Elastohydrodynamic Lubrication Theory Research Articles

Elastohydrodynamic Traction and Film Thickness at High Speeds

A renewed interest in elastohydrodynamic lubrication (EHL) phenomena at high speeds, for which thermal effects strongly influence both traction and film thickness, has grown out of the challenges presented by high-speed geared transmissions in electric vehicles. This study uses a new ball-on-disc set-up employing the well-known ultra-thin-film interferometry technique to simultaneously measure EHL film thickness and traction at entrainment speeds up to 20 m/s and slide-roll ratios up to 100%. The effect of fluid composition is examined for Group I, II and III mineral oils, for two polyalphaolefins in Group IV, and for the traction fluid Santotrac 50. The effect of viscosity in the range 4–180 mPa.s is investigated by varying bulk fluid temperature. At high speeds, both film thickness and traction are considerably lower than predicted by conventional EHL theory. The contact is seen to be fully-flooded for all conditions tested. The widely-used thermal EHL correction of Gupta is shown to overcorrect for the film thickness reduction even at modest SRRs. Finally, the influence of the sliding direction on traction and film thickness is discussed for this set-up, and a thermal model is proposed to explain the observed behaviour.Graphical abstract

ANALYSIS OF THE MIXED ELASTOHYDRODYNAMIC LUBRICATION CHARACTERISTICS OF DOUBLE CIRCULAR ARC GEARS CONSIDERING MICRO-MORPHOLOGY

Different machining methods result in diverse morphologies on the surface of gears. Under mixed lubrication, the friction and contact behavior of the real morphology interface becomes more complex. This study aims to analyze the influence of different process tooth surface micro-morphologies on the lubrication performance of the meshing area of double circular arc gears. Focusing on elastohydrodynamic lubrication (EHL) characteristics of the double circular arc gears as the research object, the study involved measuring the three-dimensional morphology of the meshing position of the double circular arc gears. Non-Gaussian simulation technology was then used to characterize the micromorphology of the tooth surface resulting from different processes (i.e. hobbing process and skiving process). The tooth surface suction speed was determined based on the meshing characteristics of double circular arc gears. Based on the theory of point contact EHL, Reynolds equation and film thickness equation considering micromorphology were derived, and numerical solutions were obtained using the multi-grid method. A point contact EHL model for double circular arc gears was established considering the micromorphology of tooth surfaces in different processes. Results show that, the oil film pressure is positively correlated with rotational speed and torque. The oil film thickness is positively correlated with rotational speed, and negatively correlated with input torque. The negative of micro-morphology on the tooth surface on the lubrication performance could lead to an increase in pressure fluctuations and the absence of the second pressure peak. The uneven distribution of oil film and the lager roughness value could result in obvious fluctuations. The lubrication performance of the contact area in the gear hobbing process is superior to that in the gear skiving process. This study lays the foundation for further exploring the coupling characteristics between the double circular arc gear transmission system and elastic fluid dynamic lubrication. Keywords: Double circular arc gears, Point contact, Mixed EHL, Lubrication characteristics, Micro- morphology.

Modeling and analysis of elastohydrodynamic lubrication of orthogonal face gear with installation errors

Installation error is one of the most prominent factors affecting the lubrication of face gear. To analyze the lubrication performance of the face gear with installation errors, the installation error model of the orthogonal face gear transmission system is established. Then, the contact path, equivalent curvature radius, load distribution and entrainment velocity are studied using the face gear loaded tooth contact analysis (LTCA). On this basis, the lubrication governing equations of the face gear are established according to the elastohydrodynamic lubrication (EHL) theory. In addition, the oil film thickness, oil film pressure and coefficient of friction in the process of face gear drives are calculated using the method of progressive mesh densification (PMD). Finally, the effects of axis intersection angle error, axis intersection error and axial displacement error on lubrication characteristics are analyzed. The results reveal that when the axial intersection angle error and axial displacement error are negative and the axial intersection error is positive, the minimum oil film thickness of the face gear tooth surface is less than that without error. When the error values are the same, the minimum oil film thickness and coefficient of friction have larger changes with the axial displacement error than with the axis intersection error, and the contact path has a bigger movement range.

