Elastohydrodynamic Lubrication Line Contact Research Articles

TVMS Calculation and Dynamic Analysis of Cracked Gear considering Oil Film Stiffness

A time-varying meshing stiffness (TVMS) model that includes oil film stiffness in the elastohydrodynamic lubrication (EHL) line contact is proposed for tooth root cracking. This model employs the oil film thickness to estimate the stiffness of the oil film in gear contact by considering the profile variation of the oil film induced by tooth root cracks, to provide the evolution principle of TVMS in EHL line contact to study the effects of oil film stiffness of cracked gear on the TVMS. The results of the analysis reveal that the overall result of TVMS decreases owing to the stiffness of the oil film, whereas the combined TVMS depends mainly on the rotation speed of the gear system because the thickness of the oil film in the tooth crack is affected by the velocity of the entrainment. Furthermore, a six-degree-of-freedom (DOF) dynamic model is introduced to analyze the vibration behavior of the gear system using the combined TVMS results for different crack levels, and the influence of the combined TVMS on the vibration response of the tooth root crack is exhibited from the time-domain analysis, frequency-domain analysis, and statistical indicator analysis.

Improved mesh stiffness model of spur gear considering spalling defect influenced by surface roughness under EHL condition

Gear tooth spalling is a typical tooth surface defects in gear transmission. The accurate calculation of the time-varying mesh stiffness of the gear pair with spalling defect under mixed elastohydrodynamic lubrication (EHL) plays an important role in tooth damage prediction and fault feature analysis. In this work, an improved time-varying mesh stiffness (TVMS) model of spalling faulty gear in mixed EHL line contact considering the coupled effect of rough surface topography is established. The proposed model considers the combined effect of spalling defect, surface roughness topography, and lubrication on the contact characteristics of the meshing interface to obtain a revised contact stiffness, which is further used to determine the comprehensive TVMS. The cylindrical contact coefficient for curved meshing interface with spalling fault is derived and incorporated into the statistical micro-contact Greenwood and Williamson model (GW model) to obtain the asperity contact stiffness. The revised contact stiffness at the rough faulty gear interface is obtained from the parallel action of the asperity contact stiffness and oil film stiffness under load-sharing concept. The dynamic responses of the gear system are analyzed using the established mesh stiffness model through the six degrees of freedom translational-torsional dynamic model, in which the dynamic meshing force is calculated iteratively using the transit surface topography and geometrical parameters along the line of contact instead of a quasi-static meshing force. Effects of multi-parameters as surface roughness, spalling fault size, and lubricant on the mesh characteristics and dynamic responses of the gear system are further investigated and discussed.

Experimental and Theoretical Study on Forming Film Properties of Hollow Cylindrical Rollers

Bending deformation of a hollow cylindrical roller (HCR) was calculated by curve bending theory and slice technology. Furthermore, an elastohydrodynamic lubrication (EHL) model involving hollow rollers was established by coupling the finite line EHL model and bending deformation. Measurements of film thickness for hollow rollers were carried out by using a line-contact optical EHL test rig, and the experimental data and theoretical results agreed well with each other. For a roller with a straight-line profile, the hollow structure could reduce pressure peak at the roller ends, but the edge effect was still present. The film thickness at the ends unfortunately could not be improved by such hollow structures, unless a profile modification for the operating surface is designed.

Surface effects on elastohydrodynamic lubrication contact of piezoelectric materials with non-Newtonian fluid

Using surface piezoelectricity theory, this article investigates the elastohydrodynamic lubrication (EHL) line contact of a transversely isotropic piezoelectric half-plane with consideration of the surface effect under a rigid cylindrical punch. The surface effect in the surface piezoelectricity theory is mainly described by the following parameters: surface piezoelectric constant, surface dielectric constant, surface elastic constant, and residual surface stress. The punch is treated as an electrical insulator. The lubricant, whose viscosity and density are dependent on fluid pressure, is chosen as a non-Newtonian fluid. Firstly, by analyzing the frictionless dry contact of piezoelectric materials vith the surface effect, the dry contact pressure distribution and the EHL film thickness equation are obtained. Then, an iterative method is proposed to obtain the fluid pressure and film thickness in the lubricant contact region by calculating the fluid–solid coupled nonlinear equations. The effects of the surface dielectric constant, surface piezoelectric constant, surface elastic constant, residual surface stress, punch radius, entraining velocity, and slide/roll ratio on the film thickness and fluid pressure are examined. Our analysis indicates that the surface effect has an essential effect on the EHL contact behavior of piezoelectric materials at micro-/nano-scales.

