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Noncircular journal bearings are used in industry because of their simplicity, efficiency and low cost. During the life time of a machine, these are required to be operated over a number of years and are submitted to several stops and starts. As a result, the bush becomes progressively worn out and the bearing performance changes. The purpose of this paper is to study theoretically the influence of wear on the performance of a non‐circular 2‐lobe four‐pocket multirecess hybrid journal bearing system.

The Reynolds equation governing the flow of lubricant in the clearance space of a non‐circular 2‐lobe multirecess worn hybrid journal bearing system has been solved using FEM along with appropriate boundary conditions. The defects caused by wear are centered on the load line and range from 10 per cent to 50 per cent of the bearing radial clearance.

The numerically simulated results based on a Newtonian lubricant and the steady state flow field system have been presented in terms of maximum fluid film pressure, minimum fluid film thickness, lubricant flow rate, direct fluid film stiffness and damping coefficients and stability threshold speed margin. The paper demonstrates that, for the bearing configurations studied, the bearing behavior is clearly affected by wear. The numerically simulated results indicate that for an offset factor of δ=1.2, the value of h¯_min reduces by 21.21 per cent at δ¯_w=0.5.

The presented results have valuable data in case of 2‐lobe four pocket hybrid journal bearing compensated with constant flow valve restrictor. The paper outcomes are sure to be of interest for researchers and useful for bearing designers.

In recent years, researchers have focused a great deal of attention on multirecess hybrid journal bearing systems. The non‐circular journal bearings are widely used in industry on account of their better stability, simplicity, efficiency and low cost. The purpose of this paper is to present a theoretical investigation into the performance of a two‐lobe multirecess hybrid journal bearing system.

The Reynold's equation governing the lubricant flow in the clearance space between the journal and bearing together with restrictor flow equations has been solved using finite element method. The bearing static and dynamic performance characteristics have been presented for the various values of the offset factors (0.75, 1, 1.25 and 1.50) for the hybrid mode of operation of the journal bearing system compensated by capillary and orifice restrictors for the commonly used bearing operating and geometric parameters. The offset of the journal has been accounted for by defining a non‐dimensional factor called offset factor delta.

The numerically simulated results indicate that a two‐lobe four recessed hybrid journal bearing provides a better performance than the corresponding similar circular recessed journal bearing system. The study further reveals that in order to get an improved performance of a two‐lobe four recessed journal bearing, a proper selection of bearing offset factors along with type of restrictor (capillary or orifice) is essential.

The results presented in this paper are useful for bearing designers.

In the present scenario of high-speed machines, the use of non-circular hole-entry bearing configuration, i.e. two-lobe, multi-lobe, lemon bore, etc., has becomes unavoidable, as the journal bearings with non-circular configurations provide better stability at high operating speed and heavy dynamic loading. Further, this research aims to show that the presence of micro particles in the lubricants greatly affects performance of the bearings, as their presence leads to non-Newtonian behaviors of the lubricant. Therefore, to consider the effect of these micro particles, the lubricant is modeled as a micropolar lubricant. The present work analyzes the effect of these micropolar lubricants on the performance of hole-entry circular and non-circular (two-lobe) hybrid journal bearings compensated with constant flow valve restrictor and compares with that of Newtonian lubricants.

The modified Reynolds equation governing the laminar flow of iso-viscous, incompressible micropolar lubricant in the clearance space of a journal bearing system has been solved using finite element method and appropriate boundary conditions. Further, a comparative analysis between circular and non-circular (two-lobe) hybrid journal bearing compensated with constant flow valve restrictor operating with Newtonian and micropolar lubricant has been presented.

The numerically simulated results reveal that the non-circular bearing configuration provides better performance vis-à-vis the circular bearing configuration. Further, the increase in the micropolar effect of the lubricant enhances the performance of circular and the non-circular bearing configurations compared with the Newtonian lubricant. Also, in the case of the non-circular bearing configuration with an offset factor (δ = 1.5), the bearing performance improved compared with (δ = 1.25).

Many research studies have been done in the area of non-circular hybrid journal bearing with Newtonian lubricants with different types of restrictors, but the non-circular hole-entry constant flow valve-compensated hybrid journal bearing operating with the micropolar lubricant has not been analyzed. Therefore, in the present work, an effort has been made to fill this research gap.

This paper aims to study the static characteristics of the hydrostatic conical journal bearings by utilizing single-action membrane restrictors to compensate the working pressures of recesses.

The flow resistance network method is used to analyze the influences of load capacity and static stiffness of bearing with the design parameters, including the number of recesses, radial eccentricity ratio, axial displacement ratio, restriction constant, membrane compliance, length-diameter ratio, circumferential land width ratio, axial land width ratio and half of cone angle.

This study shows the infinite stiffness of the oil produced in the first and second recesses while single-action membrane restriction constant of 2 and 3, respectively, as well as in the fourth recess while single-action membrane restriction constant of 0.01 and 0.1, respectively.

This article provides the hydrostatic conical bearings in static and unbiased states for analyses of design parameters. The analyses ignore dynamic pressure effect and do not use the Reynolds equation, and assuming that each oil recesses pressure is constant.

The influences of the design parameters including the number of recesses, membrane restriction, membrane compliance, length-diameter ratio, half of con-angle, circumferential land width ratio, and axial land width ratio are discussed to the load capacity and static stiffness of conical bearing.

