Mixed Elastohydrodynamic Lubrication Research Articles

An analytical friction model for point contacts subject to boundary and mixed elastohydrodynamic lubrication

An analytical EHL model suitable for highly loaded point contacts operating in mixed and boundary regimes of lubrication is presented. The results are compared and validated with the experimental measurements of friction coefficient from an MTM tribometer. Measurements are carried out upon a PAO40 oil at medium to high temperatures. In general, a good agreement in trend and magnitude over a wide range of operating conditions is observed. Both the experimental findings and the model predictions show an inverse relationship between friction and contact load in mixed and boundary regimes of lubrication, an effect not hitherto reported in literature.

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.

Prediction of mechanical efficiency of spur gear pairs based on tribo-dynamics model of multi-tooth meshing

The prediction of load-dependent losses of gear pairs is a topic of constant concern, which depends largely on the modelling of friction coefficient in tooth meshing. Although the current load-sharing based models can handle the friction coefficient in mixed elastohydrodynamic lubrication regimes, dynamics behaviour of each tooth pair or the time variation of direction of normal contact load is not taken into consideration. This study proposes a new method for modelling efficiency of spur gear pairs in transient operating conditions by coupling the multi-tooth meshing model with the friction coefficient model. The friction coefficient is modelled through load-sharing function, and the gear dynamics model is established with regard to alternate meshing of single-double tooth pair and time variation of direction of normal load and mesh stiffness. The model is validated by comparing the calculated results of friction coefficients and load-dependent losses with experimental data in published literatures, showing good agreement. At the end, the efficiency model is applied to two types of gear pairs to investigate the influence of tooth shapes and operating parameters on the load-dependent losses of gear pairs.

Modeling and analysis of 3D mixed lubrication in marine cam–tappet pair

During the operation of the marine cam–tappet pair, affected by periodic dynamic load, transient velocity, and micromorphology, it usually operates in a mixed lubrication state. Under extreme operational conditions, contact is likely to occur at the asperity of the interface, leading to problems such as stress concentration and dry contact. Considering the transient dynamics and three-dimensional roughness of cam–tappet pair, a mixed-elastohydrodynamic lubrication model is developed in this article, while the effects of surface waviness on the lubrication state are also investigated. The results show that the film thickness can be increased by 0.098 μm, and the coefficient of friction can be reduced by 10.6% when the wavelength ratio ranges from 1/6 to 6. However, when the amplitude exceeds 0.6 μm, the coefficient of friction may reach 0.10. Under conditions of low speed and high load, the film thickness decreases and contact load ratio increases. And about 30% reduction in film thickness is achieved on cam–tappet pair, potentially leading to increased wear or scuffing failure.

A fully coupled finite element solution for the mixed elastohydrodynamic lubrication of finite line contacts

A fully coupled FE model for mixed EHL of finite line contacts is proposed, integrating all of the governing equations into a monolithic system. The solution reveals the fully coupled model achieves 5% higher accuracy and 50% greater efficiency compared to the weakly coupled one. Additionally, there is evidence to support the assertion that profiling contributes to the mitigation of surface roughness contact. Logarithmic profiling can increase the minimum film thickness by a factor of 30, resulting in a reduction of up to 64.6% in the maximum asperity contact pressure, and thus, the boundary friction force is decreased by more than 19%, under heavy-load low-velocity condition. This contributes to the reduction of abrasive wear.

Dynamic performances of novel misaligned non-uniform distributed tilting-pad bearing

