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The locally oriented roughness is a common feature of surface finished by a machining process, such as the surface of the cylinder liner, and may significantly influence lubrication characteristic. A homogenised transient Reynolds equation for the locally oriented roughness is derived. The Jacobsson–Floberg–Olsson (JFO) boundary conditions was implicitly incorporated into the transient Reynolds equation to ensure the mass flow conservation. On this foundation, a model for the transient lubrication in the cylinder liner‐piston ring considering the effects of the surface roughness and cavitation is established. Then, the results of model developed here are compared with those from the stochastic model by Patir and Cheng. and the effect of the direction of roughness on the lubrication properties is analysed. The homogenised transient Reynolds equation and the lubrication model developed here have great potential for understanding and optimising the transient lubrication considering the surface local roughness orientation, cavitation and starved lubrication. [ABSTRACT FROM AUTHOR]

Polymer based additives with long chain of suspended particles in oil retain polarity effect in the presence of couple stresses. Further, at high speed of journal bearing, the oil film experiences substantial agitation due to pressure-viscosity interaction which evolve piezo-viscous dependency of the lubricant. The present article addresses the combined effects of piezo-viscous dependency and couple stresses of lubricant on the characteristics of multi-recessed hybrid journal bearing under misaligned operation. To govern the flow of piezo-viscous-polar lubricant in clearance space of the journal bearing, a piezo-polar function is used to obtain the modified form of Reynolds equation. Galerkin's technique is employed to obtain the finite element formulation in the form of algebraic equation, which is solved to determine the unknown pressure field in the bearing system. The present results reveal that the use of piezo-viscous-polar lubricant offers an enhancement in performance characteristics of bearing system, i.e., a significant hike of 13–36%, 27–30% and 7–10% in the values of S ¯ ij , C ¯ ij and ω ¯ th respectively vis-à-vis Newtonian lubricant. The numerically simulated non-dimensional results presented in the article may be useful to generate the bearing design data of the hybrid journal baring system functioning in realistic and stringent operating conditions. [ABSTRACT FROM AUTHOR]

The current paper is aimed to investigate the deformability effects of the bearing surface on the lubrication performance of cylindrical journal bearing with finite length under turbulent conditions. The bush is coated with a thin resilient layer with a smooth surface, the radial distortions of which are of the same order of magnitude as the film thickness. The elastohydrodynamic problem is studied under elasticity conditions in accordance with the plain strain hypothesis (Winkler model). The modified Reynolds equation is carried out on the base of the turbulent lubrication model of Hirs (bulk flow model). The partial differential equation is solved numerically by successive over-relaxation technique on a finite difference grid, considering different values of coating materials, lubricant viscosity, and journal speed. Results for the performance characteristics of the bearing are given for several selected values of Reynolds number and elasticity parameters of the soft liner on the bush. [ABSTRACT FROM AUTHOR]

In this paper, the tribological characteristics of an oil-soluble magnetic fluid additive under mixed lubrication are studied by experiments and numerical simulation. [bmim][FeCl4] is dissolved in CF10W-40 lubricating oil as a magnetic liquid additive, and its friction coefficient is tested by a point contact friction tester at different temperatures, rotational speeds and magnetic field intensities. The transition condition of lubrication state is obtained through analyzing the Stribeck curves based on the experiments, and the strength model of boundary film is established accordingly. A mixed lubrication model is established by substituting the boundary film strength model and the surface roughness model into the hydrodynamic lubrication model based on Reynolds equation. The results show that the magnetic solution as an additive can obviously reduce friction and wear, and the effect is more obvious under the condition of magnetic field. The boundary film strength model can accurately reflect the transition characteristics of lubrication state in the presence of boundary film, and the mixed lubrication model based on boundary film strength model can more precisely reflect the tribological characteristics of friction pairs, so this study provides a new theoretical method for the related research on the influence of boundary film on lubrication characteristics. [ABSTRACT FROM AUTHOR]

The long-term wear of the piston/cylinder pair is the main failure reason for axial piston pumps. In this paper, the dynamics of textured films to enhance the lubrication performance of piston/cylinder pairs is investigated systematically. The oil film is divided into three regions: the head region, the texture region, and the tail region. The Reynolds equation is used to predict the dynamics, which includes the carrying capacity and the friction. Influences of the texture geometries and the working conditions are presented in sequence. The results show that the texture enhances the lubrication performance by the collective effect. A shorter head length and a larger area ratio always benefit the lubrication performance, while increasing the texture region length does not always lead to positive effects, and the cell length is found to have negligible influences. The texture effect is found to be enhanced with larger shearing velocities and to be restrained with higher inlet pressures. It is also shown that the texture is effective for small inclination angles. Furthermore, a one-dimensional model is performed to unravel the mathematical mechanism, and an explicit expression is given for the texture region length. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this research is to study the dynamic behavior of hydrostatic squeeze film dampers made of four hydrostatic pads, fed through four capillary restrictors with micropolar lubricant. Design/methodology/approach: The modified version of Reynolds equation is solved numerically by the finite differences and the Gauss–Seidel methods to determine the pressure field generated on the hydrostatic bearing flat pads. In the first step, the effects of the pad dimension ratios on the stiffness and damping coefficients are investigated. In the second step, the damping factor is evaluated with respect to the micropolar properties. Findings: The analysis revealed that the hydrostatic squeeze film dampers lubricated with micropolar lubricants produces the maximum damping factor for characteristic length of micropolar lubricant less than 5, while the same bearing operating with Newtonian lubricants reaches its maximum damping factor at eccentricity ratios larger than 0.4. Originality/value: The results obtained show that the effects of micropolar lubricants on the dynamic performances are predominantly affected by the pad geometry and eccentricity ratio. [ABSTRACT FROM AUTHOR]