Dynamic characteristics investigation of a dual rotor-casing system considering the comprehensive stiffness of the intermediate bearing

This paper focuses on the vibrational properties of a dual rotor-casing coupled system with nonlinear clearance in the intermediate bearing, considering both the oil film stiffness and Hertzian contact stiffness between rolling elements and raceways. A comprehensive stiffness model for the intermediate bearing has been developed based on elastohydrodynamic lubrication (EHL) and Hertz contact theory. Subsequently, a dynamical model of the dual rotor-bearing-casing system is established using the finite element method, thereby verifying the feasibility of simulating the casing with beam elements. The dimensionality of the system equation is reduced using the fixed-interface component mode synthesis (CMS) method, and the resulting reduced-dimensionality equation is solved using the improved Newmark-β method. The effects of casing support, rotational speed, and radial clearance on the vibration characteristics of the system are investigated. Then, the comprehensive stiffness and coupled vibration characteristics of the system are analyzed to elucidate its intrinsic mechanism. Finally, the contact characteristics within the intermediate bearing under dynamic load are also studied. The results indicate that the support stiffness of the casing has a more significant impact on the second resonance caused by both the inner and outer rotors. The system is prone to experiencing varying compliance (VC) resonance at low rotational speeds. The excessive bearing clearance leads to complex vibrational characteristics of the system, making it challenging to predict its motion. The impact of minor changes in stiffness on system vibration is small when the comprehensive stiffness is large. At this time, the limited effect of oil film stiffness allows it to be disregarded in terms of comprehensive stiffness. Furthermore, the speed significantly influences the contact characteristics within the intermediate bearing under the unbalanced force of the rotor and gravity.

Establishment of the dynamic BTAP model and load-sharing analysis of herringbone gear planetary system with cracks

To reveal the influence of component cracks on the dynamic load-sharing characteristics of the herringbone gear planetary system (HGPS), a 55-DOF bending-torsional-axial-pendular (BTAP) nonlinear dynamic model of the system was constructed, taking into account parameters of different crack degrees (depth, angle, length), as well as factors such as manufacturing error (ME) and installation error (IE), time-varying mesh stiffness (TVMS), time-varying support stiffness, damping, and friction. The TVMS model of components with cracks was established using the cumulative potential energy method, and the mathematical quantification relationship between different crack parameters and TVMS was studied. Based on the theory of elastohydrodynamic lubrication (EHL), calculate the time-varying friction coefficient and friction force of each gear pair. Using the nonlinear elastic theory of rolling elements and raceways, the time-varying support stiffness of each component is obtained. Using the Runge-Kutta numerical integration method to solve the dynamic differential equations, and analyzed the load-sharing characteristics and sensitivity influence law of the system when the sun gear, planetary gear, and internal gear ring contain cracks respectively. Built a vibration test bench for the HGPS with cracks, and the experimental results were compared with the theoretical results. The results show that as the crack intensifies, the TVMS value decreases at the crack tooth. When the sun gear contains cracks, there will be obvious protruding excitation in the system’s load-sharing curve, and the internal meshing load-sharing characteristics are better than the external meshing load-sharing characteristics. At the same time, as the degree of cracks increases, the system load-sharing characteristics first improve and then deteriorate. At the same crack, as manufacturing and installation errors increase, the load-sharing characteristics of the internal and external meshing pairs deteriorate. When the internal gear ring contains cracks, the dynamic load-sharing coefficients of the internal and external meshing pairs of the system are 7.96 and 4.10, respectively, which have the highest impact on the dynamic load-sharing coefficient and sensitivity of the internal and external meshing pairs of the system. The experimental results are consistent with the theoretical results, verifying the correctness of the model.

