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This paper explores the impact of MHD couple stress and slip velocity over a conical bearing in the presence of magnetic field. The flow is considered as incompressible. A uniform magnetic field is imposed perpendicular to the bearing along y -axis. The modified Reynolds equation is solved using appropriate boundary conditions in dimensionless form to find the pressure distribution which is then used to obtain the expression for load carrying capacity paving the way for the calculation of response time. Numerical computations of the results show that the MHD couple stress on the conical bearings indicates that enhances the pressure distribution, load carrying capacity and squeeze film time of the conical bearings. Further, decrease in these characteristics was observed for the increased values of slip velocity and cone angle. [ABSTRACT FROM AUTHOR]

In this research, the combined effect of magnetohydrodynamics (MHD) and slip velocity on squeeze film lubrication of long cylinders and infinite plates with couple stress fluid has been studied. Combining the Stokes couple stress theory and the Lorentz force theory yields analytical solutions for the modified Reynolds equation. Using the Reynolds equation, the mathematical expressions for squeeze film pressure, load-carrying capacity and squeeze film time are obtained. The pressure, load carrying capacity and squeeze film time increase with the combined effect of MHD, couple stress fluids and slip velocity. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical analysis of the effects of a magnetic field, couple stress fluid, and slip velocity on squeeze film lubrication between a sphere and a flat plate. The modified Reynolds equation is derived using Stokes micro continuum theory of couple stress fluids. The nondimensional governing equations of the flow model are solved analytically for pressure, load-carrying capacity and squeezing time. The results are graphically presented and analyzed for various parameters. The study shows that the couple stress parameter and magnetic field significantly enhance the film pressure, load-carrying capacity, and squeeze film time compared to the Newtonian and nonmagnetic cases. Also from the results, it is observed that the squeeze film properties can be significantly reduced by the effect of the slip parameter. [ABSTRACT FROM AUTHOR]

The current communication aims to discuss the influence of MHD slip velocity on curved circular and rough flat plate under the non-Newtonian fluid is considered. MHD momentum equation is reduced to ordinary differential equation and solved analytically. Christenson Stochastic theory is used to derive the radial and azimuthal surface roughness expression. From the Stochastic theory we derived non dimensional Reynolds equation also mathematical derivations for squeeze film pressure, load and squeezing time are derived analytically. Applied numerical method to illustrate pressure, load support & response time graphically. In contrast to the smooth case, the load-carrying capacity and response time for azimuthal (radial) roughness patterns are affected by the roughness parameter. Also the impact of MHD couple stress with slip velocity provides the rise of squeeze film attributes than the case of non-magnetic, Newtonian and smaller values of slip velocity. • MHD slip velocity impact on curved plates. • Christenson Stochastic theory for surface roughness analysis. • Analytical solutions for squeeze film attributes. • Numerical methods for graphical representation. • Influence of MHD couple stress on squeeze film. [ABSTRACT FROM AUTHOR]

In view of the large temperature rise and impact load of thrust bearings in the main shaft system of large wind turbines, this article takes the circular tilting pad thrust bearings in large wind turbines as the research object, and analyses the basic theory of bearing lubrication. The lubrication performance calculation model established for this bearing includes the Reynolds equation, energy equation, film thickness equation, and elastic deformation equation. Theoretically analysing and calculating the lubrication performance of the circular tilting pad thrust bearing, the key performance parameters have identified such as minimum film thickness (hmin), temperature rise (ΔT), power consumption (W), and flow rate (Q). The calculation results show that the eccentricity ratio has a significant impact on the lubrication performance of the circular tilting pad thrust bearing. When both radial and circumferential eccentricity ratios are around 0.5, the bearing exhibits a high temperature rise, leading to a potential risk of bearing burnout. The results also show that at a radial eccentricity ratio of approximately 0.54, the minimum film thickness reaches its maximum value of 10.34 μm. Similarly, at a circumferential eccentricity ratio of about 0.60, the minimum film thickness reaches its peak value of 21.89 μm. This indicates that the eccentricity ratio plays a crucial role in the lubrication performance. In addition, the lubrication performance of the bearing under varying loads has been calculated at a speed of 9.5 r/min. The results demonstrated that the applied load significantly impacts the thrust bearing's performance. The findings elucidate the critical role of considering the eccentricity ratio and operational external load during the bearing design process. This study validates the potential of replacing rolling bearings with sliding bearings in wind turbine main shafts. It also provides a theoretical reference for the future design of sliding bearings. [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]

A numerical investigation on the film cooling performance of a symmetrical turbine blade is carried out for reverse injection (RH), forward injection (FH), and opposite injection (OH) which combines forward and reverse injection holes. Another objective of this work is to study the effect of the distances between the injection holes, and three different distances are considered. Five configurations are computed for five blowing ratios. A coolant flow is injected through holes inclined at 110 and 70o for reverse and forward jets, respectively. The laterally averaged film cooling effectiveness is obtained using commercial software ANSYS-CFX. In addition, several velocity vectors and contours are presented for analyzing the thermal behavior. The numerical model is based on the Navier–Stokes equations and the Reynolds stress turbulence model (SSG-RSM). The obtained results enable one to choose configurations with high film cooling effectiveness for different blowing ratios. [ABSTRACT FROM AUTHOR]

