Elastohydrodynamic Lubrication Conditions Research Articles

An enhanced water-lubrication method: Friction-reducing and diffusion properties of secondary lubricants

To prevent severe friction between water-lubricated bearings (WLBs) and stern shafts under harsh conditions, a method is introduced that uses a lubrication pump to supply a small amount of secondary lubricant into the bearing for a short period of time. The effect of the secondary lubricant viscosity on friction-reducing performance is investigated by a modified block-on-ring friction and wear tester. The transfer process of the secondary lubricant within the bearing is observed with a self-designed visualization experimental platform. A flow model for capturing the diffusion of the secondary lubricant is developed, and the flow velocity equations are used as a “bridge” to link the mixed lubrication model and Volume-of-Fluid (VOF) model. The results indicate that injecting the secondary lubricant in the mixed lubrication state has the effect of rapidly reducing the friction coefficient, while supplying the lubricant in the elastohydrodynamic lubrication state tends to increase the friction coefficient. The backflow zones are primarily located at the bearing inner surface and the upper half of the fluid. The high-viscosity secondary lubricant separates into “free lubricant” and “adhesive lubricant” during the transfer process. The “oil-free zone” appears in the lubricating film due to the obstruction of lubricant diffusion by the “backflow effect”. The area of the “oil-free zone” decreases with increasing lubricant viscosity and decreasing load. This study provides a reference for friction-reducing technologies of friction pairs under water-lubrication conditions.

Enhancing practical modeling: A neural network approach for locally-resolved prediction of elastohydrodynamic line contacts

When modeling bearings in the context of entire transmissions or drivetrains, there are practical limits to the calculation resources available to calculate single bearings or even contacts. In settings such as these, curve-fitting methods have historically been deployed to estimate the elastohydrodynamic lubrication conditions. Machine learning methods have the potential to enable more sophisticated physical modeling in the context of larger computation environments, as the evaluation time of a trained model is typically negligible. We present a neural network that accurately evaluates the locally variable elastohydrodynamic film pressure and film thickness distributions and explore its application to (e.g.) cylindrical roller bearings. Employing a neural network for the EHL film thickness calculations rather than the curve-fitted, simplified methods that are today’s standard can enable a more physically precise modeling strategy at almost no additional computational cost.

Tribo-dynamic modelling and analysis for a high-speed helical gear system with time-varying backlash and friction under Elastohydrodynamic Lubrication condition

Tribo-dynamic modelling and analysis for a high-speed helical gear system with time-varying backlash and friction under Elastohydrodynamic Lubrication condition

Numerical study on mixed lubrication performance of misaligned microgroove water-lubricated bearings considering cavitation and turbulence effects

This study presents a mixed lubrication model for misaligned microgroove water-lubricated bearings (WLBs). The model considers the effects of cavitation and turbulence to assess the mixed lubrication performance of WLBs with various microgroove morphologies. The equations are discretized using the control volume method (CVM) and solved by using the Fischer–Burmeister–Newton–Schur method for dealing with the constrained system. A comparison of the experimental data from the published literature demonstrates the model and methodology's validity. On this basis, the effects of rotational speed, load, and misalignment angle on the mixed lubrication performance of microgroove WLBs are investigated. The numerical results indicate that the left-triangular microgroove exhibits the best-mixed lubrication performance. Under elastohydrodynamic lubrication and mixed lubrication conditions, there are significant discrepancies in microgroove morphology. However, this discrepancy diminishes with increasing misalignment angles. The edge contact problem resulting from journal misalignment can be efficiently mitigated by selecting the proper microgroove morphology. This study provides useful guidance for the optimal design and mixed lubrication performance improvement of WLBs.

Enhancing the Elastohydrodynamic Lubrication and Vibration Behavior of Rolling Bearings Using a Hybrid Bio-Grease Blended with Activated Carbon Nanoparticles

In recent years, bio-lubricants have received a growing interest for industrial applications. Still, a full-scale implementation in machinery lubrication requires a thorough evaluation of their performance through tribological and operational tests to stand upon their performance. Additionally, the promising outcomes achieved by nanoadditives in improving the performance of synthetic lubricants have prompted research efforts to identify suitable nanoadditives for bio-grease. This paper introduces a bio-grease from a hybrid vegetable oil and glycerol monostearate as a thickener for the lubrication of rolling bearings. Activated carbon nanoparticles (ACNPs) as nanoadditives were synthesized, characterized, and incorporated into the bio-grease at concentrations of 0.5, 1, and 2% by weight. Tribo-tests were conducted on these bio-grease blends, and running tests were carried out using 6006 ball bearings on a custom test rig. Throughout a 30-min test run under a radial load of 10% of the bearing’s dynamic load rating, mechanical vibrations and power consumption were measured and analyzed for each bearing. The bio-grease with ACNPs exhibited a substantial reduction in wear scar diameter (WSD) and coefficient of friction (COF), achieving improvements of up to 73.6 and 65%, respectively, in comparison to lithium grease. Furthermore, the load carrying capacity was enhanced by 200%. The study revealed a strong correlation between measured vibration amplitudes and the viscosity of the bio-grease. The absence of high frequency resonant bands in vibration spectra indicated that the test grease samples satisfied the conditions of elastohydrodynamic lubrication, and these findings were corroborated through calculations of the minimum oil film thickness.

