Elastohydrodynamic Lubrication Model Research Articles

A Mixed Elasto-Hydrodynamic Lubrication Model for Wear Calculation in Artificial Hip Joints

The aim of this paper was to propose a novel in silico mixed elasto-hydrodynamic lubrication model with the purpose of wear prediction in Total Hip Replacements (THRs). The model considers the progressive wear contribution in the calculation of the meatus filled by the non-Newtonian synovial fluid. The results were referred to the gait cycle kinematics, calculated by using musculoskeletal multibody software, while the loading was assumed by literature in vivo measurements. The simulations allow evaluating the fluid and the contact pressure fields and the acetabular cup wear over the time. The results were obtained considering a Ultra High Molecular Weight PolyEthylene, UHMWPE, cup and were compared with results from the literature, showing a good agreement in terms of total volume wear of the cup.

Influences of transient impact and vibration on the lubrication performance of spur gears

In this paper, the mathematical model of gear elastohydrodynamic lubrication is presented. The transient impact operating condition and underdamped load condition are considered. Taking thermal effect and squeeze effect into account, the full numerical solution of gear pairs is obtained. In this numerical calculation, multigrid method is applied to compute the film pressure; multigrid integration technique is used to calculate the solid surface deformation; column by column scanning technique is employed to calculate temperature. The simulation results show that an entrapped film dimple forms under transient impact condition; transient impact causes remarkable increases in film pressure and film temperature. Compared with the normal case the minimum thickness of the impact case is smaller, which is not beneficial to teeth lubrication. Thermal effect induces some decreases in film thickness because of the viscosity–temperature relationship. Vibrational load with high damped frequency causes greater increases in film thickness and greater decreases in the coefficient of friction than that of low damped frequency. However, the film temperature of high damped frequency is higher than that of low damped frequency.

Subsurface stress-field analysis of generating ground helical gear based on finite line-contact mixed elastohydrodynamic lubrication

Tooth surface roughness and lubrication status have significant influence on the contact performance and fatigue life of helical gear pair. Yet, despite the development in elastohydrodynamic lubrication-based contact analysis and solution of subsurface stress field, researches in subsurface stress field of helical gears considering both lubrication and surface roughness are not quite comprehensive. In this study, three-dimensional surface roughness of generating ground gear is measured, a finite line-contact mixed elastohydrodynamic lubrication model is established to perform the contact analysis, and, on this basis, the influence of tooth surface roughness on the subsurface stress field is studied. Results show that compared with the smooth surface, the overall level of subsurface stress is raised; maximum stress values and plastic zones occur in the close vicinity of tooth surface, which adds to the risk of surface failure; within sections in the valley regions of roughness, locations of maximum stresses are generally similar to the smooth surface situation, i.e. in relatively deep zones, while within sections in the peak regions, the majority of locations with maximum stresses shift much closer to the surface; contact pressure and stress status see only mild undulation between different sections distributed along the contact line, but intense changes between sections distributed along the entraining direction.

Multi-ellipsoid contact elastohydrodynamic lubrication performance for deep groove ball bearing

The multi-ellipsoid contact elastohydrodynamic lubrication (MECEHL) model for the deep groove ball bearing considering the forces and moments applied on the rolling elements is established and solved with optimization method. In doing so, the Newton-Raphson method is used to calculate the contact load of rolling elements, and the fast Fourier transform (FFT) is employed to accelerate the calculation of the elastic deformation. The complex method and dichotomy one are proposed to obtain the revolution velocity and rotational angular velocity of all the rolling elements. Based on the validation of the elastohydrodynamic lubrication model, the MECEHL performances for the outer-inner rings are studied and compared at the varied radial load and clearance, inner ring's rotational speed, rolling element number and initial lubricant viscosity. Through the above comparison, some rules about the MECEHL of the bearing are obtained.

