Dynamic Characteristics Of Bearing Research Articles

A study on the temperature rise characteristics of high-speed ball bearings under starvation lubrication

Purpose This paper aims to study the problem of starvation lubrication of high-speed ball bearings due to temperature rise during operation and to avoid thermal failure of bearing lubrication. Design/methodology/approach Under the quasi-statics model of grease lubrication, both the oil film dragging force and the rolling friction between the balls and raceways collectively counteract the gyroscopic torque. Initially, the static model for grease lubrication is solved, followed by calculating the generated heat using the local heat generation method and ultimately the multinodal thermal network model is solved, and the solved results of the quasi-statics are updated by the temperatures of the grease nodes based on the relationship of the grease temperature and viscosity, as well as the relationship of the viscosity and the film thickness. Findings By comparing the numerical calculation results of bearings under different working conditions, the influence of starvation lubrication on the oil film thickness, oil film drag force and rolling friction of bearings is discussed, and it is found that the numerical calculation results of the outer ring temperature of bearings under the starvation lubrication due to the consideration of temperature rise are closer to the experimental values. Originality/value This study reveals the dynamic characteristics of bearings under starvation lubrication, which is more practical and engineering guiding significance for the design of bearings, and introduces a new method and basis for the calculation of temperature rise of rolling bearings. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2024-0208/

Theoretical Evaluation of Lubrication Performance of Thrust-Type Foil Bearings in Liquid Nitrogen

The development of reusable liquid rocket turbopumps has gradually highlighted the disadvantages of rolling bearings, particularly the contradiction between long service life and high rotational speed. It is critical to explore a feasible bearing scheme offering a long wear life and high stability to replace the existing rolling bearings. In this study, liquid nitrogen is adopted to simulate the ultra-low temperature environment of liquid rocket turbopumps, and theoretical evaluations of the lubrication performance of thrust-type foil bearings in liquid nitrogen are conducted. A link-spring model for the bump foil structure and a thin-plate finite element model for the top foil structure are established. The static and dynamic characteristics of the bearings are analyzed using methods including the finite difference method, the Newton–Raphson iteration method, and the finite element method. Detailed analysis includes the effects of factors such as rotational speed, fluid film thickness, thrust disk tilt angle, and the friction coefficient of the bump foil interface on the static and dynamic characteristics of thrust-type foil bearings. The research results indicate that thrust-type foil bearings have a good load-carrying capacity and low frictional power consumption. The adaptive deformation of the foil structure increases the fluid film thickness, preventing dry friction due to direct contact between the rotor journal and the bearing surface. When faced with thrust disk tilt, the direct translational stiffness and damping coefficient of the bearing do not undergo significant changes, ensuring system stability. Based on the results of this study, the exceptional performance characteristics of thrust-type foil bearings make them a promising alternative to rolling bearings for the development of reusable liquid rocket turbopumps.

Study on static and dynamic characteristics of water-lubricated hydrostatic thrust bearings – Effect of feed hole inlet shape on bearing characteristics

Recently, water-lubricated hydrostatic bearings have been attracting attention. However, when water is used as the lubricating fluid, the flow velocity of the feed hole used as a restrictor is higher than that of conventional oil-lubricated hydrostatic bearings, resulting in a larger feed hole inlet flow velocity, making it difficult to analyze its characteristics using conventional hydrostatic bearing analysis methods. Therefore, in this study, a general-purpose fluid analysis tool has been used to numerically analyze the internal flow of two types of pocket-type water-lubricated hydrostatic thrust bearings with different feed hole inlet geometries and found that the pressure loss at the feed hole inlet is large for water-lubricated bearings and that the flow inside the feed hole is different from that of oil-lubricated hydrostatic bearings. The orifice effect at the feed hole inlet is found to account for most of the restrictor function. Furthermore, it was shown that the pressure loss at the feed hole inlet can be increased by adopting a right-angle inflow structure for the feed hole inlet geometry, which can improve the static and dynamic characteristics of the bearing.

