Elastohydrodynamic Lubrication Line Contact Research Articles

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.

Elastohydrodynamic Lubrication Line Contact Based on Surface Elasticity Theory

Abstract Using surface elasticity theory, this article first analyzes the surface effect on the elastohydrodynamic lubrication (EHL) line contact between an elastic half-plane and a rigid cylindrical punch. In this theory, the surface effect is characterized with two parameters: surface elastic modulus and residual surface stress. The density and viscosity of the lubricant, considered as Newtonian fluid, vary with the fluid pressure. A numerical iterative method is proposed to simultaneously deal with the flow rheology equation, Reynolds equation, load balance equation, and film thickness equation. Then, the fluid pressure and film thickness are numerically determined at the lubricant contact region. Influences of surface elastic modulus, residual surface stress, punch radius, resultant normal load, and entraining velocity on the lubricant film thickness and fluid pressure are discussed. It is found that the surface effect has remarkable influences on the micro-/nano-scale EHL contact of elastic materials.

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.

Elastohydrodynamic Lubrication Line Contact of a Functionally Graded Material Coated Half-Plane

Abstract The elastohydrodynamic lubrication line contact problem between a functionally graded material (FGM) coated half-plane and a rigid cylindrical punch is investigated. The inhomogeneous elastic properties of the FGM coating are expressed by the exponential model. The lubricant between two solids is supposed to be the Newtonian fluid. The fluid viscosity and density are considered to be dependent on the fluid pressure. To determine the unknown film thickness and fluid pressure at the lubricant contact region, a numerical iterative method is employed to simultaneously solve the flow rheology equation, Reynolds equation, load balance equation, and film thickness equation. Influences of the stiffness ratio of the FGM coating, the resultant normal load, the punch radius, and the entraining velocity on the lubricant film thickness and fluid pressure are analyzed.

Jacobian-free Newton-Krylov subspace method with wavelet-based preconditioner for analysis of transient elastohydrodynamic lubrication problems with surface asperities

This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication (EHL) line contact. The governing equations are discretized by the finite difference method. The resulting nonlinear system of algebraic equations is solved by the Jacobian-free Newton-generalized minimal residual (GMRES) from the Krylov subspace method (KSM). Acceleration of the GMRES iteration is accomplished by a wavelet-based preconditioner. Profiles of the lubricant pressure and film thickness are obtained at each time step when the indented surface moves through the contact region. The prediction of pressure as a function of time provides an insight into the understanding of fatigue life of bearings. The analysis confirms the need for the time-dependent approach of EHL problems with surface asperities. This method requires less storage and yields an accurate solution with much coarser grids. It is stable, efficient, allows a larger time step, and covers a wide range of parameters of interest.

An improved stiffness model for line contact elastohydrodynamic lubrication and its application in gear pairs

PurposeThe purpose of this paper is to propose an simple and efficient stiffness model for line contact under elastohydrodynamic lubrication (EHL) and to investigate the gear meshing stiffness by the proposed model.Design/methodology/approachThe method combines the surface contact stiffness and film stiffness as EHL contact stiffness. The EHL contact stiffness can be calculated by the external load and displacement of the load action point. The displacement is the sum of deformation of the film and contact surface and is equal to the distance of the mutual approach of two contact bodies.FindingsThe conclusion is drawn that the contact stiffness calculated by the proposed model is smaller than that by the minimum film model and larger than that by the mean film model. It is also concluded that the gear meshing stiffness under EHL is slightly smaller than that under dry contact.Originality/valueThe EHL contact stiffness can be obtained by the increment of external load and mutual approach directly. The calculation of oil film stiffness and surface contact stiffness separately is avoided.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2019-0465

Analysis of Line Contact Elastohydrodynamic Lubrication with the Particles under Rough Contact Surface

A numerical solution for line contact elastohydrodynamic lubrication (EHL) occurring on the rough surface of heterogeneous materials with a group of particles is presented in this study. The film thickness disturbance caused by particles and roughness is considered into the solution system, and the film pressure between the contact gap generated by the particles and the surface roughness is obtained through a unified Reynold equation system. The inclusions buried in the matrix are made equivalent to areas with the same material as that of the matrix through Eshelby’s equivalent inclusion method and the roughness is characterized by related functions. The results present the effects of different rough topographies combined with the related parameters of the particles on the EHL performance, and the minimum film thickness distribution under different loads, running speeds, and initial viscosities are also investigated. The results show that the roughness morphology and the particles can affect the behavior of the EHL, the traction force on a square rough surface is smaller, and the soft particles have more advantages for improving the EHL performance.

