Elastohydrodynamic Lubrication Research Articles

Understanding the Influences of Multiscale Waviness on the Elastohydrodynamic Lubrication Performance, Part II: The Partial-Film Condition

This paper is the second part of a two-part report studying the responses of a typical point-contact elastohydrodynamic lubrication (EHL) system to multiscale roughness mimicked by wavy surfaces. The wavy surfaces are defined by three key parameters: amplitudes, frequencies, and directions. The previous Part I paper focuses on the full film lubrication condition, while the current paper focuses on the partial film regime where asperity contacts occur. A transient thermal EHL model simulates lubrication problems with different waviness parameters, loads, and speeds. The total number of simulations is 1600. Performance parameters, including the asperity contact ratio, minimum film thickness, maximum pressure, central point film thickness, central point pressure, mean film thickness, coefficient of friction (COF), and the maximum temperature rise, are obtained for each simulation. These performance parameters are post-processed in the same manner as those in the previous Part I paper. The influences of the waviness parameters, load, and speed values on the eight performance parameters are discussed.

Application of the Hybrid Model to EHL Reference Liquids for Pressure Extrapolation

Reference liquids can be useful in the new quantitative approach to elastohydrodynamic lubrication calculations only if the properties of these liquids are accurately modeled. The pressures in the contact sometimes exceed the pressures of the available viscometer measurements, requiring extrapolation. The previtreous piezoviscous response is always faster-than-exponential with an apparent divergence pressure. Therefore, any model used for extrapolation must possess these characteristics and up to now published work in EHL, where extrapolation of the viscosity of squalane is performed, has not. To date, the only model that has been shown to accurately extrapolate to high pressure is the Hybrid model. This expression was applied to six reference liquids for use in quantitative investigations in EHL. Viscosity measurements for trioctyl trimellitate were extended to 1.1 GPa. The results obtained with high pressure viscometers are preferable over molecular dynamics results if they are different. Molecular dynamics calculations are not currently capable of reliable results for viscosity at very high pressures.

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.

Non-Newtonian thermal elastohydrodynamic mixed lubrication in elliptical contact for nutation-driven double circular-arc spiral bevel gear pair

The new type of nutation reducer with double circular-arc bevel gears as the core is characterized by advantages such as high load-bearing capacity, large transmission ratio, and simple structure. The existing research focuses on the machining methods of gears and the analysis of tooth contact. This article first time establishes an elastohydrodynamic mixed lubrication model for nutation double circular-arc bevel gear. The model's accuracy is verified by comparing it with existing test results. On this basis, combined with the finite element method and tooth contact analysis, the meshing characteristics, tooth contact characteristics, and lubrication characteristics of the double circular-arc bevel gear tooth surface are analyzed. The results show that the entrainment velocity at the contact point of the tooth surface during transmission is much higher than the sliding velocity. Consequently, the meshing motion is close to pure rolling. In constant-speed transmission, the oil film thickness at the engaging-in and exit points near the edge of the tooth surface is smaller than that at other meshing points on the tooth surface. This phenomenon can easily lead to mixed lubrication and lubrication failure, as well as tooth surface wear. During deceleration, i.e., when the speed drops to 50 r/min, the oil film thickness approaches zero, indicating that the gear has entered a mixed lubrication state. The proposed model can be used for lubrication analysis and improving transmission accuracy of nutation double circular-arc bevel gears.

Implementation of a New Smart-Lubricant Model Using Generalized Newtonian Approach in Soft Elastohydrodynamic Lubrication

Abstract This is an inceptive attempt to replace the classical Bingham fluid model with a continuous double Newtonian power-law-based constitutive equation for smart lubricants like magneto-rheological, electro-rheological, and ferro-fluids. The implementation of Bingham model in hydrodynamic (HD) and elastohydrodynamic (EHD) lubrication analyses is highly challenging and inconvenient due to its inherent discontinuity. Therefore, the present work demonstrates the use of an already existing rheological model with an appropriate set of parameters to describe the flow behavior of smart lubricants in a soft-EHD lubrication algorithm based on the generalized Newtonian approach. The formation of both floating and adherent cores validates the proposed model. An extensive parametric study is also performed to explore the effects of operating speed, load, and slide-to-roll ratio on the soft-EHL characteristics. The results are very promising, showing that it's possible to customize smart lubricants to match specific operating conditions. This is achieved by adjusting the yield stress value accordingly, allowing for the desired variation in lubrication characteristics.