In this work, the influence of magneto-rheological fluid embedded on journal bearings in the dynamic behavior of rotors is considered. The modified Reynolds equations for Bingham viscoplastic materials are used for calculation of the nonlinear hydrodynamic forces. Flexible rotors are modeled by the finite element method. The static weight of the rotor, unbalance and bearing hydrodynamic forces are included in the equations of motion. Non-linear hydrodynamic forces calculation depends on the relative positions of the journal bearings. The dynamic system response is computed by the Newmark method modified to obtain the calculation of the differential displacements and velocities for each time step. By incorporating the Newton-Raphson method the necessary corrections are included in the equations of motion. Time and frequency responses are presented for two of the case studies. The sudden elevation in oscillation magnitudes due to the oil whip phenomenon is not observed in the 1-un-up test after the application of electromagnetic induction on the MR fluid. Furthermore, the controlled variation in the viscosity of the MR fluid causes significant changes in the bearing movements, as demonstrated by the orbit graphs. [ABSTRACT FROM AUTHOR]

Aerodynamic noise resulting from the flow around cylinders is a significant engineering challenge in aviation and wind engineering. The phenomenon of alternating vortex shedding in the flow leads to vibration and noise generation. However, accurately describing both the flow field and the sound field is challenging due to the significant difference in magnitude between them. To tackle this issue, this work introduces the application of the spectral element method (SEM) and flow-acoustic monolithic simulation for solving the two-dimensional compressible Navier–Stokes equations at low Reynolds numbers. This study is to investigate the reduction of flow-induced noise through the implementation of slotting technology on a circular cylinder. This study focuses on examining two different slit width ratios, s/d = 0.15 and 0.25, with a slit angle of attack of 0°. A comparative analysis is conducted between a complete circular cylinder and a slotted circular cylinder. The findings indicate that the slotted cylinder exhibits reduced intensity of vortex shedding and an extended region of downstream vortex generation compared to the complete cylinder. Notably, when s/d = 0.25, the slotted cylinder demonstrates minimal noise generation. Even at s/d = 0.15, a significant reduction in flow-induced noise is observed. These results highlight the potential of utilizing slotting technology on cylinders to effectively mitigate aerodynamic noise. The application of SEM and flow-acoustic monolithic simulation shows their relevance in analyzing and designing noise mitigation techniques in aerodynamics. This work can develop innovative solutions to reduce noise and improve the performance of various applications in aviation and wind engineering. [ABSTRACT FROM AUTHOR]

This study delves into the dynamic behavior of ultra-high-speed rotor systems underpinned by helium hydrostatic gas bearings, with a focus on the impact of rotational velocity on system performance. We have formulated an integrative dynamic model that harmonizes the rotor motion equation with the transient Reynolds equation. This model has been meticulously resolved via the Finite Difference Method (FDM) and the Wilson-Θ technique. Our findings unveil intricate nonlinear dynamics, including 2T-periodic and multi-periodic oscillations, and underscore the pivotal role of first-order temporal fluctuations, which account for over 20% of the transient pressure at rotational speeds exceeding 95.0 krpm. Further, we have executed empirical studies to evaluate the system's performance in practical settings. It is observed that when the ratio of low-frequency to fundamental frequency approaches 0.3 and the amplitude ratio exceeds 3, the vigilant monitoring of system stability and reliability is imperative. Collective insights from both computational simulations and experimental studies have enriched our understanding of the dynamic attributes of ultra-high-speed rotor systems. These revelations are crucial for the advancement of more efficacious and resilient rotor systems designed for high-speed applications. [ABSTRACT FROM AUTHOR]

A hydrodynamic thrust bearing could be forced to operate in mixed lubrication regime under various circumstances. At this state, the tribological characteristics of the bearing could be affected significantly and the developed phenomena would have a severe impact on the performance of the mechanism. Until recently, researchers were modeling the hydrodynamic lubrication problem of the thrust bearings either with analytical or with numerical solutions. The analytical solutions are very simple and do not provide enough accuracy in describing the actual problem. To add to that, following only computational methodologies, can lead to time consuming and complex algorithms that need to be repeated every time the operating conditions change, in order to draw safe conclusions. Recent technological advances, especially on the field of computer science, have provided tools that enhance and accelerate the modeling of thrust bearings' operation. The aim of this study is to examine the application of Artificial Neural Networks as Machine Learning models, that are trained to predict the coefficient of friction for lubricated pad thrust bearings in mixed lubrication regime. The hydrodynamic analysis of the thrust bearing is performed by solving the Average 2-D Reynolds equation numerically. In order to describe the roughness of the profiles, both the flow factors suggested by N. Patir and H.S. Cheng (1978) and the model of J.A. Greenwood and J. H. Tripp (1970) are taken into consideration. Three lubricants, the SAE 0W30, the SAE 10W40 and the SAE 10W60, are tested and compared for a variety of operating velocities and applied coatings. The numerical analysis results are used as training datasets for the machine learning algorithms. Four different ML methods are applied in this investigation: Artificial Neural Networks (ANNs), Multi- Variable Quadratic Polynomial Regression, Quadratic SVM and Regression Trees. The coefficient of determination, R 2 is calculated and used to determine the most accurate ML method for the current study. The results showed that ANNs provide very good accuracy in the prediction of friction coefficient compared to the rest of the ML models discussed. [ABSTRACT FROM AUTHOR]

