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Moving contact line dynamics calculations include two models: precursor film models and slip models. The lubrication approximation method is used to establish a three-dimensional mathematical model to analyze the droplet thermocapillary migration behavior on a non-uniformly heated solid substrate with a wettability track. The contact line dynamics in the slip model and the disjoining pressure effect in the precursor model are proposed to regulate the substrate wettability. Both models are numerically implemented to investigate droplet spreading for three cases: free spreading on an isothermal substrate, thermocapillary migration on a uniform wettability substrate, and thermocapillary migration on a wettability-confined track. For the case of free spreading on an isothermal substrate, the three-dimensional results of the slip and precursor contact line models are essentially consistent with two-dimensional slip model results. For the case of thermocapillary migration on a uniform wettability substrate, the results of the two models essentially agree with the experimental results. Decreasing the thermal gradient reduces the discrepancies between the two models that result from the coordinate transformation method used in the slip model, which reduces the contact angles measured in the y-direction and enlarges the advancing contact angle in the migration direction. For the case of thermocapillary migration on a wettability-confined track, the slip model gradually shows a "dynamic-pinning" behavior with increasing equilibrium contact angle in the hydrophobic region. By contrast, the precursor film model maintains a stationary pinning behavior but separates a residual liquid outside the track. The precursor film model is preferred over the slip model in lubrication approximations for three-dimensional fluids when calculating complex moving contact dynamics caused by wettability differences. However, the precursor film model must be further optimized to prevent numerical instability. [ABSTRACT FROM AUTHOR]

We consider a cylinder immersed in viscous fluid moving near a flat substrate covered by an incompressible viscoelastic fluid layer, and study the effect of the fluid viscoelasticity on the lift force exerted on the cylinder. The lift force is zero when the viscoelastic layer is not deformed, but becomes non-zero when it is deformed. We calculate the lift force by considering both the tangential stress and the normal stress applied at the surface of the viscoelastic layer. Our analysis indicates that as the layer changes from the elastic limit to the viscous limit, the lift force decreases with the decrease of the Deborah number (De). For small De, the effect of the layer elasticity is taken over by the surface tension and the lift force can become negative. We also show that the tangential stress and the interface slip velocity (the surface velocity relative to the substrate), which have been ignored in the previous analysis, give important contributions to the lift force. Especially for thin elastic layers, they give dominant contributions to the lift force. [ABSTRACT FROM AUTHOR]

ABSTRACT In numerical studies of grease lubrication, thermal effect is often neglected and surface plastic deformation is almost not considered. This paper has developed a deterministic thermal plasto‐elastohydrodynamic lubrication (PEHL) model for grease‐lubricated rolling bearing. The influence of tangent modulus, rheological index and texture orientation on lubrication characteristics and temperature rise is analysed. The results show that increasing the rheological index of grease and decreasing the wavelength factor are obviously positive for improving lubrication behaviour. Since surface plastic deformation in the EHL state is at nanoscale, film thickness, friction coefficient and temperature rise of solid surfaces decline slightly with the decrease of tangent modulus. [ABSTRACT FROM AUTHOR]

ABSTRACT The accuracy and efficiency of the wheel‐rail adhesion model are important to the wheel‐rail rolling contact issues. The purpose of this study is to develop a simplified non‐Hertzian wheel‐rail adhesion model under interfacial contaminations to predict the wheel‐rail adhesion coefficient. Firstly, a non‐Hertzian full elasto‐hydrodynamic lubrication (EHL) model was developed and applied to determine the wheel‐rail contact pressure and film thickness under interfacial contaminations. Then, the empirical formula of central film thickness available to non‐Hertzian wheel‐rail normal contact relating to train speeds, axle loads and material parameters were proposed based on a large number of non‐Hertzian full EHL simulation for smooth surface under interfacial contaminations using linear regression. The empirical non‐Hertzian central film thickness formula and minimum film thickness formula for wheel‐rail contact obtained in this paper show certain differences from the formulas based on Hertzian contact. Using the proposed non‐Hertzian central film thickness formula, a simplified non‐Hertzian wheel‐rail contact adhesion model was developed, and the adhesion coefficient was obtained at different speeds and compared with the field test data. The numerical results showed good agreement with field test data. [ABSTRACT FROM AUTHOR]

In many engineering applications, including coating and lubrication operations, analyzing the temperature behavior of thin film flows on a vertically upward-moving tube is crucial to improving predictive models. This paper examines a steady third-grade fluid film flow with a surface tension gradient on a vertical tube. The mechanisms responsible for the fluid motion are upward tube motion, gravity, and surface tension gradient. This analysis focuses on heat transfer and stagnant ring dynamics. The formulated highly nonlinear ordinary differential equations are solved using the Adomian decomposition method. The conditions for stagnant rings and uniform film thickness are attained and discussed. The inverse capillary number C, Stokes number S t , Deborah number De, and Brinkman number Br emerged as flow control parameters. The temperature of the fluid film rises with an increase in the C, S t , De, and Br, whereas it decreases with an increase in thermal diffusion rate. The radius of stagnant rings tends to shrink by the increase in C, S t , and De. When the value of De is high, third-grade fluid behaves like solids; only free drainage happens with smaller radius stagnant rings and high temperatures. A comparison between Newtonian and third-grade fluids regarding surface tension, velocity, temperature, stationary rings, and fluid film thickness is also provided. [ABSTRACT FROM AUTHOR]

