Hydrodynamic Bearings Research Articles

A model-based technique to identify lubrication condition of hydrodynamic bearings using the rotor vibrational response

Faults related to hydrodynamic bearing can imply in high maintenance costs when late-detected and lead to system shutdown. Thus, techniques of early fault diagnosis have high relevance to the reliability of rotating machinery. However, a common fault caused by inadequate bearing oil supply has not yet received appropriate attention. This paper presents a new approach to model and identify oil supply in hydrodynamic bearings. The developed identification technique is a model-based process that uses the rotor vibration to access the bearing lubrication. Numerical identifications were performed and the results showed that the proposed method satisfactorily estimates the oil flowrate in bearings under starved and flooded lubrication conditions, representing a useful and promising tool for fault diagnosis applied to rotating machinery.

Scaled boundary finite element method for hydrodynamic bearings in rotordynamic simulations

The behavior of rotor systems with hydrodynamic bearings can be affected crucially by the nonlinear bearing forces. These forces are incorporated in rotordynamic simulations by solving the Reynolds equation in every step of a time integration scheme. Since closed-form analytical solutions of the Reynolds equation are known only for simplified boundary conditions, numerical methods and look-up table approaches are applied. To obtain accurate and convergent results, numerical solutions require a fine discretization, while the look-up tables require a fine grid of interpolation points. In both cases, the numerical effort of the rotordynamic simulation is dominated by the computation of the bearing forces.In this study, a semi-analytical solution of the Reynolds equation based on the Scaled Boundary Finite Element Method (SBFEM) is developed to reduce the numerical effort of the overall simulation. In contrast to a purely numerical solution, the two-dimensional pressure field is discretized in only one coordinate direction, whereas in the other direction, an analytical formulation is used. This results in a system of non-homogeneous ordinary differential equations, which is solved under consideration of the boundary conditions. Since the complexity of the SBFEM model and the resulting numerical effort depend on the modeling of the oil supply groove, three different models are analyzed in this paper. The equations are derived, the solutions are verified, and their numerical efficiency is investigated in comparison to an FEM solution, which is one of the standard numerical approaches.

Fluid-asperity interaction induced random vibration of hydrodynamic journal bearings towards early fault diagnosis of abrasive wear

One of difficulties to detect abrasive wear in journal bearings through vibration analysis is the lack of obvious fault characteristics in an early stage. To carry out an in-depth investigation on the relationship between wear occurred inside and vibration signals acquired outside is meaningful from the diagnostic point of view. In this paper, a tribo-dynamic model is developed for the fluid-asperity interaction in journal bearings. The microscopic pressure fluctuation induced random excitation is derived. The effects of surface roughness and operating condition on the random excitation are investigated. It is found that wear induced narrowband spatial components of journal surface can excite random vibration of bearing. The speed dependent vibrational behaviour is found to be an effective indicator of surface defects.

Kriging Approach Dedicated to Represent Hydrodynamic Bearings

Abstract The mathematical modeling of journal bearings has advanced significantly since the Reynolds equation was first proposed. Advances in the processing capacity of computers and numerical techniques led to multiphysical models that are able to describe the behavior of hydrodynamic bearings. However, many researchers prefer to apply simple models of these components in rotor-bearing analyses due to the computational effort that complex models require. Surrogate modeling techniques are statistical procedures that can be applied to represent complex models. In this work, Kriging models are formulated to substitute the thermohydrodynamic (THD) models of three different bearings found in a Francis hydropower unit, namely, a cylindrical journal (CJ) bearing, a tilting-pad journal (TPJ) bearing, and a tilting-pad thrust (TPT) bearing. The results determined by using the proposed approach reveal that Kriging models can be satisfactorily used as surrogate THD models of hydrodynamic bearings.

Load-Carrying Capacity Prediction of Magnetic Fluid Hydrodynamic Bearing Under External Magnetic Field

To decrease the negative influence of the poor working environment on lubricating performance, a new hydrodynamic bearing with magnetic fluid is developed, whose lubricating performance can be significantly improved by external magnetic field. The mathematical model of magnetic intensity generating by a solenoid, which is designed as external magnetic field, is deduced according to Biot-Savart Law and validated by measurement experiment. The direct relationship of load-carrying capacity of bearing and magnetic intensity of external magnetic field is built, through analyzing the effect of magnetic flux density on magnetic fluid viscosity. The results showed that solenoid is reasonable to apply as external magnetic field, and its theory works. Magnetic intensity of external magnetic field can enhance and monitor the bearing load-carrying capacity until magnetic fluid reaches magnetic saturation.