An Integrated Model to Characterize Comprehensive Stiffness of Angular Contact Ball Bearings

The bearing dynamic behaviors will be complicated due to the changes in the geometric sizes and relative positions of the bearing components at high speed. In this paper, based on the Hertz contact theory, elastohydrodynamic lubrication (EHL) model, and Jones’ bearing theory, the comprehensive stiffness model of the angular contact ball bearing is proposed in consideration of the effects of elastic deformation, centrifugal deformation, thermal deformation, and the ball spinning motion. The influences of these factors on bearing dynamic stiffness are investigated in detail. The calculation results show that the centrifugal deformation and thermal deformation increase with the increase in rotation speed. When the centrifugal deformation and thermal deformation are considered, the bearing radial contact stiffness increases as the speed increases, whereas the axial contact stiffness and the angular contact stiffness decrease. When the deformations and the EHL are all considered, the comprehensive bearing stiffness decreases with the increasing speed. It is also found that the spinning motion of the ball causes the comprehensive bearing stiffness to increase.

Maximizing the Lubricant Film Thickness Between a Rigid Microtextured and a Smooth Deformable Surface in Relative Motion, Using a Soft Elasto-Hydrodynamic Lubrication Model.

We design a pattern of microtexture features to increase hydrodynamic pressure and lubricant film thickness in a hard-on-soft bearing. We use a soft elastohydrodynamic lubrication model to evaluate the effect of microtexture design parameters and bearing operating conditions on the resulting lubricant film thickness and find that the maximum lubricant film thickness occurs with a texture density between 10% and 40% and texture aspect ratio between 1% and 14%, depending on the bearing load and operating conditions. We show that these results are similar to those of hydrodynamic textured bearing problems because the lubricant film thickness is almost independent of the stiffness of the bearing surfaces in full-film lubrication.

A thermal EHL investigation on plate-pin hinge pairs in silent chains using a narrow finite line contact

Purpose The purpose of this paper is to numerically study the variations of oil film pressure, thickness and temperature rise in the contact zone of plate-pin pair in silent chains. Design/methodology/approach A steady-state thermal elastohydrodynamic lubrication (EHL) model is built using a Ree–Eyring fluid. The contact between the plate and the pin is simplified as a narrow finite line contact, and the lubrication state is examined by varying the geometry and the plate speed. Findings With increase in the equivalent radius of curvature, the pressure peak and the central film thickness increase. Because the plate is very thin, the temperature rise can be neglected. Even when the influence of the rounded corner region is less, a proper design can beneficially increase the minimum film thickness at both edges of the plate. Under a low entraining speed, strong stress concentration results in close-zero film thickness at both edges of the plate. Originality/value This study reveals the EHL feature of the narrow finite line contact in plate-pin pairs for silent chains and will support the future works considering transient effect, surface features and wear.

Effect of roughness on meshing power loss of planetary gear set considering elasto-hydrodynamic lubrication

Meshing power loss is one of the most important parts in power loss calculation of planetary gear set. However, most of the conventional methods assumed the friction coefficient between gears as a constant value in the meshing power loss calculation, and most importantly, the influence of gear tooth surface geometry is usually ignored, for example, roughness. Therefore, a new meshing power loss calculation model for planetary gear set that considers tooth surface roughness is proposed on the basis of elasto-hydrodynamic lubrication method. With the proposed model, a planetary gear set dynamic model that considers friction force between gears is first established to study the time-varying meshing forces, sliding speeds, and curvature radii of the gear pairs. Then, an elasto-hydrodynamic lubrication model of the gear pair contact interface is constructed to investigate and modify the friction force distribution in the gear meshing process of the dynamic model iteratively until the meshing forces converge to stable values. Furthermore, the relationship between the tooth surface roughness and film thickness is studied in the elasto-hydrodynamic lubrication model. After that, the meshing power loss is calculated based on the obtained meshing forces, friction coefficients, sliding speeds, and so on. The results show that there is a sudden growth of the meshing power loss at the end of the meshing cycle, which has a good agreement with the meshing force impact. And, it is found that tooth surface roughness has a direct influence on the meshing power loss of sun–planet gear pair, which yields an increasing tendency as the surface roughness growing.

