Elastohydrodynamic Lubrication Theory Research Articles

Dynamic analysis of double-helical gear system considering effect of oil film among meshing teeth

The oil film among meshing teeth is just like a spring-damping element, and it can dominate the friction and meshing characteristics of the gear pair and influence its dynamic performances further. Thus, this article focuses on a double-helical gear system and makes efforts to consider the effect of the oil film among meshing teeth more deeply, which can enhance the precision of dynamic analysis for the gear system. First, based on the elasto-hydrodynamic lubrication theory and “microtomy” method, the models of friction and meshing characteristics are developed including the friction state and spring-damping effect of the oil film among meshing teeth; then, the dynamic models of the double-helical gear system with the effect of the oil film among meshing teeth are established, and finally, the experiments are carried out to verify the value of the models developed in this article. According to the theoretical and experimental analyses, it can be seen that the dynamic model considering the effect of the oil film among the meshing teeth is more precise and practical, and the effect of the oil film should be considered in the dynamic analysis of the gear system, especially at the condition with heavy load or high speed.

Parametric analysis of the elastohydrodynamic lubrication efficiency on induced seismicity

SUMMARY During reservoir stimulations, the injection of fluids with variable viscosities can trigger seismicity. Several fault lubrication mechanisms have been invoked to explain the dynamic stress drop occurring during those seismic events. Here, we perform a parametric analysis of the elastohydrodynamic fault lubrication mechanism to assess its efficiency during fluid-induced earthquakes. The efficiency of the mechanism is measured with the dimensionless Sommerfeld number S. Accordingly, we analysed eight well-documented cases of induced seismicity associated with the injection of fluids whose viscosities range from 1 mPa s (water) to 100 mPa s (proppant). We collected information related to the in situ stress field, fault orientation and geometry, moment of magnitude and static stress drop of the events. These parameters allow us to analyse the variation in the Sommerfeld number. Our results show that the estimated dynamic friction on the fault during the event is compatible with the fault weakening predicted by the elastohydrodynamic lubrication theory, particularly for highly viscous fluids.

Numerical investigation on the high‐speed wheel/rail adhesion under the starved interfacial contaminations with surface roughness

AbstractThis paper presents a new numerical model of wheel/rail in rolling contact to study the adhesion mechanism under the starved interfacial contaminations at high speed considering surface roughness. A thermal starved mixed elastohydrodynamic lubrication (EHL) theory is hired in the model. The empirical equations for analysing the contact force of rough surfaces that are based on amount of accurate finite element analysis (FEA) of an elastic‐plastic single‐asperity contact over a rigid flat are proposed. Multilevel method is used to solve the modified Reynolds equations, and sweeping column method is used to solve energy and heat conduction equations. The pressure field, the fractional film content, and the temperature field are obtained through the present model. In addition, the influences of train speed, surface roughness amplitudes, and inlet film thickness on the adhesion coefficient are investigated. The results from the present model have been compared with those from flooded analyses for water and oil‐contamination cases. The numerical results show that the inlet film thickness and the train speed had a significant effect on the wheel/rail adhesion ability.

The Calculation of Friction Heat and Thermal Analysis of Spur Gears Based on Thermal Elastohydrodynamic Lubrication Theory

In order to predict the temperature distribution of gears more accurately, the influence of oil film on frictional heat generation should be taken into account in computational model. In this paper, based on the theory of thermal elastohydrodynamic lubrication, the calculation of frictional heat flux in the meshing process and the steady thermal analysis of spur gears is completed. The reliability of the model is verified by comparing the calculated results with the value of empirical formulas and experimental data. This paper provides an effective analysis method for gluing prediction, failure analysis and lubrication state analysis of aero-engine transmission gears.