Numerical and Experimental Evaluation of Hydrodynamic Bearings Applied to a Jeffcott Test Bench

Merging analytical and numerical models with experimental results improve the behaviour predictions of mechanical elements applied to rotor machinery, such as the bearings. This work aims to present the design of a hydrodynamic bearing prototype, a comparison and validation between the numerical and experimental results of critical speeds, and the differences of behaviour when the bush geometries and lubrication are changed. The bush geometries and the fluid film properties are analysed by measuring the dynamic behaviour of a rotor supported by these bearings. The experimental evaluation is based on measuring the Jeffcott test bench supported in a pair of bearings, showing the anisotropic behaviour caused by the stiffness difference in horizontal and vertical directions. It also presents an optimization of bushings for isotropic conditions when they were changed for different geometries (elliptical, offset halves) and different materials with boundary lubrication. This detailed study shows how the dynamic behaviour of rotating machinery can be predicted using numerical models and its validation by a test rig. Results also show how the vibration occurs if the bushes geometries are modified or its lubrication condition is changed.

Tilting Pad Bearing Pivot Friction and Design Effects on Thermal Bow-Induced Rotor Vibration

Abstract The Morton effect (ME) is a thermally induced vibration problem observed in a rotor supported by hydrodynamic bearings. The journal’s synchronous orbiting induces nonuniform viscous heating on its circumference, and the ensuing thermal bow often causes unacceptable vibration levels in the rotor. This paper investigates the influence of the tilting pad journal bearing (TPJB)’s pivot design on the severity and instability speed range of ME vibration. Simulations are conducted with two different types of pivots: cylindrical (CYL) and spherical (SPH), which produce different pad degrees-of-freedom and nonlinear pivot stiffness due to their geometries. The friction between pad and pivot, which only exists with the spherical pivot, is modeled, and its impact on the ME is evaluated. The example rotor model, as obtained from the literature, is single overhung, with experimentally measured excessive vibration and large journal temperature differentials, near 8000 rpm. The bearing and journal are modeled with three-dimensional (3D) finite elements, and the shaft with flexible beam elements for ME simulation. Nonlinear transient simulations are carried out for a wide operating speed range with varying pivot design parameters. Simulation results indicate that the predicted ME instability is sensitive to the pivot shape, pivot flexibility, and pad-pivot friction.

Study of the influence of surface treatment on the wear development under quasi-static loading of the levers of a newly designed thrust bearing

Hydrodynamic thrust bearings are generally used to absorb axial forces in machinery, especially where the use of rolling bearings is inappropriate in terms of dimensional constraints, service life, high loads or difficult access during assembly. Misalignment between the stator and the rotor, especially on large rotary machines, can lead to a reduction in the load capacity and damage to the entire device. To eliminate misalignment between stator and rotor (especially in large rotary machines) the thrust bearing with a system of very precise manufactured levers has started to be used.The article deals with the study of the influence of surface treatment on the development of wear and damage under quasi-static loading of the levers, which are critical parts of a newly designed axial bearing. The presented research has been carried out in two phases. In the first phase, basic samples that represented the types of geometries coming into contact in real conditions of bearing operation were manufactured and experimentally tested. Based on the results obtained at this stage, it was found that electroless nickel-plated samples showed the best results in terms of surface treatment. Due to this, real levers were produced in three sizes, which are estimated to have the potential for the greatest use in turbines, and these were surface treated with electroless nickel plating. In the second phase, the surface integrity and stiffness of the levers were examined. All samples and levers were made of 34CrNiMo6 steel. The evaluation was performed using stereomicroscope and a scanning electron microscope. Based on the results, it could be stated that the integrity of the surface was not significantly violated in any simple sample or lever. Thus, the tests confirmed the suitability of the proposed method of surface treatment of levers and their sufficient rigidity under quasi-static static loading.