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

A simplified mathematical model has been developed for understanding combined effects of surface roughness, viscosity variation and couple stresses on the squeeze film behaviour of a flat and a curved circular plate in the presence of transverse magnetic field. The Stokes (1966) couple stress fluid model is included to account for the couple stresses arising due to the presence of microstructure additives in the lubricant. In the context of Christensen's (1969) stochastic theory for the lubrication of rough surfaces, two types of one-dimensional roughness patterns (radial and azimuthal) are considered. The governing modified stochastic Reynolds type equations are derived for these roughness patterns. Expressions for the mean squeeze film characteristics are obtained. Numerical computations of the results show that the azimuthal roughness pattern on the curved circular and flat plate results in more pressure buildup whereas performance of the squeeze film suffers due to the radial roughness pattern. Further the Lorentz force characterized by the Hartmann number, couple stress parameter and viscosity variation parameter improve the performance of the squeeze film lubrication as compared to the classical case (Non-magnetic, Newtonian case and non-viscous case). [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to study the impact of transient velocity changes on sealing performance during reciprocating sealing processes. Design/methodology/approach: Establish a model of transient mixed lubrication, solve the transient Reynolds equation, consider the effect of temperature rise at the seal interfaces, and determine the behavior of the seal interfaces, such as film thickness and fluid pressure. Evaluation with friction and leakage rate, calculate the variation of sealing performance with reciprocating velocity under different working conditions, and verify it through bench experiments. Findings: Within a reciprocating stroke, the frictional force decreases with increasing velocity, and the frictional force of the outstroke is greater than that of the instroke; at the time of the stroke transition, the fluid pressure is smallest and the rough peak contact pressure is greatest. At present, the dynamic pressure effect of fluids is the largest, and the friction force also increases, which increases the risk of material wear and failure. Friction and leakage increase with increasing pressure and root mean square roughness. As temperature increases, friction increases and leakage decreases. In studying the performance variations of seal components through a reciprocating sealing experiment, it was found that the friction force decreases with increasing velocity, which is consistent with the calculated results and more similar to the calculated results considering the temperature rise. Originality/value: This study provides a reference for the study of transient sealing performance. [ABSTRACT FROM AUTHOR]

An endeavor has been made to study the performance of a ferrofluid based squeeze film in circular cylinder near a plane resorting to Shliomis model, considering slip velocity. The stochastic model of Christenson and Tonder has been brought in here to evaluate the effect of surface roughness. The associated stochastically averaged Reynolds type equation is solved to obtain the pressure distribution. Then load bearing capacity has been calculated. The results show that Shliomis model based ferrofluid lubrication is relatively better as compared to the Neuringer-Rosensweig model for magnetic fluid lubrication of this type of bearing system, even if the slip is higher. The adverse effect of roughness can be reduced considerably at least in the case of negatively skewed roughness with a suitable choice of curvature parameters. It is observed that this type of bearing system supports some amount of load even when there is no flow, unlike the case of conventional lubricants. Some of the results presented here establish that the adverse effect of slip velocity can be minimized with suitable magnetic strength, irrespective of the fact that the roughness induces adverse effect. [ABSTRACT FROM AUTHOR]

This research investigates the mixed lubrication of anisotropic non-Gaussian rough surfaces. An adaptive fluid Reynolds equation is proposed, which takes into account multiple factors such as pressure-flow factors, contact factors, and shear flow factors. The aim is to evaluate the lubrication performance of anisotropic non-Gaussian rough surfaces with transverse and longitudinal textures. We find that statistical parameters of asperities height distribution on non-Gaussian rough surfaces exert a crucial influence on contact lubrication performance, with kurtosis and skewness proving to be particularly significant. Moreover, directional effects of anisotropic rough surface textures on lubrication performance of non-Gaussian rough surfaces are complex and vary. This study proposes an innovative conclusion that optimizing asperities height distribution parameters can significantly refine the surface lubrication performance, subsequently improving operational efficiency and machinery lifespan. Furthermore, the fluid Reynolds equation developed in the paper offers theoretical support and experimental guidance for the in-depth investigation of the contact lubrication performance of non-Gaussian rough surfaces. [ABSTRACT FROM AUTHOR]

Purpose: The study aims to the distribution rule of lubricating oil film of full ceramic ball bearing and improve its performance and life. Design/methodology/approach: The paper established an analysis model based on the fluid–solid conjugate heat transfer theory for full ceramic ball bearings. The distribution of flow, temperature and pressure field of bearings under variable working conditions is analyzed. Meanwhile, the mathematical model of elastohydrodynamic lubrication (EHL) of full ceramic ball bearings is established. The numerical analysis is used to study the influence of variable working conditions on the lubricant film thickness and pressure distribution of bearings. The temperature rise test of full ceramic ball bearing under oil lubrication was carried out to verify the correctness of simulation results. Findings: As the speed increased, the oil volume fraction in full ceramic ball bearing decreased and the surface pressure of rolling element increased. The temperature rise of full ceramic ball bearings increases with increasing speed and load. The lubricant film thickness of full ceramic ball bearing is positively correlated with speed and negatively correlated with load. The pressure of lubricating film is positively correlated with speed and load. The test shows that the higher inner ring speed and radial load, the higher the steady-state temperature rise of full ceramic ball bearing. The test results are in high agreement with simulation results. Originality/value: Based on the fluid–solid conjugate heat transfer theory and combined with Reynolds equation, lubricating oil film thickness formula, viscosity temperature and viscosity pressure formula. The thermal analysis model and EHL mathematical model of ceramic ball bearings are established. The flow field, temperature field and pressure field distribution of the full ceramic ball bearing are determined. And the thickness and pressure distribution of lubricating oil film in the contact area of full ceramic ball bearing were determined. Peer review: The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2023-0126/ [ABSTRACT FROM AUTHOR]