Thermoelastohydrodynamic Lubrication Simulation of Radial Shaft Sealing Rings

Abstract Regarding the increasing demand in seal lifetime and energy efficiency, a detailed microscopic simulation is necessary—as an addition to experimental investigations—to better understand and improve radial shaft seals. For this purpose, typically thermoelastohydrodynamic lubrication (TEHL) simulations are used. The published models range from rather simple elastohydrodynamic lubrication (EHL) models to very sophisticated TEHL models. Only very few models take into account the roughness or microstructure of both contact surfaces, though, since this would require the consideration of transient effects. In this article, a transient TEHL model for the contact of radial shaft seals is presented. Studies of the sealing contact are conducted, and the possibility of investigating shaft microstructuring is shown.

A thermal EHL investigation for size effect of finite line contact on bush-pin hinge pairs in industrial chains

PurposeThis paper aims to study the influence of the dimension change of bush-pin on the pressure, oil film thickness, temperature rise and traction coefficient in contact zone by using a thermal elastohydrodynamic lubrication (EHL) model for finite line contact. Concretely, the effects of the equivalent curvature radius of the bush and the pin, and the length of the bush are investigated.Design/methodology/approachIn this paper, the contact between the bush and pin is simplified as finite line contact. The lubrication state is studied by numerical simulation using steady-state line contact thermal EHL. A constitutive equation Ree–Eyring fluid is used in the calculations.FindingsIt is found that by selecting an optimal equivalent radius of curvature and prolonging the bush length can improve the lubrication state effectively.Originality/valueUnder specific working conditions, there exists an optimal equivalent radius to maximize the minimum oil film thickness in the contact zone. The increase of generatrix length will weaken the stress concentration effect in the rounded corner area at both ends of the bush, which can improve the wear resistance of chain.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-10-2019-0448.

Lubrication mechanisms of rubbing interface in internal meshing teeth with small clearance

AbstractInternal gears with small tooth number difference are widely used as core component in robotics, medical, and other fields. The clearance between the entire meshing teeth is much smaller compared with other gear transmissions, indicating that the entire tooth profile can significantly affect the mixed elastohydrodynamic lubrication (EHL) state of a certain meshing point. Thereby, available lubrication analysis is limited with the assumption of effective radius at each meshing point. In the present study, the entire tooth profile with gear flank modification is studied to improve lubricating characteristics. A mixed EHL model for predicting the film, pressure, power loss, and subsurface stress is presented with consideration of the entire tooth geometry. We find that the tooth geometry away from the meshing location shows a remarkable influence on the film and pressure distribution as well as power loss of tooth rubbing interface, which is commonly unrecognised in previous study. Optimization of modification parameters is observed under different operating conditions, highlighting the critical role of entire tooth geometry in mixed EHL behaviour for internal gears with small tooth number difference.

A mixed thermal elastohydrodynamic lubrication model of rotary lip seal.

Rotary lip seal is used in various applications where the rotation shaft needs to be sealed, such as hydraulic pumps, fuel pumps, camshafts, crankshafts, and so on. Many thermal elastohydrodynamic lubrication models of rotary lip seal have been introduced, and most of these models neglect the asperity contact. This article proposes a mixed thermal elastohydrodynamic lubrication model of rotary lip seal, in which the microstructure of sealing lip surface, influence of temperature on fluid viscosity, and deformation of lip surface, as well as the asperity contact, are taken into consideration. Simulation study is carried out, and the results show that the asperity contact should not be neglected for analyzing the sealing performance of the rotary lip seal. The influence of speed on the sealing performance is also analyzed based on the proposed model.