Stochastic model updating of rotor support parameters using Bayesian approach

Uncertainties due to assembling, installation, and operational conditions are extensively involved in rotating systems' parameters. Stochastic characteristics of these parameters may seriously affect rotating systems' vibrational characteristics, such as their critical speeds and vibration amplitudes. These effects make the variability of parameters in the modeling of rotary machines inevitable. In rotating machinery, material properties and geometric parameters of the rotor, bearing characteristics and supports stiffness determine the system's dynamic response. Stochastic model updating methods consider model response variability and allocate them to the model parameters; however, they are not commonly employed in rotor dynamics, and deterministic approaches are still prevalent in this field. Due to the cost and efforts needed to set up experiments and obtain outcomes that reflect the machine's actual characteristics, stochastic updating practices of industrial rotating systems are rarely reported in the literature. This paper adopts an appropriate parameter selection procedure and suitable sampling strategy for stochastic model updating to investigate variability in the dynamic behavior of a complex turbo compressor rotor-bearing-support system, leading to successful parameter identification results. The compressor rotor is mounted on hydrodynamic journal bearings with speed-dependent stiffness and damping. Due to the rotating system complex model, a variance-based global sensitivity method is employed for parameter selection to eliminate non-influential parameters in the model updating and to alleviate updating complexity and computational burden. The Bayesian approach in the stochastic model updating is applied to estimate parameter uncertainty in the rotor with speed-dependent characteristics. Advanced Markov chain Monte Carlo sampling method using delayed rejection adaptive Metropolis algorithm is employed in the stochastic model updating. The updating procedure obtains marginal posterior probabilities of parameters, and uncertain parameter distributions are evaluated using the maximum entropy criterion.

Three-dimensional computational fluid dynamic analysis of high-speed water-lubricated hydrodynamic journal bearing with groove texture considering turbulence

Water-lubricated bearings have attracted increasing attention in the field of high-speed machine tools for their low friction due to low viscosity. However, new problems, in particular, insufficient load capacity, are on the way. To the point, groove-textured journal bearing is adopted in this study. Aiming at investigating the effects of groove texture on high speed, water-lubricated, hydrodynamic journal bearing precisely, and thoroughly, three-dimensional computational fluid dynamic analyses considering cavitation and turbulence are undertaken to assess the tribological performances of the bearing. To reduce the amount of three-dimensional modeling and meshing work, mesh deformation is presented. The numerical results are compared with experiments to verify the validity of the present models and calculation procedures. Pressure distribution, load capacity, and friction of groove-textured water-lubricated journal bearing are analyzed with respect to operating conditions and geometric parameters. Comparisons between groove-textured water-lubricated journal bearing and smooth bearing are carried out to find out the influence of groove texture. It is found that the groove texture can achieve a remarkable improvement of load capacity at a smaller eccentricity ratio and higher rotary speed. The load capacity is affected by the combined effects of groove depth, width, and length. However, generally, the friction force of water-lubricated journal bearing is slightly influenced by groove texture. Results can provide theoretical guidance for the optimal design of groove-textured water-lubricated journal bearing under different operating parameters.

Analysis of Incomplete Film in Parallel Plates Including Inlet Tube and Groove

Abstract To clarify the realistic upstream boundary conditions of hydrodynamic bearings, the oil spread in a complex system of parallel plates including an inlet tube and axial groove is studied by the computational fluid dynamics (CFD) method. The effects of various design parameters including clearance, velocity of bottom plate, and inlet mass flowrate on oil spread-length are presented and explained. By intensive parametric study for these parameters, an empirical expression for the oil spread-length is derived. A groove with blind ends significantly increases the efficiency of the system. A comparison with experimental observation validates the present model as a proper one for accurately solving oil spread in similar systems.

Modal parameters identification of a rotor-journal bearing system using operational modal analysis

The paper investigates the use of operational modal analysis (OMA) techniques applied directly into a rotating machinery with hydrodynamic journal bearings. OMA has proven to be a strong tool for analyzing the dynamics of large structures, especially to its capabilities in civil engineering; however, its application in rotordynamics is still very incipient. The objective here is to make a broader analysis of how this technique can be used in the universe of rotating machines and how the results become reliable. The application of this technique in rotating machines implies some care due to the inherent operating conditions of the system, especially regarding the presence of harmonic forces. The study emphasizes resonance problems with the early natural modes of the structure and its damping. The main novelty of the paper is to present a simple procedure, tapping throughout the rotor, which made possible the application of OMA to extract the modal parameters with satisfactory results in a system in which the classical EMA steeped sine technique was insufficient to provide a good analysis of the rotor. In this type of system, the hydrodynamic bearings and misalignments caused by the coupling of shaft and motor (something quite common in real systems) may cause difficulty in extracting modal parameters depending on the technique used. However, when applying traditional OMA methods, using both the frequency domain (enhanced frequency domain decomposition) and the time domain (stochastic subspace identification), it was possible to make a good identification of the modal parameters of the rotor, with promising results to encourage a broader modal identification of rotating machinery in operating conditions.