A Micropitting Study Considering Rough Sliding and Mild Wear

Micropitting is a typical surface contact fatigue in rolling–sliding contact. The kinematic sliding is of great significance in the initiation and progression of micropitting. A numerical surface fatigue model considering rolling–sliding contact and surface evolution is developed based on mixed-EHL (elastohydrodynamic lubrication) theory, rainflow cycle counting method and Archard’s law. Surface evolution is evaluated using Archard’s wear law based on measured teeth surface topography. Surface damage is determined via the Palmgren–Miner line rule and Goodman diagrams. The effect of rolling speed and surface roughness are discussed in detail. Results show that stress micro-cycles are introduced by rough sliding in the rolling–sliding contact. The mild wear reduces the height of asperities, the maximum pressure and alleviates subsurface stress concentration. For rolling–sliding contact, the faster moving surface dominates the composite height of asperities, then decides the fluctuations of pressure, as well as stress ranges. The combination of surface topography should be considered in the surface design.

Mapping the friction coefficient of AISI 316L on UHMWPE lubricated with bovine serum to study the effect of loading and entrainment at high values of sliding-to-rolling ratio

From an experimental point of view, determining the lubrication regime established between contact surfaces of joint prosthesis using the theory of elastohydrodynamic lubrication is rather impractical due to the intrinsic hindrances to measure the thickness of the lubricant film at the contact area. This claim is supported by the results obtained by experts using optical interferometry to perform such measurements using synovial like fluids. Similarly, research has shown that the complex rheology of the synovial fluid complicates the direct application of EHL theory and plays an important role in the lubrication mechanisms at work in prosthetic devices. Since the natural response of all tribological systems is the frictional force, rather than trying to measure the thickness of the lubricant film to determine the lubrication regime, we measured the effect of loading and entrainment on the friction coefficient at the contact point of an AISI 316L stainless steel sphere loaded against an ultra-high molecular weight polyethylene disc, lubricated with fetal bovine serum solution, at high values of sliding-to-rolling ratio. Applying statistical analysis, we obtained a best-fit model that shows a smooth transition from mixed to full-film lubrication regime

Thermo-elastohydrodynamic mixed-lubrication model for reciprocating rod seals

Abstract A thermo-elastohydrodynamic lubrication model of a typical VL combined reciprocating rod seal is established to analyze thermal-viscous effects on the reciprocating rod sealing system. Both the inverse and elastohydrodynamic lubrication theories are interactively applied to calculate the pressure and thickness of the lubrication film. The influence coefficient method is used to couple the fluid mechanics, macroscopic solid mechanics, and microscopic contact mechanics. The temperature field is solved using the finite-difference method. With the alternating direction implicit method, the classical heat transfer equation is discretized. The calculation results obtained with the present model are compared with those of a model without thermal correction. A considerable difference is found between the two calculations especially at high rod velocities.

Size effect on thermal elastohydrodynamic lubrication of industrial chain bush-pin hinge pair

PurposeThe purpose of this paper is to use elastohydrodynamic lubrication (EHL) theory to study the variation of the equivalent curvature radius “R” on the change of oil film thickness, pressure, temperature rise and friction coefficient in the contact zone between bush-pin in industrial chain drive.Design/methodology/approachIn this paper, the contact between bush and pin is simplified as infinitely long line contact. The lubrication state is studied by numerical simulation using steady-state line contact thermal EHL. The two constitutive equations, namely, Newton fluid and Ree–Eyring fluid are used in the calculations.FindingsIt is found that with the increase of equivalent curvature radius, the thickness of oil film decreases and the temperature rise increases. Under the same condition, the friction coefficient of Newton fluid is higher than that of Ree–Eyring fluid. When the load increases, the oil film thickness decreases, the temperature rise increases and the friction coefficient decreases; and the film thickness increases with the increase of the entraining speed under the condition “R < 1,000 mm”.Research limitations/implicationsThe infinite line contact assumption is only an approximation. For example, the distances between the two inner plates are 5.72 mm, by considering the two parts assembled into the inner plates, the total length of the bush is less than 6 mm. The diameter of the pin and the bore diameter of the bush are 3.28 and 3.33 mm. However, the infinite line contact is also helpful in understanding the general variation of oil film characteristics and provides a reference for the future study of finite line contact of chain problems.Originality/valueThe change of the equivalent radius R on the variation of the oil film in the contact of the bush and the pin in industrial chain drive was investigated. The size effect influences the lubrication characteristic greatly in the bush-pin pair.