Characteristics in hard conformal EHL line contacts

PurposeInternal gearings are commonly used in transmissions due to their advantages like high-power density. To ensure high efficiency, load-carrying capacity and good noise behavior, a profound knowledge of the local gear mesh is essential. The tooth contact of internal gears relates to a convex and concave surface that form a conformal contact. This is in contrast to external gears, where two convex surfaces form a contraformal contact. This paper aims at a better understanding of conformal contacts under elastohydrodynamic lubrication (EHL) to improve the design of internal gearings.Design/methodology/approachAn existing numerical EHL model is used for studying the characteristic properties of a hard conformal EHL line contact. A hard contraformal EHL line contact is studied as reference. Non-Newtonian fluid behavior and thermal effects are considered. By taking into account the local contact conformity and kinematics, the effects and relevance of the curvature of the lubricant gap and micro-slip are analyzed. In a parameter study, scale effects of the contact radii on film thickness, temperature rise and friction are examined.FindingsThe curvature of the lubricant gap and effects of micro-slip are small in hard conformal EHL line contacts. For high micro-slip, it can be neglected. Hence, the modeling of conformal contacts using an equivalent geometry of the contact problem is reasonable. The parameter study shows beneficial tribological aspects of the conformal contact compared to the contraformal contact. Higher film thickness and lower fluid coefficient of friction are observed for conformal contacts, which can be attributed to lower pressures for the case of the same external normal force, or to a higher contact temperature rise for the case of equivalent contact pressure.Originality/valueDespite its widespread existence, the local geometry and kinematics in hard conformal EHL line contacts like in internal gearings have been rarely studied. The findings help for a better understanding of local contact characteristics and its relevance. The quantified scale effects help to improve the efficiency and load-carrying capacity of machine elements with hard conformal EHL contacts, like internal gearings.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-12-2022-0366/

Newton-GMRES-Method for the Scritinization of electric double layer and surface roughness on EHL line contact problem

The electric double layer phenomenon exists on the solid interface under the water-liquid condition. The water molecules are ionized and adhered in the interface forming the sturn layer is a diffused layer in which molecules can move with the movement of bulk of molecules. Because of these two characteristics, the boundary layer of water molecules is called the electric double layer. The aim of present study is to explore the impact of two fraction surfaces of electric double layer (EDL) on a thin water lubricating film on an elastohydrodynamic lubrication (EHL) line contact problem with a sinusoidal surface roughness. The governing modified Reynolds and film thickness equations are based on mathematical model of electro-viscosity of asymmetrical electrical double layer is analyzed numerically. The viscosity-pressure relation of water and theoretical evaluation pertaining to the effect of electric double layer on film-thickness and pressure distribution of EHL with water film of line contact problem is discussed in detail. The effect of zeta potential on film thickness and pressure is determined using Newton’s-GMRES method with Daubechies D6 wavelet as a pre-conditioner. The results predict that, EDL has less impact on pressure distribution and significant impact on film thickness. The obtained results are compared with results of Dowson and Higginson which are comparable.

A thermal EHL investigation for finite line contact under starved condition on bush-pin hinge pairs in industrial chains

During the operation of the industrial chains, serious starvation may happen so that the oil film is often too thin to effectively separate the bush-pin surfaces, resulting in surface damage of the pin since the bush surface is harder. In this paper, the effects of oil supply and equivalent radius of curvature on the variations of pressure, film thickness and temperature in the contact area are studied based on the thermal elastohydrodynamic lubrication (EHL) theory and a finite line contact lubrication model under oil starvation condition is employed. It is found that oil starvation and the increase of equivalent curvature radius will aggravate the stress concentration at the end of the contact area, and more oil supply is required in the contact area if the thermal rise is considered. An oil starvation mechanism of finite line contact EHL is proposed, in which in addition to the direct influence of oil supply, the interaction of film thickness, pressure and temperature in the contact area also play important roles. The reduction of minimum film thickness is proposed to measure the degree of oil starvation at the ends of the contact area. The oil starvation process of finite line contact is divided into four typical stages.