A Mixed TEHL Model for the Prediction of Thermal Effect on Lubrication Performance in Spiral Bevel Gears

Arbitrary velocity vectors on two meshing surfaces in spiral bevel gears could generate large sliding velocity, which may cause a tremendous temperature rise, especially when surface roughness is involved. However, available studies are primarily concentrated on full-film lubrication without considering temperature rise and surface topography. The purpose of present study is to develop a mixed thermal elastohydrodynamic lubrication (TEHL) model taking into account the velocity vector and surface roughness. The obtained results are compared with those from an elastohydrodynamic lubrication (EHL) model and measurements in previous literature to demonstrate the accuracy of the present model. Further, the TEHL model has been applied to predict the film thickness, pressure, and temperature rise of spiral bevel gears over one meshing period by considering thermal effects.

Calculation of Gear Meshing Stiffness Considering Lubrication

Abstract Gear meshing stiffness is the key parameter to study the gear dynamic performance. However, the study on the calculation of gear meshing stiffness considering lubrication, especially mixed lubrication, is still insufficient. Based on the three-dimensional linear contact mixed elastohydrodynamic lubrication model and the contact stiffness calculation method of rough surface, a method for calculating the gear meshing stiffness under mixed lubrication is proposed in this paper. According to the proposed calculation method, the effects of speed, external load, and roughness amplitude on gear meshing stiffness are further explored. The method can take into account the real rough surface topography and lubrication in the meshing process, so it may be more advantageous than the conventional method to some extent.

Effect of imperfect coating on the elastohydrodynamic lubrication: Dislocation-like and force-like coating-substrate interfaces

Abstract The commonly existed imperfect coatings may cause the displacements and forces transmitting discontinuously at the coating-substrate interface. This paper reports an elastohydrodynamic lubrication (EHL) model of ball-coated half space with coupled dislocation-like and force-like coating-substrate interface. Reynolds equation is solved to obtain the pressure. The surface elastic deformation and subsurface stress are calculated with the discrete convolution and fast Fourier transform (DC-FFT) method with the influence coefficients (ICs) obtained through corresponding frequency response functions (FRFs). The model is validated by the available data, and then implemented to study the pressure, film thickness, and subsurface stress distributions under imperfect coating-substrate interfaces of dislocation-like, force-like, and the coupled conditions, with various displacements and stresses jumping coefficients.

Analysis of the Surface/Interface Damage Evolution Behavior of a Coating–Substrate System under Heavy-Load Elastohydrodynamic Lubrication

Keeping a coating–substrate system undamaged during heavy-load elastohydrodynamic lubrication (EHL) conditions is challenging. To overcome this problem, an EHL model with a coated gear pair was built. Firstly, based on the full-system finite element method, the effect of the coating elastic modulus on the oil film pressure was obtained. Secondly, the failure mode was predicted after the stress analysis. Finally, the surface/interface damage evolution behavior of the coating–substrate system was analyzed visually by embedding cohesive zone elements. In the numerical calculation, stiffer coatings tended to increase the film pressure and secondary pressure spike, compared with more compliant coatings. As the coating stiffness decreased, the maximum equivalent stress in the system reduced, and its location tended to develop close to or at the substrate. The coating cracking and interfacial delamination were individually caused by the shear stress in the coating and shear stress on the interface, and both of them initiated in the region of the secondary pressure peak. The interfacial delamination increased the crack failure probability of coating and vice versa. Therefore, through analyzing the EHL model, the exact damage growth location and its evolution in the coated solids can be determined, and the failure mechanism can be comprehensively revealed.