Fractured crystalline rocks have been chosen or are under consideration by several countries as host rock formations for deep geological repositories for spent nuclear fuel. In such geological formations, flow and solute transport are mostly controlled by a network of connected natural fractures, each of them being characterised by internal heterogeneity, also denoted as roughness. Fractures are, in turn, subject to variable load caused by various factors, such as the presence of thick ice sheets formed during glaciation periods. Understanding how coupled hydro-mechanical (HM) processes affect flow and transport at the scale of a single natural fracture is crucial for a robust parameterisation of large-scale discrete fracture network models, which are not only used for nuclear waste disposal applications but are also of interest to problems related to geothermics, oil and gas production or groundwater remediation. In this work, we analyse and model an HM experiment carried out in a single natural fracture and use the results of both, the experimental and the modelling work, to get insights into fundamental questions such as the applicability of local cubic law or the effect of normal load on channeling. The initial fracture aperture was obtained from laser scanning of the two fracture surfaces and an equivalent initial aperture was then defined by moving the two fracture surfaces together and comparing the results obtained using a Navier–Stokes based computational fluid dynamics (CFD) model with the experimental flowrate obtained for unloaded conditions. The mechanical effect of the different loading stages was simulated using a high-resolution contact model. The different computed fracture apertures were then used to run groundwater flow simulations using a modified Reynolds equation. The results show that, without correction, local cubic law largely overestimates flowrates. Instead, we show that by explicitly acknowledging the difference between the mechanical aperture and the hydraulic aperture and setting the latter equal to 1/5 of the former, cubic law provides a very reasonable approximation of the experimental flowrates over the entire loading cycle. A positive correlation between fluid flow channeling and normal load is also found. [ABSTRACT FROM AUTHOR]

Aiming at the compliant end face gas film seal structure, based on the linearized Boltzmann equation, the Poiseuille flow coefficient is introduced, and the generalized Reynolds equation and the sealing performance parameter solution formula considering the boundary slip flow effect are established. Through Newton–Raphson iterative calculation, the degree of influence of the slip flow effect under different working conditions is analyzed, and the internal relationship between structural parameters and sealing performance is compared. The results show that the slip flow effect can have a large impact on the pressure distribution in the fluid field close to the low-pressure side. Due to the existence of the step phenomenon of boundary velocity, it is not conducive to increasing the gas film opening force and controlling the mass leakage rate, but it can play a positive role in reducing the viscous friction power consumption. In the case of a smaller sealing gas film thickness and lower medium pressure, the slip flow effect is significant, which will have a greater impact on the sealing performance, and at this time, the slip flow effect can not be ignored. In addition, the change in seal structure parameters will also have a large impact on the sealing performance. With an increase in the wave foil thickness, the compliant end face evolves towards the rigid end face, the fluid wedge effect is weakened, and the gas film opening force and mass leakage rate are reduced. The stiffness-to-leakage ratio shows a strong nonlinear decreasing trend with an increase in the wave foil chord length and pitch, which eventually tends to a stable value. The results of this paper provide a theoretical basis for the matching design of the structural parameters of compliant end-face gas film seals under different service conditions. [ABSTRACT FROM AUTHOR]

In various systems of energy, such as turbo-machinery and viscous-lock system, squeeze film plays a crucial role for improving transport systems. The importance of the aforementioned applications led us to explore the physical behavior of Rabinowitsch fluid flow for several values of viscosity, Q ∈ [ 0 − 1 ] , load capacity (W ∗) , nonlinear factor, ω = [ − 2 × 1 0 − 4 , 0 , 2 × 1 0 − 4 ] , dimensionless film thickness (h ∗) , dimensionless radius of the capillary tube (R 0 ∗) , dimensionless thickness of porous pad (H 0 ∗ = 0 , 0. 1 , 0. 2), inner and outer radius ratio (Ω = 0 , 0. 2 , 0. 4) , roughness parameter (c ∗ = 0 , 0. 1 , 0. 2 , 0. 3 , 0. 4) through a squeeze film with two rough porous annular discs. Five-point Gauss quadrature integral formula has been used to examine the characteristics of annular discs, and small perturbation method has been used to discretize the governing Rabinowitsch fluid flow (RFF) equations. The modified Reynolds equation for rough, porous and viscosity change with film thickness is developed using Christensen's stochastic theory, modified Darcy's theory and the association between viscosity and film thickness agreement. The impacts of ω on the behavior of porosity and viscosity variability of RFF have been visually depicted in terms of film pressure, load capacity and squeeze reaction time of annular discs. It has been determined that for RFF with variable viscosity and roughness parameter on a porous media, the performance of the annular disks enhances for ω = − 2 × 1 0 − 4 (dilatant lubricant), and diminishes for ω = 2 × 1 0 − 4 (pseudo-plastic lubricant). It has been found that the film pressure in case of dilatant lubricant is increased by the influence of Rabinowitsch fluids on porous walls, but the behavior of pseudo-plastic lubricants has an opposite tendency relative to Newtonian lubricants. It has also been found that the impact of variability in porosity, roughness and viscosity diminishes the load-carrying capacity (LCC) with increased film thickness than the case of nonporous, smooth surface and constant viscosity of Rabinowitsch fluid. [ABSTRACT FROM AUTHOR]

Rotordynamic simulations with nonlinear hydrodynamic bearing forces require a solution of the Reynolds equation at every time step. As a computationally efficient alternative to the standard numerical methods, a semi‐analytical solution based on the scaled boundary finite element method (SBFEM) was developed recently. Through a discretization of the hydrodynamic pressure (dependent variable) along the circumferential but not the axial coordinate, the partial differential equation is transformed into a system of ordinary differential equations. This system of differential equations is referred to as SBFEM equation and can be solved exactly if the influence of shaft tilting is neglected. In common numerical models, this influence can be taken into account without difficulties, but as far as this semi‐analytical approach is concerned, shaft tilting complicates the equations substantially. Therefore, previous studies on the SBFEM solution of the Reynolds equation were conducted without consideration of this effect. The formulation presented in the work at hand no longer requires this simplification. The terms representing the influence of shaft tilting in the SBFEM equation are handled by the perturbation method. The pressure field is expressed by a series expansion, where the solution of order k$k$ correlates to the kth$k\mathrm{th}$ power of a perturbation parameter chosen proportional to the tilting angle. The differential equation governing the kth$k\mathrm{th}$ solution contains lower‐order solutions on its right‐hand side, implying a recursive computation of the series from lowest to highest order. A universal expression for the general solution is formulated, where only the coefficients and the maximum power of the axial coordinate differ for every k$k$. This allows the implementation of a general algorithm with no inherent limitation regarding the maximum order of perturbation. For verification, the pressure fields computed by the proposed method are compared to a numerical reference solution, showing that the series converges to the correct result for the investigated set of parameters. [ABSTRACT FROM AUTHOR]