Based on the characteristics of the conical bearing through analysis, this article suggests the front bearing with hard membrane restrictor (capillary) and the back bearing with soft membrane restrictor are the most appropriate for axial stiffness.

Every high speed machine, demanding high level of perfection, can operate successfully through a precise design of bearings. Such a design can be formulated after carefully studying both static and dynamic characteristics of the journal bearing. The present paper aims to describe the study of static and dynamic performance of a hole‐entry hybrid journal bearing system compensated with capillary restrictor by considering the combined influence of thermal effects and non‐Newtonian behavior of the lubricant.

The variation of the viscosity due to the non‐Newtonian behavior of the lubricant and temperature rise is considered in the study. The numerical solution of the generalized Reynold's, equation governing the flow of the lubricant having variable viscosity along with the energy and heat conduction equations is obtained using finite element method. The non‐Newtonian lubricant has been assumed to follow the cubic shear stress law. The study includes performance of a double row symmetric hole entry hybrid journal bearing configuration containing 12 holes per row.

The results indicate that change in viscosity of lubricant affects the bearing design parameters.

The paper shows that accurate theoretical modeling of the bearing is an effective tool for the selection of design parameter such as bearing land width ratio (a_b), restrictor design parameter (C_s2), and non‐linearity factor (K).

This paper aims to investigate the effect of plugging of holes on the static performance characteristics of a constant flow valve compensated hole‐entry hybrid journal bearing system operating with Newtonian and non‐Newtonian lubricants. The analysis considers the generalized Reynolds equation governing the flow of lubricant having variable viscosity in the clearance space and equation of flow of lubricant through constant flow valve restrictor. The non‐Newtonian lubricant is assumed to follow the power law. The performance characteristics are computed for the two values of power law index (n=1.0 and 0.566). The computed results indicate that the blockage of holes during operation will not be the likely causes for the imminent failure of a well‐designed non‐recessed hole‐entry hybrid journal bearing.

Finite element method has been used to solve generalized Reynolds equation governing the flow of lubricant having variable viscosity in the clearance space and equation of flow of lubricant through constant flow valve restrictor.

The computed results indicate that the blockage of holes during operation will not be the likely causes for the imminent failure of a well‐designed non‐recessed hole‐entry hybrid journal bearing. The bearing configuration with plugged holes provides sufficient fluid film thickness and low power requirement as less lubricant is required to be pumped in the bearing.

To the best of the author's knowledge, no study which considers the influence of plugging of holes on the static performance characteristics of a constant flow valve compensated hole‐entry hybrid journal bearing system operating with Newtonian and non‐Newtonian lubricant is yet available in the literature.

This paper aims to describe the theoretical study concerning the effect of non‐linear behavior of the lubricant on the performance of symmetric constant flow valve compensated hole‐entry hybrid journal bearing. The bearing performance characteristics have been computed for various values of non‐linearity factor, land width ratio, aspect ratio and external load.

The analysis considers the generalized Reynolds equation governing the flow of lubricant having variable viscosity in the clearance space and equation of flow of lubricant through constant flow valve restrictor. The non‐Newtonian lubricant is assumed to follow the cubic shear stress law.

The study indicates that for generation of accurate bearing characteristics data, the inclusion of non‐linear effects of lubricant in the analysis is essential.

The performance characteristics in terms of minimum fluid‐film thickness, fluid‐film stiffness and damping coefficients, critical mass and threshold speed for a wide range of values of the non‐linearity factor and external load are presented. The results presented are expected to be quite useful to bearing designers.

An electrorheological (ER) fluid consists of dielectric particles blended in a nonconducting oil. ER lubricants are often considered smart lubricants. This paper aims to examine the steady state and dynamic response of multilobe journal bearings using an ER lubricant.

Reynold’s equation has been used to describe the lubricant flow in the journal-bearing clearance space. The Bingham model is used to characterize the nonlinear behavior of the lubricant. The solution of the Reynolds equation is obtained using the Newton–Raphson method, with gaseous cavitation in the fluid film numerically addressed by applying a mass-conserving algorithm. The effects of lobe geometry and the applied electric field are investigated on film pressure profile, fluid film thickness, direct stiffness and damping parameters. The equation of motion for journal center coordinates is solved using the fourth-order Runge–Kutta method, to predict journal center motion trajectories.

Using ER lubricant combined with two-lobe journal bearing significantly improved the minimum film thickness by 49.75%, the direct stiffness parameter by 132.18% and the damping parameter by 206.3%. However, the multilobe configuration was found to negatively impact the frictional powerloss of the bearing system. In the case of multilobe configurations of journal bearings using ER lubricant, linear motion journal trajectories are observed to be reduced and exhibit increased stability.

This study presents the effect of an ER lubricant and multilobe configuration on the rotor-dynamic performance and stability analysis of hydrodynamic journal bearings.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2024-0201/

The purpose of this paper is to study the influence of different flow regimes on the dynamic characteristics of four-pad hydrostatic squeeze film dampers (SFDs) loaded between pads.

A numerical model based on Constantinescu’s turbulent lubrication theory using the finite difference method has been developed and presented to study the effect of eccentricity ratio on the performance characteristics of four-pad hydrostatic SFDs under different flow regimes.