Coupling Study on Quasi-Static and Mixed Thermal Elastohydrodynamic Lubrication Behavior of Precision High-Speed Machine Spindle Bearing with Spinning

In this work, a modified numerical algorithm that couples the quasi-static theory with the mixed thermal elastohydrodynamic lubrication (mixed-TEHL) model is proposed to examine the mechanical properties and lubrication performance of the spindle bearing that is used in a high-speed machine tool with spinning. The non-Newtonian fluid characteristics of the lubricant and the non-Gaussian surface roughness are also considered. Moreover, the mechanical properties and lubrication state of the bearing are examined in various service environments. The results indicate that the temperature reduces the lubrication efficiency, which in turn exerts a significant impact on the mechanical properties. The lubrication that either behaves in the manner of Newtonian or non-Newtonian fluid has a relatively negligible influence on the bearing working state, while the non-Gaussian surface roughness significantly alters the oil film thickness and temperature. Calculations with different operating conditions demonstrate that the operating parameters (i.e., axial load, rotation speed) will directly affect the performance of the bearings via the changes in the oil film thickness and the temperature.

A stiffness model for EHL contact on smooth/rough surfaces and its application in mesh stiffness calculation of the planetary gear set

A method for calculating time-varying mesh stiffness (TVMS) is proposed by developing a stiffness model for elastohydrodynamic lubrication (EHL) contact and integrating it into three-dimensional loaded tooth contact analysis (3D-LTCA). To enhance the accuracy and efficiency of the calculation, three projects have been implemented: Firstly, the contact deformation is modified, and the average slope is employed for calculating contact stiffness. Secondly, the lubricant film and EHL contact deformation are introduced into the deformation compatibility equations. Finally, the polynomial chaos expansion (PCE) surrogate model is employed to enhance computational efficiency. The proposed method is used to calculate TVMS of the planetary gear set, and the influence of speed, torque, and rough surface are analyzed. The results show that the previous method underestimating the TVMS of planet-ring gear pair in double-teeth meshing area under fluid lubrication, while the proposed method effectively addresses the issue. The different effects of the torque and speed on TVMS under mixed and fluid lubrication also have been revealed, emphasizing the significance of surface topography in gear meshing characteristics.

Quantitative Elastohydrodynamic Lubrication—Seventeen Years In

Abstract Seventeen years have passed since the first full elastohydrodynamic lubrication (EHL) simulation employed the real pressure and shear dependence of viscosity measured in viscometers to accurately predict film thickness and friction. This is the appropriate time to enumerate the advances in understanding brought on by the application of high-pressure rheology to the EHL problem. The pressure dependence of the low-shear viscosity, which has been measured in viscometers for nearly a century, differs from the narratives taught to tribology students and often used to justify inaccurate models. The central film thickness often depends on the shear-thinning at low pressure and time–temperature–pressure superposition demands that the same shear dependence be active at the high pressure where friction is generated. In this article, some of the revelations resulting from quantitative EHL are reviewed. For example, it has been discovered that the minimum film thickness in point contacts depends upon the viscosity at the highest pressures of the contact. This explains the errors in the classical formulas, which were based upon the fictional narratives concerning piezoviscous response, and the assumption of film thickness governed by inlet conditions. Quantitative EHL provides quantitative predictions of contact behavior.

Research on Prediction Methods for Eccentric Wear of the Slipper Pair in Axial Piston Pumps and Lubrication Performance Analysis

Abstract The axial piston pump (APP) is the core power component of hydraulic systems. Its friction pair wear can cause the degradation of piston pump performance until the function is completely lost or the service life is terminated. The slipper pair, prone to wear failure, is selected as the research object in this paper. The prediction method for the eccentric wear of the slipper pair is established, and the gradual change rules of the performance with wear accumulation are explored. The micro-surface rough peak contact and the stress state of the slipper pair are analyzed, and the mixed lubrication model of the slipper pair is established based on the elastohydrodynamic lubrication (EHL) model of the slipper pair. Grid discretization of a sealing belt of the slipper pair is carried out based on two-body abrasive wear and Archard adhesive wear models to improve the prediction method for eccentric wear of the slipper pair. The effectiveness of the proposed method is verified by a surface morphology analysis of the worn slipper. The results showed that the wear depth and wear width of the outer edge of the slipper bottom surface are positively correlated with the oil discharge pressure and the inclination angle of the swashplate, and negatively correlated with the rotational speed and the dynamic oil viscosity. The outer edge of the slipper is wedged after eccentric wear, and the hydrodynamic effect of the lubricating oil film of the slipper pair is enhanced. Hence, proper wear can improve the lubrication performance of the slipper pair.

