The Morton effect (ME) occurs when a bearing journal experiences asymmetric heating due to synchronous vibration, resulting in thermal bowing of the shaft and increasing vibration. An accurate prediction of the journal's asymmetric temperature distribution is critical for reliable ME simulation. This distribution is strongly influenced by the film thermal boundary condition at the pad inlets. Part I utilizes machine learning (ML) to obtain a two-dimensional radial and axial distribution of temperatures over the leading-edge film cross section. The hybrid finite volume method (FVM)—bulk flow method of Part I eliminated film temperature discontinuities and is utilized in Part II for improving accuracy and efficiency of ME simulation.

Uncertainty in mixing coefficients (MCs) for estimating pad leading-edge film temperature in tilt pad journal bearings reduces the reliability of predicted characteristics. A three-dimensional hybrid between pad (HBP) model, utilizing computational fluid dynamics (CFD) and machine learning (ML), is developed to provide the radial and axial temperature distributions at the leading edge. This provides an ML derived, two-dimensional film temperature distribution in place of a single uniform temperature. This has a significant influence on predicted journal temperature, dynamic coefficients, and Morton effect response. An innovative finite volume method (FVM) solver significantly increases computational speed, while maintaining comparable accuracy with CFD. Part I provides methodology and simulation results for static and dynamic characteristics, while Part II applies this to Morton effect response.

When simulating elastohydrodynamic lubrication, two main approaches are usually followed to predict the pressure and fluid film thickness distribution throughout the contact. The conventional approach relies on the Reynolds equation to describe the thin lubricant film, which is coupled to a Boussinesq description of the linear elastic deformation of the solids. A more accurate, yet a time-consuming method is the use of computational fluid dynamics in which the Navier–Stokes equations describe the flow of the thin lubricant film, coupled to a finite element solver for the description of the local contact deformation. This investigation aims at assessing both methods for different lubrication conditions in different elastohydrodynamic lubrication (EHL) regimes and quantify their differences to understand advantages and limitations of both methods. This investigation shows how the results from both approaches deviate for three scenarios: (1) inertial contributions (Re > 1), i.e., thick films, high speed, and low viscosity; (2) high shear stresses leading to secondary flows; and (3) large deformations of the solids leading to inaccuracies of the Boussinesq equation.

A mathematical modeling approach to determine fluid film thickness on the vane tip in a vane pump transmission is developed. The transmission is based on a double-acting vane pump with an additional output shaft coupled to a floating ring. Owing to the floating ring design, the internal viscous friction helps to drive the output shaft, whereas the friction is turned into heat in a conventional vane pump. To study the mechanical efficiency, it is crucial to investigate the fluid film thickness between the vane tip and the ring inner surface. The modeling approach in this study takes the interactions between vane radial motion and chamber pressure dynamics into consideration, without using a computational fluid dynamics approach. The lubrication on the vane tip is considered as elasto-hydrodynamic lubrication and the fluid film thickness calculation is based on the Hooke lubrication diagram. Results show that the developed simulation model is capable of revealing the fluid film thickness change and vane radial motion in different operation regions. Sensitivity studies of several parameters on the minimum fluid film thickness are also presented.

Hydrostatic worm-rack-drive has obvious advantages on large-sized machine tools, and its performance is significantly affected by pitch errors. This paper theoretically researches the axial static and dynamic characteristics of hydrostatic worm-rack-drive, including the effects of the amplitude, period, and phase of pitch errors. Based on the expanded view of the helicoid of threads, a numerical calculation method is implemented where the Reynolds’ equation and flow continuity equation are solved simultaneously. The influence rule of pitch errors on pocket pressure, flow, axial fluid-film force, axial stiffness coefficient, and axial damping coefficient are discussed in detail, for providing beneficial guidance for the design and performance optimization of hydrostatic worm-rack-drive.

To improve the performance accuracy of a conical journal bearing system, the surface error needs to be considered in the analysis since a tiny difference in dimensional values can alter the performance; the consideration of surface error may degrade the performance behavior of bearing. However, a better way to overcome such degradation may be to make use of magnetohydrodynamics (MHDs) of fluid. Therefore, the present work is planned to investigate the impact of taper error and MHD lubricant in recessed conical hybrid journal bearing. In this article, the Reynolds equation is derived under stated assumptions along with frictional power loss expression and finally solved using the finite element analysis, Newton–Raphson method, and generalized minimum residual method. The conducted research helped in determination of optimum values of recess width, land width ratio, and restrictor design parameter, and also obtaining the results corresponding to distinct performance indices. The outcome of these results may inspire practicing designers for the development of better tribo components.

