Elastohydrodynamic Lubrication Model Research Articles

Determination of Critical Temperature of Scuffing for AISI 8620 Steel Gear Contacts Lubricated by Dexron 6 Through Computational Simulation of Experiment

Abstract This study establishes the critical temperature of scuffing for contacts of gears made of AISI 8620 steel alloy, lubricated by Dexron 6 oil. Through thermal mixed elastohydrodynamic lubrication modeling, experimental scuffing failures are simulated to determine the associated maximum surface temperature, which consists of bulk and flash components. This temperature is referred as the limiting/critical temperature of scuffing and is believed to be independent of operating conditions, while vary for different solid material and lubricant pairs. It is found that sump lubricant temperature rise affects surface temperature by contributing to the bulk component. The flash component is largely dictated by asperity interactions within the contact zone, where Hertzian pressure is not an appropriate measure of micro-scale asperity contact loading. The observed scuffing scars are shown to be in good agreement with the high temperature zone predicted by the computational model.

Prediction of tribological and dynamical behaviors of spur gear pair considering tooth root crack

Variations in gear tooth meshing stiffness and tribological characteristics caused by tooth root cracks seriously affect the dynamic performance of gears, limiting the development of durable high strength gears. Therefore, the potential energy method was applied to obtain the time-varying meshing stiffness of the spur gear pair, and the finite element method was applied to verify the calculation results. Secondly, the load distribution of the gear with the cracked tooth root was derived using coordinated deformation conditions, and the effect of the tooth root crack on the tribological characteristics of the tooth surface was obtained based on the elastohydrodynamic lubrication (EHL) model. Finally, the tribo-dynamic behaviors of the gear under the action of the root cracks were investigated. The results indicated that root cracks change the load distribution ratio in the double-tooth meshing zone, which leads to corresponding changes in the tooth surface film thickness and friction coefficient. In addition, when the cracked teeth are engaged in meshing, the reduction in meshing stiffness causes vibration and shock, which causes the appearance of sidebands near the main meshing frequency. The amplitude of the dynamic meshing force increased with the increase in the degree of root cracks.

A solution for mixed elastohydrodynamic lubrication modeling considering effects of solid particles and surface roughness

To investigate the effects of solid particles on the point contact mixed lubrication, this paper aims to introduce solid particles into rough interfaces under mixed hydrodynamic lubrication. Statistical three-body micro-contact is utilized in modeling mixed EHL. The model is verified by comparing results without considering particles and roughness with those from classical EHL formula. Factors, such as particle physical parameters, surface roughness and operating condition acting on the system are discussed. The results show that the distribution of hydrodynamic pressure and oil film thickness on the point contact with particles still show typical characteristics of elastohydrodynamic lubrication. The physical parameters of particles and operating condition change the proportion of each part to the load carrying capacity, where an increase in particle size, concentration and surface orientation parameters increases the load ratio of particle and conversely an increase in surface roughness and sliding velocity decreases it. Both an increase in particle size and surface roughness result in an increase in the minimum oil film thickness, with the effect of surface roughness being more significant. In addition, the shear strength, size and concentration of the particles play an important role in the friction characteristics.

Tribological properties of a helical gear pair considering interfacial slip between lubricant and tooth surface

AbstractIn this study, an interfacial slip model including the limiting shear stress is proposed and applied to the thermal elastohydrodynamic lubrication (EHL) analysis of a helical gear pair. The main difference between the proposed model and the classical EHL model is that, the term of entrainment velocity in Reynolds equation is modified. The influences of interfacial slip, thermal effect, initial limiting shear stress and operating conditions on the tribological properties are evaluated. Due to the interfacial slip, the pressure distribution moves towards the inlet region, and the fluctuation distributions of entrainment velocity and film thickness are similar to the trigonometric function. The influence of thermal effect on interfacial slip cannot be ignored, especially in the case of high speed and heavy load. As the input torque and input rotational speed increase, the interfacial slip gradually extends to the whole meshing process.

Thermal Analysis of Herringbone Gears Based on Thermal Elastohydrodynamic Lubrication Considering Surface Roughness

To predict the temperature distribution of the tooth surface of a herringbone gear pair, a numerical method for the determination of frictional heat generation was proposed by establishing a thermal elastohydrodynamic lubrication (TEHL) model in the meshing zone taking surface roughness into account. According to the real micro topography of the tooth surface measured by a non-contact optical system and loaded tooth contact analysis, the friction coefficient was obtained by a TEHL analysis and then the heat generation in the contact zone was determined. With the combination of heat generation and heat dissipation analysis, the single tooth model of the herringbone gear pair due to the finite element method (FEM) was proposed and the steady-state temperature distribution of the tooth surfaces was predicted by FEM simulations. The simulation and the experimental results demonstrated good agreement, which verified the feasibility of the present numerical method.