Purpose: This study aims to present a numerical solution for the analysis of the influence of surface roughness as presented by a sinusoidal ripple of different amplitude and wavelength on the performance of transient elastohydrodynamic lubrication at motion start-up under different operational parameters of entraining speed and load as well as different acceleration rates. Design/methodology/approach: A statistical asperity micro-contact model represented by a sinusoidal ripple expressed by two parameters (wavelength and undeformed amplitude) is considered. The ball equation of motion is used to calculate the force on the ball as it starts to move. The time-dependent Reynolds equation is solved together with surface deformation and statistical asperity models using the Newton–Raphson technique with the Gauss–Seidel iteration method. Findings: The behaviour of the film thickness was found to be strongly influenced by the acceleration rate for different ripple amplitude and wavelength parameters. The effect of increasing the final entraining speed will eventually lead to rapid film thickness build-up and increase the film thickness jump at the moment of motion start-up. The effect of increasing applied load is to reduce the deviation of the minimum film thickness jump at the start-up of motion, making its value approximately equal to the steady-state value over the entire run-time period. Originality/value: Influence of surface roughness for various wavelength and undeformed amplitude on the performance of transient elastohydrodynamic lubrication at motion start-up is presented at different acceleration rates as well as for different operating parameters of entraining speed and load. Ball equation of motion is used to calculate the force on the ball as it starts to move. [ABSTRACT FROM AUTHOR]

The anti-scuffing bearing capacity of gears is a significant issue for their service lives, especially for the cases with heavy loads or high speeds. Generally, the anti-scuffing bearing capacity is evaluated according to the surface contact temperature that can be calculated with either analytical methods or finite element analysis (FEA) methods. The analytical methods usually apply the theory of Blok to efficiently obtain the results by simplifying some actual physical conditions, which are well considered in the FEA methods with accurate results but more computation time. Conversely, a new efficient and accurate analytical method is proposed by introducing the actual lubricant film thickness and continuous heat transfer for the theory of Blok. These two physical conditions are the key issues for the calculation of the two parts of surface contact temperature, flash temperature and bulk temperature, respectively. For the calculation of flash temperature, elastohydrodynamic lubrication (EHL) is introduced to consider the lubricant film thickness for the theory of Blok, and the result is obtained by solving the Reynolds equation efficiently with the finite difference method. For the bulk temperature, the result for a contacting point on the gear tooth surface is directly obtained according the theory of Blok, and the continuous heat transfer among the adjacent contacting points is considered with Gaussian heat morphology, which can accurately construct the bulk temperature field distribution in the contact region. The proposed method is validated as in good agreement with the FEA method and with less computation time. [ABSTRACT FROM AUTHOR]

The piston/cylinder pair is one of the most important friction pairs in the axial piston pump; reducing the friction of it can improve the axial piston pump efficiency. In this paper, the Reynolds equation coupled with the Half–Sommerfeld boundary condition is applied to predict the dynamics of the textured piston/cylinder pairs, and the characteristic function is used to predict the optimal geometry parameters. The analysis results show that the combination of the shearing coefficient and the characteristic function can predict the cavitation region and the critical inclination angle. The results of this paper provide theoretical guidance for the surface texture design on piston/cylinder pairs. [ABSTRACT FROM AUTHOR]

The novelty of this paper is to numerically investigate the effect of manufacturing error and misalignment on the transient lubrication behavior of dynamically loaded journal bearings with micro-groove. Based on the average Reynolds equation considering the mass conservation cavitation algorithm, the asperity contact model, and the force balance equation, the mixed lubrication model under time-varying dynamic loads is developed. Meanwhile, mathematical functions are given for the bearings with different surface profiles, including the circumferential and axial manufacturing errors of the bearing, the horizontal and vertical deflection angles of the journal, and the micro-grooves with different distribution forms. According to this model, the lubrication characteristics of the bearing are systematically investigated at different horizontal and vertical deflection angles, amplitudes, spatial numbers, and phase angles of the circumferential waviness, as well as shape profiles of the axial error. In addition, the performance parameters of dynamically loaded journal bearings with ideal and actual surfaces under different micro-groove distributions are comparatively evaluated. Numerical results show that manufacturing errors and misalignment have a remarkable effect on the transient behavior of dynamically loaded journal bearings, and the coupling effect will be more consistent with practical engineering. It can be found that the distribution form of the micro-groove surface directly affects the friction reduction effect of bearing systems. The numerical model can serve as a meaningful guideline for the optimum design of dynamically loaded journal bearing with micro-groove. [ABSTRACT FROM AUTHOR]