This paper introduces a concise data set formulation for efficient modeling of dynamically loaded conformal elastohydrodynamic lubrication (EHL) problems. The data set represents the structural elasticity of the bearing members and is constructed independently of the lubricant film model. Data set construction involves modification of a previously published mode-based EHL formulation such that the resulting structural information is insensitive to changes in finite-element mesh density and thus to the modeling process itself. Curve-fitted expressions of modal information are introduced for elastic structures, which otherwise would normally be represented by large structural matrices. A data set is formulated for the sample case of a dynamically loaded big-end connecting-rod bearing, and the resulting bearing performance agrees well with previously published node- and mode-based EHL methods.

This paper presents the performance behaviors (coefficient of friction, minimum film thickness, and pressure distributions) of a fluid film thrust bearing using a newly conceived micro-texture on pads. In the numerical investigation, the Reynolds equation has been discretized using the finite element formulation followed by the solution of algebraic equations employing the Fischer-Burmeister-Newton-Schur (FBNS) algorithm, which satisfies the mass-conservation phenomenon arising due to the commencement of cavitation in the lubricating film. The effects of parameters (micro-texture/pocket depth, circumferential/radial length of micro-texture and pocket, etc.) of new texture on the performance behaviors of the thrust bearing have been explored and presented herein for the range of input data. It has been found that the minimum film thickness has increased up to 48%, and the friction coefficient reduced up to 24% in comparison to conventional plain pad case.

There exist laminar and turbulent flow in the inner and outer fluid film of the hybrid floating ring bearing at high speed. The finite element method (FEM) and finite difference method (FDM) are used to solve the thermohydrodynamic (THD) lubrication model within the laminar and turbulent mixed flow regime which governs the pressure, temperature, viscosity, and Reynolds number of the two-layer fluid films together for a type of the journal hybrid floating ring bearing with deep/shallow pockets. The static and dynamic characteristics are analyzed including the load capacity, the friction moment, the volume flowrate, the stiffness, and damping coefficients with consideration of the mixed flow and thermal effect based on the floating ring balance. The unitized kinematic model of the shaft and floating ring is proposed to deduce the instability criteria and calculate the threshold rotational speed of a rigid Jeffcott rotor system supported on two hybrid floating ring bearings by the Routh–Hurwitz method. The results present that there are non-uniform pressure and temperature profile within the fluid film field, and the laminar flow and turbulent flow appear at certain positions of film through theory and experiment, separately. The mixed flow effect promotes the bearing load capacity and the friction moment at high speed and eccentricity, and the system threshold speed drops within the mixed flow regime. Therefore, the thermal effect and mixed flow existing in the fluid film should be considered into the lubrication analysis for the floating ring bearing.

The performances of the tribo-pairs are greatly influenced by introducing the grooved surfaces. Developments of the newer type of lubricants have made a great impact on the performance of fluid film bearings. This article investigates the non-Newtonian behavior of electrorheological lubricant on the performance of grooved hybrid spherical journal bearing. The effect of different arrangements of grooves, i.e., partially grooved or fully grooved on the bearing surface, has been studied. The finite element method is used to numerically simulate the results. Furthermore, a parametric study is performed for optimizing the groove attributes. The present work demonstrates that the different grooved arrangements have a substantial influence on the bearing performance. It is revealed that the provision of grooves on the bearing surface decreases frictional losses and enhances the stiffness coefficients of the bearing. Furthermore, numerically simulated results indicate that the electrorheological lubricant enhances the value of minimum fluid film thickness and the stiffness coefficients ( S ¯ x x a n d S ¯ y y ) of spherical hybrid journal bearing. Improved bearing performance can be achieved by using the optimized grooved attributes together with the electrorheological lubricant.

The position of fluid film in journal bearing will change while the journal moving in bearing, which can be named fluid film boundary migration (FFBM). It is usually ignored in the calculation of linear dynamic coefficients. While, the errors brought by this neglection was not ever investigated in detail. In this paper, the influence of FFBM on bearing dynamic coefficients and rotor system dynamic behaviors are investigated. A new perturbation-based model is proposed to take the FFBM into account by modifying the boundary conditions of governing equations. It is then verified by the experimental results and analytical results from previous research. Furthermore, the effects of FFBM on stiffness and damping in two typical journal bearings are investigated. The result indicates that the FFBM has a significant influence on dynamic coefficients of full circular journal bearing but little impact on journal bearing with axial grooves. Moreover, it affects the stiffness and damping more significantly in the cases of large length-to-diameter ratios or small eccentricity ratios in full circle bearing. Finally, the dynamical behavior of a rotor-bearing system with considering the FFBM is also investigated. The result shows that the FFBM of oil film has remarkable influences on the instability threshold and imbalance responses of the rotor system, which should not be ignored. The conclusions obtained in this research are expected to be helpful for the design of full circular journal bearings or rotor-bearing systems.