The non-uniform distributed tilting-pad journal bearings (NDTPJB) in large wind turbine main shafting has become an important development trend for high-power wind turbines due to the advantages of improving reliability and reducing maintenance costs. However, studies involving NDTPJB have not been reported under specific conditions such as low speed, wide range variable direction and magnitude of heavy-load in wind turbine. A new transient mixed elastohydrodynamic lubrication (mixed EHL) model for NDTPJB is established, taking into account the misalignment effect of the shaft tilt and the swinging of pads in the circumferential and axial directions, as well as the influence of pivot friction and elastic deformation effects. Based on the mathematical model, the dynamic characteristics and structural parameter effects of NDTPJB are systematically studied under low speed, wide range variable direction and magnitude of heavy-load. The results indicate that the NDTPJB exhibits a more significant sensitivity to the heavy load direction due to the different functional roles of the above distributed pads (ADP) and bottom distributed pads (BDP). The modified mixed EHL model can more accurately evaluate the lubrication performance of NDTPJB, and combine the characteristics in individual pad swing and the overall effect of the pads to comprehensively analyze the dynamic lubrication behavior of NDTPJB. By setting the pivot coefficient to 0.55, reducing the distribution angle of BDP, and increasing the distribution angle of ADP, a better load-carrying capacity can be achieved. The research results have guiding significance for further monitoring and analyzing the experimental performance of NDTPJB, as well as designing and optimizing such bearing structures.

Numerical Point Contact Model of Mixed Elastohydrodynamic Lubrication for Transversely Isotropic Coating

Abstract Transverse isotropy, a typical property of coating providing protection or lubrication for transmission parts, is different from isotropy focused in most of previous research, catching increasing attention in recent years. This study aims to make the lubricating contact behavior of transversely isotropic coating under different working conditions better understood, with the assistance of a proposed mixed elastohydrodynamic lubrication (EHL) model for a rigid ball in contact with transversely isotropic coating. Explicit analytical expressions of frequency response functions (FRFs) of the elastic field for transversely isotropic coating were derived, which could be used to work out surface/subsurface displacement and stress if surface pressure is known. The proposed EHL model for transversely isotropic coating was verified by comparing the film thickness and pressure distribution with those from literature by an uncoated model. Furthermore, the effects of coating elastic property, coating thickness, velocity, and load on lubrication performance and mechanical responses are investigated. In addition, the results under different coating parameters are also compared and discussed with those obtained by the Hamrock–Dowson equations to demonstrate the effectiveness of the latter. This investigation may provide a potential application for coating optimal design considering lubrication.

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.

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.

Dynamic misalignment effects on performance of dynamically loaded journal bearings

The lubrication characteristics of dynamically loaded journal bearings are significantly affected by misalignments. However, existing research on misalignment primarily focuses on fixed misalignment models, and studies on the nonlinear dynamic response of dynamically loaded bearings under dynamic misalignment are yet to be reported. To address this research gap, this study proposed a dynamic misalignment model coupled with rotor dynamics and transient mixed elastohydrodynamic lubrication. The model comprehensively considers factors such as journal eccentric translation, surface topography, oil film cavitation, and bearing elastic deformation. Upon model validation, numerical simulations are conducted to reveal the single-cycle nonlinear tribological characteristics of dynamically loaded bearings subjected to transient time-varying dynamic loads and time-varying misalignment moments. Based on the dynamic misalignment model, a series of parameter studies were conducted to explore the influence of operating conditions such as load magnitude and rotational speed on lubrication characteristics. The research also evaluated the impact of various structural parameters, including surface roughness, bearing bush thickness, and radial clearance, on the performance of dynamically loaded bearings. The numerical results indicate that the impact of fixed-value misalignment on the performance is highly dependent on the manually set deflection angles. Under light-load and high-speed nonstationary operating conditions, the effect of dynamic misalignment on the lubrication characteristics of dynamically loaded journal bearings was significantly amplified. Furthermore, a smoother surface, thicker bearing bush, and smaller radial clearance intensify dynamic misalignment's influence, compared to fixed-value misalignment, on the transient rough contact behavior at the interface. The findings of this study provide valuable guidance and references for the theoretical analysis and optimization design of dynamically loaded journal bearings.

Study on mixed elastohydrodynamic lubrication performance of point contact with non‐Gaussian rough surface

AbstractA numerical method is proposed to evaluate the effect of non‐Gaussian roughness on point contact elastohydrodynamic lubrication (EHL). A mixed EHL model of point contact, considering non‐Gaussian roughness, is developed. The oil film pressure in the model was controlled by the Reynolds equation of average flow, and the contact pressure of asperity was obtained by the rough surface micro‐contact model. The influence of non‐Gaussian roughness parameters on contact pressure distribution, film thickness profile and the ratio of asperity pressure to contact load (asperity load ratio) are investigated based on the mixed EHL model. The results show that the asperity pressure increases as root mean square (RMS) roughness increases, skewness and kurtosis. The film thickness also increases with RMS roughness and skewness, but is not sensitive to kurtosis.