It was found that the influence of turbulent flow on the dimensionless damping of four-pad hydrostatic SFDs appears to be essentially controlled by the eccentricity ratio. It was also found that the laminar flow presents higher values of load capacity compared to bearings operating under turbulent flow conditions.

In fact, the results obtained show that the journal bearing performances are significantly influenced by the turbulent flow regime. The study is expected to be useful to bearing designers.

The present paper proposes a theoretical analysis of the stability characteristics of a rigid rotor‐hybrid bearing system. It is intended that on the basis of the numerical results drawn from this study, the optimal restriction parameter for stable operation can be determined for use in the bearing design process.

A rigid rotor supported by hybrid oil film bearings with six recesses and capillary‐compensated restrictors is studied. In order to facilitate the calculation of film dynamics, using the perturbation method, the Reynolds equation was linearized and subsequently solved using finite difference techniques, whilst the stability maps were determined by the Routh‐Hurwitz method.

The data reported here suggest that the stability characteristics of the rigid rotor‐bearing system could be improved by the use of shallow, dual‐recessed hybrid bearings with capillary compensation. For the same restriction parameter and the same land‐width ratio used in large eccentricity case the stability characteristics of a shallow‐recessed bearing is superior to that of a deep‐recessed bearing, however, a deep‐recessed bearing with a small land‐width ratio and a small restriction parameter can provide better stability than a shallow‐recessed bearing with a large land‐width ratio or with a large restriction parameter.

This study proposes an extensive database as a critical requirement in the design of hybrid bearings, in order to ensure that a rotor bearing system is operating stably.

This study examines the influence of the restriction parameters on the stability of a Jeffcott rotor supported by single‐row, six‐recessed hybrid bearings with orifice compensation. The Reynolds equation governing oil‐films is solved using the finite difference method, whilst the determination of stability of the Jeffcott rotor‐bearing system uses the Routh‐Hurwitz method. The load capacity, stability threshold, and the critical whirl ratio versus the changing restriction parameters, are each simulated for the shallow‐recessed bearing and the deep‐recessed bearing with various land‐width ratios. The simulation results indicate that with the appropriate design of restriction parameters and land‐width ratio, a deep‐recessed bearing may be relatively superior. Although the performance of a shallow‐recessed bearing is, by and large, superior to that of a deep‐recessed bearing, it does nevertheless hinge upon the design of both restrictor and bearing.

The present paper proposes a theoretical analysis of the stability characteristics of a Jeffcott rotor‐hybrid bearing system. It is intended that on the basis of the numerical results drawn from this study, appropriate recess depth, land size, orifice location and speed parameter for stable operation can be determined for use in the bearing design process.

A Jeffcott rotor supported by hybrid oil film bearings with dual‐row recesses and orifice‐ compensated restrictors is studied. In order to facilitate the calculation of film dynamics, using the perturbation method, the Reynolds equation was linearized and subsequently solved using finite difference techniques, whilst the stability maps were determined by the Routh‐Hurwitz method.

The data reported here suggest that the stability characteristics of the Jeffcott rotor‐bearing system could be improved by the use of shallow, dual‐recessed hybrid bearings with orifice compensation. In addition to greater eccentricity ratios, smaller land‐width ratios and greater shaft stiffness may also provide shallow‐recessed bearings with better stability. In all cases, the stability provided by upstream orifice‐sited bearings is better than that provided by center orifice‐sited bearings, whilst high‐speed parameters may also provide a greater stability threshold.

This study proposes an extensive database as a critical requirement in the design of hybrid bearings, in order to ensure that a rotor bearing system is operating stably.

This paper aims to describe a theoretical and experimental research concerning influence of recess shape on comprehensive lubrication performance of high speed and heavy load hydrostatic thrust bearing with a constant flow.

The lubrication performance of a hydrostatic thrust bearing with different recess shape under the working conditions of high speed and heavy load has been simulated by using computational fluid dynamics and finite volume method.

It is found that the comprehensive lubrication performance of a hydrostatic thrust bearing with circular recess is optimal. The results demonstrate that recess shape has a great influence on the lubrication performance of the hydrostatic thrust bearing.

The simulation results indicate that to get an improved performance from a hydrostatic thrust bearing with constant flow, a proper selection of the recess shape is essential.

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.

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.

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.

The results obtained show that the effects of micropolar lubricants on the dynamic performances are predominantly affected by the pad geometry and eccentricity ratio.

Hybrid conical journal bearings have received great attraction by design engineers and researchers due to their incomparable performance. However, performance of these bearings is affected due to wear. This paper aims to present an analytical study concerning the performance of hole entry worn hybrid conical journal bearings.

The Reynolds equation governing the flow of lubricant in the clearance space along with the restrictor flow equations has been solved using finite element method.

The numerically simulated results of worn bearing performance parameters indicate significant change in the performance due to wear. Therefore, for semi cone angle γ = 25^°, the value of C¯₂₂ reduces by 24.6 per cent at the wear value of about 50 per cent of radial clearance for the given configuration of bearing.

The present results are original of its kind and surely useful to bearing designers and researchers in predicting actual performance of worn hole entry hybrid conical journal bearing.

This paper aims to study the influence of thermal effect on the performance for a high-speed conical hybrid bearing including stability and minimum oil film thickness.