For inherently compensated aerostatic bearings, the traditional modeling method of describing an air supply orifice with a nodal point results in computational errors when numerical discretization methods, such as the finite difference method, are used particularly for a small air-film thickness. To address this problem, this paper proposes an equivalent pressure-equalizing chamber model (EPECM) to consider the pressure depression around the orifice. First, numerical simulations of the circular centrally fed aerostatic thrust bearing (CCFATB) were conducted using computational fluid dynamics. The discharge coefficient and the radius of the pressure-depression region under various operation conditions were obtained. Subsequently, by combining these two key parameters, the EPECM was applied to analyze the static performances of the CCFATB and annular aerostatic thrust bearing (AATB). The air domain of the AATB was divided into non-uniform grids. The five-point difference scheme and nine-point difference scheme were adopted to solve the Reynolds equation respectively, and the computational results were compared. The proposed model and discretization method were verified by comparing the results with experimental and published data. It is found that the EPECM has a high computational accuracy and superior numerical iteration efficiency compared with the commonly used point-source assumption. The five-point difference scheme is able to deal with the non-uniform mesh model accurately. Moreover, the modified discharge coefficient and pressure-depression region radius calculated in this study provide useful data for performance analysis of inherently compensated air bearings. [Display omitted] • The computational error of the point-source assumption in the modeling of aerostatic bearings is studied. • An improved model is proposed to consider the pressure depression around the orifice. • 576 bearing models are established through CFD dynamic mesh method and the modified discharge coefficient and pressure-depression region radius are obtained. • High computational accuracy and superior numerical efficiency are achieved by using the improved model. [ABSTRACT FROM AUTHOR]

Porous aerostatic bearings and seals offer several advantages in precision engineering applications. The static performance of aerostatic elements, i.e., bearings and seals, is investigated both experimentally and numerically. This study presents a method, a test setup, and a measurement of the air gap pressure distribution with high spatial and temporal resolution. This study presents experimental and numerical results of the load capacity, air gap height, static stiffness, air consumption, and air gap pressure distribution. The experimental results are compared to a numerical model based on the modified Reynolds equation. Furthermore, boundaries for the operating parameter space of the investigated seal are determined by stiffness and leakage. The experimental results and the numerical model showed good correlation, providing corroborative evidence for the accuracy of the measurement setup and the feasibility of the pressure measurement method. [Display omitted] • Porous aerostatic seals and bearings are investigated under static conditions. • Experiment and model to obtain load capacity, stiffness, air gap height, and pressure. • A method and a robust test setup for measurement pressure distribution in an air gap. • Characterisation of operating domain of an aerostatic seal by leakage and stiffness. [ABSTRACT FROM AUTHOR]

Near-field ultrasonic levitation (NFUL) technology is increasingly attracting attention for its advantages of non-contact nature, compactness, and environmental friendliness. Nevertheless, the development of NFUL is hindered by challenges such as carrying capacity and stability. To date, most studies have focused on the static stability of NFUL, primarily through analysis of the restoring force. However, there remains a significant gap in the literature regarding the motion prediction of levitated objects, which is the focus of this paper. A numerical model coupling the levitated object and the squeeze film is established, and then, the Reynolds equation considering the motion parameters of the levitator is derived. Since the misalignment and inclination of the levitator are concurrent cases, its inclination needs to be considered in the film thickness expression. Subsequently, due to the introduction of an imaginary levitator with a groove, the eight-point discrete method is applied to solve the discontinuous film thickness problem. Thereupon, the pressure profile is obtained by determining the inclination angle of the levitator using the spline interpolation. The motion trajectory and frequency of the levitator are estimated utilizing the time-marching method and corroborated through experimental measurements. Both numerical and experimental results indicate that the motion frequency initially increases sharply with rising the preset eccentricity, before gradually diminishing. Additionally, higher motion frequencies are observed at larger amplitudes of the vibrator and lower weights of the levitator. Comparatively, the motion frequency of a levitator under a flexible vibrator is also found to be higher than that under a rigid vibrator. [ABSTRACT FROM AUTHOR]

The effect of surface roughness, magnetic field, and couple stress on the performance of secant slider bearing is studied in this paper. The effectiveness of the bearing is assessed by using a couple stress liquid as the lubricant in the process. Because of microstructural impacts, couple stress fluids have distinctive rheological characteristics. These features have the potential to make a major impact on the bearing's performance. The novel aspect of this study is that the roughness of the secant slider is taken into consideration. The modified Reynolds equation is derived using Christensen's stochastic theory for roughness. Here, both transverse and longitudinal roughness patterns are considered. The analytical solutions are obtained for steady-state pressure, load-carrying capacity, film stiffness, and damping coefficient. The results are presented for various parameters through graphs and tables. The combined effect of the magnetic field and couple stress is significant on bearing characteristics. It is noticed that the bearing features increase with the longitudinal roughness parameter, and the reverse phenomenon is observed with the transverse roughness parameter. When a transverse roughness pattern is assumed on a secant slider bearing, characteristics like pressure, load, stiffness of the film, and damping coefficient increase significantly. [ABSTRACT FROM AUTHOR]