The oil film separates the shaft-bearing system to reduce the frictional force of contact surfaces with large temperature variations owing to thermal conduction. Multiple impact factors seriously affected the lubrication behavior of the bearing during actual working process. An applicable model regarding the lubrication analysis of a hydrodynamic-static hybrid bearing with deep-shallow chambers is proposed and validated with published literature. The lubrication behavior includes film pressure, load capacity, bearing stiffness and flow rate is numerically calculated with centered finite difference method by solving the Reynolds equation. The influence of film thickness and working temperature are considered, over a range of eccentricity ratio. Moreover, the temperature variation caused by thermal conduction is analyzed in details. To investigate the influence of thermal conduction on the lubrication behavior, the results show that the load capacity, bearing stiffness, friction power, and flow power significantly decline with the consideration of thermal conduction. This study proposes an accurate model that is helpful for the design of hydrodynamicstatic hybrid bearings with deep-shallow chambers under low rotational speed, heavy load, and high temperature conditions. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to investigate mixed lubrication performances of stern bearing in a misaligned state considering turbulence and bearing deformation impacts. Design/methodology/approach: A mixed lubrication model of stern bearing is established. The generalized average Reynolds equation governing the turbulent flow of lubricant is analyzed by considering the interaction of bearing elastic deformation, asperity contact pressure and film pressure. The bearing behaviors including minimum film thickness, hydrodynamic pressure, asperity friction force and frictional coefficient are studied under different models. The correctness of this model is verified by comparing it with that of the published data. Findings: Numerical results indicate that elastic deformation noticeably decreases the maximum film pressure, the asperity contact force and the friction coefficient in the mixed lubrication stage. The effect of elastic deformation and turbulence reduces the transition speed from mixed to liquid lubrication. Originality/value: This model includes both turbulence and bearing deformation impacts on journal bearing performances. It is expected that the numerical results can provide useful information to establish a stern bearing exposed to mixed lubrication conditions. Peer review: The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2022-0352/ [ABSTRACT FROM AUTHOR]

The fuel injection system heavily relies on the high-pressure fuel pump, which plays a critical role in its overall performance. The fuel pump plunger is subjected to high levels of stress and experiences irregular lubrication during dynamic loads, causing premature wear. In the industrial sector, laser surface micro-texturing has been utilized to reduce friction and enhance anti-wear properties, and its positive impact has been supported by both theoretical and experimental evidence. This article presents a method for determining the hydromechanical characteristics of plunger pairs under conditions of hydrodynamic friction. The microgeometry of friction surfaces was taken into account through the cavitation effect of the lubricating fluid, described by the modified Reynolds equation. Software was developed according to the proposed method. The developed software can be used to analyze the contacting surfaces of plunger pairs and evaluate their tribotechnical characteristics based on the microgeometry parameters of the friction surfaces. The article also discusses the impact of the microgeometry parameters on the quality criteria of the hydromechanical characteristics of the plunger pairs. Computational examples are given for the analysis of contacting surfaces of plunger pairs separated by a lubrication layer. The technical characteristics are evaluated depending on the parameters of the microgeometry of the roughness of the friction surfaces. The influence of the microgeometry parameters on the quality criteria of the hydromechanical characteristics of the plunger pairs is presented. [ABSTRACT FROM AUTHOR]

As operating under quite high bearing speed with quite narrow clearance, the slip effect generally inevitable exists and closely relates to the performance of Gas Journal Bearing (GJB). However, singly the conventional macroscopic method may not be capable of fully exploring the influence of slip effect and seize tiny details such as slip velocity and flow vortex. In this article, both the Lattice Boltzmann Method (LBM) and the Reynolds equation method are applied to analyze the distributions of lubricant viscous dissipation heat, velocity, slip velocity, pressure, journal position and film thickness versus different operating parameters at multiscale. It shows that the slip effect weakens the squeezing function on lubricant film, reduces the viscous dissipation heat peaks, consumes the maximum pressure peaks, and decreases the bearing capacity, which is more obvious at larger Knudsen number. At higher bearing speed, the high viscous dissipation heat and pressure zone rapidly magnifies, in contrast, under larger bearing load, the high viscous dissipation heat zone concentrates. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to investigate the performance of an ultra-thin film lubricated conjunction through the elastohydrodynamic lubrication of point contacts for various ridge shapes and sizes located within the contact zone including flat-top, triangle and cosine wave profiles, considering the influence of surface forces of solvation and Van der Waals' in addition to the hydrodynamic effect to predict an optimum geometric characteristics for surface texture for lubricated conjunctions. Design/methodology/approach: Surface features are simulated in a variety of sizes and shapes including flat-top, triangle and cosine wave profiles. While estimating the elastic deformation of the contacting surfaces, surface forces of solvation and Van der Waals' are taken into account. The Reynolds equation is solved using the Newton–Raphson method to get the pressure profile and film thickness including the elastic deformation, and surface feature. Findings: The geometrical characteristics of the ridge, its placement in relation to the contact zone and its height all have a significant impact on the performance of ultra-thin film lubricated conjunction. When the triangular-shaped ridge is present in contact, it forecasts even sharper peaks in film thickness and pressure. More friction, wear and eventually contact fatigue are brought on by this more acute pressure and film thickness peaks. The flat-top ridge shape shows a better performance for lubricated conjunction where, the minimum film thickness value is comparable to that obtained for the case of a smooth contact surface. This behavior is attributed to the effect of intermolecular force of solvation. An increase in the size of the ridge results in a step increase in the film thickness for different ridge shapes, particularly for the flat-topped ridge pattern. Originality/value: Evaluation of the performance of elastohydrodynamic lubricated ultra-thin film conjunction related to film thickness and pressure profile for various ridge surface features of different amplitudes, shapes and sizes located through the contact zone considering the influence of surface forces of solvation and Van der Waals' in addition to the hydrodynamic effect. Peer review: The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2023-0062/ [ABSTRACT FROM AUTHOR]