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.

Study on the subsurface characteristics of textured surfaces under EHL condition

PurposeThe purpose of this study is to investigate the influence of surface texture on the subsurface characteristics of contact interfaces under elastohydrodynamic lubrication condition. As a typical contact form of gears and bearings, the optimization of friction characteristics at the elastohydrodynamic lubrication (EHL) interface has attracted the attention of scholars. Laser surface texturing is a feasible optimization solution, but there have been concerns about whether the surface texture of high-pair parts will affect their fatigue life.Design/methodology/approachTo examine the impact of texture preparation on the subsurface characteristics of high-pair interfaces under EHL conditions, a point contact EHL model is developed that takes into account the effect of textured surface topography. The pressure and thickness of the oil film are calculated as input parameters under different loads and entrainment velocities. The finite element method is used to simulate the impact of textures with varying diameters, densities and depths on the subsurface characteristics of the elastohydrodynamic interface. According to ISO 25178, analyze the relationship between 3D topography parameters and subsurface characteristics and study the trend of friction characteristics and subsurface characteristics based on the results of the ball on disc friction tests.FindingsThe outcomes suggest that under different rotational velocity and load conditions, the textured surfaces exhibit improved friction reduction effects; however, the creation of textures can result in significant subsurface plastic deformation and local peeling. The existence of texture makes the larger stress zone in the subsurface layer closer to the surface, leading to fatigue failure near the surface. Reasonable design parameters can help enhance the attributes of the subsurface. A smaller Sa and a Str greater than 0.5 can achieve ideal subsurface properties on the textured surface.Originality/valueThis paper investigates the influence of surface texture on the friction and subsurface characteristics of EHL interfaces and analyzes the impact of surface texture on interface contact performance while achieving lubrication improvement functional characteristics. The results provide theoretical support for the optimization design and functional regulation of surface texture in EHL interfaces.Peer reviewThe peer review history for this article is https://publons.com/publon/10.1108/ILT-10-2023-0324/

A time‐varying meshing stiffness model for gears with mixed elastohydrodynamic lubrication based on load‐sharing

AbstractIn mixed elastohydrodynamic lubrication (EHL), the load distribution between the gear meshing surfaces is shared by the oil film and the asperities of the gear's rough surface. Based on the load‐sharing concept, this paper proposes a time‐varying meshing stiffness (TVMS) model for gears with mixed EHL. The initial step involves the utilization of the Greenwood‐Williamson model to calculate the contact stiffness of surface asperities, while the lubricating film is assessed using a curve‐fitting formula to investigate the influence of gear surface morphology on TVMS. Subsequently, the incorporation of gear fillet foundation deformation and friction enables accurate TVMS determination. The proposed method is employed to examine the meshing stiffness of the gear pair under both dry lubrication and EHL conditions. Comparative analysis reveals favorable agreement between the proposed model and experimental results obtained under dry lubrication, thereby highlighting the superior performance of the proposed approach. Moreover, the time‐varying friction coefficient under EHL is computed, and the impacts of gear surface morphology parameters, temperature, speed, and load on lubrication conditions and TVMS are investigated. The findings presented in this paper contribute significantly to advancements in gear design and performance.

Experimental Analysis of Rolling Torque and Thermal Inlet Shear Heating in Tapered Roller Bearings

The investigation in this article focuses on the rolling resistance torque and thermal inlet shear factor in tapered roller bearings (TRBs) through systematic experiments using a modular test setup. TRBs typically operate under Elastohydrodynamic Lubrication (EHL) conditions. At sufficiently high speeds, the majority of rolling friction is due to a significant shift of the pressure centre in the EHL contact. While at lower speeds, sliding friction in the roller-rib contact becomes dominant, which operates under mixed lubrication conditions. Limited literature exists on the impact of inlet shear heating on effective lubricant temperature (Tin_c) and rolling friction in TRBs. To fill this gap, experimental measurements of the total frictional torque under axial loading at different speeds and oil temperatures are performed. With existing models for different friction contributions described in the literature, the rolling resistance due to EHL has been determined for various operating conditions. The effects of dimension-less speed (U), material (G), and load (W) parameters have also been investigated. Under fully flooded conditions, it was observed that the influence of material (G) and load (W) parameters on rolling friction is minor, while the impact of velocity (U) is significant. In the context of rolling resistance, the heating due to shear of the lubricant in the inlet zone plays a significant role. For higher rotational velocities, the estimated rotational torque reduction resulting from inlet shear heating was found to be approximately 6–8%.