A thermal hydrodynamic (THD) model and dynamic model of single mass rigid rotor system were established by taking conical hybrid bearing with shallow and deep pockets as the research object, dynamic coefficient and stability parameters of bearing-rotor system were obtained by using finite element method (FEM) and finite difference method (FDM) to solve computational models of Reynolds equation, energy equation and viscosity-temperature equation. Minimum oil film thickness was obtained based on bearing force balance. Dynamic coefficient was compared with previous findings.

After considering thermal effect, the dimensionless critical mass decreases, a significant decrease in the instability speed, and the stability of the system decreases greatly; the minimum oil film thickness decreases because of thermal effect.

The thermal effect is combined with dynamic characteristics to analyze stability of the rotor system for a conical hybrid bearing. Influence of thermal effect on minimum oil film thickness is studied.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-12-2019-0542/

This paper’s aim is modeling and simulation of an advanced controller design for a novel mechatronics system that consists of a hydrostatic journal bearing with servo control. The proposed mechatronic system has more worth in tribology applications as compared to the traditional hydrostatic bearing which has limited efficiency and poor performance because of lower stiffness and load-carrying capacity. The proposed mechatronic system takes advantage of active lubrication to improve stiffness, rotor’s stability and load-carrying capacity.

The current work proposes extended state observer-based controller to control the active lubrication for hydrostatic journal bearing. The advantage of using observer is to estimate unknown state variables and lumped effects because of unmodeled dynamics, model uncertainties, and unknown external disturbances. The effectiveness of the proposed mechatronic system is checked against the traditional hydrostatic bearing.

Proposed mechatronics active hydrostatic journal bearing system is checked against traditional hydrostatic journal bearing. It is found that novel active hydrostatic journal bearing with servo control has good tribology performance factors such as stiffness, less rotor vibration, no wear and friction under starting conditions and high load-carrying capacity under different conditions of spindle speed, temperature, initial oil pressure and external disturbance. The result shows that proposed mechatronics system has more worth in rotary tribology applications.

The current manuscript designs a novel active hydrostatic journal bearing system with servo control. The mathematical model has advantages in term of estimating unknown state variables and lumped effects because of unmodeled dynamics, model uncertainties and unknown external disturbances. The result shows improvement in dynamic characteristics of a hydrostatic journal bearing under different dynamic conditions.

To meet the high stiffness requirement of bearings used in high-precision spindles, this paper aims to propose a novel kind of bearing composited by hydrostatic cavities and tilting pads with preload.

Cavities are cut on the oil seal surface of a hybrid bearing, in which the tilting pads are set up. The load of the bearing is carried by the hydrostatic cavities and tilting pads. The structural features of this compound bearing and the controlling variables of the main stiffness coefficient are presented. Two basic design principles are proposed on the basis of equal machining clearance (EMC) and equal installation clearance (EIC).

The theoretical analysis indicates that the stiffness of compound bearings under the EMC condition increases to infinity monotonously when the preload coefficient of the tilting pad tends to 1, while the stiffness under the EIC condition has a peak value. Therefore, a synthetic design principle is proposed by synthetically using the above-mentioned two principles. The applicable range of the three principles is discussed through an example.

The study about technological combination of hydrostatic cavity and tilting pad in this paper can provide suggestions for the design of a high-stiffness bearing in a precision spindle.

This paper aims to propose a method for finding the maximum rotational speed of an inclined turntable at which the stability of the bearing oil film is maintained.

The finite difference method was used to solve the Reynolds equation. Variation of bearing capacity of a tilted hydrostatic turret over time was determined. The combined effect of tilt and rotational speed of the turret on the oil film stability was also analyzed.

When the turntable is operated at low speeds with only small angle of tilt, stability of the oil film is maintained. At lower rotational speeds, a smaller angle of tilt improves the bearing capacity and ensures stability of the oil film. Whereas, higher rotational speeds can have a considerable influence on the bearing capacity.

The results demonstrate that the inclination or tilt of the turntable significantly affects the stability of the oil film.

This paper aims to establish an accurate mathematical model of a piezoelectric membrane restrictor that can be applied to control the shaft’s centerline orbit.

The methodology uses three coupled equations to establish a mathematical model of the piezoelectric membrane restrictor – Reynolds equation, the membrane deformation equation and the flow rate equation. A data identification method is used to propose the flow rate formulas for the piezoelectric membrane restrictor.

It has been found that the structural parameters, the membrane center deformation and the inlet and outlet pressures of the piezoelectric membrane restrictor have an effect on the static performance of the restrictor. The identified flow rate result of the piezoelectric membrane restrictor is consistent with the models.

The paper provides an accurate mathematical model of the piezoelectric membrane restrictor which can also be applied to other membrane restrictors.

This paper aims to provide a new method for fast calculation of the recess pressure for hydrostatic bearing compensated by orifice restrictor.

Three methods (new method, old method and finite difference method) are used to calculate recess pressure for hydrostatic bearing at different eccentricity ratios and radial clearances, and the results with the three methods are compared.

From the results, the conclusion is that the new method has a simple calculation process and a quick calculation speed.

The new method can be used to calculate the recess pressure of hydrostatic bearing with high precision and simple computing process.

The purpose of this paper is to establish a simplified model of the closed hydrostatic guideway for the rapid analysis of static and dynamic characteristics. Further, the influence of compressibility and dynamic frequency are taken into consideration in the new dynamic model.