For investigating the rail corrugation characteristics of metro small curve track under the combined effect of rail side lubrication and slip rate dependence, by developing a three-dimensional vehicle-track coupling numerical model, the wheel-rail (WR) contact stick-slip (SS) characteristics under different transition areas of rail side lubrication in the presence of corrugation were analyzed. Meantime, on the basis of considering the friction slip rate dependence, the SS vibration characteristics under different rail side lubrication conditions were further analyzed to understand the effect mechanism of rail surface friction characteristics on corrugation. The results show that, when there is rail side lubrication, both inner and outer WR systems have the possibility for SS vibration, and the longitudinal SS vibration intensity is greater than the transverse SS vibration intensity; the SS vibration intensity of the inner WR system is greater than that of the outer WR system, indicating that the inner rail is more susceptible to corrugation and the corrugation is more acute. With the expansion of the rail side lubrication range, the standard deviations of longitudinal and transverse adhesion coefficients decrease, illustrating that the expansion of the lubrication range can reduce the SS vibration intensity of WR system. When the co-effects of rail side lubrication and slip rate dependence are considered, the increase of the rail side lubrication range leads to the increase of standard deviations of adhesion coefficients, which may be related to the enhancement of slip effect induced by the increase of the lubrication range. The introduction of slip rate dependent effect can reduce the standard deviation of the WR adhesion coefficient, which demonstrates that the slip rate dependent effect can ease the degree of SS vibration of WR system, thus reducing the probability of corrugation occurrence caused by the SS vibration. [ABSTRACT FROM AUTHOR]

A theoretical model for the calculation of thermal elastohydrodynamic lubrication performance of the flow distribution pair of piston pumps is established, which is composed of the oil film pressure governing equation and energy equation, and solved by means of numerical solution and simulation. We carry out quantitative analysis of the influence of various parameters on the thermal elastohydrodynamic lubrication characteristics of the flow distribution pair. The results indicate that both the oil film thickness and the cylinder tilt angle of the flow distribution pair vary in a periodic manner. The increase in the rotational speed of the cylinder block will increase the film thickness of the oil film and reduce the fluctuation, and the inclination angle of the cylinder block and its fluctuation amplitude will decrease. An increase in working pressure will lead to a decrease in the average oil film thickness, an increase in fluctuations, and an elevation in both the tilt angle of the cylinder block and its fluctuation amplitude. The increase in the rotational speed of the cylinder block and the increase in the working pressure will lead to the increase in the viscous friction dissipation of the flow distribution pair, the increase in the oil film temperature and the increase in the leakage. The reduction in the sealing belt will lead to the reduction in oil film friction torque and leakage. [ABSTRACT FROM AUTHOR]

Engineering practice has demonstrated that seal failure can result in severe leakage and wear, reducing the efficiency of hydraulic systems and even leading to major safety risks. Currently, analyses of the thermal aspect of seal interfaces are relatively limited, with most studies focusing on mechanical analysis. However, in actual applications, temperature has a significant impact on sealing performance. In this paper, nonlinear elastomechanics, viscous fluid mechanics, micro-contact mechanics, micro-deformation theory, and thermodynamics are coupled to establish a mixed lubrication model considering the thermal effect. The reliability of the mixed lubrication model is verified through experiments, and the temperature distribution of the oil film in the sealing area and the temperature distribution of the seal ring are simulated. Finally, the effects of the reciprocating speed, root mean square roughness, fluid medium pressure, and seal pre-compression on seal friction force and leakage are investigated. The results show that the heat generated in the sealing area accumulates at the bottom of the V-ring. Under the same conditions, compared with the instroke, the temperature-rise area of the outstroke is biased to the left and the increase in temperature is greater. In addition, the piston rod speed and the preliminary compression of the seal ring have a greater impact on the overall seal friction force and leakage. Under a lower seal pre-compression, the RMS roughness has a great influence on the leakage and friction in the outstroke, while the impact of the internal stroke is limited. [ABSTRACT FROM AUTHOR]

The reduction of frictional power losses in power transmitting gears takes a crucial role in the design of energy- and resource-efficient drivetrains. Water-containing lubricants like glycerol and polyalkylene glycols have shown great potential in achieving friction within the superlubricity regime with coefficients of friction lower than 0.01 under elastohydrodynamic lubrication. Additionally, a bio-based production of the base stocks can lead to the development of green lubricants. However, one challenge associated with the application of water-containing lubricants to gearboxes is the evaporation of water and its impact on the lubricant properties. In this study, the influence of water evaporation on elastohydrodynamic friction and film thickness was investigated for three water-containing polyalkylene glycols. Two nominal water contents of 20 wt% and 40 wt% and two viscosities were considered. The results show that the friction increases continuously with higher evaporated water content, while the overall friction level remains low in nearly water-free states. A similar trend is observed for film thickness, where the strong increase in viscosity results in a notable increase in film thickness. Nevertheless, the sensitivity of friction and film thickness to water evaporation is low for small amounts of evaporated water. This allows generous thresholds for permissible variations in water content. [ABSTRACT FROM AUTHOR]

The benefits of surface textures on rolling and sliding tribological contacts have been an exciting field of study over the last three decades. Laser surface texturing (LST) is a comparatively newer texturing methodology that yields repeatable precise microtextures. A detailed overview of the available literature on the various works in this field is consolidated in this review. The main focus is on the effect of surface textures (with focus on laser ablation) for nonconformal contacts with elastohydrodynamic lubrication (EHL), as in rolling element bearings. A review of literature on textured contacts for the EHL regime, emphasizing its effect on friction, wear, rolling contact fatigue, vibration, texture geometry, and numerical simulation studies, is carried out with possibilities of future works. Basic details on LST processes and various parameters of the laser beam that determine the texture geometry are discussed. Being a field of continuing research, the review paper will aid in understanding the present developments and future directions in laser‐based surface texturing for nonconformal tribological contacts. [ABSTRACT FROM AUTHOR]

ABSTRACT The scuffing load capacity of gear is closely related to the meshing temperature rise of tooth surface. The key to predict the temperature rise is to establish an accurate meshing temperature rise model. In the paper, a tribo‐dynamic model of helical gear is established through coupling of tooth surface lubrication parameters, and the influence of temperature rise on ambient temperature during meshing process is considered. Then, the effects of oil supply temperature, input speed and torque on tooth surface temperature rise, film thickness, friction excitation and gear dynamic characteristics are discussed. The results show that the temperature rise of the gear is higher during the engaging‐in and engaging‐out regions. Meanwhile, there is local high temperature at the end of the contact line due to the end effect. The vibration of gear along the off‐line‐of‐action direction is mainly determined by friction excitation. With the increase of oil supply temperature, input speed and torque, the risk of scuffing failure increases and the influence of oil supply temperature and input load is more significant. The conclusions of this paper may provide some valuable suggestions for the anti‐gluing failure design of gear in engineering. [ABSTRACT FROM AUTHOR]