Study on Thermal Characteristics of Angular Contact Ball Bearings Considering Roundness Error

To develop an angular contact ball bearing with low power consumption, a heat generation calculation model for angular contact ball bearings has been established based on bearing quasi dynamics, elastohydrodynamic lubrication theory, heat transfer theory, and Kirchhoff’s law of energy conservation, considering the effects of roundness error, bearing preload, centrifugal effect, and thermal expansion. The correctness of the model is verified through experiments. The influence of different operating conditions and roundness errors on the thermal characteristics of angular contact ball bearings is analyzed. The results of the calculation indicate that when the roundness error order is equal to the number of balls n/2 ± 2 (where n = 1, 2, 3, …), the overall heat generation of the bearing is lower than that without considering the roundness error. When the roundness error order is equal to (2n − 1)/4 ± 2 (where n = 1, 2, 3, …), the overall heat generation of the bearing is higher than that without considering the roundness error. At the same rotating speed, the overall heat generation fluctuates as the roundness error order changes, and the trend becomes more pronounced as the rotating speed increases. The maximum overall heat generation is achieved when the roundness error order equals (2n − 1)/4 times (where n = 1, 2, 3, …) the number of balls. When the roundness error order is equal to n/2 times the number of balls (where n = 1, 2, 3, …), the bearing’s overall heat generation is minimal. The variation in the total heat generated by the bearing is directly proportional to the amplitude of the roundness error. With the increase in roundness error harmonic order, the bearing integral heat generation shows a periodic change, and the change period has a mapping relationship with the number of balls.

Influence of manufacturing surface topography on torque and load bearing capacity of hydro-viscous drive clutch under mixed lubrication stage

PurposeHydro-viscous drive (HVD) clutches are widely used in equipment requiring soft start, such as fans and pumps, to transmit torque and adjust speed by changing the gap distance between friction pairs. This paper aims to propose a novel two-parameter evaluation method for HVD during the mixed lubrication stage. The objective is to develop an effective model that establishes the relationship between these parameters and the actual surface topography.Design/methodology/approachIn the presented methods, the fractal features of the real manufacturing surface are calculated based on the power spectrum function by the ultra-depth three-dimensional microscope. After that, the hybrid friction model of the friction plate is established based on mixed elasto-hydrodynamic lubrication theory, boundary friction model and fractal theory. Then the torque and load bearing characteristics of the clutch are obtained, and the influences of the surface fractal features are investigated and discussed. Finally, the Weierstrass–Mandelbrot function is adopted for the surface topography characterization and evaluation.FindingsThe results indicate that the proposed method exhibits good accuracy, while the speed difference between the friction pair exceeds 2,500 rpm. It is concluded that this paper proposed a way to evaluate the torque and loading capacity of HVD considering the real manufacturing surface topography and is helpful for surface optimization.Originality/valueThe originality and value of this study lie in its development of a novel torque and load bearing capacity evaluation method for HVD in mixed lubrication stage, considering manufacturing surface topography and describing the real manufacturing surface.

Investigation of rail damage considering impact at a welded joint under wet condition

PurposeThe purpose of this study is to develop a transient wheel–rail rolling contact model to primarily investigate the rail damage under wet condition when the train passes through the welded joints.Design/methodology/approachThe impact force induced by welded joints is obtained through vehicle–track coupling dynamics. The normal and tangential wheel–rail contact pressures were solved by elastohydrodynamic lubrication (EHL) theory and simplified third-body layer theory, respectively. Then, the obtained tangential pressure and normal pressure were applied to the finite element model as moving loads, simulating cyclic loading. Finally, the shakedown map and critical plane method were used to predict rolling contact fatigue (RCF) and the initiation of fatigue cracks.FindingsThe results indicate that RCF will occur and fatigue cracks are more prone to appear on the subsurface of the rail, specifically around 2.7 mm below the rail surface in the vicinity of the welded joint and its heat-affected zone.Originality/valueThe cosimulation of numerical model and finite element model was implemented. The influence of surface roughness and fluids was considered. In this model, the normal and tangential wheel–rail contact pressure, the stress and strain and the rail fatigue cracks were obtained under a rail-welded joint excitation.