Effect of roundness and coaxiality error on the lubrication performance of ICE main bearings

Nowadays, with higher power density trend and lightweight design requirements in internal combustion engine, more factors are considered in bearing lubrication analysis to improve the lubrication performance and to decrease the risk of failure. The effect of roundness and coaxiality on the lubrication performance of a V-type diesel engine main bearings were investigated systematically and comprehensively using numerical simulation method based on elasto-hydrodynamic lubrication theory. The average flow model, the asperity contact theory and the multi-body dynamics based on component mode synthesis were used to improve simulation accuracy and efficiency. The results showed that out-of-roundness has an apparent negative effect on the lubrication performance of main bearings and the out-of-roundness wave height and the wave number should not exceed 2μm and 10 respectively. In addition, the lubrication performance increased slightly when the bearing house coaxiality tilt angle is the same as the journal load bending direction. The study has some guiding significance for improving the lubrication performance and tolerance requirements design of main bearings.

The effect of contact severity on micropitting: Simulation and experiments

Abstract A numerical contact fatigue model combining the effects of rolling contact fatigue and wear has been developed based on mixed elastohydrodynamic lubrication (EHL) theory, continuum damage mechanics (CDM) and the Archard's wear law. A series of benchtop tests were conducted using a triple-contact test rig to study the influence of surface roughness, speed and load on micropitting. The proposed surface damage model was used to simulate the rolling-sliding line contact of surfaces having different surface topography. The film thickness, contact pressure and sub-surface stress were determined by solving the generalized Reynolds equation and using the well-developed discrete convolute and fast Fourier transformation (DC-FFT) method. The jump-in-cycle was assumed to evaluate the accumulated damage based on the tested fatigue life and sub-surface stress histories. Surface topography was updated by calculating the wear height with the Archard's wear equation. Results reveal that micropitting occurs under the combined effect of wear and contact fatigue. The micropitting rate increased then turn to decreased as the lambda ratio ( λ ) increased. The contact pressure significantly affected the contact fatigue life and the micropitting rate.

Elastohydrodynamic Lubrication Modeling by a Cosserat Continuum Theory for Small Polymer Journal Bearings

Abstract Recent experiments have shown that the elastic deformation behaviors of a polymeric material are consistent with the Cosserat elasticity under nonuniform deformation at a millimeter scale. Thus, an elastohydrodynamic lubrication model in the framework of the Cosserat continuum theory is proposed to explore the lubrication performance that deviates from the classical elastohydrodynamic lubrication theory for the small polymer journal bearings with millimeter size. The elastic deformation of the bearing sleeve made of polymeric material and the pressure distribution in a lubricating film are obtained through an iterative solution of the equation of the Cosserat elasticity and the modified Reynolds’ equations with considering the boundary slippage. The effect of bearing size and Cosserat characteristic lengths for torsion and bending on the lubrication performance of the small polymer journal bearings is studied using the proposed Cosserat elastohydrodynamic lubrication model. It was found that the small changes in film thickness due to the Cosserat effect can result in large changes in film pressure. The Cosserat characteristic length of bending possesses a significant effect on the lubrication behaviors of the journal bearings, because the size effect is mainly caused by the increased apparent modulus due to the bending elastic deformation of the bearing sleeve. The boundary slip behaviors dependent on the Cosserat characteristic length are also studied using the Cosserat elastohydrodynamic model, and the numerical results show that the Cosserat characteristic length changes the optimal geometric parameters of the slip zone in terms of load carrying capacity for the small polymer journal bearings.

The prediction of load distribution in four-row cylindrical roller bearings under the elastohydrodynamic lubrication based on boundary element method

In order to get the prediction of load distribution in four-row cylindrical roller bearing under the elastohydrodynamic lubrication (EHL), a new bearing Boundary Element Method (BEM) is proposed, which is based on the elastic contact BEM and EHL theory. Firstly, the basic theories of the bearing BEM are introduced. Secondly, the basic equations of the EHL theory of finite length line contact are described, and the calculation program is compiled by the Finite Difference Method (FDM), by which the EHL characteristics of four-row cylindrical roller bearing under smooth condition are analyzed. Thirdly, the thickness of lubricant oil film and the surface roughness are coupled with the boundary integral equation in the form of contact clearance, and also the friction coefficient equation derived by EHL theory. The boundary integral equation of bearing BEM under the EHL condition is established, and the calculation program is compiled. Then, load and pressure distributions of a four-row cylindrical roller bearing are simulated numerically under different surface roughness conditions. Finally, the load distribution of the four-row cylindrical roller bearing is tested, and the experimental data and the simulation results are compared, which proves the validity and effectiveness of the new bearing BEM.