Numerical Analysis of the Effect of Temperature on the Pressure and Film Thickness for Line Contact Elastohydrodynamic Lubrication Using Bio-Based Oils as Lubricants

This paper develops a numerical model to study the effect of lubricant’s temperature on generated pressure and film thickness formation for the line contact elastohydrodynamic lubrication (EHL) using some bio-based oils as lubricants. In this study, a contact between inner ring and cylindrical roller of rolling element bearing is modelled as the line contact of EHL. The Reynolds equation is simultaneously solved with elastic deformation equation and pressure-viscosity equation. This aims to calculate the pressure distributions and film thickness profiles with a range of seven vegetable oils as bio-based lubricants at the various temperature. Moreover, the minimum film thickness is investigated in more detail to show the effect of the lubricant’s temperature. Obtained results show that palm oil has the highest of the minimum film thickness among other vegetable oils. However, all vegetable oils simulated in this study are suitable to replace mineral oil as lubricant for application of roller element bearing.

A Fast Thermoelastic Model Based on the Half-Space Theory Applied to Elastohydrodynamic Lubrication of Line Contacts Involving Free Boundaries

Abstract This study allows contact models based on semi-analytical methods including the impacts of thermoelastic deformations in contacts of finite dimension bodies. The proposed method controls heat flows crossing free boundaries. A comparison with finite element analysis (FEA) reveals that the proposed method can reduce the calculation times by more than 98%. The paper introduces the thermoelasticity effects into thermal-elastohydrodynamic lubrication (TEHL) modeling of line contact problems. The analysis reveals that including thermoelastic deformations changes the pressure profile and tends to localize the pressure close to the distribution center. Compared to TEHL simulations, the examined configurations caused an overall increase in the maximum pressure by about 9%, an overall film thickness reduction of about 7%, and an overall temperature increase of about 2 K.

Study on the Lubrication Characteristics of Spur Gear Pairs With Low Sliding Ratio Under Mixed Elastohydrodynamic Lubrication

Abstract The relative sliding at the meshing point directly affects the contact and lubrication characteristics of the gear pair and is an important factor of gear wear and power loss. In this study, for investigation of a new type of low sliding ratio (LSR) gear pair whose tooth profile is constructed by a cubic function, a three-dimensional (3D) mixed elastohydrodynamic lubrication (EHL) line contact model was established with consideration of the effect of tooth profile geometry, transient motion characteristics, load distribution, and machining roughness. The distribution of the center film thickness of the LSR gear along the meshing line was predicted through an example the result of which was compared with a typical line contact EHL formula to verify the model. In addition, the difference was investigated in film thickness distribution of friction coefficient and temperature rise between LSR spur gears and involute spur gears. Hence, the effect of 3D rough tooth surface on the contact lubrication characteristics of LSR gears was discussed. The results demonstrated that the minimum center film thickness of the LSR gear appeared at the alternating point of the concave and convex tooth surfaces. At the same time, compared with the involute gear, the LSR gear significantly increased the film thickness at the start and ending points of the meshing and reduced the friction coefficient and the flash temperature rise.

Effects of spalling fault on dynamic responses of gear system considering three-dimensional line contact elasto-hydrodynamic lubrication

Spalling is a common fault in gear system, which directly degrades the performance of the gear system and increases the risk of downtime of the entire system. Until now, lots of efforts have been done to study the underlying mechanism of the spalling fault and its effects on dynamic characteristics for the purpose of accurate diagnosis. However, the lubrication characteristics affected by the spalling fault are usually neglected, which degrades the modelling accuracy of gear system with spalling fault. Therefore, a new dynamic modelling method with spalling fault considering three-dimensional (3D) line contact elasto-hydrodynamic lubrication (EHL) is proposed in this paper. With the established model, the contact characteristics of the lubrication film between gear teeth affected by the spalling fault and the dynamic responses of the gear system can be studied. The main differences of the proposed model are that the meshing force over the lubrication film is calculated iteratively instead of a given quasi-static meshing force and the comprehensive meshing stiffness is obtained considering the effects of both spalling fault and lubrication film. The effects of spalling fault on film pressure distribution, film thickness distribution, film stiffness, comprehensive meshing stiffness and dynamic responses are studied based on the proposed method. Finally, the proposed 3D line contact EHL model is verified by comparing to a traditional EHL model. Effects of the spalling fault size on the comprehensive meshing stiffness and the dynamic responses of the gear system are investigated and discussed. The results reveal that this work can provide a more reasonable analytical method for understanding the contact characteristics and dynamic responses of gear system with spalling fault.