The new model is based on the second kind of Lagrange equation. In this model, the closed hydrostatic guideway is supported by 12 pads, and each oil pad is equivalent to a nonlinear spring-damper system. The equivalent spring coefficient and damper coefficient of the oil pad are extracted by the three different equivalent methods. Finally, the validation experiments of step load response and dynamic stiffness are conducted on a hydrostatic guideway.

For solving the step response, the linear spring-damper model and the nonlinear spring-damper Model 1 are better than the nonlinear spring-damper Model 2. The accuracy of the three methods are very high for static stiffness calculation. For the calculation of dynamic stiffness, the nonlinear spring-damper Model 2 is better than the nonlinear spring-damper Model 1. The linear spring-damper model has low precision for dynamic stiffness calculation, especially at high frequency. The accuracy of the new model is validated by experiments.

The equivalent method of nonlinear spring-damper system has higher accuracy. Different equivalent methods should be adopted for different load types. The computational speeds of the new dynamic model with the three methods are much better than finite element method (about ten times).

The purpose of this paper is to study the influences of recess configurations on the performances of high-speed hybrid journal bearing. Hybrid journal bearing earns increasing attention in high-speed machine tool spindle owing to its intrinsic outstanding performances of low temperature rise and high stability.

To investigate the coupled effects of temperature, turbulence and the interaction between lubricant and journal/bearing bush, a thermal fluid-structure interaction approach is presented and validated by the experimental results.

Ladder-type recess has excellent tribological characteristics in decreasing temperature rise, improving stability and inhibiting cavitation, which are all beneficial to improve the performances of high-speed spindle system.

This work can be a valuable guide for the future high-speed hybrid journal bearing design.

The purpose of the paper is to analyze the bearing capacity of hydrostatic bearing during the change of film thickness under different working conditions and to improve the processing efficiency and precision of equipment.

In this study, Q1-205 double rectangular cavity hydrostatic thrust bearing is selected as the research object. The dynamic mesh method and ANSYS/FLUENT software are used to simulate the curves of oil film thickness and oil pressure under different operating conditions. Finally, the change of pressure in the oil cavity at different operating speeds under a certain inlet flow rate was tested through design experiments.

When the film thickness was thick, the maximum pressure in the oil cavity at different inlet velocities showed little difference. With a larger inlet flow, the maximum pressure in the oil cavity was higher. The pressure at the edge of the oil seal was linearly distributed. The oil pressure in the downstream side was greater than that in the counter flow side. When the working pressure was low, the pressure in the oil cavity slightly decreased with the increase of working speed. Moreover, the pressure loss at high speed was considerable.

Based on the lubrication theory, the mathematical model of the bearing oil film was set up. The bearing capacity equation of the hydrostatic cavity was derived. The double-rectangular-annular hydrostatic guides studied in this paper have not been reported in previous research literature and the method of dynamic mesh dynamic simulation of variable viscosity is seldom studied before. The bearing characteristics and the change of oil film thickness under different working conditions have been studied systematically and comprehensively. The theoretical analysis results are basically consistent with the experimental results.

When the clearance oil film of hydrostatic bearing friction pair is in critical lubrication state, the phenomenon of zero flow of local lubricating oil will aggravate the oil film temperature rise, which needs to be solved.

In this paper, the critical lubrication parameter equation and the oil film temperature rise mathematical model are derived for the new type q1-205 double rectangular cavity hydrostatic bearing. Based on a combination of theoretical analysis, simulation and experimental verification, this paper analyzes the flow characteristics and temperature rise characteristics of the lubricating oil when the hydrostatic bearing is in a critical lubrication state under different operating conditions and finally obtains the critical lubrication state of the oil film.

This study found that the numerical simulations and the derived formulas agree with the results. When the oil film is in critical lubrication, the cross-section side flow of the oil side is almost zero. The heat cannot be taken away in time, resulting in the local temperature rise of the oil film, which causes serious heat accumulation.

It is concluded that the operating condition parameters corresponding to the critical lubrication state provide a theoretical basis for the selection of actual hydrostatic bearing operating conditions, which is of great scientific significance.

The present paper aims to analyse the synergistic effect of pocket orientation and piezo-viscous-polar (PVP) lubrication on the performance of multi-recessed hybrid journal bearing (MHJB) system.

To simulate the behaviour of PVP lubricant in clearance space of the MHJB system, the modified form of Reynolds equation is numerically solved by using finite element method. Galerkin’s method is used to obtain the weak form of the governing equation. The system equation is solved by Gauss–Seidal iterative method to compute the unknown values of nodal oil film pressure. Subsequently, performance characteristics of bearing system are computed.

The simulated results reveal that the location of pressurised lubricant inlets significantly affects the oil film pressure distribution and may cause a significant effect on the characteristics of bearing system. Further, the use of PVP lubricant may significantly enhances the performance of the bearing system, namely.

The present work examines the influence of pocket orientation with respect to loading direction on the characteristics of PVP fluid lubricated MHJB system and provides vital information regarding the design of journal bearing system.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2023-0241/

This study aims to investigate the impact of surface waviness on the static performance parameters of hydrodynamic journal bearings operating with lubricants containing copper oxide (CuO) and cerium oxide (CeO₂) nanoparticles.

The static performance parameters of bearings with surface waviness and the addition of nanoparticles in lubricants were calculated using the nondimensional form of Reynolds equation and finite element method. Static performance parameters are calculated at different waviness numbers in the circumferential, axial and both directions at various wave amplitudes with variable viscosities of lubricants with nanoparticles using the viscosity equation forming a relationship between the relative viscosity, temperature and weight fraction of nanoparticles in lubricant developed from the experimental results.