Stick–slip is a standard friction-induced self-excited vibration that usually occurs in the boundary or mixed lubrication regimes. Broadening of the hydrodynamic lubrication regime is conducive to suppressing stick–slip motion. In this paper, the load carrying capacity of a magnetic fluid (MF) film in the presence of a magnetic field is derived based on the modified Reynolds equation. An additional lifting force produced by MF under the magnet was applied between the tribopairs to achieve the full fluid lubrication. Thus, the stick–slip is expected to be inhibited in a lower speed scope. The effect of magnet thickness on the lifting force is investigated experimentally and theoretically. Special attention is given to the influence of the lifting force on the friction and the critical transition speed of the hydrodynamic lubrication regime. Results demonstrate that the lifting force increases with the increment of the magnet thickness. The presence of the additional lifting force expands the hydrodynamic lubrication and makes the critical transition speed move left, as shown by the friction transitions on the Stribeck curve. Therefore, stick–slip motion can be suppressed at a lower sliding speed. Such beneficial effects are more pronounced in thicker magnets. It can be confirmed that, so long as the lifting force is higher than the normal load, the friction will invariably operate in the full film lubrication and the stick-slip motion may be eliminated theoretically. [ABSTRACT FROM AUTHOR]

Aiming at the key problems such as serious friction and wear and large leakage of aviation piston pumps operating under high-speed and high-pressure harsh conditions, the lubrication characteristics of aviation plunger pumps are studied in this paper. In order to improve the lubrication performance of the plunger pump, as well as its working efficiency and service life, the equations of pressure, the thickness, and the leakage of the plunger pair oil film under the combined actions of viscosity temperature and pressure under pressure flow, shear flow, and cylinder elastic deformation are established. The finite difference method is used to analyze the lubrication characteristics and the leakage of the plunger pair under these four different conditions: considering, respectively, the effect of viscosity temperature and pressure, only considering the effect of viscosity temperature or viscosity pressure, without considering the effect of viscosity temperature and viscosity pressure. As a result, coupled by the effects of viscosity temperature and viscosity pressure, when the temperature increases from 20 to 60 °C, the oil film pressure increases, and the thickness decreases faster. When the temperature increases from 60 to 120 °C, the oil film pressure increases and the thickness decreases slower When the contact length of the plunger pair increases from 17 to 37 mm, the leakage ratio decreases more rapidly, and when it is greater than 37 mm, it decreases more slowly. The following conclusions were obtained: the viscosity of lubricating fluid is greatly affected by temperature and pressure. The viscosity decreases and increases hyperbolically with the increase in temperature and pressure, the maximum oil film pressure when considering the effect of viscosity temperature and pressure was significantly greater than that without considering the viscosity temperature and pressure, and the minimum oil film thickness was much smaller than that without considering the viscosity temperature and pressure. The leakage curve when considering the viscosity temperature and pressure effect was obviously different from when only considering a single factor or not considering the viscosity temperature and pressure effect. The magnitude of leakage in the four cases is: considering the viscosity temperature effect, considering the viscosity temperature and pressure effect, not considering the viscosity temperature and pressure effect, and considering the viscosity pressure effect. This study can provide a reference for the accurate theoretical design and safe and stable operation of the plunger pair in the plunger pump. [ABSTRACT FROM AUTHOR]

In the modeling of elastohydrodynamic lubrication problems considering mixed friction, strongly coupled dependencies occur due to piezo-viscous effects and asperities, which can make a numerical solution exceptionally difficult. A fully implicit coupled scheme for solving mixed elastohydrodynamic lubrication problems is presented. Our scheme uses finite-volume discretization and co-allocated grids for hydrodynamic pressure and elastic deformation. To provide strong coupling between pressure and deformation even in the highly loaded zone, a correction term that adds numerical diffusion is used. The resulting linear equation system of this scheme can be efficiently solved by Krylov subspace methods. This results in an improved accuracy and computational efficiency compared to the existing methods. This approach was validated and has been shown to be accurate. [ABSTRACT FROM AUTHOR]

Dynamical modeling of spur gears with typical faults is crucial research topic for understanding fault features and vibration mechanisms. Meanwhile, the lubrication plays an important role in dynamic model. In this work, a novel coupled model combined dynamic model with elastohydrodynamic lubrication model is proposed by considering typical faults action mechanisms. A modified backlash error model takes into account the deformation and oil film backlash to calculate the time-varying backlash. The Runge–Kutta, multigrid integral and five-level Dmeyer wavelet transform method are combined to calculate the lubrication properties and dynamic characteristics at each meshing position along the line of action. Influences of typical faults on the contact performance, such as pressure distribution, oil film thickness, vibration response and bifurcation chaotic behavior are studied. The results show that the typical faults have a significant impact on both the lubrication and dynamic characteristics of the system. The spatial placement of faults can significantly alter the distribution of lubrication parameters. The disturbance of gear faults cause the system attractor unfold and the phase trajectory diffuse and make the system tend to be unstable. The typical faults are more sensitive at low excitation frequencies and less affected at high excitation frequencies. The research provides a basis for the fault diagnosis and detection of gearbox. [ABSTRACT FROM AUTHOR]

: In order to explore formation and evolution mechanism of lubrication failure of friction pair in mechanical transmission system under harsh working conditions, a point contact elastohydro-dynamic lubrication model was established considering oil film interface slip, and simulation calcula¬ion was carried out. The two-color light interference elastohydrodynamic lubrication test was carried out to study the influences of load on oil film interface slip in elastohydrodynamic lubrication, and hen variation characteristics of entrainment velocity, hydrodynamic pressure, oil film thickness and lip parameters with load were studied under interface slip state. The results show that with the in¬rease of load, the slip amplitude and slip range of interface increase significantly and the entrainment velocity in slip region decreases obviously. The dynamic pressure distribution in slip region tends to be uniform. In addition, slip region produces film thickness accumulation and inlet depression character¬istics. The shape of slip region gradually presents the characteristics of "half crescent". [ABSTRACT FROM AUTHOR]