Influence of Nitrile Butadiene Rubber (NBR) Shore Hardness and Polytetrafluoroethylene (PTFE) Elastic Modulus on the Sealing Characteristics of Step Rod Seals

The influence of NBR Shore hardness and PTFE elastic modulus on the sealing characteristics of step rod seals is analyzed in this paper based on the developed mixed elastohydrodynamic lubrication (EHL) model. The optimized selection studies of NBR Shore hardness and PTFE elastic modulus under different operating conditions are carried out based on the principle of minimizing net leakage and friction power loss. Results show that the Shore hardness of the NBR O-ring and, in particular, the elastic modulus of the PTFE ring has a significant effect on the sealing characteristics. Although the high values of these parameters result in high friction forces, they are beneficial for leakage control. To achieve both low leakage and low friction, it is recommended that high hardness and low modulus are selected for moderate-low pressure or high speed conditions, but low hardness and high modulus are selected for high pressure or low speed conditions.

Finite element modeling and simulation of mixed elastohydrodynamic lubrication for the finite line contact under tilting loads

Misalignment is a prevalent problem in rotor machinery. This paper proposes a numerical analysis for the mixed EHL of finite-line contacts considering tilting loads based on FEM. The Reynolds and linear elasticity equations, and Greenwood-Tripp contact model are coupled in an iterative process to solve the fluid-solid/solid-solid interaction under the compound external force and moment. Lubrication characteristics at both ends of the cylinder are analyzed and an asymmetric profile design scheme is presented to improve the lubrication performance at the cylinder's lower end. It is found that proper profile parameters can reduce EHL pressure by 40%, increasing the minimum oil film thickness by up to 100%, and thus reduce asperity contact pressure by up to 50%.

Transform of parameter and teeth surface modification for non-standard planetary spur gear train with X-gears

In view of the lack of ready formulae for modification calculation of non-standard planetary spur gear trains, the paper is focused on new modification methods of non-standard planetary spur gear trains with X-gears. Firstly, a novelty transform method from the parameters on the pitch circle to the parameters on the reference circle for a non-standard planetary spur gear train with X-gears is proposed in order to study the modification method. Secondly, a scheme of teeth surface modification for non-standard planetary spur gear train with X-gears is put forward. Thirdly, the calculation method of loaded transmission error and flash temperature on the tooth surface under mixed elastohydrodynamic lubrication for external meshing spur gear pairs is proposed using tooth contact analysis as well as loaded tooth contact analysis. Then, a new modification optimization method for non-standard planetary spur gear train with X-gears is proposed, and formulae of the maximal modification length along the tooth height are derived. Finally, the effectiveness of the modification optimization method is confirmed by an example, and the transform formulae of the optimized modification parameters for sun gear are derived.

Study on gear meshing power loss calculation considering the coupling effect of friction and dynamic characteristics

Gear transmission system is widely used in many mechanical equipment to achieve power transmission and rotational speed changes. Meshing power loss is one key index to assess the performance of a gear system, which directly influences heat generation and lubrication, etc. Over the past decades, many computational models of gear meshing power loss have been proposed to support gear design and optimization. However, the coupling effect between the gear friction and dynamic characteristics are usually ignored, including time-varying meshing stiffness (TVMS) and dynamic meshing force (DMF), which are not conducive to accurate calculation and improvement of meshing power loss. Therefore, an improved gear meshing power loss calculation method is proposed to settle this problem in this paper. With the proposed method, the friction calculation model is established considering the effect of DMF and surface roughness based on mixed elastohydrodynamic lubrication (EHL). Then the TVMS is obtained with the friction force along the meshing line and DMF was taken into consideration. On the basis of modelling of friction and TVMS, a six degrees-of-freedom (DOF) gear dynamic model, as well as a power loss iteration calculation process are established and studied. The effects of gear surface manufacturing quality and loads on power loss are analyzed. Furthermore, a gear meshing power loss experimental setup is constructed to verify the effectiveness of the proposed method. The results show that this method is in better agreement with the experimental results than the traditional method which does not consider the coupling effects.