The computed results indicate that the impact of waviness on the bearing surface enhances the load capacity, reduces friction coefficient, and is more effective in the circumferential direction than in the axial direction or in both directions. The addition of CuO and CeO₂ to the lubricant enhanced its viscosity which further improved the steady-state parameters of the wave bearing.

This study is based on a numerical technique, which has significant limitations, and the simulated results must be tested experimentally.

The current findings will be beneficial for designers to improve the performance of hydrodynamic journal bearings.

The calculated results demonstrate that the combined effect of the surface waviness on bearings and the addition of nanoparticles to lubricants can greatly increase the performance of hydrodynamic journal bearings.

The purpose of this paper is to provide a solution for Reynolds equation with both throttling term and reverse throttling term and provides a reference for changing damping of hydrostatic bearing.

The reverse throttling term is introduced into the Reynolds equation, and the adaptive damping factor is used in the Newton iteration method to improve convergence of numerical calculations. The static and dynamic performances of this bearing are numerically investigated by the finite-element method.

The results indicate that the reflux orifices lead to a decrease in load capacity at a high eccentricity ratio. Additionally, the mass inflow rate is increased; however, the additional inflow increase can be controlled by enhanced backpressure of the reflux orifice. Nevertheless, the bearing with the reflux orifice shows superiority in resisting high-frequency disturbances and enhances direct damping by 20% under a high backpressure.

This work presents an adaptive Newton damping iterative method for solving Reynolds equation with both throttling term and reverse throttling term. This work also provides a new idea for bearing structure design in improving damping.

Hybrid journal bearing have long been used in machines requiring large load and high speed capacity operating under wide range of temperatures. Different compensating devices are used in for efficient operation of bearings. This paper aims to help in selection of optimum compensating device by evaluating the comparative performance of constant flow valve, capillary compensated and slot entry hybrid journal bearing under the combined influence of thermal effects and micropolar nature of lubricant.

The variation in micropolar parameters and viscosity change due to temperature increase of lubricant are considered in present study. Finite element method is used for combined iterative solution of micropolar Reynolds, energy and conduction equations. Micropolar lubricant is assumed to be governed by two parameters, coupling number and characteristic length. The results in the study are presented for symmetric and asymmetric configurations of hole entry and slot entry non-recessed hybrid journal bearings

The results indicate that constant flow valve compensated hole entry hybrid journal bearing is the highest performing bearing for the given range of micropolar parameters of lubricant in terms of maximum fluid pressure and dynamic coefficients.

The performance variations of various configurations of hybrid journal bearing are presented in a single paper. The reader can get overview of combined effects of micropolar parameters and viscosity decrease due to temperature increase of the lubricant.

Bearing performance characteristics, such as stiffness and load capacity, are related to the viscosity of the fluid circulating through the gap. Nanoparticle additives in lubricant are one way to enhance of the viscosity. This study aims to investigate the effect of nanoparticle additives on the thermohydrodynamic performance of journal bearing with different bearing parameters.

The temperature distribution is modeled using a three-dimensional energy equation. The velocity components are calculated on the pressure distribution governed by Dowson’s equation. Moreover, the heat transfer between the journal and lubricant is modeled with Fourier heat conduction equation. On the other hand, the viscosity equation is derived for Al₂O₃ nanoparticles as a function of the volume ratio and the temperature. An algorithm based on the finite difference method is developed, and a serial simulation is performed for different parameters and different volume ratio of nanoparticle.

With the increase in the nanoparticle volume ratio, the maximum temperature decreases for the lower clearance values, but the addition of the nanoparticle influence on the maximum temperature reverses when the clearance grows up. The nanoparticle additives increase further the maximum temperature for higher values of L/D ratios. Moreover, the effects of the nanoparticle additives on the pressure are stronger at high eccentricity ratios for all bearing parameters.

This paper provides valuable design parameters for journal bearing with lubricant containing the nanoparticle additives.

The current trend of modern industry is to use machineries which rotate at high speed along with the capability of carrying heavy rotor loads. This paper aims at static thermal analysis of two different profiles of non-circular journal bearings – a true elliptical bearing and orthogonal bearing.

The Reynolds equation has been solved through finite difference method to compute the oil film pressure. Parabolic temperature profile approximation technique has been used to solve the energy equation and thus used for computation of various bearing performance characteristics such as thermo-hydrodynamic oil film pressure, temperature, load capacity, Sommerfeld number and power loss characteristics across the bearing. The effect of ellipticity ratio on the bearing performance characteristics has also been obtained for both the elliptical and vertical offset bearing using three different commercially available grades of oil (Hydrol 32, 68 and 100).

It has been observed that the thermo-hydrodynamic pressure and temperature rise of the oil film is less in orthogonal bearing as compared to the true elliptical bearing for same operating conditions. The effect of ellipticity ratio of non-circularity on bearing performance parameters have been observed to be less in case of elliptical bearing as compared to orthogonal bearing. It has been concluded that though the rise in oil film temperature is high for true elliptical bearing, but still it should be preferred over orthogonal profile under study, as it has comparably good load-carrying capacity.

The performance parametric analysis will help the designers to select such kind of non-circular journal bearing for various applications.