Lateral Dynamic Response of Helical Pile in Viscoelastic Foundation Considering Shear Deformation

Helical piles are a new type of pile that has good application prospects, and researchers have carried out an in-depth investigation into their vertical uplift and compressive bearing capacity. However, there is relatively little research on the dynamic bearing characteristics of helical piles. Therefore, the lateral vibration of a helical pile embedded in the viscoelastic foundation is systematically studied in this article. Utilizing the equivalent stiffness method to transform a helical pile into a cylindrical pile of special diameter, the lateral vibration model of the helical pile considering shear deformation is established based on the Winkler foundation model and the Timoshenko beam theory. The analytical solutions for the lateral dynamic displacement, bending moment, and shear force of the helical pile are strictly derived, and the rationality of the present solutions is also verified by comparing them with existing solutions. Based on the present solutions, a parametric study is carried out to investigate the influence of the pile and soil properties on the lateral dynamic response of the helical pile. It is found that the load excitation frequency and pile–soil stiffness ratio have a significant influence on the lateral dynamic displacement, bending moment, and shear force of the helical pile with space and time response.

A study on the influences of journal axial vibration on ship shaft stern bearing dynamic characteristics

PurposeThis paper aim to take the ship shaft stern bearing as the research object, and studies the influence of journal axial vibration on bearing dynamic characteristics under different misaligned angles and rotation speeds.Design/methodology/approachComputational fluid dynamics (CFD) and harmonic excitation method were used to build bearing unstable lubrication model, and the dynamic mesh technology was used in calculation.FindingsThe results indicate that journal axial vibration has a significant effect on bearing dynamic characteristics, like maximum oil film pressure, bearing stiffness and damping coefficients, and the effect is positively correlated with journal misaligned angle. The effect of shaft rotation speed and journal axial vibration on bearing dynamics characteristics are independent; they have no coupling. Bearing axial stiffness is mainly affected by the journal axial displacement, bearing axial damping is mainly affected by journal axial velocity and they are positively correlated with the misaligned angle. The influence of rotational speed on bearing axial stiffness and axial damping is not obvious.Originality/valueThis paper establishes the bearing dynamic model by CFD and harmonic excitation method with consideration of cavitation effect and analyzing the influence of journal axial vibration on the dynamic characteristics. The results are benefit to the design of ship propulsion shaft and the selection of stern bearing. Also, they are of great significance to improve the operation stability of the shaft bearing system and the vitality of the ship.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2022-0337/

Discussion on dynamic characteristics of long journal bearings considering surface roughness

The hydrodynamic bearing is the key part of many rotating machines, and dynamic characteristics of the bearing would affect the operation performance of machines directly. Thus, this study focused on dynamic characteristics of long journal bearings and tried to illustrate the influence of surface roughness on dynamic performances of long bearings. Applying Christensen stochastic model and long bearing approximation, the modified Reynolds equation was established. To solve the modified Reynolds equation, the numerical integration method was applied. It is found that the surface roughness would significantly weaken the stability threshold speed, normal stiffness coefficients ([Formula: see text], [Formula: see text]), and crossed dampness coefficients ([Formula: see text] and [Formula: see text]) for the long bearing with a large eccentricity ratio. In summary, the influences of surface roughness cannot be ignored during discussing dynamic characteristics of long journal bearings.

Horizontal Vibration Characteristics of a Tapered Pile in Arbitrarily Layered Soil

A tapered pile (TP) is a new type of pile with a good bearing capacity, and scholars have conducted in-depth research on its static bearing characteristics. However, there is relatively little research on its dynamic bearing characteristics. In this paper, the horizontal vibration behavior of a tapered pile in arbitrarily layered soil is studied. Utilizing the Winkler foundation model and Timoshenko beam model to simulate pile-surrounding soil (PSS) and a tapered pile, respectively, the horizontal vibration model of a tapered pile embedded in layered soil was built. The analytical solutions for the horizontal displacement (HD), bending moment (BM), and shear force (SF) of a tapered pile were derived, and then the solutions for the horizontal dynamic impedance (HDI), rocking dynamic impedance (RDI), and horizontal-rocking coupling dynamic impedance (HRDI) of pile head were obtained. Using the present solutions, the effects of soil and pile properties on the horizontal vibration characteristics of a tapered pile were systemically studied. The ability of a tapered pile–soil system to resist horizontal vibration can be improved by strengthening the upper soil, but this ability cannot be further improved by increasing the thickness of the strengthened upper soil if its thickness is greater than the critical influence thickness.