The modeling of engineering systems considering fractional approach configures a tendency as due to the generalization of traditional models that use integer order and to the number of applications in different science fields that can benefit from this approach. The present contribution aims to analyze the physical parameters of a near-field acoustic levitation system, as described by the Reynolds equation, and to evaluate the influence of fractional orders on the obtained profiles. For this purpose, both time and space fractional derivatives found in the fractional differential model are approximated using Caputo and Grünwald–Letnikov formulas, respectively. The discretized nonlinear algebraic system is solved considering the Newton method. The proposed methodology was able to solve the time–space fractional near-field acoustic levitation model for both integer and fractional orders. The performed sensitivity analyses demonstrated the influence of the model parameters and the fractional orders on the pressure fields and levitation force. Physically, for a squeeze film levitation system, the increase of the squeeze number is necessary for levitation purposes. In addition, the maximum achievable levitation capacity of a squeeze film levitation system is determined by the excitation amplitude. As expected, the levitation domain is reduced as the mass increases and the reduction rate of the integer model is higher than the one of the fractional order. In this case, for mass bigger than 1.629 Kg, the levitation domain is larger for the fractional order model. It is worth mentioning that the proposed methodology can be used to solve other dynamic systems modeled by time–space fractional differential equations. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to investigate the dynamic characteristics of a high-speed mechanical seal by considering the flow regime, cavitation phenomenon and inertia effect. Design/methodology/approach: Based on the high-speed conditions of a mechanical seal with a low-viscosity fluid, a multi-factor coupled lubrication model of a mechanical seal is established. The perturbation Reynolds equation set is derived using the perturbation method, and the effects of turbulent flow and inertia on sealing performance are discussed. Findings: The results indicate that turbulence significantly influences the dynamic characteristics of low-viscosity fluids under high-speed conditions. Originality/value: The results of the dynamic characteristics presented in this study are expected to provide guidance for the design of mechanical seals. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to evaluate three types of textures designed to enhance the tribological performance of static and dynamic pressure thrust bearings. Design/methodology/approach: To explore the effects of different types of textures on tribological performance, the Reynolds equation is modified using lubrication theory and computational fluid dynamics methods while considering the influence of cavitation and turbulence on the physical field. In addition, the tribological performance is optimized through an improved selection algorithm based on Pareto envelope (PESA). Findings: The results indicate that textured thrust bearings exhibit superior tribological performance compared to untextured ones. The circular texture outperforms other textures in terms of load-bearing and friction performance, with improvements of approximately 28.8% and 18.9%, respectively. In addition, the triangular texture exhibits the most significant temperature improvement, with a reduction of approximately 1.93%. Originality/value: The study proposes three types of textures and evaluates the friction performance of thrust bearings by modifying the Reynolds equation. In addition, the optimal texture design is determined using an improved selection algorithm based on PESA. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to study the impact of different types of textures on the friction lubrication performance of cylindrical roller bearings. Design/methodology/approach: In the present study, the composite texture hydrodynamic lubrication model that takes into account the effects of surface roughness is established, and the Reynolds equation for the oil film is numerically solved using the finite difference method. The study investigates the oil film carrying capacity and maximum pressure of bearings under two different arrangements of four composite textures and conducts a comparative analysis of the oil film characteristics under various texture parameters and surface roughness levels. Findings: When the roughness of the inner texture surface and the contact surface are equal, the bearing capacity of the composite texture is intermediate between the two textures. The impact trend of surface roughness on fluid dynamic pressure effects varies with the type of composite texture; the internal roughness of the texture affects the micro-hydrodynamic pressure action. Composite textures with different depths exhibit improved bearing capacities; elliptical cylindrical parallel and elliptical hemispherical parallel textures perform better when their area densities are similar, while other types of composite textures show enhanced bearing performance as the ratio of their area densities increases. Originality/value: This paper contributes to the theoretical investigations and analyses on designing the textured rolling bearings with high lubrication performance. Peer review: The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-02-2024-0050 [ABSTRACT FROM AUTHOR]

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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 article investigates the influence of textured shapes and electrorheological fluid (ERF) behavior on slot entry hybrid conical journal bearing system (HCJBs). The slot entry restrictor is used as a compensating element to supply the lubricant in the clearance space. Spherical, rectangular, and triangular textured shapes over the surface of conical bearings have been employed. Furthermore, the intelligent properties of ERF on the behavior of textured slot entry HCJBs have been analyzed. The finite element method (FEM) and the successive iteration-based Gauss-Seidel method have been used to solve the modified Reynolds equation. The results drawn from this study show different influences on the bearing performance for different textured shapes. Using textured surfaces and ERF improves the minimum fluid film thickness, stability, and bearing stiffness compared to the non-textured bearing. [ABSTRACT FROM AUTHOR]

Squeeze film dampers are used to reduce vibration in aircraft jet engines supported by rolling element bearings. The underlying physics of the squeeze film dampers has been studied extensively over the past 50 years. However, the research on the SFDs is still ongoing due to the complexity of modeling of several effects such as fluid inertia and the modeling of the piston rings, which are often used to seal SFDs. In this work, a special experimental setup has been designed to validate the numerical models of SFDs. This experimental setup can be used with various SFD geometries (including piston ring seals) and simulate almost all conditions that may occur in an aircraft jet engine. This work also focuses on the inertia forces of the fluid. The hydrodynamic pressure distribution of a detailed 3D-CFD model is compared with the solution of the Reynolds equation including inertia effects. Finally, the simulation results are compared with experimental data and good agreement is observed. [ABSTRACT FROM AUTHOR]