Study on contact fatigue of a wind turbine gear pair considering surface roughness

Contact fatigue issues become more and more crucial in gear industry as they significantly affect the reliability and service life of associated mechanical systems such as wind turbine gearboxes. The contact fatigue behavior is mostly determined by the mechanical properties of materials and stress fields near the contact area, which is further influenced by the lubrication and surface roughness due to pressure fluctuations. In this study, a numerical model incorporating the lubrication state, tooth surface roughness, residual stress, and mechanical properties of the material is developed to determine the contact fatigue behavior of a megawatt level wind turbine carburized gear. The variations of the hardness and residual stress along the depth were characterized by the Vickers hardness measurement and X-ray diffraction test, respectively. The elastohydrodynamic lubrication theory was applied to predict the contact pressure distribution, highlighting the influence of the surface roughness that stemed from the original measurement through an optical profiler. The stress histories of the studied material points during a complete contact loading cycle were fast calculated using the discreteconcrete fast Fourier transformation (DC-FFT) method. Modified Dang Van diagrams under different working conditions were determined to estimate the contact fatigue failure risk. The effect of the root mean square (RMS) value of the surface roughness on the failure risk at critical material points were discussed in detail. Results revealed that the surface roughness significantly increases the contact fatigue failure risk within a shallow area, and the maximum risk appears near the surface.

Parameter design methodologies for vertical skewed line gears taking lubrication performance into account

Based on the elastohydrodynamic lubrication (EHL) theory, design methodologies are proposed aiming to improve the EHL state of the vertical skewed line gear (VSLG) in this article. First of all, the parametric equations of the driving and driven VSLG surfaces are established and then converted into equivalent Hertz contact model. Then, the influences of the design parameters of the VSLG on the ellipticity are analyzed by its equivalent Hertz contact model. Finally, the parameter design method for improving the EHL state of VSLG is deduced. The results of optical elastohydrodynamic experiment and simulation experiment indicate that the parameter design method is effective for the formation of EHL film without changing the kinematic characteristics of VSLG. In short, this paper provides reliable and convenient parameter design methods for VSLG in consideration of EHL.

Research progress on calculation method of tooth surface friction coefficient

Firstly, the research significance of tooth surface friction is introduced. The difficulties in calculating the friction factor of tooth surface are analysed. Secondly, the current calculation method of the friction factor of the tooth surface is introduced systematically, the method of calculating the friction factor of the tooth surface based on elastohydrodynamic lubrication theory and the method of calculating the friction factor of the tooth surface based on the friction characteristics test of the tooth surface.

Mechanical behaviour of fluid-lubricated faults

Fluids are pervasive in fault zones cutting the Earth's crust; however, the effect of fluid viscosity on fault mechanics is mainly conjectured by theoretical models. We present friction experiments performed on both dry and fluid-permeated silicate and carbonate bearing-rocks, at normal effective stresses up to 20 MPa, with a slip-rate ranging between 10 μm/s and 1 m/s. Four different fluid viscosities were tested. We show that both static and dynamic friction coefficients decrease with viscosity and that dynamic friction depends on the dimensionless Sommerfeld number (S) as predicted by the elastohydrodynamic-lubrication theory (EHD).Under favourable conditions (depending on the fluid viscosity (η), co-seismic slip-rate (V), fault geometry (L/H02) and earthquake nucleation depth (∝σeff)), EHD might be an effective weakening mechanism during natural and induced earthquakes. However, at seismic slip-rate, the slip weakening distance (Dc) increases markedly for a range of fluid viscosities expected in the Earth, potentially favouring slow-slip rather than rupture propagation for small to moderate earthquakes.