Numerical solution of thermal EHL line contact with bio-based oil as lubricant

ABSTRACT The paper presents the numerical solution of line contact thermal elastohydrodynamic lubrication (EHL) with bio-based lubricant. The model comprises Reynolds equation, film thickness, load balance and energy equations with appropriate boundary conditions by incorporating viscosity–pressure–temperature and density–pressure–temperature relations. Second-order finite difference scheme is used for the discretised form and their equation. The multigrid method with full approximation scheme is used to solve the Reynolds equation along with multilevel multi-integration method for film thickness equation. The pressure, film thickness and temperature distributions for two rolling velocities and various loads with a bio-based lubricant are presented in detail. The present findings yield a reduction in the minimum film thickness for high speed. Details of pressure spike as a function of relevant parameters are given. The results are compared with earlier findings based on different methods.

Elastohydrodynamic lubrication line contact of piezoelectric materials

This paper investigates the elastohydrodynamic lubrication (EHL) line contact between a rigid cylindrical punch and a transversely isotropic piezoelectric half-plane. The punch is supposed to be a perfect conductor, and its electric potential is constant within the contact region. The lubricant is assumed as a kind of Newtonian fluid. The lubricant density and viscosity are considered as the function of the fluid pressure. An iterative method is developed to solve the film thickness equation, Reynolds equation, flow rheology equation and load balance equation simultaneously. The effects of the total electric charge, maximum normal pressure, entraining velocity and material properties on the EHL film thickness and fluid pressure are discussed. Furthermore, the EHL contact of the insulating punch is also discussed to analyze the influences of conductivity of punch and piezoelectric effect of materials. The present results could be applied to improve the wear and contact damage of piezoelectric devices.

Soft-Elastohydrodynamic Lubrication Line Contact Analysis on a Strip of Bio-Materials

Abstract The characteristics of anisotropic material, finite deformation, and lubrication in biological system diminish the friction and wear between soft tissues with relative motion. In this research, the lubrication between pleura surfaces in relative motion is analyzed by soft elastohydrodynamic lubrication (soft-EHL) line contact with an equivalent model. The model is a soft, transversely isotropic (TI) elastic strip with finite thickness sliding under a rigid sinusoidal surface, which is used to simulate the surface irregularities, with lubricant in between. The material nonlinearity and the curvature effects due to finite deformation, which are significant in soft-EHL, are considered in the present study. The pressure distribution, film thickness, von Mises stress, and material deformation are analyzed and discussed under various combinations of elastic moduli and Poisson's ratios for the transversely isotropic models. The simulation results reveal that the soft-EHL modeling fit actual result better than the traditional EHL (t-EHL) modeling. The Poisson's ratio νp = 0.1 and νpz = 0.49 situation will have more gentle stress distribution. The present soft-EHL solver can be used to realize some desired stress distributions and to identify the mechanical properties bio-materials under the aids of experiments.

Experimental Analysis of Chromium Molybdenum Coatings Under Mixed Elastohydrodynamic Lubrication for Film Thickness, Friction, and Wear Characterizations

This research aims to evaluate the tribological performance of chromium molybdenum (CrMo) coatings under point and line-contact mixed elastohydrodynamic lubrication. This article studies the coatings made from two different methods and treated in an electrifying process of different durations, which produced microchannels and micropockets in the surfaces. The resulting surface topographies had varying impacts on lubricant film thickness, friction, and wear. Root-mean-square roughness (Sq) and porosity are used to characterize the surfaces and their performances in terms of film thickness, friction, and wear. The results suggest that the coated surfaces with a lower Sq and porosity density tended to yield higher film thickness. However, their influence on friction is complicated; lower roughness and porosity are preferred for lower wear, but certain levels of small roughness and surface pores may help to reduce boundary lubrication friction when compared with the frictional behaviors of porosity-free surfaces and those with higher roughness and higher porosity.

An adhesive wear model for helical gears in line-contact mixed elastohydrodynamic lubrication

Adhesive wear in mixed elastohydrodynamic lubrication (EHL) has been one of the most prominent problems for heavy-loaded helical gears. However, this issue was rarely investigated in previous researches. In this work, an adhesive wear model for helical gears is established in line-contact mixed EHL. The contact parameters of the pinion and gear are derived according to the equivalent tapered roller contact model, and the load is attained in consideration of the varying contact line ratio. Then the asperity contact pressure is calculated according to Hertz's elastic contact theory and load sharing. Moreover, the sliding distances of the points on tooth surface of driving pinion and driven gear are achieved by a single point observation method, and Archard theory in dry contact is extended to the mixed lubrication to estimate the wear rate in mixed EHL by using fractional film defect. The modified Archard's wear model is then employed in formulating and accounting for the gear tooth wear. Effects of surface roughness, geometrical parameters and working parameters on wear depth of the driving pinion are furtherly investigated. The results show that the wear depth in mixed EHL is lower than that under dry contact, which indicates that tooth wear can be reduced with the reasonable lubricants. As the surface roughness becomes large, the asperity contact pressure, the tooth surface temperature and wear depth are increased. Additionally, the wear depths decrease with the increase in module, helix angle, pressure angle, tooth width or rotation speed but increase with input torque.