Fractal simulation of surface topography and prediction of its lubrication characteristics

A machined surface has observable fractal characteristics, with infinite local and overall self-similar consistency. Therefore, the fractal theory is considered to provide a better description of the morphological characteristics of rough surfaces, which accurately reflects the randomness and multi-scale characteristics of rough surfaces and it is not comparable with the surface characteristics obtained based on statistical parameters limited by sampling length and device resolution. In this study, the Weierstrass-Mandelbrot (W-M) function was applied to construct a fractal reconstruction surface, and the mixed elastohydrodynamic lubrication model was used to investigate the lubrication characteristics of real and reconstructed surfaces under the same fractal parameters. The effects of the fractal parameters on the fractal surface lubrication characteristics were further analyzed. The results demonstrate that the lateral roughness fractal surface provides greater resistance to the entrained flow of lubricant, which leads to a larger average film thickness, than the longitudinal roughness and isotropic fractal surface. With the increase in fractal dimension, the surface roughness peak density increases, which reduces the surface film thickness by 47%, and the friction coefficient increases by 46%. The lubrication parameter fluctuates slightly with the change in the number of overlapping ridges M of the fractal surface. Generally, M has little effect on the surface lubrication characteristics.

Duncan Dowson: Pioneer of elastohydrodynamic lubrication of gears

The paper briefly reviews Duncan Dowson's ground-breaking contribution to the theory of elastohydrodynamic lubrication in relation to the understanding of lubrication of gear tooth contacts. His early work with Higginson on numerical modelling of elastohydrodynamic lubrication finally explained how gears can operate successfully, and avoid wear, due to the generation of a stiff, protective oil film. The resulting minimum film thickness equation stands as a reliable reference formula for calculations in gear design standards. The paper includes examples of how elastohydrodynamic lubrication theory has been developed by the present authors and their co-workers, and applied to aid the design of engineering components such as worm gears, thrust rims and profile-modified helical gears. Also included is its extension to include the important effects of surface roughness at the asperity level (micro-elastohydrodynamic lubrication) and its relevance to the current, troublesome problem of micropitting.

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.

Study of the friction and wear of dimple textured surfaces based on mixed elastohydrodynamic lubrication

In recent years, many study results have indicated that surface texture may have a positive effect on the improvement of the tribology properties of an interface. The novelty of this work is the study of the friction and wear of a line contact textured surface with consideration of the real surface topography and a discussion of the relationship between the roughness and the dimple depth. In this work, the mixed elastohydrodynamic lubrication model is employed to investigate the friction and wear of a line contact textured surface. In order to obtain the optimal texture form that is beneficial to improve the surface tribology performance, the friction coefficient and wear losses of different textured surfaces are compared. In addition, the influences of the dimple depth, roughness amplitude, and applied loads on the friction and wear of the interface are explored. The most important finding is that the textured surface has better tribology performance when the standard deviation of the surface roughness is close to the dimple depth.

Fractal variation of three-dimensional surface topography during sliding wear under mixed elastohydrodynamic lubrication

The surface morphology variation of the friction pair during the wear process directly affects the local lubrication effect and contact strength, and this variation is difficult to quantify in mixed lubrication. In this study, a numerical simulation and characterization model method of sliding wear surface morphology evolution based on deterministic elastohydrodynamic lubrication (EHL) model and surface three-dimensional morphology fractal method is established. The effectiveness of the lubrication model is verified by the film thickness measurement, and the actual surface wear coefficient is obtained through the wear experiment. On this basis, the variation of surface morphology and fractal parameters in the sliding wear process is investigated, and the effect of contact load and sliding speed on surface lubrication characteristics and fractal parameters is analyzed. The results show: wear will cause the higher wave peaks on the ground surface to be gradually worn away and the fine structure of the surface is reduced, and the fractal dimension of the morphology is therefore reduced. In addition, the contact area ratio and contact load ratio, as well as the coefficient of friction and surface evolution under different loads and sliding speeds are consistent.