Much research and practical experience have shown that the utilization of textures has an enhancing effect on the performance of dynamic seals and the dynamic pressure lubrication of gas bearings. In order to optimize the performance of floating ring seals, this study systematically analyzes the effects of different texture shapes and their parameters. The Reynolds equation of the gas is solved by the successive over-relaxation (SOR) iteration method. The pressure and thickness distributions of the seal gas film are solved to derive the floating force, end leakage, friction, and the ratio of buoyancy to leakage within the seal. The effects of various texture shapes, including square, 2:1 rectangle, triangle, hexagon, and circle, as well as their parameters, such as texture depth, angle, and area share, on the sealing performance are discussed. Results show that the texture can increase the air film buoyancy and reduce friction, but it also increases the leakage by a small amount. Square textures and rectangular textures are relatively effective. The deeper the depth of the texture within a certain range, the better the overall performance of the floating ring seal. As the texture area percentage increases, leakage tends to increase and friction tends to decrease. A fractal roughness model is developed, the effect of surface roughness on sealing performance is briefly discussed, and finally the effect of surface texture with roughness is analyzed. Some texture parameters that can significantly optimize the sealing performance are obtained. Rectangular textures with certain parameters enhance the buoyancy of the air film by 81.2%, which is the most significant enhancement effect. This rectangular texture reduces friction by 25.8% but increases leakage by 79.5%. The triangular textures increase buoyancy by 28.02% and leakage increases by only 10.08% when the rotation speed is 15,000 r/min. The results show that texture with appropriate roughness significantly optimizes the performance of the floating ring seal. [ABSTRACT FROM AUTHOR]

This paper presents a nonstandard numerical manifold method (NMM) for solving Burgers' equation. Employing the characteristic Galerkin method, we initially apply the Crank–Nicolson method for temporal discretization along the characteristic. Subsequently, utilizing the Taylor expansion, we transform the semi-implicit formula into a fully explicit form. For spacial discretization, we construct the NMM dual-cover system tailored to Burgers' equation. We choose constant cover functions and first-order weight functions to enhance computational efficiency and exactly import boundary constraints. Finally, the integrated computing scheme is derived by using the standard Galerkin method, along with a Thomas algorithm-based solution procedure. The proposed method is verified through six benchmark numerical examples under various initial boundary conditions. Extensive comparisons with analytical solutions and results from alternative methods are conducted, demonstrating the accuracy and stability of our approach, particularly in solving Burgers' equation at high Reynolds numbers. [ABSTRACT FROM AUTHOR]

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]

Micro/nanoscale lubrication must take into account the fractal profile of the shaft and bearing surfaces. A new fractal rheological model is proposed to describe the properties of the non-Newtonian fluid, and a fractal variational principle is established by the semi-inverse method, and finally the Lagrange multipliers can be found in the obtained variational formulation. This work provides a new fractal approach to nano/micro lubrication. [ABSTRACT FROM AUTHOR]

Bubble inclusion in the tribo-pair leads to two-phase fluid lubrication. Upon the initial introduction of air bubbles to the tribo-pair, it can lead to instability in the operational state. A numerical model is formulated by coupling the fluid Reynolds equation, bubble dynamics equation, and rotor dynamics equation. Various parameters, such as hydrodynamic pressure, fluid carrying capacity, rotor trajectory, and equilibrium position, are employed to characterize the impact of operational and fluid interface parameters on the bubble entrainment process. The findings reveal that the hydrodynamic pressure plays a crucial role in establishing the correlation between velocity and fluctuations in kinetic parameters. Surface tension predominantly influences bubbles within the dispersion region, while surface dilatational viscosity affects the entire domain. Lower surface dilatational viscosity or neglecting surface tension can trigger larger fluctuations in the rotor trajectory. Changes in liquid-phase viscosity result in fluctuations in bubble behavior and dynamics parameters, influenced by the equilibrium position and the effect of hydrodynamic pressure. Higher initial gas-phase volume fractions lead to a more pronounced reduction in fluid-carrying capacity and increased system instability. [ABSTRACT FROM AUTHOR]

When studying the characteristics of aerostatic bearings with orifices by solving the Reynolds equation, it is usually assumed that the discharge coefficient is a constant of 0.8,which may affect the accuracy of solving the Reynolds equation. A method which combined Fluent and Reynolds equation was proposed to obtain the discharge coefficient in the aerostatic thrust bearings with inherent orifices. The discharge coefficients were calculated by comparing the mass flow rate obtained by FLUENT and Reynolds equation simulations. The influence of parameters such as gas film thickness, gas supply pressure,and orifice diameter on the orifice coefficient was analyzed. The results indicate that the discharge coefficient increases first and then decreases with the increase of film thickness,decreases with the increase of gas supply pressure,and increases with the increase of orifice diameter. However, the discharge coefficient is not sensitive to changes in bearing radius and orifice length. The bearing capacity from solution of Reynolds equation with the discharge coefficient obtained by this solution method is agreement with that from FLUENT, verifying the correctness and feasibility of this solution method. [ABSTRACT FROM AUTHOR]

The Reynolds equation was modified in response the problem that the continuity equation used in the derivation of the conventional master Reynolds equation was not applicable at the throttle bore of a hydrostatic gas bearing. Based on the angle-preserving transformation method, Newton's iteration method, finite difference method and relaxation iteration method, the modified Reynolds equation was calculated for the region of the bearing gas film flow field, and the distribution of gas film pressure along the circumferential direction at the apex angle of the orifice distribution cone was obtained under different air supply pressures. The influence of air supply pressure and radial eccentricity on the radial load capacity and axial load capacity of aerostatic air spherical bearings was analyzed. The results show that the radial bearing capacity and axial bearing capacity of aerostatic spherical air bearings are affected by the coupling of static pressure effect and dynamic pressure effect. The greater the air supply pressure, the greater the radial bearing capacity and axial bearing capacity,and the greater the air consumption. The greater the radial eccentricity, the greater the radial bearing capacity and axial bearing capacity,and the radial eccentricity has little effect on the gas consumption.The larger the diameter of the orifice, the greater the radial bearing capacity, axial bearing capacity and air consumption. [ABSTRACT FROM AUTHOR]