This paper aims to present a simplified method to predict the pressure of the recess, no matter whether the tilt center coincides with the geometric center of the hydrostatic journal bearings.

To validate the effectiveness of the presented model, computational fluid dynamics (CFD) method and experimental method are performed in this study.

By comparing the CFD results and the experimental results, the pressure of the recess is related to the tilt direction, the tilt center, the width of the land and the circumferential angle of the land.

The mathematic model requires equivalent resistance of land edge – tilt position, tilt direction, tilt angle and the thickness of oil film instead of any digital iteration. Furthermore, a novel experimental apparatus including a circular hydrostatic bearing called ball bearing is designed to study the tilt effect produced by manufacturing error and offset load force on the pressure of the recess.

Hybrid bearings have found increasing applications in various machines owing to their large number of favorable characteristics like high load carrying capacity, increased minimum fluid film thickness, long life and increased damping making them attractive for various applications such as turbo machinery, machine tool spindles, precision grinder spindles, etc. A careful design of such bearing for optimum performance has always been among the key issues of the researchers. The present work has been carried out to study the effect of bearing geometric parameters on performance of hybrid journal bearing and supply cut‐off behavior has also been studied for the improved performance.

The generalized Reynold's equation governing the fluid flow in the clearance space between bearing and journal has been solved using finite element method to determine the pressure distribution, subsequently performance of hole‐entry hybrid journal bearing are computed. The journal centre equilibrium position for the given load is computed and the formulation is explained. The geometric parameters include aspect ratio, land width ratio, number of rows and number of holes per row. Further, performance of the bearing is computed with increasing the load, which induces negative pressure or the backpressure at the supply holes subsequently those are plugged to support the higher load.

The obtained results are presented in graphical form and logical conclusions are drawn and the modified configurations with reduced number of holes are suggested for higher load. It is observed that the bearing configuration with aspect ratio = 1.0 and land width ratio = 0.2 is best for high load support for low power requirement as less lubricant is required to be pumped in the bearing yet it provides sufficient fluid film thickness and lower values of maximum pressure. The load carrying capacity of the bearing can be further increased by plugging the holes on which backpressure is obtained for same bearing configuration. A feedback control with hybrid bearing system will sustain the sudden increase of load by shutting off the supply of the lubricant through supply hole where negative pressure is encountered.

The paper addresses the performance of non recessed hybrid journal bearings with wide range of geometric parameter. The results are quite useful for the bearing designer. The supply cut‐off is another aspect of originality of the paper as it provides the better load support.

Wear in journal bearings occurs when the operating conditions (high load, high temperature, low angular velocity or low viscosity), downgrade the ability of the bearing to carry load. The wear depth increases because the rotor comes in contact with the bearing surface. Wear in journal bearings affects their characteristics because of its influence on the thickness of the fluid film. This influence can be detected in the dynamic behavior of the rotor and especially in the dynamic stiffness and damping coefficients. The paper aims to discuss these issues.

In this paper, the effect of wear on the rotor dynamic stiffness and damping coefficients (K and C) of a short journal bearing is investigated. K and C in this work are estimated by using two methods a semi-analytical method and finite element (FE) analysis implemented in the ANSYS software.

The main goal of this research is to make the identification of wear in journal bearings feasible by observing the alternation of their dynamic coefficients. Both of the methods implemented are proven to be useful, while FE analysis can provide more accurate results.

This paper is original and has not been published elsewhere.

Hydrostatic thrust bearing is a key component of the vertical CNC machining equipment, and often results in friction failure under the working condition of high speed and heavy load. The lubricating oil film becomes thin or breaks because of high speed and heavy load and it affects the high precision and stable operation of the vertical CNC machining equipment; hence, it is an effective way of avoiding friction failure for achieving the oil film shape prediction

For the hydrostatic thrust bearing with double rectangular cavities, researchers solve the deformation of the friction pairs in hydrostatic bearing by using the computation of hydrodynamics, elasticity theory, finite element method and fluid-thermal-mechanical coupled method. The deformation includes heat deformation and elasticity deformation, the shape of gap oil film is got according to the deformation of the friction pairs in hydrostatic bearing, and gets the shape of gap oil film, and determines the influencing factors and laws of the oil film shape, and achieves the prediction of oil film shape, and ascertains the mechanism of friction failure. An experimental verification is carried out.

Results show that the deformation of the rotational workbench is upturned along its radial direction under the working condition of high speed and heavy load. However, the deformation of the base is downturned along its radial direction and the deformation law of the gap oil film along the radius direction is estimated; the outer diameter is close but the inner diameter is divergent wedge.

The conclusion can provide a theoretical basis for the oil film control of hydrostatic thrust bearing and improve the stability of vertical CNC machining equipment.

Large scale is a trend of the ball mill, so the loads on their bearings become very large, bearing operating conditions turn into more severe. The moment of inertia to their pivot of the pad increase significantly, so it leads to the difficult of the pad attitude adjustment and makes the pad tilting angles time response slow, the key factor to effects attitude adjustment is the oil film moment to the pad pivot at unbalance position. the oil film moment and its effect factors must be studied in the design of the bearing used in ball mill.