This paper adopts Rotem and Shinnar's modification of the Rabinowitsch fluid model for the 1-D non-Newtonian lubrication problem, a variational principle is established by the semi-inverse method, and a generalized Reynolds-type equation is obtained. This article opens a new avenue for the establishment of Reynolds-type equation of complex lubrication problems. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to investigate the effects of inertia of the lubricant on the performance parameters of journal bearings textured with spherical-shaped textures. Design/methodology/approach: The lubricant is assumed to be Newtonian, and the flow is considered laminar. Considering the lubricant inertia effects, the modified Reynolds equation is discretized using the finite difference method and solved with the Gauss–Seidel successive over-relaxation scheme using the progressive mesh densification method. Findings: The results from this numerical study indicate that the lubricant inertia improves textured journal bearing performance characteristics significantly. The improvement is more significant in the case of heavily loaded bearings. Furthermore, it is observed that protruded texturing in journal bearings shows better results compared to dimple textured journal bearings. Originality/value: Understanding the effect of lubricant inertia is essential for efficiently designing textured journal bearings. Thus, the results shown here would be helpful for the researchers and the bearing designers. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to describe and observe the influence of boundary slip associated with an arbitrary entrainment angle on the contact lubrication properties of ellipses. Design/methodology/approach: Based on the modified Reynolds equation, the boundary slip of any angle is considered in the elliptic contact, and numerical simulation is carried out. In the above calculation, the progressive mesh densification method is used, which greatly reduces the computation time. Findings: The results indicate that the variation of film thickness corresponding to different entrainment angles is distinct from those without considering boundary slip. In addition, boundary slip reduces the central film thickness and minimum film thickness, which makes the hydrodynamic pressure distribution smoother. Originality/value: The present study focuses on the specific condition with the arbitrary direction of rolling and sliding velocity found in hypoid gears and worm, and some other components. The influence of boundary slip associated with arbitrary entrainment angle on the lubrication film thickness in elliptical contacts is first revealed, which improves a good understanding of elastohydrodynamic lubrication characteristics. [ABSTRACT FROM AUTHOR]

In this paper, the combined effects of the characteristic size and concentration of inorganic fullerene-like tungsten disulphide nanoparticles (IF-WS2 NPs) or molybdenum disulphide nanoparticles (IF-MoS2 NPs) on the nonlinear dynamic behaviour of a gasoline engine crankshaft bearing subject to an arbitrary force torsor (effective applied force and moment vector) are theoretically and numerically investigated using the V. K. Stokes micro-continuum theory. These NPs are the most common additives for lubrication purposes due to their excellent tribological characteristics along with their effect on reducing friction and wear. It is assumed that the journal (crankshaft) currently made of a forged steel is rigid and the main bearing consists of a thin poroelastic liner made of low elastic modulus materials like Babbitt metals fixed in a stiff housing as defined by ASTM B23-00. The Krieger-Dougherty law is included in the proposed EHD model to account for the viscosity variation with respect to the volume fraction of nanoparticles dispersed in the base lubricant. On the other hand, the characteristic size of nanomaterials is introduced by a new material entity, denoted l, which is responsible for a couple-stress property. The Reynolds equation is derived in transient conditions and modified to account for the size of nanoparticles and the bearing-liner permeability property. For an arbitrary force torsor, the hydrodynamic pressure distribution, the squeeze film velocities, and the misalignment angular velocities are determined simultaneously by solving the discretized Reynolds equation and the equilibrium equations with the damped Newton-Raphson iterative method at each crank angle step. The crankshaft center trajectories in three sections of the main journal axis as well as the misalignment angles are deduced from the squeeze film velocities and the misalignment angular velocities by means of a Runge-Kutta scheme. According to the obtained results, the combined effects of the size and concentration of fullerene-like nanoparticles on the dynamic behavior of a compliant dynamically loaded crankshaft bearing operating with dynamic misalignment are significant and cannot be overlooked. [ABSTRACT FROM AUTHOR]

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

Due to the relatively low load-carrying capacity, low-viscosity lubricated bearings can easily operate in a mixed-lubrication regime. Furthermore, low lubricant viscosity may cause local turbulence in the area with relatively thick film. To analyze the influence of local turbulence on the transient characteristics of mixed-lubrication bearings, a simulation approach for unsteady mixed-lubrication bearings considering local turbulence effects is proposed. Transient journal center locations are solved via journal dynamic equations and numerical integration. The ratio of the film thickness to the roughness determines whether each node of the bearing is in the mixed-lubrication area or the pure hydrodynamic lubrication area. The liquid film in the mixed-lubrication area is analyzed by a transient average Reynolds equation to account for the surface roughness effect. A liquid film in the hydrodynamic lubrication area is analyzed by a transient generalized Reynolds equation to consider local turbulence. The transient average Reynolds equation and transient generalized Reynolds equation are derived in a form convenient for coupling with the governing equations of the journal center. The proposed model is experimentally validated. The influence of local turbulence on unsteady mixed-lubrication bearings is analyzed. The results show that local turbulence and asperity contact can coexist in low-viscosity lubricated bearings, even if the journal speed is relatively low. In the mixed-lubrication regime, local turbulence increases the minimum film thickness and decreases the friction coefficient as well as the journal speed at which the mixed-lubrication transitions to hydrodynamic lubrication. [ABSTRACT FROM AUTHOR]