In order to study the effects of the distribution,number,density,placement angle and depth of different shapes of texture on the bearing performance of the misaligned gas foil thrust bearing,the Reynolds equation for the gas foil thrust bearing was solved by combining Successive Over Relaxation (SOR) and the finite difference method (FDM), and the load carrying capacity and frictional moment of the bearing were obtained by MatLab simulation under different texture parameters.The results show that the bearing load carrying capacity is significantly increased when the texture is distributed at the junction of the base area and the wedge area of the thrust bearing compared to other distribution methods. The load carrying capacity and frictional moment of the bearing increase first and then decrease with the increase of the proportion of micro-texture.The bearing performance is best improved when the maximum cross section of different shaped texture is placed along the radial direction of the thrust bearing. The micro-texture can improve the bearing performance only when its depth reaches a certain range.It is found that there exists optimal number, density,and depth of micro-textures that can make the thrust bearing have a higher bearing load capacity at a smaller friction torque. Compared to the bearings without texture, the elliptical micro texture with optimal micro-texture parameters can increase the load carrying capacity by 41.22% and reduce the friction torque by 0.81%. [ABSTRACT FROM AUTHOR]

In order to explore the influence of the structural parameters of the split type carbon ring seal on the radial deformation of the sealing surface,the numerical calculation was used to solve the pressure control Reynolds equation to obtain the gas film pressure. The fluid-solid thermal coupling simulation was conducted in combination with the finite element analysis software to explore the influence of different structural parameters on the radial deformation of the carbon ring under specific working conditions,and the radial deformation characteristics of the main sealing surface was analyzed. The results show that the installation position of the anti-rotation pin has the greatest influence on the radial deformation of the carbon ring, and the radial deformation can be reduced by selecting the appropriate installation position. When the external convex structure is uneven and the ratio of the center angle is large, the radial deformation is small. The larger the ratio of the lap joints on both sides, the smaller the radial deformation. The selection of tension spring and compression spring has little influence on the radial deformation of carbon ring.The larger the spring pressure, the smaller the radial deformation. However, when the spring pressure is too high,it can easily lead to increased wear, fracture of the carbon ring,and even the failure of seal. The refore, appropriate spring pressure should be selected based on actual working conditions. The research results provide a reference for the structural optimization design of split carbon ring seals. [ABSTRACT FROM AUTHOR]

This paper presents the results of extensive testing of four recently proposed algebraic laminar-turbulent transition (LTT) models, which are significantly more computationally effective than differential models, while being potentially equally accurate. The models chosen for evaluation, namely, SST KD, SST kγ, SST alg-γ, and SA BCM, are implemented in the in-house code NTS and verified by comparing the obtained results with those published by the models' authors. The experimental database used for the evaluation of the models includes transitional boundary layers at different free-flow turbulence intensities with and without the pressure gradient, four airfoil flows with different LTT scenarios, and a tandem of two airfoils. It is found that at low levels of turbulence, the results of the SA BCM and SST kγ models may depend on the initial approximation, which does not allow them to be recommended for engineering applications. The best results, comparable in accuracy to those of differential models, are obtained using the SST alg-γ model. [ABSTRACT FROM AUTHOR]

The longevity of prosthetic hip implants is significantly influenced by wear. Surface textures of various length scales can reduce the friction coefficient and wear of lubricated bearing surfaces. The optimization of multiscale texture parameters, aimed at maximizing lubricant film thickness, was achieved through hydrodynamic lubrication simulations that solve the Reynolds equation with a mass-conserving cavitation model under various operating conditions. The outcomes indicate that adding "interstitial" texture features to a pattern of microscale texture features can further increase the lubricant film thickness. Additionally, the lubricant film thickness increases as the interstitial texture feature aspect ratio and texture density decrease. Pin-on-disc experiments align with simulation findings, demonstrating that multiscale texturing with ultra-fast laser ablation on Ti6Al4V discs significantly improves wettability and reduces the friction coefficient of ultra-high molecular weight polyethylene pins when compared to untextured and microscale textured surfaces. The multiscale surface texturing also changes the evident wear mechanisms on the pins, reducing the incidence of abrasive scratches and adhesive wear compared to both untextured and just microscale textured surfaces. [ABSTRACT FROM AUTHOR]

We proposed a numerical method to investigate the thermo-fluid–structural coupled characteristics of a mechanical seal of a reactor coolant pump (RCP), especially during extended loss of AC power (ELAP) operation. We developed a finite element program for the general Reynolds equation, including the turbulence effect to calculate the pressure, opening force, and leakage rate of fluid lubricant and the two-dimensional energy equation to calculate the temperature distribution of the fluid lubricant. We verified the accuracy of the developed program by comparing the simulated temperature distribution and leakage rate of this study with those of previous research. Heat conduction and elastic deformation due to pressure and temperature changes at the seal structure were analyzed using an ANSYS program. The results showed that temperature more significantly affected the elastic deformation of the seal structure near clearance than pressure both under normal and ELAP operating conditions. High temperature and pressure of the coolant under ELAP operating conditions deform the seal structure, resulting in a much smaller clearance of the fluid film than normal operating condition. However, even with a small clearance under ELAP operation, the leakage rate slightly increases due to the high internal pressure of the coolant. This research will contribute to the development of robust mechanical seals for RCPs by accurately predicting the characteristics of mechanical seals, especially when the RCP is operating under ELAP. [ABSTRACT FROM AUTHOR]