Theoretical model and experimental study of the influence of bearing inner clearance on bearing vibration

During the installation and operation of transmission equipment, bearing clearance problems occur, which are also one of the main reasons for bearing failure. Therefore, research on bearing clearance has theoretical significance and engineering value. To determine the influence of bearing clearance on bearing vibration, the theoretical model of a 2-degree-freedom rolling bearing was established based on the dynamic characteristics of the bearing vibration. Based on Hertz elastic contact theory analysis of the dynamic characteristics of the rolling bearing, it was observed that for the tested bearings, the number of balance points of the inner ring of the bearing depends on the clearance of the bearing. When bearing inner clearance (e)e<4.5μm is present in the bearing, a stable equilibrium point exists, and periodic vibration occurs in the inner ring of the bearing near the centre of the balance point. When a gap of (e⩾4.5μm) is present, and the gap and rotational speed of the bearing increase continuously, the system generates chaotic vibrations, and the area in which the chaotic vibration occurs also increases. The experimental results of the ϕ127mm rolling bearing indicated that under the same damping parameters, bearing size and rotational speed, the results of the singular attractors obtained from the experimental data are similar to those obtained by solving the equation of motion. This qualitative result not only confirms the existence of chaotic bearing behaviour, but also verifies the reliability of the theoretical model.

Optimal Design of Clearances of Cylindrical Roller Bearing Components Based on Dynamic Analysis

With the continuous advancement in bearing speed, bearing assembly clearance (pocket, radial, and guide clearances) has a particularly significant impact on dynamic characteristics of bearing. In order to improve its performance, it is necessary to generate an optimized design for assembly clearance based on dynamic analysis. In this paper, a dynamic model of cylindrical roller bearing has been put forth based on the variable step fourth-order Runge–Kutta method, while the simulation results have been verified by a high-speed bearing cage motion testing machine. Considering pocket, radial, and guide clearances as independent variables and maximum impact force, whirl deviation ratio, and minimum power loss as the objectives, a multiobjective optimized model of cylindrical roller bearing has been developed using central composite experimental design (CCD) and response surface method. After optimization, the maximum impact force was reduced by 9.26%, the whirl deviation ratio was reduced by 2.87%, and power loss was reduced by 1.45%.

Thermohydrodynamic investigation for supercritical carbon dioxide high speed tilting pad bearings considering turbulence and real gas effect

A global heat balance method for supercritical carbon dioxide (S-CO2) high speed tilting pad bearings was developed, in which the real gas effect, variable thermodynamic properties, and turbulence effect were considered. The bearing characteristics can be obtained by the partial derivative method embracing dynamic variations of complete variables. Then thermohydrodynamic lubrication mechanisms for S-CO2 bearings are studied, and results indicate that the real gas effect of thermal compressibility is significant. The influence of the thermal effect on the static and dynamic characteristics of bearings is caused by changes in density, specific heat, and thermal expansion coefficient rather than viscosity, which is totally different from oil bearings. In general, the influence of thermohydrodynamic lubrication on static characteristics of S-CO2 tilting pad bearings is more obvious than that on dynamic coefficients. For example, the maximum deviation of damping coefficients of a bearing with parameters in this research at a certain speed range is 8%, and that of the load capacity at the corresponding speed is 10.7%. However, the influence of the thermal effect on dynamic coefficients is varied at different rotating speeds.