Modelling of rolling-contact fatigue pitting phenomena by phase field method

The paper proposes a novel numerical framework for modelling of the pitting damage mechanism, based on the application of the three-layered residual control staggered phase-field algorithm. Proposed numerical framework can be applied to all contacting mechanical elements subjected to rolling contact fatigue, but in this paper, it is applied on gears. More precisely, gear teeth flanks subjected to the rolling-contact fatigue conditions are investigated, which consequently results in governing pitting mechanisms. Loading of the teeth flanks is imposed via moving load, with assumption of the full-film lubrication and pressure distribution according to the elastohydrodynamic lubrication theory, as well as Hertzian theory. The Coulomb's law is used to compute the friction force distribution. The numerical framework is embedded into finite element software ABAQUS via user subroutines. The validity of the proposed numerical scheme is tested by comparison to the examples from the literature. The main mechanisms of the pitting formation have been verified, i.e., surface- and subsurface-initiated pitting formation. Furthermore, an influence of the microstructure has been considered in the modelling of pitting phenomena. It has been demonstrated that the proposed numerical framework provides satisfactory results, and it is able to capture governing pitting mechanisms.

A New Thermal Elasto-Hydrodynamic Lubrication Solver Implementation in OpenFOAM

Designing effective thermal management systems within transmission systems requires simulations to consider the contributions from phenomena such as hydrodynamic lubrication regions. Computational fluid dynamics (CFD) remains computationally expensive for practical cases of hydrodynamic lubrication while the thermo elasto-hydrodynamic lubrication (TEHL) theory has demonstrated good accuracy at a lower computational cost. To account for the effects of hydrodynamic lubrication in high-power transmission systems requires integrating TEHL into a CFD framework such that these methodologies can be interfaced. This study takes an initial step by developing a TEHL solver within OpenFOAM such that the program is prepared to be interfaced with a CFD module in future versions. The OpenFOAM solver includes the Elrod–Adams cavitation model, thermal effects, and elastic deformation of the surfaces, and considers mixing between the recirculating flow and oil feed by applying energy and mass continuity. A sensitivity study of the film mesh is presented to show the solution variation with refinement along the circumferential, axial and radial directions. A validation case is presented of an experimental single axial groove journal bearing which shows good agreement in the pressure and temperature results. The peak pressure in the film is predicted within 12% and the peak temperature in the bush is predicted within 5% when comparing the centerline profiles.

Influence of lubricant material in the point contact zone of rolling friction on fatigue life for friction bearing units

Although lubrication is necessary for the satisfactory operation of rolling bearings, the effect of lubricant on the fatigue life of the bearing has not been sufficiently studied. In recent times, the theory of elastohydrodynamic (EHD) lubrication [1] has been used to explain the different effects of lubricants. According to this theory, the thickness of the lubricating layer separating the moving elements of the bearing is determined by the viscosity-pressure dependence of the lubricant. The contact of surface micron irregularities does not occur if it is possible to maintain a sufficient thickness of the lubricating layer - in this case, the long-term durability of the bearing is ensured. If the film thickness is reduced to a level where surface irregularities are encountered, the fatigue life rapidly decreases with increasing contact frequency. In any case, a comprehensive calculation methodology is needed that would allow to take into account the influence of lubricant on the fatigue life of bearing units.