In practice, due to bearing load there is a generation of pressure in the lubricant film, which leads elastic deformation on the bounding surfaces and causes variation in the film thickness. As film thickness plays an important role in performance of the slider‐bearing designs; an attempt has been made to study numerical simulation of elastic deformation effect in one‐dimensional inclined slider‐bearing with ferrofluid (FF) lubricant. The modified Reynolds equation is derived using ferrohydrodynamic theory by Shliomis with transverse uniformly strong magnetic field, and continuity equation. Using this equation dimensionless load‐carrying capacity (W¯$\bar{W}$) is studied for different parameters. The results show the better performance of W¯$\bar{W}$ for lower convergence ratio and higher effective viscosity. However, elastic deformation has no effect on W¯$\bar{W}$. Some comparisons are also made with the previous literature. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to investigate the performance improvement of journal bearing by applying the arc-shaped textures on various regions of bearing expressly full, second half and pressure increasing regions operating with and without nanoparticles in the lubricant. Design/methodology/approach: The Reynolds equation is solved numerically by using the finite element method to obtain static performance parameters such as load-carrying capacity (LCC) and coefficient of friction (COF), which are then compared with untextured bearing at eccentricity ratios of 0.2 to 0.8. Aluminum oxide (Al2O3) and copper oxide (CuO) nanoparticles additives are used, and viscosity variation due to the addition of additives in the base lubricant is computed for considering the range of temperatures 50 to 90°C at a weight fraction of 0.1 to 0.5% by using an experimentally validated regression model. Findings: The results indicate that the maximum LCC and the lower COF are found in the pressure-increasing region. A maximum increase of 34.42% is observed in the pressure-increasing region without nanoparticles, and furthermore, with the addition of Al2O3 and CuO nanoparticles in lubricants in the same region, the LCC increased to 21 and 24%, respectively. Originality/value: Designers should use optimal parameters from the present work to achieve high bearing performance. [ABSTRACT FROM AUTHOR]

Lubrication is essential to minimize wear and friction between contacting surfaces in relative motion. Oil based lubricants are often enhanced via polymer additives to minimize self-degradation due to the shear thinning effect. Therefore, an accurate estimate of the load carrying capacity of the thin lubricating film requires careful modeling of shear thinning. Available models such as the generalized Reynolds equation (GR) and the approximate shear distribution have drawbacks such as large computational time and poor accuracy, respectively. In this work, we present a new approach, i.e., the modified viscosity (MV) model, based on calculating the strain rate only in one point along the vertical direction. We investigate, for both MV and GR, the load, the maximum pressure, and the computational time for (i) sliding (non-cavitating) contacts, (ii) cavitating, and (iii) squeezing contacts. We observe that the computational time is reduced (i) considerably for non-cavitating sliding and rolling contacts and (ii) by several orders of magnitudes for cavitating and squeezing contacts. Furthermore, the accuracy of MV is comparable with the GR model within an appreciable range of bearing numbers. Finally, for each type of boundary motion, we have determined the optimal vertical location to calculate the shear strain rate for MV; while this optimal value is close to half the height of the contact for sliding configurations, for rolling dominated and squeezing contacts it is around one quarter (or three quarter) of their height. We finally provide an analysis to a priori estimate the optimal location of the strain rate. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to compare the spherical protruded and dimple textured journal bearings performance characteristics with the untextured bearing. Design/methodology/approach: The governing Reynolds equation considering the mass conserving (JFO) boundary conditions is solved using the computationally efficient progressive mesh densification (PMD) method. The central difference scheme is used for the discretization of the governing Reynolds equation. The numerical code developed is validated with the experimental results available in the literature. Findings: From this numerical study, it has been observed that the protruded textured journal bearing gives better performance compared to the dimple textured and untextured journal bearing for friction variable, whereas dimple textured journal bearing provides better performance compared to the protruded textured and untextured journal bearing for load carrying capacity and flow coefficient. For better performance, dimple and protruded textured bearings must be textured in second-half textured region configuration. Practical implications: The results shown here would be quite useful for the researchers generally and the bearing designers particularly. Originality/value: The load carrying capacity should be maximum whereas, the friction coefficient should be minimum and also the adequate flow of lubricant is necessary to maintain hydrodynamic lubrication and to remove the heat generated within the bearing due to friction, which impacts the bearing performance and life. Thus, this study would be significant in effective bearing design aspect. [ABSTRACT FROM AUTHOR]

In this study, an interfacial slip model including the limiting shear stress is proposed and applied to the thermal elastohydrodynamic lubrication (EHL) analysis of a helical gear pair. The main difference between the proposed model and the classical EHL model is that, the term of entrainment velocity in Reynolds equation is modified. The influences of interfacial slip, thermal effect, initial limiting shear stress and operating conditions on the tribological properties are evaluated. Due to the interfacial slip, the pressure distribution moves towards the inlet region, and the fluctuation distributions of entrainment velocity and film thickness are similar to the trigonometric function. The influence of thermal effect on interfacial slip cannot be ignored, especially in the case of high speed and heavy load. As the input torque and input rotational speed increase, the interfacial slip gradually extends to the whole meshing process. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to present a numerical model to examine the finite magneto-hydrodynamic (MHD) journal bearings performances including both non-Newtonian couple stress and bearing deformation impacts. Design/methodology/approach: Based upon the MHD and Stokes theories, a novel expression of modified Reynolds equation including bearing deformation is obtained. The bearing elastic deformation impact is predicted by means of the Winkler model. Using the numerical differentiation approach, the film pressure is iteratively solved. Different bearing characteristics are then numerically calculated. The validity of the proposed model was verified by comparing with some particular cases from literature. Findings: From the numerical presented results, it is demonstrated that the conducting couple stress lubricant with an applied radial magnetic field results in an induced electric current density and thus significantly improves the performances of elastic journal bearings. Particularly, the load-carrying capacity is increased, whereas a reduction in friction factor is observed. Originality/value: This numerical model is original, which combines both non-Newtonian couple stress and bearing deformation impacts on finite MHD journal bearings performances. It provides useful information in designing MHD journal bearings, given the lack of experimental studies. [ABSTRACT FROM AUTHOR]