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.

Influence of cashew nut shell liquid on corrosion and tribocorrosion behavior of metallic alloys

Cashew Nut Shell Liquid (CNSL) has been explored in several applications within the sustainability principles and circular economy of agro-industrial product waste. To understand the anticorrosive and lubricant properties of CNSL solutions, a multi-faceted approach, incorporating electrochemical analyses, immersion test, tribological measurements, and tribochemical characterization was carried out for mild steel AISI 1012, stainless steel AISI 420 and Aluminium Alloy 6061. Electrochemical analyses reveal a positive impact of CNSL, inducing a shift in corrosion potential to more positive values and a decrease in corrosion current, indicating effective corrosion inhibition for stainless steel and aluminium alloy. In mild steel, CNSL exhibits a mixed-type inhibition with efficiency increasing in correlation with oil concentration. The lubricating properties of CNSL are evident according to the coefficients of friction (COF) obtained and the elastohydrodynamic lubrication regime observed during tribological tests. Tribochemical tests demonstrate a reduction in wear and an improvement in tribocorrosion behavior under sliding conditions. CNSL emerges as a promising tribocorrosion mitigator, demonstrating multifaceted benefits. The concentration-dependent effects highlight the need for optimization in specific applications, particularly for passive materials. CNSL not only inhibits corrosion through film formation but also provides effective lubrication, reducing friction, wear, and chemical-mechanical degradation. This research contributes valuable insights to corrosion science. It proposes practical applications for CNSL in diverse industrial contexts, showcasing its potential as an environmentally friendly and sustainable solution for tribocorrosion challenges.

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.

Mesh stiffness calculation of defective gear system under lubrication with automated assessment of surface defects using convolutional neural networks

As typical failure mode of gear system, the tooth surface pitting, spalling can be detected in most long-running gear system, especially under heavy-load and high-speed condition, or under lubricant-starvation condition, the tooth pitting is characterized by irregular contour and random distribution. Most previous study on the defective gear system mainly based on manually detection of defective region, or just rely on geometric simplification of defects, leading to inaccurate results with low-efficient method, therefore, the machine-vision-based defect inspection method is proposed in the study of defective gear system. First, the pitting defects on gear tooth surface is detected and segmented based on involutional neural network U-net, then the tooth surface with segmented defective region is mapped to the elastohydrodynamic lubrication model of spur gear system, finally, the tribological behavior in addition to the mesh stiffness under lubrication condition of defective spur gear system are investigated and discussed. The results reveal that the machine-vision-based defects inspection could improve the accuracy and efficiency of the failure study for gear system.

A general kinematic model for lubricated ball bearings based on the minimum energy hypothesis

Accurately predicting the performance of lubricated rolling elements is critical for certain key bearing applications. A widely employed simulation technique is quasi-static models, which although computationally efficient to implement, lack accuracy in predicting the kinematics of bearing components. This problem arises from their construction under kinematic assumptions, instead of solving the kinematic based on real frictional interactions. This paper presents a quasi-static model based on the minimum energy hypothesis for lubricated contacts, which determines the kinematic of the ball considering the effects of the frictional interactions governed by the elastohydrodynamic lubrication mechanism. The influence of kinematic variables on the sliding patterns and power loss distribution of the contact are analysed. The results are compared with other published quasi-static models, revealing substantial differences. The influence of the kinematic hypotheses on power losses are also studied at a bearing component scale. Finally, the effect of the governing lubrication mechanism of the contact is discussed, concluding that the limiting shear stress of the lubricant and the centrifugal forces have a significant effect on the kinematic of the ball.