Simulation evaluation of dynamic characteristic identification accuracy of sliding bearing considering test error

Aiming at the dynamic characteristics test bench of sliding bearings, the dynamic model is established. Based on the forward and inverse dynamic problems of the bearing, a simulation evaluation method for the identification accuracy of the sliding bearing dynamic characteristics is proposed and the algorithm is verified. The identification errors of dynamic characteristic coefficients under different excitation frequencies are analyzed, the sensitivities of single frequency excitation method and dual-frequency excitation method to test error are contrastively analyzed, and the influence laws of dynamic characteristic identification accuracy of sliding bearing are evaluated. Based on which the traditional single frequency excitation method has been improved. The dynamic characteristic test should be carried out respectively in the low frequency range and the high frequency range. The main stiffness and cross damping are the average of two tests, the main damping is the identification value in the high frequency, and the cross stiffness is the identification value in the low frequency. That will effectively reduce the impact of test error. The obtained data and laws could support the improvement of the dynamic characteristics test method of sliding bearings and the confirmation of test parameters, thereby the accuracy of dynamic characteristics identification is improved.

Influences of bidirectional shaft inclination on lubrication and dynamic characteristics of the water-lubricated stern bearing

This paper investigates the lubrication and dynamic characteristics of water-lubricated stern bearing (WSB) under service conditions. A test scheme of bearing film pressure distribution and spatial shaft position is proposed. The experiment reveals the pressure bias and bidirectional shaft inclination phenomenon of full-size WSB, according to which the transient fluid–solid coupling dynamic model of the bearing is established, considering bidirectional shaft inclination and lining deformation. The calculation method of 16 dynamic coefficients is proposed. Influences of eccentricity ratio, shaft inclination angle, and bearing structure parameters on lubrication and dynamic characteristics are explored systematically. Results indicate that the rotating shaft produces apparent horizontal deflection during the working condition of low speed and heavy load. Under the existence of attitude angle, the horizontal and vertical shaft inclinations both affect the film thickness and pressure distribution, especially at low eccentricity ratio, the horizontal shaft inclination has a greater impact on the bearing. As the length to diameter ratio increases or as the clearance ratio decreases, the effect of vertical shaft inclination on lubrication and dynamic characteristics of the bearing decreases, and that of horizontal shaft inclination increases. Research results are instructive for further study on the effect of misalignment on the structural design and optimization for such bearings.

Structural optimization and dynamic characteristics of the new type 3-degrees of freedom axial and radial hybrid magnetic bearing

A new type of three degrees of freedom axial-radial hybrid magnetic bearing (3-DOF ARHMB) with compact structure, shorter axial length and smaller volume is proposed for the flywheel energy storage system. The axial direction adopts the permanent magnet biased thrust bearing (PMB) made of soft magnetic composite materials (SMCs). In the radial direction, the laminated structure is used to reduce the eddy current, and the Halbach array is introduced to strengthen the magnetic density of the radial air gap. Firstly, the dynamic magnetic flux distribution of the 3-DOF ARHMB is analyzed by the finite element method (FEM). Based on the equivalent magnetic circuit method, the equivalent reluctance model with comprehensive consideration of eddy current effect and magnetic leakage effect is established, and then the frequency responses are analyzed. Secondly, a constraint model coupled with structural parameters, equivalent reluctance and magnetic leakage coefficient is established, and an adaptive particle swarm optimization algorithm (APSO) is used to optimize the bearing parameters. Finally, based on the equivalent reluctance model, the axial and radial force-current factor and force-displacement factor are derived, and the dynamic characteristics of bearings with different structures and materials are compared and analyzed. The results show that the new 3-DOF ARHMB made of SMCs can provide much larger and more stable magnetic force and larger bandwidth than that made of carbon steel materials, and has better dynamic characteristics under higher-frequency conditions, which can meet the industrial requirements of flywheel energy storage system.