Dynamic response of rolling element bearing with compound fault considering defect-rolling-element interaction

Dynamic modelling of rolling element bearing (REB) is a significant method to explore the vibration mechanism generated by fault, and it is the theoretical basis of fault diagnosis of REBs. Aiming at the complexity of defect-rolling-element interaction under radial load, the whole contact process of rolling element (RE) passing over defective area of outer or inner ring is analysed in detail. The impact force excitation function is derived by rotation and revolution velocity of RE. A four degree-of-freedom (DOF) dynamic model of REB with compound fault of both inner and outer raceway surface is developed by considering the time-varying displacement, impact force excitative and elastohydrodynamic lubrication (EHL) condition, and the novelty of the model is that the improved impact force excitation function is used. The experimental validation is carried out on test tig of Machinery Fault Simulator. The change of impact force with shaft speed and defect size is analysed. It is shown that the simulation results of the proposed model are closer to experimental results. A mapping method from defect-rolling-element-defect (DRED) behaviour to time is proposed to study the vibration characteristics of DRED behaviour, the results show that the amplitude of vibration will decrease when the same RE collides with inner and outer raceway defects simultaneously. When the same RE collides with inner and outer raceway defect successively, the amplitude of vibration will reach the maximum during the inner raceway defect rolling over each RE once. The proposed model can be used in practical application to study the influence of compound defects on vibration response of REB.

Interaction Between Gear Surface Wear and Contact Fatigue

Abstract A methodology is proposed to study the interplay between tooth wear and contact fatigue under elastohydrodynamic lubrication condition. The modeling methodology includes the influence of contact fatigue on wear and the influence of wear on contact fatigue. First, the changes in film pressure and film thickness of oil at each meshing point caused by contact fatigue are introduced according to the surface wear model, and the change of wear model is analyzed to study the effect of contact fatigue on wear. Then, according to the elastohydrodynamic lubrication theory, the change in film pressure affected by tooth surface wear is analyzed to study the effect of wear on contact fatigue. Finally, the influence of lubrication conditions on the interplay between tooth surface wear and contact fatigue is analyzed. In addition, an experimental fatigue study is performed and introduced into the model predictions to improve the accuracy of the proposed methodology.

Influence of water content on elastohydrodynamic friction and film thickness of water-containing polyalkylene glycols

Lubricants with a functional water portion have demonstrated a drastic reduction in friction under elastohydrodynamic lubrication conditions. With water-containing polyalkylene glycols, superlubricity with coefficients of friction <0.01 have been measured in model and gear contacts. In addition to the low friction, their calorimetric properties make them particularly interesting for application in electrified vehicles because the liquid can simultaneously serve as lubricant for the gearbox and coolant for the electric motors and the power electronics. In this study, the influence of water content between 8 wt% and 40 wt% of water-soluble polyalkylene glycols on friction and film thickness in elastohydrodynamically lubricated rolling-sliding contacts such as in gears and bearings is investigated. A polyalphaolefine oil is used as a reference. Friction has been measured on a ball-on-disk tribometer and film thickness on an optical tribometer. For a water content of 40 wt%, superlubricity with coefficients of friction down to 0.004 are found. The decrease in friction is up to 95% compared to the polyalphaolefine reference. The measured film thickness decreases with increasing water content. For a water content of 8 wt%, the film thickness is similar to that of the polyalphaolefine reference while at the same time friction is still reduced by 81%. Depending on the friction and film thickness requirements of a specific tribosystem, the water content of a water-containing polyalkylene glycol can be chosen accordingly.