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.

Temperature Effect on Load Distribution, Friction, and Wear of a Grease-Lubricated Spherical Roller Bearing (SRB)

This article investigates the effect of temperature on the lubrication and wear behavior of a grease-lubricated spherical roller bearing (SRB) assuming mixed-elastohydrodynamic lubrication (mixed-EHL) where the contact load is shared between the lubricant film and contact asperities. Temperature effects on internal load distribution and elastic modulus and their subsequent effect on the wear are also analyzed. The effect of temperature is investigated, first on the film thickness and load sharing, and then on the friction and wear. If the temperature rises from ambient to 110 °C, the increase in the contact patch dimensions, due to the decrease of elastic modulus, is only approximately 1% and the decrease in mean contact pressure is approximately 2%. Moreover, the load at decreases by approximately 4%, and the load zone increases by approximately 5%. As the temperature rises from 50 to 110 °C, the asperity portion of the contact load at position is increased by 350%. At 50 °C, only 20% of the total traction is contributed by the contact asperity, which is 80% at 110 °C. For the temperature rise from 50 to 110 °C, the wear volume loss increases by 238% and nonlinearly, due to viscosity reduction and its effect on the reduction of film thickness. The isolated change of internal load distribution and elastic modulus due to temperature rise causes a relatively insignificant change in wear. Hence, the predominant effect of temperature rise on wear is due to a decrease in lubricant film thickness causing the asperity component of the contact load to increase.

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.

An Improved Modeling and Numerical Analysis Method for Tooth Surface Wear of Double-Arc Harmonic Gears

Tooth surface wear is one of the most common failure modes of harmonic gears, especially in space drive mechanisms. Due to difficulty accurately modeling its wear failure model and the complex mechanism, its dynamic behavior and wear mechanism have not been deeply investigated, and study of the double-arc tooth profile wear model is relative lacking. Therefore, an improved wear modelling and analysis method that is more in line with actual conditions for double-arc harmonic gears is here proposed. Firstly, a tooth surface wear model under mixed elastohydrodynamic lubrication (EHL) was established based on the Archard formula, which combines the Reynolds equation and double-arc tooth profile equation, and considering the meshing offset caused by elastic deformation. Then, the wear analysis method combined with mixed EHL was derived, and numerical simulation analysis of the wear characteristics in lubrication state was carried out, including wear depth calculation and wear output comparison of different tooth profiles. Furthermore, the influence of main working parameters and design parameters on the wear quantity was analyzed. The results show that wear depth for mixed EHL is significantly less than at dry contact. The double-arc tooth profile can withstand more wear cycles than the involute tooth profile, and the input torque and the number of cycles significantly affect the amount of tooth wear. This study further reveals the tooth wear mechanism for harmonic gears, and provides a theoretical basis for the structural optimization design, wear reduction, and life prolonging of harmonic gears.

Wear prediction considering dynamic load for spur gear in mixed elastohydrodynamic lubrication

In this work, a wear prediction model considering the dynamic load is proposed for spur gears in mixed elastohydrodynamic lubrication (EHL). The dynamic load is calculated by gear dynamic model. Combining gear wear model and dynamic model, the wear depth under the dynamic load is determined and compared with that under quasi-static load. The comparative results show that the maximum wear depth under dynamic load is significantly larger than that under quasi-static load near engaging-in point. The effects of fractional film defect coefficient on wear depth are considerable under dynamic load, which is closely related to gear contact temperature. Furthermore, the effects of surface roughness and gear geometrical parameters on wear depth are studied. The investigation reveals that the wear depth decreases with the increased tooth width, module and pressure angle, but increases with the surface roughness. It illustrates that gear wear depth under the dynamic load can be reduced by optimizing gear geometrical parameters.