In this work, a new method to solve the Reynolds equation including mass-conserving cavitation by using the physics informed neural networks (PINNs) is proposed. The complementarity relationship between the pressure and the void fraction is used. There are several difficulties in problem solving, and the solutions are provided. Firstly, the difficulty for considering the pressure inequality constraint by PINNs is solved by transferring it into one equality constraint without introducing error. While the void fraction inequality constraint is considered by using the hard constraint with the max-min function. Secondly, to avoid the fluctuation of the boundary value problems, the hard constraint method is also utilized to apply the boundary pressure values and the corresponding functions are provided. Lastly, for avoiding the trivial solution the limitation for the mean value of the void fraction is applied. The results are validated against existing data, and both the incompressible and compressible lubricant are considered. Good agreement can be found for both the domain and domain boundaries. [ABSTRACT FROM AUTHOR]

Traditional oil seals are insufficient for the high-speed and bi-directional rotation of new energy electric vehicles. Therefore, we developed a Python program focusing on micro-groove pump seals and examined the unexplored non-contact oil–air biphasic internal end-face seals. Real gas effects were described using the virial and Lucas equations. We introduced an oil–air ratio to determine the equivalent density and viscosity of the two-phase fluid in the seal. Furthermore, we solved the compressible steady-state Reynolds equation using the finite difference method. Analysing the seal's pumping mechanisms and the effects of operating parameters on sealing performance, we assessed 17 types of hydrodynamic grooves. The results demonstrate that inverse fir tree-like grooves perform well under typical sealing conditions. Under the conditions given in this study, the pumping rate of the optimal groove type compared to other groove types even reached 633.54%. In the oil–air biphasic state, the micro-groove pump seal exerts significant dynamic pressure on the sealing surface. Seal opening force increases with rotational velocity, oil–air ratio, and inlet pressure but decreases with temperature. The pumping rate first increases and then decreases with rotational velocity, increases with oil–air ratio and temperature, and then decreases with inlet pressure. Some special working points require consideration in sealing design. Our results provide insights into designing micro-grooved pumping seals for new energy electric vehicles. [ABSTRACT FROM AUTHOR]

Local wellposedness for a nonlinear parabolic-hyperbolic coupled system modeling Micro-Electro-Mechanical System (MEMS) is studied. The particular device considered is a simple capacitor with two closely separated plates, one of which has motion modeled by a semilinear hyperbolic equation. The gap between the plates contains a gas and the gas pressure is taken to obey a quasilinear parabolic Reynolds' equation. Local-in-time existence of strict solutions of the system is shown, using well-known local-in-time existence results for the hyperbolic equation, then Hölder continuous dependence of its solution on that of the parabolic equation, and finally getting local-in-time existence for a combined abstract parabolic problem. Semigroup approaches are vital for the local-in-time existence results. [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 effect of fluctuating coagulation on particle distribution in multiphase turbulence of nanoparticles was studied based on the Reynolds averaged equation of turbulence flow and the general dynamic equation of particles. A one-order closed model was proposed to relate the fluctuating coagulation term to the average particle size distribution function for closing the particle equation. The proposed model and equations were applied to a turbulent jet flow using the k-ε turbulent model and the Taylor-series expansion moment method. The results showed that there is a difference in the values of particle number density M0, geometric average diameter dpg and geometric standard deviation σg of particle diameter with and without considering fluctuating coagulation. Larger Damkohler number leads to smaller M0, higher particle polydispersity M2, larger dpg and σg. Along the x direction of the flow, M0 decreases, while M2, dpg and σg increase. From the centerline to the outer edge of the jet, M0, M2 and dpg decrease, while σg increases first and then decreases. Finally, the further research that can be carried out has been proposed. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to study the influence of cylindrical texture parameters on the lubrication performance of static and dynamic pressure thrust bearings (hereinafter referred to as thrust bearings) and to optimize their lubrication performance using multiobjective optimization. Design/methodology/approach: The influence of texture parameters on the lubrication performance of thrust bearings was studied based on the modified Reynolds equation. The objective functions are predicted through the BP neural network, and the texture parameters were optimized using the improved multiobjective ant lion algorithm (MOALA). Findings: Compared with smooth surface, the introduction of texture can improve the lubrication properties. Under the optimization of the improved algorithm, when the texture diameter, depth, spacing and number are approximately 0.2 mm, 0.5 mm, 5 mm and 34, respectively, the loading capacity is increased by around 27.7% and the temperature is reduced by around 1.55°C. Originality/value: This paper studies the effect of texture parameters on the lubrication properties of thrust bearings based on the modified Reynolds equation and performs multiobjective optimization through an improved MOALA. [ABSTRACT FROM AUTHOR]

Purpose: To guide the stable radius clearance choice of water-lubricated bearings for single screw compressors, this paper aims to analyze the effects of turbulence and cavitation on bearing performance under two conditions of specified external load and radius clearance. Design/methodology/approach: A modified Reynolds equation considering turbulence and cavitation is adopted, based on the Jakobsson–Floberg–Olsson boundary condition, Ng–Pan model and turbulent factors. The equation is solved using the finite difference method and successive over-relaxation method to investigate the bearing performance. Findings: The turbulent effect can increase the hydrodynamic pressure and cavitation. In addition, the turbulent effect can lead to an increase in the equilibrium radius clearance. The turbulent region exhibits a higher load capacity and cavitation rate. However, the increased cavitation negatively impacts the frictional coefficient and end flow rate. The impact of turbulence increases as the radius clearance decreases. As the rotating speed increases, the turbulence effect has a greater impact on the bearing characteristics. Originality/value: The research can provide theoretical support for the design of water-lubricated journal bearings used in high-speed water-lubricated single screw compressors. Peer review: The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-01-2024-0029/ [ABSTRACT FROM AUTHOR]