Stability analysis of horizontal symmetric flexible rotor mounted on hydrodynamic bearing and squeeze film damper using analytical approach

The paper deals with the development of a close form solution to find the stability of flexible symmetric horizontal rigid and tuned flexible rotor mounted on hydrodynamic bearing with squeeze film damper system. The correlations are developed analytically to find the static equilibrium position of a rigid and flexible rotor-bearing-damper system and stability threshold of the system about its static equilibrium position under isoviscous conditions. Modified Reynolds equation with short damper approximation is used to derive the forces of hydrodynamic bearing and squeeze film damper using π-film approximation under both laminar and turbulent conditions. A simple iterative method is used to predict the stability threshold. Effects of shaft flexibility, damper support flexibility, damper mass and turbulence on stability are discussed. Deployment of squeeze film damper increases the stability limit of horizontal symmetric tuned flexible rotor-bearing system to nearly two times of its original limit and mass of damper play important role to increase the stability threshold of the system. Stability threshold of rigid system can be increased significantly by increasing the damper mass and stiffness. Insertion of turbulence reduces the limits of stability. Further work has been extended to find Thermo-hydrodynamic analysis of rotor -bearing -damper system by solving the Energy equation with adiabatic boundary conditions simultaneously with Reynolds equation with analytical approach. In case of rigid rotor bearing damper system, Thermo-hydrodynamic analysis overestimates the stability threshold as compared to isoviscous conditions, stability limit of horizontal symmetric tuned flexible rotor-bearing -damper system under estimates in comparison with isoviscous conditions till k⇀=1. Stability threshold of rigid system can be increased significantly by increasing the damper mass and stiffness.

Machine learning-based performance analysis of two-axial-groove hydrodynamic journal bearings

The precise prediction of a rotor against instability is needed for avoiding the degradation or failure of the system’s performance due to the parametric variabilities of a bearing system. In general, the design of the journal bearing is framed based on the deterministic theoretical analysis. To map the precise prediction of hydrodynamic performance, it is needed to include the uncertain effect of input parameters on the output behavior of the journal bearing. This paper presents the uncertain hydrodynamic analysis of a two-axial-groove journal bearing including randomness in bearing oil viscosity and supply pressure. To simulate the uncertainty in the input parameters, the Monte Carlo simulation is carried out. A support vector machine is employed as a metamodel to increase the computational efficiency. Both individual and compound effects of uncertainties in the input parameters are studied to quantify their effect on the steady-state and dynamic characteristics of the bearing.

Performance of a Direct Bonded Sub-Millimeter Peek Coating for Hydrodynamic Plain Bearings

Abstract Despite their superior tribological properties, thick-layer bearing coatings based on polyetheretherketone (PEEK) have up to now not been applied in a very high number of plain bearings for industrial applications. This can at least partly be credited to the high costs and low flexibility associated with the coating process for these materials. At the same time, while thick-layer polytetrafluoroethylene (PTFE) coatings have been successfully applied in industrial plain bearings for around 50 years, thin-layer PTFE coatings today constitute the majority of applications of PTFE in plain bearings. It is therefore reasonable to assume a similar approach for thin-layer PEEK coatings. This article reports the performance of a thin-layer PEEK coating directly applied on a mild steel substrate, with results ranging from first sample test through component tests to application in an actual machine and behavior during realistic operating conditions and induced bearing failure.

Investigation of the Tribological Performance of Heterogeneous Slip/No-Slip Journal Bearing Considering Thermo-Hydrodynamic Effects

The slip boundary has an important influence on hydrodynamic journal bearing. However, less attention has been paid to the positive effect of slip on thermal behaviour. In this study, a computational fluid dynamics (CFD) analysis investigating the thermo-hydrodynamic (THD) characteristics of heterogeneous slip/no-slip bearings running under steady, incompressible, and turbulent conditions is presented. A comprehensive analysis is made to investigate the THD behaviours of heterogeneous slip/no-slip bearings in terms of lubricant pressure, temperature distribution, volume fraction of vapor, and load-carrying capacity when they are running under different shaft rotational speeds. The multiphase cavitation model is adopted to represent the real operational condition of the journal bearing. Numerical results show that the load-carrying capacity of the heterogeneous slip/no-slip bearing can be significantly increased by up to 100% depending on the rotational speed. It is also observed that there is an optimal journal rotational speed for maximizing the load-carrying capacity. An insightful new finding is revealed in a numerical framework, wherein it is found that by introducing the heterogeneous slip/no-slip pattern, the maximum temperature can be reduced by up to 25% in comparison with a conventional bearing.