Friction remains as the primary mode of energy dissipation and components wear, and achieving superlubricity shows high promise in energy conservation and lifetime wear protection. The results in this work demonstrate that direct superlubricity combined with superlow wear can be realized for steel/Si3N4 contacts on engineering scale when polyhydroxy alcohol solution was selectively modified by amino group. Macroscopic direct superlubricity occurs because 3-amino-1,2-propanediol molecules at the friction interface could be induced to rotate and adsorb vertically on the friction surface, forming in-situ thick and dense molecular films to passivate the asperity contacts. Furthermore, amino modification is also conducive to improving the lubrication state from boundary to mixed lubrication regime by strengthening the intermolecular hydrogen bonding interaction, presenting enhanced load-bearing capability and reduced direct solid asperity contacts. Thus, direct superlow average friction of 0.01 combined with superlow wear are achieved simultaneously. The design principle of direct superlubricity and superlow wear in this work indeed offers an effective strategy to fundamentally improve energy efficiency and provide lifetime wear protection for moving mechanical assemblies. [ABSTRACT FROM AUTHOR]

The ocular lubrication, where the eyelid constantly slides on the curved corneal surface, is considered as one of primary lubrication systems in bio-tribology. Under reliable lubrication conditions, sensitive ocular tissues remain intact from fatigue damage during spontaneous blink cycles. The tear film, evenly filled between cornea and conjunctiva, is a biological fluid with dynamic adjustment ability, which provides superior lubrication with the friction coefficient of below 0.01. However, the lubrication failure may result in a variety of uncomfortable symptoms such as inflammatory reactions, tissue damage and neurological abnormalities. Therefore, it is essential to clarify the fundamental mechanism of ocular lubrication, which helps to alleviate and even recover from various ocular symptoms. This review firstly demonstrates that the ocular components, containing lipids and mucins, contribute to maintaining the lubrication stability of tear film. Furthermore, the ocular lubrication state in various physiological environments and the physical effect on tear film dynamics are further discussed. As typical applications, the therapeutic agents of dry eye syndrome and contact lens with superior lubrication effects are introduced and their lubrication mechanisms are clarified. Finally, this review summarizes a series of the latest research inspired by ocular lubrication. Overall, this work will provide a valuable guidance on the theoretical research and extensive applications in the field of biological lubrication. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

From the earliest theoretical studies on elastohydrodynamic lubrication, it was believed that film build-up is governed by lubricant rheology in the low-pressure contact inlet. Recently, it was discovered that this is only true for the theoretical line contact case, where lubricant out-of-contact lateral flow is absent. In actual contacts, though central film thickness is indeed governed by low-pressure lubricant rheology, minimum film thickness is additionally influenced by the high-pressure response. Thus, a proper prediction of minimum film thickness (either by analytical formulae, or machine-learning frameworks) would require input parameters that define the high-pressure viscous response of the lubricant. The current work identifies and formulates these parameters with the help of machine-learning regression tools. These are fed with minimum film thickness results from finite element simulations of smooth steady-state isothermal Newtonian circular contacts, lubricated with sets of hypothetical fluids having the same pressure-viscosity response at low pressure, but different high-pressure ones. It is found that conventional dimensionless groups are not sufficient to describe minimum film thickness formation, and that an additional pressure-viscosity coefficient—evaluated at half the Hertzian contact pressure—is required. [ABSTRACT FROM AUTHOR]

Antiwear additives permit energy-efficient lubrication of gearboxes, bearings, and other tribological interfaces. We study zirconia (ZrO2) nanocrystal additives, which readily form protective tribofilms in tribological contacts. Our prior work demonstrated cooperative antiwear performance between ZrO2 and the S- and P-based co-additives in fully formulated hydrocarbon gear oils. Here, we extend that work by examining the growth kinetics of the ZrO2 tribofilms, including the influence of the co-additives. In the boundary lubrication regime for mixed rolling-sliding contacts, the initial phase of ZrO2 tribofilm growth is soon overtaken by removal processes, phenomena whose importance has gone unnoticed in prior work. Tribofilm removal affects the steady-state thickness and morphology of the tribofilm as well as its growth kinetics. The S- and P-based co-additives are incorporated into the ZrO2 tribofilm, and alter the competition between the growth and removal processes, increasing initial net growth rates per contact cycle and contributing to a more polished final interface. This work highlights the significance of removal processes in determining tribofilm antiwear performance, and suggests several routes for improving tribofilm growth kinetics using co-additives. [ABSTRACT FROM AUTHOR]

This paper introduces an optimized computational domain for fully flooded circular elastohydrodynamic lubrication (EHL) contacts, enhancing the accuracy of numerical calculations of pressure and oil film thickness. First, the computational domain was configured based on Kapitza's analytical solution. Then, a resolution sensitivity study for the mesh of the 2D computational domain for the Reynolds equation was conducted to investigate the effect of mesh resolution on the accuracy of the numerical solution. Subsequently, the impact of the size of the full 3D computational domain on the simulation's accuracy and computational efficiency was analyzed. The main result is the 3D computational domain, which automatically adapts to operating conditions within the piezoviscous rigid, the isoviscous rigid, the piezoviscous elastic, and the isoviscous elastic regions, as well as in the transition regions between them. This results in a model which provides accurate predictions across a wide range of operational conditions. Another outcome is a new approximate expression for the central oil film thickness, showing a maximum relative difference of less than 4.6% compared to the numerical model. [ABSTRACT FROM AUTHOR]