Professor Duncan Dowson, a source of inspiration

The current paper highlights the contribution of the Dowson and Higginson work to numerical line contact elastohydrodynamic lubrication film thickness prediction and the Hamrock and Dowson contribution to the film thickness prediction in elliptical contacts. This paper shows that, even by today’s standards, both the numerical pressure and film thickness results and the curve-fitted film thickness predictions are very accurate. As for the elliptical results, the authors show that the original predictions remain surprisingly accurate for moderately elliptical contact. For very long elliptical contacts, their prediction does not tend to a line contact asymptote. This paper then concludes that the predicted pressure spikes by Dowson, Higginson, and Hamrock are correct in shape and amplitude, at least near pure rolling conditions.

Analysis of Transmission Efficiency of Herringbone Gear with Elastohydrodynamic Lubrication Theory

This paper takes the herringbone gear as the research object, and analyzes the transmission efficiency of the herringbone gear by using the theory of non Newtonian fluid line contact elastohydrodynamic lubrication. Firstly, the oil film pressure and thickness of the contact area are obtained, then the friction coefficient distribution and transmission efficiency in the herringbone gear mesh area are obtained. Finally, the influence of various parameters on the transmission efficiency is analyzed.

Effect of micro-textures on lubrication characteristics of spur gears under 3D line-contact EHL model

Purpose The purpose of this paper is to use a combination of numerical simulation and experiment to evaluate the performance of laser surface texturing (LST) in the field of gear lubrication, and to more accurately predict the lubrication characteristics of different surfaces. Design/methodology/approach The method used in this paper is developed on the basis of the deterministic solution of the three-dimensional (3D) mixed elasto-hydrodynamic lubrication (EHL) model and the model parameters are corrected by friction test. The film pressure, film thickness and friction coefficient of different micro-textured tooth surfaces are predicted on the basis of accurate 3D mixed EHL models. Findings The results demonstrate that the micro-texture structure of the tooth surface can increase the local film thickness and enhance the lubricating performance of the tooth surface without drastically reducing the contact fatigue life. The stress distribution and friction characteristics of the tooth surface can be optimized by adjusting the micro-texture arrangement and the size of the micro-textures. Originality/value A new evaluation method using a 3D hybrid EHL model and friction test to predict the lubrication characteristics of LST is proposed, which can effectively improve the processing economy and save time. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2020-0423

Experimental study on line-contact elastohydrodynamic grease lubrication properties of surface-textured rollers

Purpose This paper aims to study line-contact elastohydrodynamic grease lubrication properties of surface-textured rollers as well as the effect of different crown widths (dw) on oil film thickness under textured conditions. Design/methodology/approach The laser processing method was used to make the micro-texture on the surface of GCr15 steel rollers; lithium grease was used as the lubricant, and line-contact elastohydrodynamic grease lubrication experiments under pure sliding conditions were performed on light interference elastohydrodynamic-lubricated experimental table. Findings The results show that the line-contact elastohydrodynamic grease lubrication is closely related to the textured crown width of steel rollers. At low speeds and light loads, texturing has an inevitable inhibitory effect on the formation of the lubricating oil film, and the smaller the width of the crown area, the more obvious the inhibitory effect, which is not conducive to the improvement of the lubrication condition. At high speeds and high loads, the textured roller with dw = 1 mm has the largest oil film thickness and shows better lubrication performance. Originality/value At present, there is little research on the surface texture of line-contact friction pairs. This work explores the effect of different textured crown width on the lubricating properties of line-contact elastohydrodynamic grease lubrication by experiment. It provides a new theoretical basis for the subsequent practical application of surface texture technology.

Elastohydrodynamic lubrication line contact in couple-stress elasticity

By using the couple-stress elasticity theory, this article firstly analyzes the size-dependent elastohydrodynamic lubrication (EHL) line contact between a deformable half-plane and a rigid cylindrical punch. The size effect that emerged from the material microstructures is described by the characteristic material length. It is assumed that the viscosity and density of the lubricant vary with the fluid pressure. An iterative method is developed to deal with the flow rheology equation, film thickness equation, load balance equation and Reynolds equation at the same time. Then, distributions of fluid pressure, in-plane stress and film thickness are determined numerically at the lubricant contact surface. Influences of the size parameter, punch radius, resultant normal load and entraining velocity on the fluid pressure, in-plane stress and lubricant film thickness are discussed. The fluid pressure and film thickness predicted from the couple-stress elasticity theory present significant departures from the classical elasticity results. It is demonstrated that results for micro-/nano-scale EHL contact problems may be underestimated when the classical elasticity theory is employed.