Remarks on Modeling the Oil Film Generation of Rod Seals

The oil film generation of a U-cup rod seal and the oil film thickness on the rod after outstroke were analyzed analytically, numerically, and experimentally. The analyzed sealing system consists of an unmodified, commercially available U-cup, a polished rod, and mineral oil. The inverse theory of hydrodynamic lubrication (IHL) and an elastohydrodynamic lubrication (EHL) model—both based on the Reynolds equation for thin lubricating films—were utilized to simulate the oil film generation. In the EHL analysis, physical parameters and numerical EHL parameters were varied. Both the analytical and numerical results for the varied parameters show that the film thickness follows a square-root function (i.e., with a function exponent of 0.5) with respect to the product of dynamic viscosity and rod speed, also referred to as the duty parameter. In comparison to the analytical and numerical results, the film thickness obtained via ellipsometry measurements is a function of the duty parameter with an exponent of approximately 0.85. Possible causes for the discrepancy between theory and experiments are discussed. A potential remedy for the modeling gap is proposed.

The Causes of Asymmetric Deformation of Surface Roughness Asperities in Elastohydrodynamic Lubrication Contacts

Abstract This paper provides the main causes of asymmetric or directional deformation of surface roughness based on a transient non-Newtonian thermal elastohydrodynamic lubrication (EHL) model, where the contact materials have different thermal conductivities and elastic moduli. In order to obtain the actual shape of the surface asperity, the surface shapes of contact bodies are evaluated separately. It is clarified that the asymmetric deformation of the asperities appears due to two causes. One depends on the slide-roll ratio (SRR) and the difference in thermal conductivity between contact materials, and the other is caused by the contact pressure between the asperities through the oil film.

Mechanical Power Losses of Ball Bearings: Model and Experimental Validation

Abstract A tribo-dynamic model of ball bearings is proposed to predict their load-dependent (mechanical) power losses. The model combines (i) a transient, point contact mixed elastohydrodynamic lubrication (EHL) formulation to simulate the mechanics of the load carrying lubricated ball-race interfaces and (ii) a singularity-free dynamics model and establishes the two-way coupling between them that dictates power losses. The dynamic model uses a vectoral formulation with Euler parameters. The EHL model is capable of capturing two-dimensional contact kinematics, velocity variations across the contact as well as asperity interactions of rough contact surfaces. Resultant contact surface shear distributions are processed to predict mechanical power losses of example ball bearings operating under combined radial and axial forces. An experimental setup is introduced for measurement of the power losses of rolling-element bearings. Sets of measurements taken by using the same example ball bearings are compared with those predicted by the model to assess its accuracy in predicting mechanical power loss of a ball bearing within wide ranges of axial and radial forces.

A transient and time lag deformation alternating-coupling micro elastohydrodynamic lubrication model

As transient and time lag deformations occur alternately and influence each other for viscoelastic materials of dynamically loaded journal bearings, the time lag deformation per unit time is defined based on the finite element stiffness equation and the standard linear solid model, accumulating it by loop and superposing transient deformation to obtain actual deformation at every moment. Thereby, a novel temporal association deformation equation of bearing is constructed. It is used to improve the film thickness calculation method of the traditional micro elastohydrodynamic lubrication (MEHD) model. Finally, a novel transient and time lag deformation alternating-coupling micro elastohydrodynamic lubrication (TTL-MEHD) model is established. The comparison between lubrication performance parameters calculated by the new model and the MEHD model under the eccentric motion of the journal proves the new model is correct, and can effectively analyze the knocking and rough rubbing characteristics at the early stage of bearing instability. The new model is implemented to explore the effect of the time lag degree of material deformation on mixed lubrication performance. The application of the new model in connecting rod bearing of internal-combustion engine proves that it can effectively compensate for the impact lag deviation caused by the complete elasticity assumption.

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

Wear characterization under sliding–rolling contact using friction-induced vibration features

Skidding in rolling bearings often causes unexpected surface wear and early failures. Although vibration monitoring is widely used for bearing fault diagnosis, it is much less developed for wear analysis. This paper presents an investigation into characterizing the surface wear of a simplified sliding–rolling contact using friction-induced vibration features. The friction vibration mechanism under a rough sliding–rolling contact is explored by a mixed elastohydrodynamic lubrication model. It is found that the friction coefficient has a positive correlation with the surface roughness, which indicates that the friction behaviour can be used to track the wear state under the sliding–rolling contact. Furthermore, the vibration excited by different rough surfaces is studied experimentally on a roller–ring test rig. The friction-induced vibration signal is extracted and a feature parameter ( K) is defined for quantitative wear characterization. Results show that the friction-induced vibration can well reflect the surface wear under the sliding–rolling contact. Compared with traditional time-domain parameters, the proposed parameter has a better linear relationship with the surface roughness.