This work focuses on the evolution of lubrication wedge shaping in internal combustion piston engines, taking into account liquid microflows on curved surfaces and coating microgeometries. It introduces a new approach to the analysis of friction losses by simulating the microflow of lubricating oil between the surfaces of piston rings cooperating with the cylinder surface. The models used take into account three types of microgeometry and material expansion. Key results indicate that microirregularities with a stereometry of 0.1–0.2 µm significantly influence the distribution of oil film thickness in the phase of maximum working pressure, which is critical for the functioning of the seal ring. The innovation of the work consists of demonstrating that, despite small changes in the friction force and power in the piston rings, changes in the minimum values of the oil film thickness are significant. The work highlights the failure to take into account microgeometry parameters in friction models, which leads to significant errors in the simulation results, especially in terms of oil film continuity and the contribution of mixed friction. The simulations also indicate that advanced geometric models with high mesh resolution are necessary only for the assessment of changes in oil film thickness during the highest pressure increase in the combustion chamber and taking into account various mixed friction conditions. The results suggest significant progress in engine design and performance, confirming the importance of advanced fluid and mixed friction models in piston engine lubrication research. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Analyzing Phan-Thien Tanner fluid film behavior on a vertically upward moving tube can help predictive models in engineering, notably in coating and lubrication operations. This paper provides a theoretical analysis of the dynamics of stagnant rings and uniform Phan-Thien Tanner fluid film adhered to a vertically upward moving tube. Formulated ordinary differential equations are solved to get exact analytic expressions for velocity, flow rate, average velocity, shear stress components, and stagnant rings. Highly nonlinear algebraic equations are solved using Newton's method in MAPLE to find the linear and exponential Phan-Thien Tanner film thicknesses. The uniform film thickness widens with increasing constant tube velocity, while it decreases with increasing Deborah number, Stokes number, and elongation parameter. The analysis delineates that stagnant rings shrink around the tube as the Stokes number, Deborah number, and elongation parameter increase. The minimal Stokes condition for the existence of a realistic stagnant ring is also determined. It has been established that whenever the Stokes number is less than the minimal Stokes condition, stagnant rings do not form. A comparison between the exponential Phan-Thien Tanner, linear Phan-Thien Tanner, upper convected Maxwell, and Newtonian fluids is also provided for stagnant rings and fluid film thickness. Following the application of an efficient approximation on tube geometry, plate geometry is approximated, and the outcomes are consistent with existing literature. The results of this research are significant for a wide range of biofluid applications, including agrochemical uses, paint and surface coating flow behavior, thin films on the cornea and lungs, and chemical and nuclear reactor design. [ABSTRACT FROM AUTHOR]

To meet the demand for energy-efficient and, at the same time, durable, functional components, the improvement of tribological behavior is playing an increasingly important role. One approach to reducing friction in lubricated tribological systems is the microtexturing of the surfaces tailored to the application, but in most cases, this leads to increased manufacturing costs and thus often makes their use in industry more difficult. In this work, we, therefore, present an approach for an efficient design and fully integrated production process using a cam tappet as an example. For the used cam tappet contact, we first determined the optimal texture geometries using two differently complex EHL (elastohydrodynamic lubrication) simulation models. Based on these, textured tappets were manufactured in a combined manner using sheet-bulk metal-forming and deposition with a diamond-like-carbon (DLC) coating for additional wear protection without further post-processing of the coating. We show that the simulation approach used has a rather subordinate influence on the optimization result. The combined forming of components with textured surfaces is limited by the local material flow, the resulting texture distortion, and tool wear. However, a targeted process design can help to exploit the potential of single-stage forming. The applied DLC coating has good adhesion and can completely prevent wear in subsequent reciprocal pin-on-disc tests, while the friction in the run-in behavior is initially higher due to the soothing effects of the coating. The experiments also show a tendency for shallow textures to exhibit lower friction compared to deeper ones, which corresponds to the expectations from the simulation. [ABSTRACT FROM AUTHOR]

The development of high-speed motors has stimulated the demand for high-speed reducers. In response to the lack of research on high-speed reducers and the challenge of developing high-speed transmission systems, this study proposes a novel wedge-loading planetary traction drive (WPTD). First, a more accurate theoretical analysis model is established by considering the combined effects of elastic deformation, loading state, and a elastohydrodynamic lubrication (EHL) traction mechanism. Second, the mixed thermal EHL model is introduced into the performance analysis of traction drive for the first time. The fitting formulas for predicting traction contact behavior are derived, and a performance analysis method for all line-contact traction drives is presented. Third, the loading performance, transmission characteristics, and the influence of different parameters on the transmission characteristics of WPTD are analyzed. Finally, the theoretical model is validated by prototype performance tests. The results show that the loading mechanism demonstrates a good self-adaptive loading effect, and WPTD achieves a peak efficiency of 96%. Additionally, WPTD delivers superior efficiency and vibration and noise performance because of its smooth power-transfer characteristics, thereby providing a possible solution for high-speed and low-vibration transmissions. [ABSTRACT FROM AUTHOR]

Film thickness in a grease-lubricated bearing is a critical bearing operation parameter, yet there are no models available to predict it. Our recent articles demonstrated that the relative film thickness ( h g / h ff ) can be predicted using the base oil viscosity ( η ), half contact width (b), and linear speed (u) for any axially loaded deep groove ball bearing. In this article, we extend this study to include radial loads and combined—axial and radial—loads. Radial load application causes an additional replenishment in the unloaded zone, introducing a new length variable z r and surface tension σ. A universal power-law relationship between the relative film thickness in a deep groove ball bearing and the nondimensional number (η bu) / ( z r σ) for all loading and grease lubrication conditions is presented for use in predicting film thickness. [ABSTRACT FROM AUTHOR]

When the lubricant is not enough to maintain the ideal lubrication state of the bearing, the deep groove ball bearing will enter the starved lubrication state, which leads to the change of the vibration response of the deep groove ball bearing with localized defects. Previous bearing dynamics models mainly consider the lubrication state as an ideal lubrication condition, which may not reveal the effect of starved lubrication on the vibration characteristics of defective bearings. In this paper, the internal interaction of the system under starved condition is taken into account, and a dynamic model of defective deep groove ball bearings with insufficient lubricant is established to investigate the effects of different starved lubrication degrees on the contact force, friction force, cage speed, and system vibration characteristics. The results show that the lubricant insufficiency significantly changes the contact force inside the bearing, and the increase in friction caused by the increase in the degree of starved lubrication leads to the suppression of the degree of bearing slipping. The root mean square (RMS) value of the time-domain signal and the outer ring fault frequency both increase with the increase of the starved degree. The results of the study are helpful for fault diagnosis and condition monitoring of related equipment. [ABSTRACT FROM AUTHOR]