Purpose: Researchers have not reached an agreement on which biomimetic shape has the best lubrication performance. This paper aims to study the influence of microtexture size, shape and direction on bearing capacity, end leakage, friction coefficient and wear of oil film. Design/methodology/approach: Different oil film thickness equations considering the microtexture of bearing surface are gained. The two-dimensional finite difference equation and the calculation equation of wear are established. Findings: The theoretical research shows that the wear value and the wear ratio when long side is perpendicular to the axial direction of the bearing are generally lower than when the long axis is parallel to the axial direction of bearing. The theoretical and experimental results show that the appropriate microtexture shape, such as circular dimple, crescent-shaped dimple, triangular dimple and fish-shaped dimple can improve effectively the lubrication performance of journal bearing and reduce the friction coefficient. Originality/value: The research has great significance to reduce friction and improve the wear resistance of equipment. [ABSTRACT FROM AUTHOR]

In the framework of stochastic representation of surface roughness, a novel Reynolds-type Equation has been derived recently by the authors and utilized to calculate the average values of a bearing's operational parameters. To acquire an improved insight to the hydrodynamic lubrication phenomena in rough bearings, the stochasticity of the operational parameters should be described, by calculating their higher-order moments, such as the variation. The present work aims at deriving equations for calculation and quantification of these higher-order moments. More specifically, in the present paper equations for the variation of a slider bearing operational parameters (pressure, load carrying capacity, friction force and friction coefficient) are derived. The obtained results are validated against the deterministic Reynolds Equation solution, for a series of bearings with different random Gaussian surface roughness profiles, over a wide range of bearing design and operational parameters. • Stochastic implementation of the surface roughness profiles as Gaussian variables. • Hydrodynamically lubricated bearings with surface roughness on the bearing and slider. • Utilization of Stein's Lemma, novel stochastic calculus theorem of probability theory. • Mathematical derivation of novel equations for calculating the variance of critical bearing's operational parameters. • Validation of acquired equations via numerical simulations and with existing results found in literature. [ABSTRACT FROM AUTHOR]

A deterministic mixed lubrication model for parallel surfaces is proposed. The oil film force is solved by the Reynolds equation with a mass-conserving cavitation model. The contact force is predicted by using a neural network trained on a database, which was built by conducting finite element analysis on a single asperity. In addition, an extended Archard equation is introduced to predict the transient running-in wear. The contact model is proved to be suitable for Gaussian and non-Gaussian surfaces. The Stribeck curves calculated under the different wear coefficients and wear steps are compared with the experimental results. The influence of initial surface topography on the running-in behavior has also been studied. The contact database for GCr15 is provided. [ABSTRACT FROM AUTHOR]

Various anti-wear and anti-corrosion coatings are applied on the surface of journal and bearing to maximise service life of a bearing system. These coatings influence the wettability of surfaces consequently causes velocity slip phenomena in the bearing system. This article addresses a novel investigation to examine the influences of velocity slip and PVP (Piezo-viscous-polar) lubrication on multirecessed hybrid conical journal bearing (MHCJB). For various cases of velocity slip, novel forms of Reynolds equation are derived and solved numerically by using FEM. The results reveal that velocity slip severely affects the generation of oil film pressure. Consequently, it deteriorates the bearing characteristics viz. load carrying capacity, oil flow rate and rotordynamic coefficients. Further, PVP lubricant offers substantial enhancement in bearing characteristics. • Anti-wear/anti-corrosion coatings influence the wettability of surfaces consequently causes velocity slip in the bearing system. • Novel forms of Reynolds equation for various cases of velocity slip in conical journal bearing with PVP lubrication. • Velocity slip impacts oil film pressure distribution and thereby load carrying capacity, rotordynamic coefficients. • PVP lubricant offers valuable enhancement in load carrying capacity and stability characteristics of conical bearing. [ABSTRACT FROM AUTHOR]

The paper presents the numerical solution of line contact thermal elastohydrodynamic lubrication (EHL) with bio-based lubricant. The model comprises Reynolds equation, film thickness, load balance and energy equations with appropriate boundary conditions by incorporating viscosity–pressure–temperature and density–pressure–temperature relations. Second-order finite difference scheme is used for the discretised form and their equation. The multigrid method with full approximation scheme is used to solve the Reynolds equation along with multilevel multi-integration method for film thickness equation. The pressure, film thickness and temperature distributions for two rolling velocities and various loads with a bio-based lubricant are presented in detail. The present findings yield a reduction in the minimum film thickness for high speed. Details of pressure spike as a function of relevant parameters are given. The results are compared with earlier findings based on different methods. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to study the effect of isosceles triangle micro concave texture with different parameters on the performance of oil seal to obtain a reasonable combination of parameters. Design/methodology/approach: Based on the theory of elastohydrodynamic lubrication, a numerical model is established by coupling the texture parameters of isosceles triangle with concave lip with the two-dimensional average Reynolds equation considering surface roughness. Findings: The results show that there is an optimal combination of parameters to improve the performance of the oil seal. When hp = 5µm-6.5 µm, a = 110°−130°, O = 1.4, C = 1.6 mm-2.2 mm, the oil seal with isosceles triangle micro concave texture can show good lubrication characteristics, friction characteristics and sealing ability. Originality/value: The model provides a new idea for the design of new oil seal products and provides a theoretical support for the application of surface texture technology in the sealing field in the future. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to investigate the squeeze film lubrication properties of hexagonal patterned surface inspired by the epidermis structure of tree frog's toe pad and numerically explore the working mechanism of hexagonal micropillar during the acquisition process of high adhesive and friction for wet contacts. Design/methodology/approach: A two-dimensional elastohydrodynamic numerical model is employed for the squeezing contacts. The pressure distribution, load carrying capacity and liquid flow rate of the squeeze film are obtained through a simultaneous solution of the two-dimensional Reynolds equation and elasticity deformation equations. Findings: Higher pressure is found to be longitudinally distributed across individual hexagonal pillar, with pressure peak emerging at the center of hexagonal pillar. Expanding the area density and shrinking the channel depth or initial film thickness will improve the magnitude of squeezing pressure. Relatively lower pressure is generated inside interconnected channels, which reduces the load carrying capacity of the squeeze film. Meanwhile, the introduction of microchannel is revealed to downscale the total mass flow rate of squeezing contacts. Originality/value: This paper provides a good proof for the working mechanism of surface microstructures during the acquisition process of high adhesive and friction for wet contacts. [ABSTRACT FROM AUTHOR]