Numerical Calculation Method of Multi-Lip Seal Wear under Mixed Thermal Elastohydrodynamic Lubrication

The multi-lip combined seal has the advantages of multi-lip coupling, large supporting force, and can withstand high-pressure shocks. It is an irreplaceable structure for single-lip seals. However, most of the seal wear analysis focuses on the simulation method of the single-lip seal under the influence of macro factors, and very little involves the wear characteristics of multi-lip seals. In this paper, a micro numerical method is established, which combines the elastohydrodynamic lubrication theory with the modified Archard equation. The performance of a multi-lip combined seal under different working conditions is analyzed through simulation, including macro and micro factors. It is found that some of the characteristics of single-lip seals are also reflected in multi-lip seals, and there is a critical speed that makes the sealing behavior of each seal lip different.

Point Contact Thermal Mixed Elastohydrodynamic Lubrication Under Short-Period Intermittent Motion

Abstract To improve mechanical efficiency, the tribological performance of short-period intermittent motion needs to be investigated. Based on the theory of thermal elastohydrodynamic lubrication (EHL) and considering the influences of rough surface, a mixed-EHL model under point contact simple sliding intermittent motion is established. Using this model, the transition from mixed-EHL to EHL in the contact area is realized by changing the period of intermittent motion and setting the surface roughness. It is found that the thermal effect on simple sliding intermittent motion should not be ignored, and the pressure, temperature rise distribution, and friction coefficient during the stop and start-up are fluctuated obviously. Under the condition of rough surface contact, the contact area will enter the mixed-EHL state during the stop and start-up. Shortening the period of intermittent motion is beneficial to alleviate the adverse effect of the mixed-EHL.

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.

Lubrication failure analysis of camshaft bearings in V6 diesel engine

This contribution investigates the lubrication characteristics and failure causes of camshaft bearings belong to a V6 diesel engine. Numerical simulation based on the theory of elastohydrodynamic lubrication and flexible multibody dynamics is performed to analyse the lubrication characteristics of camshaft bearings. The results reveal that lubrication performance of different bearings of camshaft shows great differences. For a certain bearing, the mixed lubrication state and elastohydrodynamic lubrication state alternately occur in one engine cycle. The duration of mixed lubrication varies greatly in different bearings. For the bearing closest to the timing drive gear, the total pressure is dominated by the asperity contact pressure, and the predicted safety factors of the asperity contact pressure, hydrodynamic pressure and oil film thickness are less than 1, which means that this bearing will have lubrication failure.

Feedback control of the mechanical spindle thermal error based on thermal simulation with bearing heat sources analysis

The thermal error stability (STE) of the spindle seriously affects the machining accuracy of a machine tool, however existing empirical heating model-based active cooling strategies mainly focus on suppressing the spindle’s overall thermal deformation and cannot effectively stabilize the thermal error. This study regards the “active cooling-spindle” system as a feedback control system and employs a data-driven thermal error model to provide feedback. Thus, the spindle thermal error can be stabilized for a long time owing to the homeostasis of the feedback control system under disturbance. A mechanical spindle with an external cooling scheme is taken as the study object. Bearings are the primary heat sources of the mechanical spindle; thus, the angular contact ball-bearing heat generation is precisely modeled based on local heat sources analysis of bearing components, elastohydrodynamic lubrication, and micro-contact theory. Thermal simulation of the spindle under varying-coolant temperature cooling is conducted to pre-validate the thermal error suppression and variation trend influencing effect, and obtain the Reference Input of Thermal Error (RITE) for the feedback control under different work conditions. Subsequently, a spindle thermal error feedback control system is developed, including computation, cooling, and real-time monitoring modules with inter-communication. Finally, the thermal error feedback control strategy is applied on the mechanical spindle, and experimental comparisons with constant coolant temperature cooling show that the thermal equilibrium time is advanced by 61.46%, 59.16%, 40.51%, and 58.08%. The thermal error variation range (TEVR) after the preheating stage is reduced to1.92, 1.52, 1.91, and 1.69 μm, respectively. The significant reduction in TEVR validated the effectiveness of the proposed strategy for spindle thermal error stabilization.