A simple numerical approach is developed to predict the wear and friction of piston ring pack and cylinder liner during the break-in period and under transient speed conditions. In the model, a solution of mixed lubrications using the load-shearing concept is presented based on the selected elastic-plastic equations of asperity contacts in conjunction with well-established elastohydrodynamic equations. The model takes shear-thinning, thermal effects in elastohydrodynamic lubrication (EHL) and lubricant starvation effects into account. Modified Archard's wear coefficient to describe the piston ring against cylinder liner wear is introduced. The approach is valid for the calculations of the asperity pressure at low values of the ratio of oil film thickness to combined roughness of the interacting surfaces, that is, less than 0.5. Applications are discussed, including association of piston side thrust force on wear and friction characteristics of piston ring/cylinder bore, gas blowby through the ring pack on the cylinder liner wear, a strong coating dependence for the piston ring wear, and wear distribution across the stroke under engine operating conditions. A good agreement between the experimental and analytical data indicates that the proposed model can be used to predict the wear and friction of the piston ring pack sliding against cylinder liner. [ABSTRACT FROM AUTHOR]

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This work explores experimentally the effects of DC electrical currents on lubricant film thickness alteration in lubricated sliding steel contacts in the boundary and mixed regime as measured by ultrasound. The experiments were performed in a two-electrode cell-based pin-on-disk tester instrumented with ultrasonic transducers. Unelectrified and electrified tribological tests were conducted on steel flat-on-flat contacts under various speeds and loads using both a mineral base oil and a gear oil. Film thickness, coefficient of friction (CoF), and electrical contact resistance (ECR) were measured during short experiments (30 s) in unelectrified and electrified (1.5 and 3 A) conditions. The results suggest that film thickness, CoF, and all ECR are altered by passing DC currents through the contact. In particular, film thickness increased and decreased, respectively, by applying electricity at the different speeds and loads tested. These alterations were majorly ascribed to oil viscosity decrease by local heat and surface oxidation caused by electrical discharge and break down at the interface. [ABSTRACT FROM AUTHOR]

This study is an optimized extension based on the authors' previous research on the tribo-chemical reaction under constant temperature field of two-stroke internal combustion engines (ICEs). It establishes a coupled analysis model that considers the tribo-chemical reactions, dynamic contact, and interface lubrication of the piston ring-cylinder liner (PRCL) system under transient temperature conditions. In this study, for the first time, the prediction of the tribofilm thickness and its influence on the surface micro-topography (the comprehensive roughness) are coupled in the working temperature field of the PRCL system, forming an effective model framework and providing a model basis and analytical basis for subsequent research. This study findings reveal that by incorporating temperature and tribofilm into the simulation model, the average friction deviation throughout the stroke decreases from 8.92% to 0.93% when compared to experimental results. Moreover, the deviation during the combustion regime reduces from 39.56% to 7.34%. The proposed coupled model provides a valuable tool for the evaluation of lubrication performance of the PRCL system and supports the analysis software forward design in two-stroke ICEs. [ABSTRACT FROM AUTHOR]

Polymers are widely used in bearing applications. In the case of water-lubricated stern tube bearings, thermoplastic polyurethane (TPU)-based composites are used due to their excellent wear resistance, corrosion resistance, and tunable mechanical properties. Their tribological performance, however, depends on operating conditions. In this work, TPU was blended with carbon fiber, graphene platelet, and ultra-high molecular weight polyethylene (UHMWPE). Friction tests of TPU based-composites against copper countersurface were carried out in water to mimic the actual operating conditions of the bearing. Most of the resulting contacts were in the boundary lubrication regime, in which friction was attributed to both contact mechanics of asperities as well as water lubrication. Our results show that the viscoelasticity of TPU has a considerable impact on its tribological performance. Water lubrication at 50 °C promotes the softening of polymer surface material during sliding, resulting in higher fluctuation in the coefficient of friction and wear loss. This is attributed to the reduced thermomechanical properties. In addition, Schallamach waviness is observed on worn surface. The tribological properties of TPU are significantly improved by the inclusion of carbon fiber, graphene platelet, and UHMWPE. The formation of graphene transfer-layers and UHMWPE transfer film reduces friction and wear loss, while the inclusion of carbon fiber enhances wear resistance due to improved mechanical properties and load bearing capacity. [ABSTRACT FROM AUTHOR]

Durability and reliability have been studied for decades through intensive trial-error experimentation. However, there are numerous fields of application where the costs associated with this approach are not acceptable. In lubricated machines with severe dynamic loads, such as high-power-density engines, simulation tools offer clear advantages over intensive testing. Prototypes and multiple scenarios can be cost-effectively simulated to assess different lubricants and engine configurations. The work presented here details the study of wear based on a validated elastohydrodynamic (EHD) simulation model of the connecting rod journal bearing. This model accounts for elastic deformation through a connecting rod finite element model (FEM). In addition, multiple lubricant rheological and tribological dependences, determined by specific experimental tests, are applied in the model through their interaction with the simulation software. Correspondingly, a novel wear algorithm is proposed to predict wear depth over time evolution along a proposed wear cycle based on the typical working ranges of high-performance engines. A final assessment is presented to compare 4 different ultralow-viscosity lubricants in their protective performance under severe conditions. The results show the evolution of the wear load and wear depth over the wear cycle. This evaluation is key to describing a lubricant selection procedure for high-power-density engines. [ABSTRACT FROM AUTHOR]

A stochastic uncertain tribodynamic model is established for a spur gear pair for the first time. The stochastic uncertainty of pinion rotation speed propagated to lubrication performance is investigated. The probability density function of the minimum lubricant film thickness hmin evolves over time periodically at interval of an engagement process. Correspondence between abrupt increase in meshing force and amplification of hmin uncertainty is found. Robust and reliable lubrication performance can be achieved by suppressing the hmin uncertainty and decreasing the lubrication failure probability. This can be done by increasing lubricant viscosity, and decreasing input torque and uncertainty level of input rotation speed. This work lays a solid foundation for robust and reliability based optimization for tribodynamic gear system. [ABSTRACT FROM AUTHOR]