Models about the lubrication of multi-pocket pivoted pad hydrostatic bearing is established, the complicated relationship of the oil flow rate between the oil pockets are taken into account. Finite differential method is used to solv the model, and theroy of finite element method is use to calculate the oil flow rate out of the pocket edges. Newton’s methods are used to determine the pressure of pockets.The pad tilting moment to its pivot is numerically analyzed.

The tilting moment to its pivot is set as an indicator of the ability for a pad to adjust its attitude. The effects of the diameter of throttling capillary and the pocket area on the attitude adjusting capacity is studied. Relations between the attitude adjustment capacity for a pad and there effects factors are presented.

The methods and results have the special reference to the design and operation of multiple pockets tilted pad hydrostatic journal bearing.

Methods to studied the pad attitude adjustment are given in the article for the multi-pocket pivot pad hydrostatic beairng.The influence factors on pad attitude adjusting capacity are discussed for a this specail kind hydrostatic bearing, the how the factors influence the pad tilting angle adjustment are presented.

To solve the problem of oil film thinning when hydrostatic thrust bearings are overloaded or rotating at high speed, the dynamic pressure formed by tiny oil wedges is used to compensate, and the optimum height of oil wedges is determined by the compensation rate to improve the bearing capacity of hydrostatic thrust bearings.

This research method is aimed at the new type of double rectangular cavity static bearing with microbevel surface of q1-205. The wedge parameters of oil film were defined. The oil film lubrication performance of the bearing with the wedge parameters of 0, 0.02, 0.04, 0.06, 0.08 and 0.10 mm was simulated by the finite volume method, the comprehensive influence law of the wedge-shaped parameters on the vorticity and flow rate of the oil cavity pressure fluid was revealed. Finally, the oil cavity pressure changes of oil films with different wedge parameters under certain load and speed were tested by design experiments, and the theoretical analysis and simulation were verified.

This study found that the oil film wedge shape can well compensate the static pressure loss caused by the high-speed or heavy-duty operation of the bearing, but the dynamic pressure effect of the wedge shape does not always increase with the increase of the wedge height. The oil film exhibits superior lubrication performance in the range of 0.06–0.08 mm.

The original hydrostatic oil pad was designed as a microinclined plane, and the dynamic pressure caused by the microwedge of the oil pad was used to compensate the static pressure loss of the bearing. The lubrication performance of the oil film under the condition of varying viscosity was obtained by using the simulation method.

The paper seeks to study, theoretically, the performance characteristics of capillary compensated multi‐recessed hydrostatic journal bearings operating with micropolar lubricant. The finite element method is used to solve the modified Reynolds' equation governing the micropolar lubricant flow in the clearance space of a hydrostatic journal bearing. The performance characteristics of bearing operating with micropolar lubricant are presented and compared with that of Newtonian lubricant, for a wide range of non‐dimensional load, capillary restrictor design parameter and micropolar parameters.

The modified Reynolds' equation governing the flow of the micropolar lubricant is solved along with restrictor flow equation by finite element method so as to obtain fluid‐film pressures. The iterative procedure is repeated until the converged solution for the fluid‐film pressure field is obtained.

A study of four‐pocket hydrostatic journal bearing system capillary compensated and operating with micropolar lubricant is presented. The following conclusions are made from the results presented in this study: at a constant load, pocket pressures and minimum film thickness, stiffness coefficients and, the damping coefficients increase with increase in micropolar effect of lubricant as compared to the Newtonian lubricant; the influence of the micropolar parameters of lubricant is more significant upon the minimum fluid‐film thickness at higher values of load and lower values of restrictor design parameter; the non‐dimensional flow decreases with increase in the micropolar effect of the lubricant a given values of restrictor design parameter and load; and the stiffness coefficient in the direction of load is found to be influenced by the micropolar parameters and more significantly at lower values of restrictor design parameter and load.

Studies of capillary compensated multi‐recess hydrostatic journal bearing operating with micropolar fluid/lubricant are not available in the existing literature to the best of authors' knowledge. Although, such bearing has been studied with Newtonian lubricant and available in open literature. Therefore, this paper is an original piece of work in the area of micropolar lubrication and compensated hydrostatic bearings.

The changing technological scenario necessitated hybrid journal bearings to operate under severe conditions of heavy load and high speed resulting into temperature rise of the lubricant fluid-film and bearing surface. To predict the performance of a bearing realistically, theoretical model must consider the combined influence of the rise of temperature and non-Newtonian behavior of the lubricant. The aim of the present paper is to study the effect of viscosity variation due to temperature rise and non-Newtonian behavior of the lubricant on performance of constant flow valve compensated multiple hole-entry hybrid journal bearings.

Finite element method has been used to solve Reynolds equation along with restrictor flow equation, 3D energy equation and 3D conduction equation using suitable iterative technique. The non-Newtonian lubricant has been assumed to follow cubic shear stress law.

The thermohydrostatic rheological performances of symmetric and asymmetric hole-entry hybrid journal bearing configurations are studied. The computed results illustrate that variation of viscosity due to rise in temperature and non-Newtonian behavior of the lubricant affects the performance of hole-entry hybrid journal bearing system quite significantly.

In the present work, the influences of the viscosity variation due to temperature rise and non-Newtonian behavior of the lubricant on the performance characteristics of non-recessed hole-entry hybrid journal bearing with symmetric and asymmetric configurations compensated with constant flow valve restrictors have been investigated for generating the design data to be used by bearing designer. The design data computed in the present thesis are a contribution in field of knowledge of bearing design.