Purpose: The edge of diesel engine crankshaft main bearing is more likely to fail in its real working condition. This paper aims to study the bearing failure mechanism by finding the relationship between bearing lubrication characteristics and its working condition. Design/methodology/approach: This work builds the mixed lubrication model of crankshaft bearing to analyze the cause of bearing abnormal wear, and the finite difference method was used to solving the average Reynolds equation. During the analysis, journal misaligned angle, external load and roughness are considered. Findings: The result shows that the wear of the diesel engine crankshaft bearing happens in engine startup phase and the bottom of the bearing are more prone to be excessively worn. Under the influence of journal misalignment, bearing asperity contact load and speed range of mixed lubrication will increase markedly. The edge of the bearing will be excessively worn. The effect of misalignment on bearing lubrication performance varies under different shaft rotation speed. Originality/value: The former research studies on crankshaft bearing either just focused on its lubrication characteristics or interested in its failure types (wear, adhere, cavitation). This paper studies the relationship between bearing failure mechanism and lubrication performance. [ABSTRACT FROM AUTHOR]

Calculating the flow of a film of lubricant between rough surfaces by solving the Reynolds equation requires a very fine mesh to capture the details of the topography and is thus very time consuming. In the present paper, a multiscale method is proposed. The domain is divided into an appropriate number of subdomains on which deterministic simulations are performed. The results of this microscale solution are coupled at the macroscale by employing a macromesh on which a mass flow balance is implemented. This method has already been successfully applied to liquid lubrication and is extended to gas lubrication. A significant reduction in computation time is obtained compared to a fully deterministic solution. The calculation of the load is also accurate. [ABSTRACT FROM AUTHOR]

Most mechanical systems have mating interfaces that require effective lubrication for smooth functioning. Thus, understanding and accurately modeling lubrication regimes is an essential research task. The present work proposes a set of normalized coefficients based on homogenization and stochastic theories to model the partial and full-film lubrication regimes between a smooth and a rough surface. The modified Greenwood and Williamson theory, considering inter-asperity-interactions, was used to model the contact-zones. Subsequently, the film-thickness was evaluated and the homogenized Reynolds equations were solved to compute the normalized coefficients. The estimated coefficients were compared with Patir and Cheng's flow-factors, and the similarities and disagreements between both approaches were discussed. New sets of coefficients for running-in surfaces were proposed for modeling their lubrication regimes. • Normalized homogenization coefficients are evaluated based on stochastic analysis. • Inter-asperity interactions have been considered to model the solid contacts. • New sets of homogenization coefficients for running-in surfaces are proposed. [ABSTRACT FROM AUTHOR]

Traditional methods of evaluating the performance of journal bearings, for example thermal-elastic-hydrodynamic- lubrication theory, are limited to simplified conditions that often fail to accurately model real-world components. Numerical models that include additional phenomena such as cavitation and fully coupled effects like deformation, temperature, pressure and viscosity can be more accurate but require a large amount of computational overhead, making analysis slower and more costly. To address this limitation, a novel machine learning-driven approach is developed to predict the 2D distribution of surface deformation, film thickness, temperature, and pressure across the bearing surface as a function of design variables such as load and speed. The training dataset, generated using a fully coupled Reynolds' Equation solver implemented in OpenFOAM, contains a significantly extended range of conditions than in previous studies with approximately 39 000 000 points encompassing 4925 different test cases. Modelled bearing speeds range from 2000 to 10 000 rpm, while load values are varied between 1 and 30 kN. Predicting surface deformation, film thickness, temperature and pressure across the bearing surface results in a mean absolute percentage error below 0.4 % or better. The work also demonstrates that the trained models have a strong ability to generalise the prediction beyond the original training data range with only a 1 % error at up to 200 % of the highest trained speed. This work also demonstrates that machine learning-based processes are a practical alternative to physics-based numerical modelling, especially in cases where rapid performance evaluation is desired as real-time calculation is possible with significantly reduced computational cost. This has the potential to enable development of rapid design optimisation tools and real-time performance monitoring at high resolution and with low latency. Using consumer hardware, it is found that the neural network-based approach is faster than the existing numerical modelling technique by a factor of over 10 000, enabling real-time predictions of lubrication systems. • A neural network approach is demonstrated, using independent models to predict each variable. • Neural network models trained using an OpenFOAM numerical model display a mean error of < 0.4%. • Once trained, the neural network models are ∼ 10 000 x faster than traditional numerical models. [ABSTRACT FROM AUTHOR]