A Wear Calculation Method for Helical Gear Based on Irreversible Thermodynamics

Abstract The accurate prediction of wear depth is of great significance to the failure evaluation of gear transmission. At present, the traditional wear calculation method is still unable to accurately predict the wear depth of helical gears under variable working conditions. The present work proposes a novel wear depth prediction method of helical gear, which is based on the theory of thermodynamics and the degradation entropy generation (DEG) theorem. The method can be used in not only dry contact friction but also mixed elastohydrodynamic lubrication (EHL) condition. The degradation coefficient of helical gear material was determined by wear experiment. The advantages of using DEG theorem to calculate wear loss under variable operation conditions are demonstrated by wear experiment. Moreover, the influence of ignoring the update of tooth surface load on the calculation results in wear process is further studied. The results reveal that the wear depth prediction method of helical gear proposed in this work can obtain the consistent wear depth distribution with the traditional method. The results calculated by the traditional method are generally higher than the method in this paper, and ignoring the load update in the wear process will make the results larger. The prediction method of helical gear wear depth presented in this paper will be useful for accurately predicting the wear of helical gear.

What stress components drive mechanochemistry? A study of ZDDP tribofilm formation.

Zinc dialkyldithiophosphate (ZDDP), the most widely used antiwear additive in engine oils, has been extensively studied over the last few decades to help understand the origin of its effectiveness. Glassy phosphate-based tribofilms, approximately 100 nm thick, are often formed on surfaces sliding in ZDDP-containing oils, which help to prevent or reduce wear. Recent studies reveal that a combination of applied shear and compressive stresses drive mechanochemical reactions that promote tribofilm growth, and that growth is further accelerated by increased temperature. While recent work has shown that compressive stress alone is insufficient to form tribofilms, the individual effects of the shear stress and compressive stress are not fully understood. Here, shear and compressive stresses are studied separately by using different ratios of high-viscosity, high-traction fluids for testing. This allows the areal mean compressive and shear stresses in the fluid when confined at a loaded sliding interface, to be independently controlled while driving tribofilm growth, which is a system we refer to as a stress-controlled mechanochemical reactor. Tribofilms derived from a secondary ZDDP were generated using a tungsten carbide/tungsten carbide ball-on-disk contact in the full elastohydrodynamic lubrication (EHL) regime using a mini-traction machine (MTM), meaning that solid-solid contact is avoided. The MTM was equipped with a spacer layer imaging (SLIM) capability, permitting in situ measurement of the tribofilm thickness during its growth. The well-separated sliding surfaces generated by the high-viscosity fluids confirm that solid-solid contact is not required for tribofilm formation. Under these full fluid film EHL conditions, shear stress and temperature promote tribofilm growth in accordance with stress-augmented thermal activation. In contrast, under constant shear stress and temperature, compressive stress has the opposite effect, inhibiting tribofilm growth. Using the extended Eyring model for shear- and hydrostatic pressure-affected reaction kinetics, an activation energy of 0.54 ± 0.04 eV is found, consistent with prior studies of ZDDPs. The activation volume for shear stress is found to be 0.18 ± 0.06 nm3, while that for the compressive stress component is much smaller, at 0.010 ± 0.004 nm3. This not only confirms prior work supporting that shear stress drives tribofilm growth, but demonstrates and quantifies how compressive stress inhibits growth, consistent with the rate-limiting step in tribofilm growth involving a bond-breaking reaction. Implications of these findings are discussed.

Evaluating the Time-Varying Mesh Stiffness of Planetary Gear Set With Gear Crack Considering the Friction Force Under Mixed Elastohydrodynamic Lubrication Condition

Abstract The mesh stiffness calculation of the planetary gear system with gear crack is investigated, and gear crack is modeled into end-face and addendum extended crack. Furthermore, the mesh stiffnesses are calculated under the effect of friction force obtained under the mixed elastohydrodynamic lubrication (EHL) condition. The nonuniformly distributed gear cracks on external and internal gear pairs are comprehensively modeled and analyzed, which is rarely investigated in previous studies. Moreover, the influence of crack propagation conditions on the meshing stiffness of the planetary gear system is analyzed. The obtained results show that the mesh stiffnesses experience abrupt variation in the pitch area during meshing, the extent of change is determined by the amplitude of the friction coefficient; in addition, gear crack position and extent could cause mesh stiffness reduction at varying levels at different stages of gear meshing.