Effects of oil film stiffness and damping on spur gear dynamics

An enhanced spur gear dynamic model considering the combined stiffness and damping of both gear tooth and oil film is established. To acquire the combined stiffness and damping involved in the modified dynamics equations, Ishikawa formulas are adopted to calculate the gear mesh stiffness, and given the viscous-elastic oil film in elastohydrodynamic lubrication line contact equivalent to massless spring and damping elements, the models of oil film stiffness and damping in normal and tangential directions are then developed. The combined stiffness is deduced from the stiffness of both the gear tooth and oil film, while the combined damping is derived from the damping of these parts. Effects of oil film stiffness and damping on the gear dynamics are investigated, and the dynamic response of the developed model is in contrast to that of the conventional model. The results show that by utilizing the enhanced dynamic model, the displacement fluctuation in transient stage fast decays and displacement response reaches steady state faster. The speed and acceleration fluctuations in the period converting from transient to steady stages are obviously reduced, and the response curves of speed and acceleration in steady stage are smoother. Moreover, the oil film normal damping plays large role in the gear periodic motion. This indicates that the oil film stiffness is prone to effectively alleviate impact and the oil film damping is inclined to substantially reduce vibration and frictional heat for a gear drive.

Theoretical analysis of a rolling-sliding elastohydrodynamic lubrication line contact with a subsurface inclusion

This work investigates the transient effects of a single subsurface inclusion over the pressure, film thickness, and von Mises stress in a line elastohydrodynamic lubrication contact. Results are obtained with a fully-coupled finite element model for either a stiff or a soft inclusion moving at the speed of the surface. Two cases analyzed consider the inclusion moving either at the same speed as the mean velocity of the lubricant or moving slower. Two additional cases investigate reducing either the size of the inclusion or its stiffness differential with respect to the matrix. It is shown that the well-known two-wave elastohydrodynamic lubrication mechanism induced by surface features is also applicable to the inclusions. Also, that the effects of the inclusion become weaker both when its size is reduced and when its stiffness approaches that of the matrix. A direct comparison with predictions by the semi-analytical model of Morales-Espejel et al. ( Proc IMechE, Part J: J Engineering Tribology 2017; 231) shows reasonable qualitative agreement. Quantitatively some differences are observed which, after accounting for the semi-analytical model's simplicity, physical agreement, and computational efficiency, may then be considered as reasonable for engineering applications.

Dynamics and lubrication analyses of scotch yoke mechanism

In this paper the contact problem of a scotch yoke mechanism has been investigated in details under the elastohydrodynamic lubrication regime and line contact model is used in the analyses. The non-Newtonian oil behavior of the lubricant and the variation of the load and the surface velocities throughout the operating cycles are considered in the analyses. The results reveal that the variation of these values makes the contact problem (depending on the position in the operating cycle) to operate under lightly and heavily loaded conditions. Under these conditions, extremely thin levels of film thickness have been predicted.

Influence of piezo-viscous behavior and load on the effectiveness of inlet zone bump in unidirectional pure sliding EHL line contacts

PurposeThe purpose of this paper is to introduce the concept of stationary inlet zone bump (IZB) for film thickness enhancement in unidirectional pure sliding elastohydrodynamic lubrication (EHL) line contacts and to investigate the effects of maximum Hertzian pressure (load) and piezo-viscous response on the effectiveness of IZB.Design/methodology/approachThe numerical analysis involves the solution of Reynolds and elasticity equations. The well-established Doolittle–Tait equations are used herein to determine the lubricant viscosity and density as functions of local pressure, while the Carreau model is used to describe the lubricant rheology. The IZB is assumed to have a sinusoidal profile and it is present on the stationary surface. The governing equations are discretized using finite difference scheme and solved using the Newton–Raphson technique.FindingsTwo test oils, L7808 and SR600, with linear and exponential piezo-viscous responses in the inlet zone are considered here for comparison. The effectiveness of IZB in terms of film thickness enhancement is found to be more for SR600. Besides, IZB is found to be more effective at lower values of maximum Hertzian pressure. The bump needs to shift downstream at higher load to be as effective as at lower load.Originality/valueThis is the first paper to simulate EHL characteristics in the presence of a stationary IZB and to study the effect of various parameters on EHL effectiveness. The film thickness enhancement obtained here is remarkable and hence it is a novel and valuable contribution.

