate the TVMS of orthogonal face gears using the deformation compatibility condition. First, the tooth surface equations of orthogonal face gears are derived according to the tooth surface generation principle. Then, the oil film thickness on the tooth surface of face gears is obtained by solving the governing equations of EHL. Furthermore, the proposed model is used to calculate the TVMS of face gears along the mesh cycle and is verified. Finally, the effects of module, tooth number of shaper cutter and pressure angle on mesh stiffness are analyzed.FindingsThe results indicate that when the contact ratio is greater than 1 and less than or equal to 2, the TVMS of face gears exhibits a phenomenon of double-single tooth alternating meshing where sudden changes occur. As the module increases, the overall mesh stiffness of face gears increases, and the magnitude of the sudden change at the moment of single-double tooth alternating meshing gradually increases. As the tooth number of shaper cutter and pressure angle increase, so does the TVMS of face gears. When the effect of oil film is considered, the calculated TVMS of face gears slightly increases overall and the increase in average oil film thickness leads to a rise in the TVMS. This study provides a theoretical basis for understanding the dynamic characteristics of face gear drives.Originality/valueThis study’s originality and value lie in its comprehensive approach, which includes conducting analysis based on loaded tooth contact, considering the influence of elastohydrodynamic lubrication, proposing a novel analytical–finite–element model, calculating TVMS of face gears, verifying the proposed model and analyzing the effects of typical structural parameters and oil film thickness.

Numerical analysis of the Thermal EHL line contact problem under intermittent motion

Abstract A mathematical model of time-varying thermal elastohydrodynamic lubrication (EHL) is developed using a sleeve chain as the object of study. The effects of thermal effect, load, speed, rest time and equivalent radius of curvature on its EHL are investigated using theoretical simulations. The results show that during intermittent motion, a portion of oil is entrapped in the contact zone at the end of the deceleration phase, after which this entrapped oil gradually moves out of the contact zone with the onset of speed, and a lower film of oil at the lubrication inlet passes through the center of the contact zone. In simple sliding intermittent motion, the temperature rise plays a crucial role in the variation of the oil film, particularly during the motion phases, and is an unavoidable factor. An increase in stop time reduces the film thickness and increases the following friction coefficient in the acceleration stage. An increase in the equivalent radius of curvature increases the film thickness and thermal rise in the contact zone as well as decreases the friction coefficient. Since the sleeve chain is one of the most commonly used mechanism in industry, high priority should be given to the lubrication design of this structure.

Study on the wear characteristics of cylindrical needle bearings on the crankshaft of RV decelerator

PurposeThe purpose of this study is to systematically analyze the wear of cylindrical needle bearings in rotary vector reducers under temperature rise and identify the influencing factors.Design/methodology/approachBased on the dynamic characteristics of the RV-20E reducer, the time-varying contact force of the cylindrical needle bearing and the entrainment speed of the inner and outer raceways were calculated. A mixed elastohydrodynamic lubrication model of the needle bearing, considering friction and temperature rise, was established using a dynamic rough tooth surface model. The model solved for the oil film thickness, contact stress and wear conditions of the bearing raceway contact area. The effects of the number of rolling needles, the diameter of rolling needles and surface strength on the wear characteristics were analyzed.FindingsThe results of this study show that the oil film thickness, oil film pressure and surface scratches of cylindrical needle bearings exhibit an uneven, patchy distribution under the combined effects of friction and temperature rise. When the radius of the rolling needle is less than 1.44 mm, inner ring wear is less than outer ring wear. Conversely, when the radius exceeds 1.44 mm, inner ring wear is greater. The optimal rolling needle radius is 1.6 mm. Increasing the number of rolling needles and enhancing the yield strength of the contact surface significantly extend bearing life.Originality/valueThis study provides valuable recommendations for optimizing bearing structural parameters and material characteristics in the design of rotary vector reducers.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2024-0242/

A Fully Implicit Coupled Scheme for Mixed Elastohydrodynamic Problems on Co-Allocated Grids

In the modeling of elastohydrodynamic lubrication problems considering mixed friction, strongly coupled dependencies occur due to piezo-viscous effects and asperities, which can make a numerical solution exceptionally difficult. A fully implicit coupled scheme for solving mixed elastohydrodynamic lubrication problems is presented. Our scheme uses finite-volume discretization and co-allocated grids for hydrodynamic pressure and elastic deformation. To provide strong coupling between pressure and deformation even in the highly loaded zone, a correction term that adds numerical diffusion is used. The resulting linear equation system of this scheme can be efficiently solved by Krylov subspace methods. This results in an improved accuracy and computational efficiency compared to the existing methods. This approach was validated and has been shown to be accurate.

High-pressure rheological properties of polyalphaolefin and ester oil blends and their impact on lubrication

Different base oils are often blended to optimize lubrication effectiveness. For blends of polyalphaolefins (PAOs) and ester oils, while their boundary lubrication performance is well-studied, studies on their rheological properties and elastohydrodynamic lubrication (EHL) are limited. This study investigates the viscosity and EHL properties of PAO 8 and pentaerythritol tetra(2-ethylhexanoate) (PEB 8) blends at various blending ratios, pressures, and temperatures. Results showed that under certain conditions, viscosities of the blends are lower than either base oil. This phenomenon was explained from a molecular perspective. The pressure–viscosity relationship was fitted using the Doolittle-Tait free-volume model. Additionally, studies of EHL performance and simulations of different oils correlate the pressure–viscosity to EHL characteristics. These findings provide insights for future lubricant formulation.

Minimum zone fitting and error evaluation for arc correction type convex contour of bearing roller

The minimum zone fitting and error evaluation for the arc-modified convex contour of a bearing roller have important applications for consistency detection and quantificational research of the elastohydrodynamic lubrication of a bearing roller. Based on the definition of the shape error and the geometric characteristics of the arc corrected roller convexity line of the bearing, a new fitting and error evaluation method for the total convexity contour of a bearing roller is presented. First, the reference cutoff points of the arc segment and straight line are determined based on the curvature difference of each measurement point. Then, the measuring points on both sides of the two reference cutoff points are selected as auxiliary cutoff points for arc fitting. The fitting error is obtained based on the minimum area method. Finally, a series of tangent equations are obtained based on the tangent principle between a line and two arcs, and the straightness error is determined by calculating the distances between the measuring points and the tangents. The example results show that an arc-modified convex contour can be fitted, and its global error can be evaluated effectively and precisely using the presented method. This study also provides a new idea for the minimum zone fitting of multi-segment curves along a plane.