Influence of load and speed on tribological performance of Cu nanofluids in EHL line contacts

Abstract Nowadays, wear is the leading cause of common machine failure and significant use of lubricants is required to reduce such failure. Lubricants over the years have evolved from animal fats to mineral oils and now nanofluids. Nanofluids are the blend of nanoparticles and base lubricating oil. Copper nanofluids are used as efficient nanolubricants for contacting surfaces because of their high thermal and electrical conductivity. In this paper, influences of applied load and rotational speed on tribological performance of copper nanofluids have been investigated. The effect of viscoelasticity in terms of contact pressure and film thickness in elastohydrodynamic lubrication (EHL) has been also investigated. Experimental tests were performed on multispecimen tribometer machine in pin on roller (line contact) arrangement, using EN31-EN31, EN31-GM, EN31-PB, EN31-Al alloy as tribopairs. Results indicate that both contact pressure and film thickness do not have any significant effect after incorporation of viscoelastic effect in EHL line contacts of copper nanofluids. Coefficient of friction (CoF) for all the tribopairs have been increased with the applied load, with rotational speed for EN31-GM, EN31- Al alloy. However, for EN31-EN31, EN31-PB CoF decreases. Wear has been also shown to be increase with the increase of applied load and rotational speed.

Assessment of Thermal Effects on Mixed Elastohydrodynamic Lubrication Line Contact by Outlet Lubricant Temperature

The elastohydrodynamic (EHD) lubrication straight line contact conjunction is studied to evaluate the mixed lubrication heat generation experimentally over bordering operating conditions in a disc-on-disc machine. An experimental investigation is carried out using an accessory device that collects and measures the outlet lubricant temperature. The experimental results show the typical transition from mixed to elastohydrodynamic lubrication, tracking the difference of outlet lubricant temperature and the total average full-film EHD temperature. A new variable coupling flash temperature was introduced as an in situ approach to demonstrate the lubricant capacity of removing heat from asperity interaction in mixed lubrication contacts. It was possible to estimate the metal–metal contact area in mixed lubrication by coupling flash temperature as a direct correlation to the true flash temperature in relation to correspondence to final surface roughness characterizations.

Research on the Lubrication Characteristics of Harmonic Gear Transmission Meshing Areas

To analyse the lubrication characteristics of harmonic gears and lay the foundation for the study of its gear tooth failure performance and dynamic characteristics, based on the tooth contact geometry of harmonic gear, the integrated curvature radius, tooth load, and entrainment velocity at the meshing point of the gear teeth in the harmonic gear transmission are analysed. A finite-length line contact elastohydrodynamic lubrication (EHL) model for harmonic gears is established. The numerical calculation method is used to solve the oil film thickness and pressure distribution in the lubricating area, and the effects of rotational speed and temperature on the contacting load ratio and film thickness ratio of the meshing area are studied, as well as the change of oil film stiffness under different working conditions. The results show that along the meshing direction, the pressure is small at the end and reaches a peak at the centre, and the film thickness is the largest in the entrance area and is evenly distributed in the centre contact area. As the speed increases, the gear tooth contact load ratio decreases, the oil film thickness ratio increases, the stiffness of the oil film decreases significantly, and the lubrication effect is improved; but the temperature has the opposite effect. Proper increase of rotation speed and decrease of oil temperature can effectively improve the lubrication characteristics of the system.

Lubrication reliability analysis of spur gear systems based on random dynamics

An approach for lubrication reliability analysis of spur gear systems considering the randomness of external load and surface roughness is presented. The instantaneous failure probability of gear lubrication is captured by a gear stochastic dynamics model and a reliability model of elastohydrodynamic lubrication (EHL). The stochastic dynamics model is adopted to obtain the numerical characteristics of meshing force. The reliability model is established based on a mixed EHL line contact film thickness formula. The first-order second-moment method is employed for predicting failure probability of lubrication. The lubrication reliability of a gear pair excited by different intensity random load is studied. The results show that the lubrication failure probability in dedendum and single meshing region are higher than addendum.