The issue of lubrication in metallic artificial hip joints is discussed to prevent the two bearing surfaces from contacting each other. This study aims to analyse the characteristics of elastohydrodynamic lubrication (EHL) and investigate the effect of radial clearance and head size on the tribological performance of metallic artificial hip joints under steady-state conditions using the Fluid-Structure-Interaction (FSI) method. The average load in the z-direction and flexion-extension motion around the y-axis were used to represent normal walking. This study demonstrates that the film thickness profile from the validation study aligns with the findings of the previous study. The contour of the fluid pressure in the central contact zone changes with different time steps – the direction of fluid movement corresponds to the solid-fluid reaction. Additionally, the deformation of the cup surfaces contributes to the continuous fluid film that separates the contact surfaces. Furthermore, design parameters also influence EHL performance. It has been discovered that less radial clearance and a larger head size led to an increase in fluid film thickness. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Friction and wear are the main failure sources of face seals. When the surfaces of sealing rings exhibit greater roughness, the level of friction might increase and lead to sealing failure. Therefore, in this paper, based on the elastic contact hypothesis of rough and wavy surfaces and the influence of temperature on the elastic modulus of materials, a thermoelastic contact lubrication model of a gas-lubricated end seal is established. The novelty and advantage of this study is that it takes the effect of surface roughness into consideration during thermoelastic analysis of gas-lubricated seals. The film pressure, temperature, contact force and deformation of a gas spiral groove-faced seal are numerically determined. The influence of surface roughness on the contact distribution, deformation and temperature of the end-face seal at different speeds and pressures is analyzed. The film thickness increases as the rotational speed increases from 1 rpm to 2000 rpm, while the contact pressure sharply decreases from 0.25 kPa to 0. The analysis shows that the roughness contact mainly happens on the inner side of the rings due to convergent distortion of the seal faces, which easily causes partial wear of the seal faces. Moreover, it can also be found that the spiral grooves on the sealing surface can produce obvious hydrodynamic pressure effect due to the function of shear speed when the speed increases to 2000 rpm, while the film temperature increases from 293.3 K to about 306 K. The greater surface roughness results in a larger temperature rise under low-rotational-speed and lower-seal-pressure conditions, which further increases the risk of severe wear or even failure of the seal faces. [ABSTRACT FROM AUTHOR]

Rolling element bearings are widely used in aero engines, high-speed trains, precision machine tools, and other technical fields due to their high rotational accuracy and strong carrying capacity. With the development of rotating machinery in the direction of high speed, the working conditions of rolling element bearings are becoming more and more harsh, resulting in thermal problems that will seriously affect the mechanical properties of the bearing and the stability of the rotor system. In this paper, the four-degrees-of-freedom quasi-static model of cylindrical roller bearings was established based on the elastohydrodynamic lubrication theory combined with slicing technology. The local thermal approach and the thermal resistance network method were adopted to calculate the frictional heat generation and the transient temperature field of bearings. So the thermal-mechanical coupling model was obtained considering the correction of the thermal effect. On this basis, the influences of temperature on the vibration of the bearing-rotor system were researched. Finally, the temperature and stiffness of the bearings under various operating conditions were discussed. The coupling theory of thermal characteristics and mechanical properties of such bearing-rotor systems was improved. Practical Applications: Cylindrical roller bearings generally play a supporting role in rotating machinery and are widely used on high-speed occasions. For example, aero engines work under high-speed conditions, and high speeds in mechanical systems often bring serious thermal problems. As one of the core components, the spindle bearing must be able to overcome such a complex working environment. In this paper, cylindrical roller bearings and bearing-rotor systems are mathematically modeled for this feature in order to study their thermal and dynamic characteristics. The conclusions of this paper can provide relevant references for the design theory of this type of bearings applied in the fields of aero engines, high-speed precision machine tools, high-speed trains, etc., as well as theoretical guidance for the evaluation of their actual service performance. [ABSTRACT FROM AUTHOR]

The following study investigates the effects of Rabinowitsch fluid on journal bearing lubrication under the influence of velocity slip and variable viscosity. The finite difference method is used to produce a numerical solution to the 2D Modified Reynolds equation. The findings verify the previous results, which indicate that the dilatant (shear-thickening) fluid pressure is higher than the Newtonian and pseudo-plastic (shear-thinning) fluids. The results show that in the presence of slip, the pressure distribution rises with the piezo- viscosity parameter (variable viscosity) by up to 75%. Compared to the Newtonian, and pseudo-plastic (shear thinning) fluid, the dilatant (shear-thickening) fluid produces the highest pressure. A higher eccentricity ratio, slip-velocity, piezo-viscosity parameter, and dilatant fluid enhances the load-carrying capacity. The reduction in the attitude angle plays an integral part in the load-carrying capacity of the journal bearing. The attitude angle decreases for all values of the bearing ratio; the dilatant fluid has the most significant reduction in attitude angle compared to the Newtonian and pseudo-plastic fluids. Slip effects reduce the attitude angle, and a further reduction occurs when the piezo-viscosity and slip factors are combined. The slip-velocity, lower values of the bearing's length to diameter ratio, greater piezo-viscosity, higher values of the eccentricity ratio, and the dilatant fluid minimize friction. The Rabinowitsch fluid properties and the addition of both slip and variable viscosity increase bearing performance by increasing the pressure distribution, load-carrying capacity of the journal bearing and reduction of the frictional parameter, and should be considered when optimizing pressure, load, and friction for the creation of the ideal journal bearing. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to understand the vibration characteristics of full ceramic ball bearings under grease lubrication, reduce the vibration of the bearings and improve their service life. Design/methodology/approach: The Hertz contact stiffness formula for full ceramic ball bearings is constructed; the equivalent comprehensive stiffness calculation model and vibration model of full ceramic ball bearings are established. The dynamic characteristic test of full ceramic ball bearing under grease lubrication was carried out by using the bearing life testing machine, and its vibration was measured, and its vibration acceleration root-mean-square was obtained by software calculation and compared with the simulation results. Findings: At the rotational speed of 12,000 r/min, the root-mean-square value of vibration acceleration is maximum 10.82 m/s2, and the error is also maximum 7.49%. As the rotational speed increases, the oil film stiffness decreases. In the radial load of 600 N, the vibration acceleration root-mean-square is minimum 6.40 m/s2, but its error is maximum 6.56%. As the radial load increases, the vibration of the bearing decreases and then increases, so under certain conditions increasing the radial load can reduce the bearing vibration. With different types of grease, the best preload is also different; low-speed heavy load should be used when the viscosity of the grease is large, and high-speed light load should be used when the choice of smaller viscosity grease is made. Originality/value: It provides a theoretical basis for the application of full ceramic ball bearings under grease lubrication, which is of great significance for reducing the vibration of bearings as well as enhancing the service life of bearings. Peer review: The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2024-0094/ [ABSTRACT FROM AUTHOR]