A novel numerical scheme for the analysis of effects of surface roughness on EHL line contact with couple stress fluid as lubricant

In this article, a Jacobian-free Newton Multigrid (JFNMG) method is used for obtaining the solution of isothermal, steady and compressible elastohydrodynamic lubrication (EHL) line contact problem with surface roughness. The lubricant is a couple stress fluid. A finite difference scheme is used for the solution of EHL equations. The proposed JFNMG method, for the solution of resulting nonlinear system of algebraic equations, comprises nonlinear Newton iterations on the outer loop and linear multigrid iterations on the inner loop. It overcomes the limitations of conventional schemes for the investigation of the problems covering wide range of physical parameters of interest. For increasing values of couple stress parameter, there is an increase in minimum film thickness and considerable decrease (in height as well as spread) of pressure spike. Also, the sensitivity of height and spread of pressure spike as a function of load, couple stress parameter and other parameters are investigated.

Numerical modeling of elastohydrodynamic lubrication of line contact lubricated with micropolar fluid

This paper presents numerical investigation on elastohydrodynamic lubrication (EHL) of line contacts lubricated with micropolar fluids. Numerical model of EHL line contact has been developed by coupled solution of Reynolds equation, elastic deformation equation, load balance equation and fluid rheology equation from inlet to the outlet region. This system of equations has been solved using finite element method techniques. The influence of micropolar fluid parameters and operating parameter on the performances EHL line contacts has been investigated. Further, a comparative assessment on the micropolar and Newtonian fluid-lubricated contact has been presented. It has been observed that the use of micropolar fluid parameters enhances the values of minimum and central fluid film thickness and contact pressure within the EHL line contacts. The empirical formulae for minimum $$\left( {\bar{H}_{\hbox{min} } } \right)$$ and central $$\left( {\bar{H}_{\text{cent}} } \right)$$ fluid film thickness are formulated based on the numerically simulated results. The study reveals that overall performances of EHL line contacts increases significantly with micropolar fluid parameter. Further, it has been observed due to micropolar lubricant in EHL line contacts, chances of metal-to-metal contact reduces.

Stiffness and damping models for the oil film in line contact elastohydrodynamic lubrication and applications in the gear drive

• New stiffness and damping models are developed for oil film in normal and tangential directions. • Smaller lubricant stiffness is beneficial for alleviating gear meshing impact and shear vibration. • Meshing impact and friction heat is suppressed by either larger normal lubricant damping or smaller tangential lubricant damping. • Better combined stiffness and damping can be achieved by optimizing gear geometric parameters and operating conditions. Innovative stiffness and damping models for oil films are developed to account for the impacts in both normal and tangential directions. Given that these models are applied to a gear drive in line contact elastohydrodynamic lubrication (EHL), the combined stiffness is derived from the stiffness of both the oil film and gear tooth while the combined damping is established from the damping of these parts. The effects of three fundamental parameters (contact force, rotation speed, and tooth numbers) of the gear drive in line contact EHL on the combined stiffness and damping are then investigated. The results reveal that the small normal and tangential stiffness of the lubricant can alleviate meshing impact and shear vibration, while the impact and friction heat can be reduced by using an oil film with either a large normal damping or small tangential damping. Given that its amplitude and fluctuation are closely related to shear rate, effective viscosity, entrainment velocity, and curvature radii, the improved combined stiffness and damping can be obtained by rationally matching the geometric and operating parameters.

Investigation into the Normal Contact Stiffness of Rough Surface in Line Contact Mixed Elastohydrodynamic Lubrication

ABSTRACT In this work, the statistical asperity microcontact models in combination with the acoustic spring model and the load sharing concept are utilized to study the interfacial normal contact stiffness for a rough surface in line contact elastohydrodynamic lubrication (EHL). Two different statistical microcontact models of Greenwood and Williamson (GW) and Kogut and Etsion (KE) are employed to derive the normal contact stiffness expressions for a dry rough line contact considering the purely elastic contact and the multiple regimes elastic–elastoplastic–fully plastic contact, respectively. The liquid film stiffness is calculated based on the relationship between film thickness and bulk modulus of the lubricant. The lubricant film thickness equations are employed in conjunction with the load sharing concept and the empirical formulas for the maximum contact pressure in a dry rough contact are fitted for the GW model and the KE model, to evaluate the relationship between film thickness and motion velocity for the purely elastic GW microcontact model and the multiregime KE microcontact model, respectively. The comparison with experimental results shows that the KE model predicts closer total contact stiffness results than the GW model. The stiffness contributions from the solid asperity contact and lubricant film are obtained and effects of surface roughness, applied load, motion velocity, and type of lubricant on the normal contact stiffness are analyzed.