Energy loss and mechanical efficiency forecasting model for aero-engine bevel gear power transmission

• Numerical loaded tooth contact analysis for meshing interface. • Meshing interface state evolution under TEHL condition. • Non-Newtonian fluid ETHL model considering entrainment angle. • Separation flow method for the friction coefficient determination. • Energy loss and mechanical efficiency forecasting model. Energy loss and mechanical efficiency directly affect the service performance and reliability of aero-engine bevel gear power transmission, but there is currently a lack of effective diagnosis in early design stage due to the complex tooth meshing interface state evolution under the thermal elastohydrodynamic lubrication (TEHL) condition. A new energy loss and mechanical efficiency prediction model is proposed by using the improved TEHL analysis considering the entrainment angle and non-Newtonian fluid effect. Firstly, numerical loaded tooth contact analysis (NLTCA) is developed to determine tooth meshing kinematic relating to the entrainment and sliding states. Then, the entrainment angle is taken into account the Non-Newtonian fluid TEHL model and separation flow method is applied for friction coefficient solution. Finally, new energy loss and mechanical efficiency model is established by simulating the complex tooth meshing interface TEHL. This model is enabling ever-higher levels of aero-engine bevel gear production efficiency and design sustainability. It can provide an important access to geometric and physical assessments that can improve the energy generation, conversion, transfer and utilization of the whole aero-engine power transmission system. .

Analysis on the effect of starved elastohydrodynamic lubrication on the adhesion behavior and fatigue index of wheel-rail contact

Friction modifiers (FMs) are widely used in wheel-rail applications. This paper presents a method to analyze the starved elastohydrodynamic lubrication (EHL) of the wheel-rail surface coated with FMs. Combined with rough surface simulation techniques, starved EHL analysis and film thickness analysis, the pressure distribution and adhesion coefficient under different film thickness states are obtained. The effect of film thickness of the FM supply layers and surface roughness on the adhesion coefficient is studied. The adhesion coefficient increases with the decrease in the effective FM film thickness and increase in the surface roughness. Based on the subsurface stress model, the subsurface stress distribution is studied. Then the influence of FMs on the fatigue of wheel and rail is analyzed on the basis of the shakedown map. Finally, the fatigue index of rail is explored in starved EHL state.

Meshing Characteristics of Spur Gears Considering Three-Dimensional Fractal Rough Surface under Elastohydrodynamic Lubrication

Taking the effect of actual surface topography under elastohydrodynamic lubrication (EHL) conditions on the contact state of gear pairs into consideration, a combination model with the analytical sliced method and two-dimensional (2D) EHL model is proposed to characterize the three-dimensional (3D) meshing characteristics of spur gears. Firstly, the surface topology of gears is tested by a surface profiler, which reflects that the topography of tooth surface accords with fractal characteristics. Thus, by adopting the Weierstrass–Mandelbrot (W-M) fractal function, the gear surface is characterized. Secondly, the numerical 2D EHL model with fractal roughness is established, and distributions of oil film pressure (OFP) and oil film thickness (OFT) at different meshing positions are obtained. Finally, considering the different topography distributions in the direction of face width, time-varying mesh stiffness (TVMS) is calculated based on the analytical sliced method. Thus, the influence of 3D surface topography can be considered. The Hertz contact stiffness is substituted by the time-varying lubricating oil film stiffness (OFS). The influences of tooth surface topography and lubricant film characteristics on meshing characteristics are investigated. The results show that the 3D rough tooth surface may be well characterized by a fractal function with random phase. Moreover, there is a great difference in the distribution of OFP and OFT between rough and smooth surfaces, which certainly influences the gear meshing characteristics.

Vibration-Based Fault Diagnosis of Helical Gear Pair With Tooth Surface Wear Considering Time-Varying Friction Coefficient Under Mixed Elastohydrodynamic Lubrication Condition

Abstract Based on “slice method,” the improved time-varying mesh stiffness (TVMS) calculation model of helical gear pair with tooth surface wear is proposed, in which the effect of friction force that obtained under mixed elastohydrodynamic lubrication (EHL) is considered in the model. Based on the improved TVMS calculation model, the dynamic model of helical gear system is established, then the influence of tooth wear parameters on the dynamic response is studied. The results illustrate that the varying reduction extents of mesh stiffness along tooth profile under tooth surface wear, in addition, the dynamic response in time-domain and frequency-domain present significant decline in amplitude under deteriorating wear condition.

Effects of Raceway Convexity on Friction Moment of Tapered Roller Bearings

The Effects of raceway convexities on friction moment of tapered roller bearings were studied in this paper. A new theoretical model of friction torque of tapered roller bearings was established considering the roughness and convexities of inner and outer ring raceways. Friction between roller and raceways were analyzed under the condition of elastohydrodynamic lubrication. Based on the theoretical model and experiments, the changes of friction torque with respected to raceway convexities of tapered roller bearings were obtained. The results show that the friction moment decreases with the increase of raceway convexities, while the increase of raceway convexity leads to the increase of contact stress. Therefore, the convexity values should be balanced between friction torque and contact stress. The convexity values should be balanced between friction torque and contact stress. The optimum values of the bearing being measured raceway convexities should be 5 ~ 6μm under the test conditions.