Extrapolation of Hydrodynamic Pressure in Lubricated Contacts: A Novel Multi-Case Physics-Informed Neural Network Framework

In many technical applications, understanding the behavior of tribological contacts is pivotal for enhancing efficiency and lifetime. Traditional experimental investigations into tribology are often both costly and time-consuming. A more profound insight can be achieved through elastohydrodynamic lubrication (EHL) simulation models, such as the ifas-DDS, which determines precise friction calculations in reciprocating pneumatic seals. Similar to other distributed parameter simulations, EHL simulations require a labor-intensive resolution process. Physics-informed neural networks (PINNs) offer an innovative method to expedite the computation of such complex simulations by incorporating the underlying physical equations into the neural network’s parameter optimization process. A hydrodynamic PINN framework has been developed and validated for a variant of the Reynolds equation. This paper elucidates the framework’s capacity to handle multi-case scenarios—utilizing one PINN for various simulations—and its ability to extrapolate solutions beyond a limited training domain. The outcomes demonstrate that PINNs can overcome the typical limitation of neural networks in extrapolating the solution space, showcasing a significant advancement in computational efficiency and model adaptability.

Forecasting model for hypoid gear elastohydrodynamic lubrication considering entrainment effect

In full consideration of time-varying meshing performance and oil film characteristics, entrainment effect on elastohydrodynamic lubrication (EHL) is developed for establishing accurate forecasting model of the complex hypoid gears. Firstly, dynamic loaded tooth contact analysis (DLTCA) is employed to determine the meshing interface kinematics, load distribution and entrainment speed under dynamic load condition. Then, entrainment speed is introduced into the EHL governing equation and accurate forecasting model is established. With accurate discretization of EHL governing equation, discrete convolution and fast Fourier transformation (DC-FFT) method is employed to compute the flank elastic deformation. Finally, a hypoid gear set in automotive industrial application is exercised to verify entrainment effect on EHL assessment in the proposed model.

Optimization of lubrication characteristics of wind turbine’s transmission system based on Newton Raphson method

To improve the reliability and lifespan of wind turbines, this paper takes the two-stage fixed shaft gearbox experimental platform of wind turbines as the research object. Based on Hertz contact theory, the oil film pressure and thickness in the contact area are solved by combining the equations of elastohydrodynamic lubrication and the Newton Raphson method; And the lubrication characteristics of the transmission system were analyzed to verify the correctness of the method; At the same time, in response to partial load phenomenon caused by system coupling deformation, genetic algorithm was selected to modify the gear teeth. The results show that the max unit load on the tooth face and the maximum stress of tooth root decreased by up to 26.48 % and up to 20.35 % respectively after modification which can improve the uneven distribution of oil film and the lubrication performance of the tooth surface.

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.

Transient mixed thermal elastohydrodynamic lubrication under startup and shut down conditions

The transient mixed lubrication behaviors in thermal elastohydrodynamic lubrication (TEHL) contacts during startup and stop are investigated. A transient mixed TEHL model for point contacts under time-varying speed conditions is proposed with comprehensive consideration of surface roughness, thermal effect, and transient behavior. The model is validated by the comparison to available published data. Based on the developed model, significant differences have been found compared with transient EHL and steady TEHL models. In addition, the transient mixed TEHL performance during start–stop with different acceleration rates and surface roughness is investigated. It shows that the lubrication behaviors during start–stop have an irreversible process. The roughness can significantly enhance the transient behavior. The roughness effect has a remarkable impact on lubrication performance in mixed lubrication. The evolution of lubrication behaviors during start–stop is highly related to the acceleration rate and surface topography.

TVMS Calculation and Dynamic Analysis of Cracked Gear considering Oil Film Stiffness

A time-varying meshing stiffness (TVMS) model that includes oil film stiffness in the elastohydrodynamic lubrication (EHL) line contact is proposed for tooth root cracking. This model employs the oil film thickness to estimate the stiffness of the oil film in gear contact by considering the profile variation of the oil film induced by tooth root cracks, to provide the evolution principle of TVMS in EHL line contact to study the effects of oil film stiffness of cracked gear on the TVMS. The results of the analysis reveal that the overall result of TVMS decreases owing to the stiffness of the oil film, whereas the combined TVMS depends mainly on the rotation speed of the gear system because the thickness of the oil film in the tooth crack is affected by the velocity of the entrainment. Furthermore, a six-degree-of-freedom (DOF) dynamic model is introduced to analyze the vibration behavior of the gear system using the combined TVMS results for different crack levels, and the influence of the combined TVMS on the vibration response of the tooth root crack is exhibited from the time-domain analysis, frequency-domain analysis, and statistical indicator analysis.