Elastohydrodynamic lubrication model and failure test for micro-contact thermodynamic characteristics of friction interface

A micro-contact thermodynamic model is proposed to study the interfacial characteristics in wet friction pair based on Elastohydrodynamic Lubrication (EHL) theory. The study takes into account the asperity elastic-plastic deformation, establishing an improved model with high accuracy in verifications with experimental data and existing model. With this optimized micro-contact thermodynamic model, we systematically discussed the influence of sliding speed, oil temperature, and average surface pressure on thermodynamic behaviors such as rough contact area, pressure distribution, and temperature distribution. Additionally, experimental investigations revealed the complex failure mechanism of the friction disc. Specifically, during the failure process, the friction coefficient and the radial temperature difference gradually increase. The metal oxides form on the surface, and the graphite distribution is gradually dispersed.

Thermal Elastohydrodynamic Lubrication Analysis for Rolling Cone Enveloping End Face Worm Drive

To explore the thermal elastohydrodynamic lubrication performance of rolling cone enveloping end face worm drive, the mathematical model of thermal elastohydrodynamic lubrication is established based on the meshing theory of rolling cone enveloping end face worm drive and elastohydrodynamic lubrication theory. With the help of the numerical analysis software MATLAB, the thermal elastohydrodynamic lubrication performance under smooth conditions is selectively analyzed by the multigrid method. Besides, the effects of throat coefficient, cone apex radius and half cone angle of the rolling cone on thermal elastohydrodynamic lubrication performance are analyzed at the meshing out of the transmission pair. The results show that the thermal elastohydrodynamic lubrication film thickness at meshing out of the worm gear is the smallest; the oil film thickness, oil film pressure and oil film temperature are reduced from meshing in to meshing out. The oil film temperature at the interlayer is the largest. The oil film temperature at the end face worm surface is the smallest. The small half-cone angle of the cone apex radius and larger throat coefficient and cone apex radius may achieve better thermal elastohydrodynamic lubrication performance of rolling cone enveloping end face worm drive.

Wheel-rail contact and friction models: A review of recent advances

Rail transportation is regarded as a reliable, quick, and secure mode of transportation. The wheel-rail contact interaction is crucial to the railway operation since it is responsible for supporting, traction, braking, and steering of railway vehicles. Improper wheel-rail interactions may produce or exacerbate wheel-rail interface issues such as rolling contact fatigue (RCF) and wear, which can threaten the vehicle’s running safety and stability. A review of the evolution and recent literature on wheel-rail contact mechanics and tribology is presented here. Topics covered include the basics of wheel-rail contact problem and methodologies for modeling both the normal contact (Hertzian and non-Hertzian) and tangential contact (Kalker’s theories including CONTACT and FASTSIM algorithms, Polach’s theory, USETAB program, etc.). The paper also reviewed various effects of contaminants and environmental conditions (water, leaves, sand, temperature, humidity, etc.) in wheel-rail contact. Various wheel-rail empirical adhesion models like the Water-induced low adhesion creep force model (WILAC) model and adhesion models based on elastohydrodynamic lubrication (EHL) theory (Greenwood-Tripp [GT] and Greenwood-Williamson [GW] models) are also reviewed. Lastly, the paper discusses the need and challenges for developing and integrating the wheel-rail non-Hertz contact model and adhesion model, as well as open areas for further research.

Tribological Behaviors and Meshing Efficiency of a Novel Planar Ball Reducer Based on the Elastohydrodynamic Lubrication Theory

Abstract A novel planar ball reducer (NPBR) is invented in which the relative velocity of meshing surfaces is reduced to achieve high mechanical efficiency. In order to acquire an accurate quantitative analysis on the efficiency of a ball reducer, thorough comprehension of the reducer’s tribological behavior is required. To this end, the elastohydrodynamic lubrication (EHL) theory, for the first time, is used to reveal the tribological behavior of the planer ball reducer, and the equations of kinematics, EHL model, and theoretical efficiency of the transmission system are derived. The prototype of NPBR is developed, and its experimental efficiency is measured, which agrees well with the theoretical efficiency.