Tribo-dynamics model of a spur gear pair with gyroscopic effect and flexible shaft

This study proposes a tribo-dynamic model of a spur gear by coupling an elastic dynamic model and an isothermal elastohydrodynamic lubrication (EHL) model. In this model, the gear shafts are modelled as flexible bodies by the resultant elements of Timoshenko beam and bar elements, and the gyroscopic effect of gear rotors and shafts is also included. The transient and non-Newtonian effects are considered in the EHL model to predict tooth friction forces and moments. Then, an example is provided to analyze the interaction between gear tribology and dynamic behavior. Results indicate that the fluctuations of mesh force and surface tangential velocity caused by gear vibration considerably affect the pressure and thickness of the lubricant film. The gyroscopic effect exerts a significant influence on the dynamic and tribology properties of the gear drive at high speed. The proposed model has important guidance for the design of lubrication systems and dynamic properties in gear drives.

Thermal elastohydrodynamic lubrication analysis of helical gear pair under starved lubrication condition

AbstractIn the present study, thermal starved elastohydrodynamic lubrication (EHL) model is developed for a helical gear pair. The influences of inlet oil‐supply layer, input speed, lubricant viscosity, and surface roughness on the lubrication behaviour are investigated. The minimum film thickness, temperature rise of teeth surfaces and oil film, and the friction coefficient are predicted along the line of action (LOA). Results show that the effects of inlet oil‐supply layer, input speed, and lubrication viscosity on the tribological performance are remarkable. Under the starved lubrication, the influence of inlet oil supply on the temperature rise is insignificant. Meanwhile, the effect of surface roughness has been discussed. It reveals that the roughness texture along the entrainment velocity direction has significant influence on the lubrication characteristics. The results provide the tribological guidance for design of a helical gear pair in engineering.

Effect of arbitrary entrainment angle in elastohydrodynamic lubrication elliptical and circular contacts

Conventional elastohydrodynamic lubrication models assume parallel surface velocities such as in cam-follower and ball bearing systems. However, many important machine elements like hypoid gear and spiral bevel, the sliding and entrainment velocities are along different directions that could possibly influence the elastohydrodynamic lubrication performance characteristics significantly. For such complex conditions, the existing film thickness formulae and shear-thinning correction factors available in the literature are not suitable. Therefore, this paper investigates the effect of arbitrarily oriented surface velocity vectors on elastohydrodynamic lubrication characteristics considering realistic rheological models and experimentally established viscosity–pressure and compressibility laws. The Reynolds equation employed herein includes the surface velocity components along both the reference axes in the plane of contact. The elastohydrodynamic lubrication film thickness is found to deviate up to a maximum of 61% with respect to its conventional value. This deviation in film thickness behavior is shown to be a function of ellipticity and shear-thinning parameters.

Numerical simulation of transient mixed elastohydrodynamic lubrication for spiral bevel gears

Abstract In spiral bevel gears, the entraining velocity, contact load and radii of curvature along tooth surface are always changed dramatically, which results in remarkable transient squeezing effect on lubricating performance, especially it operates in high-speed and heavy-load conditions. Available elastohydrodynamic lubrication (EHL) and mixed EHL studies for spiral bevel gears are mainly performed under quasi-static (steady-state) assumptions which ignores these transient influences. Therefore, in this paper, a transient mixed EHL model for spiral bevel gears is presented, in which takes into account most variable parameters along meshing surface including contact load, contact radii of curvature, entraining and sliding velocity vectors. Note that all these transient parameters of spiral bevel gears are employed from the results of loaded tooth contact analysis (LTCA). In order to improve the computational efficiency and convergent accuracy with a relatively dense grids, the progressive mesh densification (PMD) method for this transient mixed EHL model is also introduced. A comparison between the present transient mixed EHL model and those data from literature is executed to verify the correctness of the newly developed model. After that, systematically investigations of transient squeezing impact are carried out for spiral bevel gears and compared with the corresponding steady-state EHL results with and without real machined surface roughness. The obtained results reveal that the transient squeezing action can significantly affect the film thickness distribution in each contact zone and along the meshing track line in spiral bevel gears, and lead to dramatic growth in asperity contact area as well. Besides, the steady-state EHL appears to be greatly overestimated the lubricating characteristics for spiral bevel gears.