Elastohydrodynamic Friction Mode as a Method of Surface Finishing Excluding Burnishing

Over the past decades the science of friction has got great development. Processes of friction and wear significantly depend on constructive junction design, selection of wear resistant materials and effective lubricants for them, as well as the conditions of the machinery operation. Currently, a large number of scientific works [7-11, 16-20] are devoted to the review of the contact interaction conditions with the use a lubricant. The method of elastohydrodynamic lubrication is of particular interest when studying different kinds of lubrication. According to the elastohydrodynamic lubrication theory, contact conditions of two elastic bodies are characterized by high pressures which cause the elastic deformation of solids and by the dependence of a lubricant viscosity from the pressure. When using the elastohydrodynamic lubrication the layer profile, the sum amount of elastic deformations, elastic deformations and the lubricant viscosity dependence from pressure are given by set equations [12-15]. The impact of elastohydrodynamic lubrication method on the surface layer of the contacting parts is of great interest.

Research on tribological characteristics of bevel gear after shot blasting based on 85-pellets model

High-speed overloading puts forward very strict requirements on the bending strength of spiral bevel gears, and shot blasting is a technological process method to increase gear bending fatigue strength significantly. During the process of shot blasting, a large number of tiny pellets bombard metal target material surface at very high speed in order to let the target material form plastic deformation and form strengthened layer at the same time. As the bombarded target, the microstructure of gear surface spiral bevel gear is inevitably changed. This paper aims at revealing how the shot peened surface microstructure of the spiral bevel gear affects lubrication of gear and establishes a reasonable microstructure description model of the shot blasting surface of the spiral bevel gear, revealing the tribological characteristics of spiral bevel gears after shot blasting treatment based on the elastohydrodynamic lubrication theory. Also, comparative research is carried out on a variety of lubrication characteristics of the microstructure surface.

On the mixed EHL characteristics, friction and flash temperature in helical gears with consideration of 3D surface roughness

PurposeThe purpose of this study is to investigate the tribological performance of helical gear pairs with consideration of the properties of non-Newtonian lubricant and the real three-dimensional (3D) topography of tooth flanks.Design/methodology/approachBased on the mixed elastohydrodynamic lubrication (EHL) theory for infinite line contact, this paper proposes a complete model for involute helical gear pairs considering the real 3D topography of tooth flanks and the properties of non-Newtonian lubricant. Film thickness, contact load and contact area ratios at the mid-point of contact line are studied for each angular displacement of pinion. Both the total friction coefficient and surface flash temperature are calculated after obtaining the values of pressure and subsurface stress. Then, the influences of input parameters including rotational speed and power are investigated.FindingsDuring the meshing process, contact load ratio and area ratio of the two rough surface cases first increase and then decrease; the maximum flash temperature rise (MFTR) on the gear is lower than that on the pinion first, but later the situation converses. For cylindrical gears, on the plane of action, there is a point or a line where the instantaneous friction reduces to a minimum value in a sudden, as the sliding–rolling ratio becomes zero. When rotational speed increases, film thickness becomes larger, and meanwhile, contact load ratio, coefficient of friction and MFTR gradually reduce.Originality/valueA comprehensive analysis is conducted and a computer program is developed for meshing geometry, kinematics, tooth contact, mixed EHL characteristics, friction, FTR and subsurface stress of involute helical gear pairs. Besides, a numerical simulation model is developed, which can be used to analyze mixed lubrication with 3D machined roughness under a wide range of operating conditions.

Numerical simulation model of a reciprocating seal based on the mixed‐lubrication theory

Based on the mixed-lubrication theory, a numerical simulation model of a reciprocating seal is established. The model includes finite element, fluid mechanics, contact mechanics and deformation mechanics analyses. The hydrodynamic analysis uses elastohydrodynamic lubrication theory and inverse hydrodynamic lubrication to obtain the relationship between fluid pressure and film thickness, while the contact mechanics analysis obtains the relationship between the asperity contact pressure and film thickness. The influence of the coefficient matrix and static contact pressure is calculated by the finite element analysis. The coupling relationship among the fluid pressure, asperity contact pressure and static contact pressure is provided by the influence coefficient method of the deformation mechanics analysis. The calculation results of the numerical model are verified by experimental results, which are measured by the bench test developed by the authors.