The tribological behavior of an addendum modified altered tooth sum optimized spur gear set were experimentally compared with that of the standard spur gear under several loading conditions including the wear morphology study and wear debris analysis. The temperature, viscosity, elastohydrodynamic oil film thickness, specific film thickness, and combined surface roughness variation under increasing operating load were analyzed experimentally. Finally, the performance impact of addendum shifted altered tooth sum optimized gear was examined. Results show that the tribological improvement strongly depends on the addendum alteration and modified tooth sum condition. The modification of the addendum in gears with a negatively altered tooth sum facilitates the transition from single-tooth contact to two-tooth contact, broadening the lubrication range while preserving optimal film thickness and improving wear resistance. However, it is reverse to decrease the film thickness and increase wear for standard and profile-modified positively altered tooth sum gear. The gear tribological performance can be significantly improved by profile modification and negatively altered tooth sum approach with a lower rate of degradation of oil and damage on the tooth contacting surface. [ABSTRACT FROM AUTHOR]

The non-slip condition is one of the acknowledged conditions in the common fluid dynamic applications. In some specific cases, this assumption is challenged. When high speed and pressure occur in a part of the flow near the surface, such as in the lubrication of non-conformal surfaces, there is a possibility of slippage on the surface. In this study, the effect of fluid slipping on the surface in elastohydrodynamic lubrication has been numerically investigated. A numerical model was derived based on the equations governing the flow of the lubricating fluid and with the assumption that the fluid is Newtonian and the flow is isothermal. The geometry includes an upper long cylindrical surface and a lower flat surface. The equations were discretized by the finite difference method and solved by the least squares method. In this investigation, in addition to proving the existence of slip, its effect was considered for various values of problem parameters, such as the speed of the surfaces, load, the ratio of the speed of the surfaces, and the limit shear stress. The results showed that with the increase in speed and load, a significant slip occurs and the no-slip condition causes a deviation of 20% till 90% in the estimation of the friction coefficient. At the speed ratio near one, the slippage is higher. As the shear stress increases, the occurrence of sliding becomes more limited. Slipping reduces the friction of lubrication. [ABSTRACT FROM AUTHOR]

We present in this article a numerical technique to simulate the hydrodynamic behaviour of a magnetic reading device. In the transient regime, the evolution of the air pressure is computed as the solution of a time dependent compressible Reynolds equation. The proposed numerical method is based on a local discontinuous Galerkin method combined with a $ \theta- $method for the time derivative. We present some numerical tests to show the good behaviour of the numerical scheme. [ABSTRACT FROM AUTHOR]

This work aims to study the tribological performance of the water-lubricated journal bearings by developing an EHL model considering non-Gaussian roughness and cavitation. An elastohydrodynamic lubrication (EHL) model is established by solving the Reynolds equation, elastic deformation and film thickness equations in a coupling manner by using the finite difference method with a successive over-relaxation scheme. The non-Gaussian flow factors and cavitation factors are incorporated in the Reynolds equation to tackle the roughness and non-Gaussian roughness effects. The result shows that the coefficient of friction increases with an increase in skewness. A significantly increase in the minimum film thickness is observed for a surface having high negative skewness. The friction coefficient decreases with an increase in the L/D ratio. [ABSTRACT FROM AUTHOR]

Present analysis deals with the impact of nonlinear convection on MHD non-Newtonian fluid flow considering exponentially stretched sheet through porous media. Additionally, the effects of radiation, Joule heating and energy dissipation have been taken into account. The considered flow situation of nonlinear PDEs is transmuted to nonlinear ODEs using similarity analysis. The numerical computations are derived using a fourth-order Runge–Kutta scheme with a shooting technique. Meaningful observations are discussed for velocity and energy profiles. Further, the impact of pertinent parameters considering pseudoplastic fluids (n = 0. 6) and dilatant fluids (n = 1. 3) is briefed through graphs. It is noted that the escalation in the values of the power-law index declines the velocity and energy profile. Higher values of the nonlinear parameter decline the energy profile. [ABSTRACT FROM AUTHOR]

In 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. [ABSTRACT FROM AUTHOR]

The lubricating medium of the aerostatic spindle is gas, with relatively low rigidity, which is easy to cause rotor offset and additional vibration under the action of external load, thus affecting the processing accuracy of the spindle. To solve the problem of unbalanced vibration of the spindle, a new type of controllable radial aerostatic bearing is designed by combining piezoelectric ceramics, which use the inverse piezoelectric effect of piezoelectric ceramics to squeeze the air film to produce corresponding control force, and the radial unbalanced vibration of the spindle is suppressed. A bearing–rotor–piezoelectric ceramic coupling model was established, and the control method of feedforward combined with feedback was used to reduce the hysteresis characteristics of piezoelectric ceramics. On this basis, the sliding mode controller of the entire system, and through research, it is found that the sliding mode controller based on the extended observer has the best vibration suppression effect compared with other sliding mode controllers in the article; this research results can improve the rotation accuracy of the spindle system and the machining accuracy of ultra-precision machine tools. [ABSTRACT FROM AUTHOR]