To compensate for an extremely heavy journal, jacking pockets can be added to the surface of pads in fluid film bearings. Jacking pockets can range in size and shape and will have an influence on the hydrodynamic performance of the bearing. Computational fluid dynamics (CFD) was used to better understand the influence of the geometry of a rectangular/stadium-shaped, jacking pocket on the performance of bearings. First, the influence of the pocket depth on the pressure profile of the bearing was investigated. A varying profile occurred with jacking pocket depths less than 6.6 × C b . After this threshold, the pocket depth ceased to have an influence on the pressure profile. A second study examined the circumferential length of the pocket, and the pressure profile was found to approach the smooth case as the pocket circumferential length decreased. Response surface models were created to map the influence of the jacking pocket geometry on the journal location in the bearing, power loss, and stiffness characteristics of the bearing. This is the first study on influence of the geometry of a jacking pocket on the operation and linear stiffnesses of the bearing in fluid film journal bearings.

To harness higher axial load capacity, a larger cone angle is used in conical bearings, resulting in an increase in the surface area which in turn increases the frictional power loss. The use of microgrooves in journal bearing helps in controlling this loss. Therefore, the present work is aimed to analyze conical hybrid journal bearing (i.e., combination of hydrostatic and hydrodynamic modes of operation) consisting of microgrooves along with shear thinning and piezo-viscous behavior of the lubricant. In this study, the microgroove attributes have been optimized by obtaining the solution of a Reynolds equation using finite element method and generalized minimum residual scheme (GMRES). These optimized groove attributes are used for numerically simulating the performance of the conical bearings. It has been observed that the best features of microgrooves and shear thinning behavior of the lubricant can be extracted to achieve better performance of the bearings. The results presented in this study are believed to be beneficial to the bearing designers and practising lubrication engineers.

Numerical and experimental analyses of the static and dynamic characteristics of the liquid annular seals with axially partial helical grooves were conducted to investigate the effects of the axial length g al of a helically grooved section in a seal stator. The numerical solution and experimental procedures were applied in the same manner as in previous studies on through-helically grooved seals, wherein the grooves extend across the seal length. The numerical results qualitatively agreed with the experimental results, demonstrating the validity of the numerical analysis. The leakage flow rate Q was lower in the partially helically grooved seals than that of conventional through-helically grooved seals across a small range of rotor spinning velocities. In contrast, the reduction in Q due to the pumping effect caused by the spin of the rotor diminished with the decrease in g al . For a small concentric whirling motion of the rotor, the radial dynamic reaction force F r and magnitude of variation in the tangential dynamic reaction force F t with the whirling angular velocity increased with the decrease in g al , and their values approached the corresponding values for the smooth-surface seal. Under the same rotor whirling velocity, the F t for the partially helically grooved seals became lower than that for the smooth-surface seal (similar to the case for the through-helically grooved seal), although decreasing g al tended to increase F t . These results suggest that partially helically grooved seals can improve the efficiency and stability margin of the pumps because of the reduction in leakage flow rate and suppression of the rotor forward whirling motion (with large radial and tangential dynamic reaction forces) as compared to conventional through-helically grooved seals.

Contact performance can be enhanced by using textured surfaces. These are also found to have influences on lubricated contacts. A procedure to find the optimal partially textured thrust bearing configuration is presented in this study. A parallel sector-pad thrust bearing is simulated by a three-dimensional (3D) computational fluid dynamics (CFD) model. The stationary surface of the bearing is textured with dimples, while the rotor surface is flat. The results of the baseline model are validated by experimental data. In this study, we compare rectangular and elliptical dimples by investigating design parameters, such as major the length of the major axis (width), the length of the minor axis (length), dimple depth, circumferential space between two dimples, radial space between two dimples, radial extent, circumferential extent are selected as design parameters. A parametric study is conducted to investigate the influence of the texture geometries and a surrogate model is created. Based on the surrogate model, a multi-objective optimization scheme is used to navigate the design space and find the optimal texture structure that provides a lower maximal temperature inside the fluid film, higher load capacity, and lower friction torque. The results show that the optimal radial extent of the texture is around 80% of the pad radial length for both cases. The optimal length of the elliptical dimples in the circumferential direction is about 30% larger than the value of the rectangular dimples. In the final optimal design, the maximal temperature reduces 1.1% and 1.3% for rectangular and elliptical dimples while the load capacities are maintained at the same level.