Numerical analysis of rough hydrodynamic bearings for various deterministic micro-asperity features

The hydrodynamic analysis of isotropic and anisotropic Gaussian surfaces has been studied well. However, the analysis reported earlier cannot simply apply to non-Gaussian and self-affine fractal rough surfaces, which demands a thorough investigation to study the effect of non-Gaussian nature of surfaces having different deterministic asperity features. This work demonstrates the effect of non-Gaussian and fractal nature of rough surfaces on hydrodynamic bearing characteristics. The modified Reynolds equation is used in this work with consideration of cavitation. The variation of asperity pressure, hydrodynamic load, and friction force with lambda ratio (the ratio of nominal film thickness to composite roughness) for various types of non-Gaussian and fractal rough surfaces is presented and discussed in detail. It is found that skewness, kurtosis, and fractal signature significantly affect the bearing load capacity and bearing friction force. No significant effect of types micro features is observed on asperity pressure. Asperity pressure is found to decrease with an increase in lambda ratio. More negative skewness results in a decrease in asperity pressure.

Influence of Surface Waviness of Journal and Bearing Bush on the Static Characteristics of Hydrodynamic Bearing

An investigation on the surface waviness of both the journal and the bearing bush and their impact on the static characteristics of the hydrodynamic journal bearing is presented in this paper. The finite difference method is introduced to solve a Reynolds equation and obtain the unknown pressure field. The static characteristics, including the load carrying capacity, attitude angle, end leakage flow rate and frictional coefficient are studied under different waviness parameters. The numerically simulated results indicate that the waviness of the bearing bush may deteriorate or enhance the bearing system, depending on the phase angle. The waviness of the journal causes periodic changes in bearing behavior, owing to the alteration in the phase angle. The profile of the journal and bearing surfaces near the attitude angle determines the performance of the bearing system.

Modelling non-Gaussian surfaces and misalignment for condition monitoring of journal bearings

In the hydrodynamic lubricated journal bearing system, the surface roughness and angular misalignment are two critical factors that affect bearing’s performance. In this paper, the coupled effects of different non-Gaussian properties and misalignments are investigated on the performance of journal bearings. Christensen’s stochastic model is extended by improving the probability density function of random roughness heights, which incorporates the Gram-Charlier expansion including skewness and kurtosis. In comparison with a Gaussian surface, the non-Gaussian rough surface has more significant influence on the bearing static performance. The negative skewness and large kurtosis increase the load capacity and decrease the friction coefficient. According to the simulations and experiments, non-Gaussian properties have more impact on the performance than misalignment when the journal bearing is operated in hydrodynamic lubrication regime based on different pressure distributions and vibration responses. These novel findings provide the basis for monitoring the conditions of hydrodynamic journal bearings.

Experimental analysis of the efficacy of vegetable oil-based nanolubricants for improving journal-bearing performance

The present experimental study explores the performance of Hydrodynamic journal bearings operating with vegetable oil-based nanolubricants. For this study, titanium oxide nanoparticles have been added to canola oil by varying the volume fraction from 0% to 0.04%. An assessment of performance characteristics has been done by using a journal-bearing test rig under different operating conditions. The outcome of the experimental results aimed at the addition of nanoparticles to base lubricants to improve the performance was observed to be favorable. However, under high operating conditions, the influence of nanoparticles is observed to be less useful. The fluid film pressure of nanolubricants increased up to a specific volume concentration of titanium oxide nanoparticles (i.e. 0.02%) beyond which no further enhancement was observed. At a load of 3000 N, the fluid film pressure increased up to 10%, when a bearing is lubricated using canola oil with a 0.02% volume fraction of nanoparticles. The heat transfer rate was found to be higher for nanolubricants in comparison to a base oil and the fluid film temperature was reduced by up to 15% at a volume fraction of 0.04%. Furthermore, rheological studies reveal that the prepared nanolubricants exhibited Newtonian behavior under the given conditions. The percentage increment of viscosity varied from 2.1% to 15.4% and 2.43% to 13.89% for a volume fraction ranging from 0.01% to 0.04% at a temperature of 40 °C and 100 °C, respectively. The dynamic light scattering results confirmed that the particles were well distributed in a base lubricant without much aggregation.