A fatigue model for spiral bevel gears under mixed elastohydrodynamic lubrication conditions

AbstractMany contributions have focused on the pitting analysis in gear transmissions. However, studies on pitting fatigue in spiral bevel gears are limited due to the complexity of tooth contact and lubrication analysis. This paper is to present a reasonable methodology to simulate the pitting crack nucleation of spiral bevel gears considering the real three‐dimensional (3D) rough surface contact where the intermittent asperity stress concentrations is prominent. The proposed model includes a loaded tooth contact analysis model, a mixed elastohydrodynamic lubrication model proposed previously, 3D stress filed formulation, and multi‐axial fatigue criterions. In order to determine an appropriate multi‐axial fatigue criterion for spiral bevel gear, a characteristic plane approach and a conventional critical plane approach are employed in this study. The predicted micro‐pitting lives are compared to published micro‐pitting investigations to assess the reliability of two fatigue criterions in simulation of the micro‐pitting failure. It is observed that the characteristic plane approach is better to reveal the failure mechanism in spiral bevel gears.

Design of logarithmic crowned roller for tapered roller bearings based on the elastohydrodynamic lubrication model

PurposeThe purpose of this paper is to study the film-forming capacity of logarithmic crowned roller for tapered roller bearing (TRB) and to design a tapered roller profile based on an elastohydrodynamic lubrication model.Design/methodology/approachA coupled model, incorporating a quasi-static model of TRBs and an elastohydrodynamic lubrication model was developed to investigate the load distribution of TRB and to evaluate the lubrication state of tapered roller/raceway contact.FindingsThe model is verified with published literature results. Parametric analysis is conducted to investigate the effect of crown drop on azimuthal load distribution of the roller, film thickness and pressure distribution in the contact area. The result shows that crown drop has little influence on the azimuthal load distribution; also, the film thickness and the pressure distribution are asymmetric. When the tapered roller is designed and manufactured, the crown drop of the small end should be larger than that in the large end.Originality/valuePrecise roller profile design is conducive to improve the fatigue life of TRBs. Currently, most crown design methods neglect the influence of lubrication, which can lead to a non-suitable roller profile. Therefore, the present work is undertaken to optimize roller profiles based on lubrication theory.

Amorphous Carbon Coatings for Total Knee Replacements-Part II: Tribological Behavior.

Diamond-like carbon coatings may decrease implant wear, therefore, they are helping to reduce aseptic loosening and increase service life of total knee arthroplasties (TKAs). This two-part study addresses the development of such coatings for ultrahigh molecular weight polyethylene (UHMWPE) tibial inlays as well as cobalt-chromium-molybdenum (CoCr) and titanium (Ti64) alloy femoral components. While the deposition of a pure (a-C:H) and tungsten-doped hydrogen-containing amorphous carbon coating (a-C:H:W) as well as the detailed characterization of mechanical and adhesion properties were the subject of Part I, the tribological behavior is studied in Part II. Pin-on-disk tests are performed under artificial synovial fluid lubrication. Numerical elastohydrodynamic lubrication modeling is used to show the representability of contact conditions for TKAs and to assess the influence of coatings on lubrication conditions. The wear behavior is characterized by means of light and laser scanning microscopy, Raman spectroscopy, scanning electron microscopy and particle analyses. Although the coating leads to an increase in friction due to the considerably higher roughness, especially the UHMWPE wear is significantly reduced up to a factor of 49% (CoCr) and 77% (Ti64). Thereby, the coating shows continuous wear and no sudden failure or spallation of larger wear particles. This demonstrated the great potential of amorphous carbon coatings for knee replacements.

Lubrication characteristics study of main bearings on crankshaft balance rate

Unbalanced inertia force and moment of crankshaft generated by cylinder pressure have a significant effect on the vibration characteristics of diesel engine, but the study on the lubrication characteristics of crankshaft by balance rate needs to be studied. Based on Greenwood-Tripp asperity contact theory and average Reynolds equation, an elastohydrodynamic (EHD) lubrication model of the main bearing for a V-12 diesel engine is developed, and the influence of different balance rates on lubrication characteristics is analyzed. On this basis, a factorial experiment of ten influencing factors including the balance rate is designed, and the factors that significantly affected the lubrication characteristics of the main bearing are screened out by factor effect diagram, statistical analysis and residual probability diagram. The results show that the crankshaft with different balance rate has a great influence on the lubrication performance. With the increase of balance rate, the minimum oil film thickness first increases and then decreases, and the maximum oil film pressure first decreases and then increases. The balance rate, bearing width, bearing clearance, bush repair and oil viscosity have significant effects on the performance of main bearing, among which the balance rate of crankshaft has the greatest effect on the minimum oil film thickness, the maximum rough contact pressure and the average friction power loss.