Numerical and experimental analyses were carried out to investigate the dynamic characteristics of liquid annular seals with helical grooves in the seal stator. In the numerical analysis, the governing equations were the momentum equations with turbulent coefficients and the continuity equation, all averaged across the film thickness and expressed using an oblique coordinate system in which the directions of coordinate axes coincided with the circumferential direction and the direction along the helical grooves. These governing equations were solved numerically to obtain the dynamic characteristics, such as the dynamic fluid-film forces, dynamic coefficients, and whirl-frequency ratio (WFR). The numerical analysis included the effect of both fluid inertia and energy loss at the steps between the helical groove and the land sections. In the experiments, the dynamic fluid-film pressure distributions, which were induced by a small whirling motion of the rotor about the seal center, were measured to obtain the dynamic characteristics. The equivalent numerical results reasonably agree with the experimental results, demonstrating the validity of the numerical analysis. The value of the tangential dynamic fluid force induced by the rotor whirling motion decreased with increasing the helix angle γ . Consequently, the values of the cross-coupled stiffness coefficient and WFR decreased with increasing γ and became negative for large γ . In general, pump rotors rotate with a forward whirling motion under normal operating conditions. Hence, the negative value of WFR for helically grooved seals contributes to rotor stability by suppressing the forward whirling motion of the rotor.

Numerical and experimental analyses were carried out to investigate the static characteristics of liquid annular seals with helical grooves in a seal stator. In the numerical analysis, the momentum equations with turbulent coefficients and the continuity equation, which were averaged across the film thickness, were numerically solved to obtain the leakage flow rate and the pressure distributions in the seal clearance. To accurately define the location of the step between the groove and the land regions in the calculation domain, these governing equations were expressed using an oblique coordinate system in which the directions of coordinate axes coincided with the circumferential direction and the direction along the helical grooves. The numerical analysis included the effects of both fluid inertia and energy loss due to expansion during the passage of fluid from the land region to the helical groove region and that due to contraction from the groove region to the land region. In the experimental analysis, the leakage flow rate and the fluid-film pressure distributions in the seal clearance were measured for the helically grooved seals with different helix angles of the helical groove. The numerical results of leakage flow rate and pressure distributions agree reasonably with the experimental results, which demonstrates the validity of the numerical analysis. The leakage flow rate of the helically grooved seals was influenced by two factors: fluid energy loss during passage through the step between the groove and the land, and the pumping effect by which the spinning motion of the rotor pushes the flow back upstream along the helical grooves. Under a low range of rotor spinning velocity, the leakage flow rate decreased with helix angle because the effect of fluid energy loss in the steps was significant. By contrast, under a high range of spinning velocity, the quantitative difference in the leakage flow rate due to the helix angle decreased compared to that under a low range because the reduction in the leakage flow rate due to the pumping effect was pronounced for a larger helix angle. The effects of helix angle and rotor spinning velocity on the leakage flow rate are explained qualitatively using a simplified model.

Mechanical face seals are constitutive components of much larger turbomachines and require consideration of the system dynamics for successful design. The dynamic interplay between the seal and rotor is intensified by recent trends toward reduced clearances, higher speeds, and more flexible rotors. Here, the “rotor” consists of the flexible shaft and the rotating seal seat. The objective here is to, for the first time, determine how the rotor affects the seal performance and vice versa. Thresholds can then be established beyond which the rotor influences the seal but not vice versa (i.e., the rotordynamics can be sent to the seal analysis as an exogenous input). To this end, a model of a flexibly mounted stator face seal is provided including the coupled dynamics of the flexible rotor. The model accounts for axial and angular deflections of the rotor and seal. Coupled rotordynamics are modeled using a lumped-parameter approach including static and dynamic rotor angular misalignments. For expediency, linearized expressions for fluid forces are used, and the resulting steady-state equations of motion are solved analytically to investigate how rotor inertia, speed, and angular misalignment influence the coupled seal dynamics. Importantly, results from the study reveal that in some operating regimes, neglecting the rotordynamics implies healthy seal operation when instead intermittent rub exists between the faces. This work also shows that when the rotor inertia is much larger than the seal inertia, the rotordynamics can be solved separately and used in the seal model as an external input.

Fluid film bearings (FFBs) provide economic wear-free performance when operating in hydrodynamic lubrication regime. In all other operating conditions, except hydrostatic regime, these bearings are subjected to wear. To get wear-free performance even in those conditions, a hybrid (hydrodynamic + rotation magnetized direction (RMD) configured magnetic) bearing has been proposed. The hybrid bearing consists of square magnets to repel the shaft away from the bearing bore. Load-carrying capacities of four configurations of hybrid bearings were determined. The results are presented in this paper. The best configuration of hybrid bearing was developed. A test setup was developed to perform the experiments on the fluid film and hybrid bearings. The wear results of both the bearings under same operating conditions are presented.

The viscous dissipation of micropolar lubricant results in temperature increase of hole-entry hybrid journal bearing. Thermohydrostatic (THS) performance characteristics are computed by the concurrent solution of micropolar Reynolds, micropolar energy, and conduction equations. The results obtained numerically indicate that bearing is significantly affected by increase in temperature. Hence, it is essential to consider the thermal effects for bearing operating with micropolar lubricant to produce realistic bearing characteristic data.