РЕКОМЕНДАЦИИ ПО ПРОЕКТИРОВАНИЮ ГИДРОСТАТОДИНАМИЧЕСКИХ ПОДШИПНИКОВ СКОЛЬЖЕНИЯ СДВОЕННОГО ТИПА

The task is to develop recommendations for the design of dual-type hydrostatodynamic plain bearings based on the existing experience in designing this type of plain bearings, as well as based on many theoretical and experimental studies performed by the author of this work. The number of the most necessary parameters for the design of dual-type hydrostatodynamic bearings is determined. Particular attention was paid to the development of recommendations for additional parameters specific to the design of double type plain bearings. Attention is paid to the selection of double-type bearing materials and it is shown that the problem of selecting materials for hydrostatic dynamic bearings is not so relevant, however, sometimes in start-up and shutdown modes, as well as in emergencies, to ensure high reliability of the designed machine, it is necessary to pay attention to the choice of bearing materials. The influence of various forms of chambers on the static and dynamic characteristics of hydrostatodynamic bearings is analyzed and it is shown that the greatest distribution in practice, they got rectangular cameras. It is shown that the flow regime of the working fluid also significantly affects both the static and dynamic characteristics of the bearing. It is noted that even with a non-rotating rotor in a hydrostatodynamic bearing, the most turbulent mode of flow of the working fluid is most often observed. The influence of the thickness of the working fluid layer on increasing the rigidity of the supports and expanding the range of stable operation is considered. It is shown that with a decrease in the clearance in the bearing, its bearing capacity increases and the range of stable operation expands, however, this increases the friction power loss, increases the likelihood of clogging of the slit bearing path, and also increases the requirements for the quality of manufacture of the bearing working surfaces. It is recommended that in the double hydrostatodynamic bearing in the outer and inner parts to assign the same clearances. It is shown that in a dual hydrostatodinamic bearing, the existing recommendation on the number of chambers can lead in some cases to large working fluid flow.

The influences of bump foil structure parameters on the static and dynamic characteristics of bump-type gas foil bearings

Bump-type gas foil bearing is a special type of sliding bearing, especially suitable for supporting rotors with light loads and high speeds. In this paper, a deformation model of bump foil is established by using elastic mechanics theory. A fluid-structure interaction algorithm is proposed according to Reynolds equation of compressible gas. On this basis, a method for calculating the static and dynamic characteristics of the bump-type gas foil bearing is established considering the structure parameters of the bump foil. The presented model is validated using the data reported in the existing research. The gas film pressure distribution, gas film thickness distribution of the bearing, and the influences of bump foil structure parameters on the static and dynamic characteristics of the bearing are studied with an example. Results show that, decreasing the bump foil thickness tB or increasing the bump pitch s will increase the limiting load-carrying capacity W and decrease the attitude angle β. And increasing tB or decreasing s will decrease the friction torque Tr and increase the side leakage flow of gas Qz, resulting in less friction heat generation and faster heat dissipation. Increasing tB or decreasing s will increase the absolute values of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] of the gas film, leading to higher equivalent stiffness of the gas film [Formula: see text].

A 3D Approach for THD Lubrication in Tilting Pad Journal Bearing—Theory and Experiment

The study of rotating machines stands out in the context of systems and structures due to the significant number of typical phenomena that may be present during the operation of such equipment. Rotating systems play an important role in industrial environments, with a wide range of application, namely, pumps, turbines, generators and compressors, and turbochargers, among others. Given this context, tilting pad journal bearings (TPJBs) can offer considerable stability to the rotor system due to its damping and stiffness characteristics, especially under high rotation speeds, whereas journal bearings with a fixed geometry may be subjected to fluid-induced instability. Consequently, thermal effects are significant in rotating machines to evaluate the behavior of hydrodynamic bearings due to the increase in shear effects in the lubricant caused by the rotation speed, leading to excessive temperature increase under specific operational conditions and, therefore, significant changes in lubricant viscosity. These effects may influence the dynamic characteristics of bearings, affecting the dynamic response of the entire system. From this perspective, a specific test rig was designed to perform the characteristic uncoupled motion of the shaft when supported by this kind of bearing. Experimental tests were directly compared with numerical models, showing promising results. In addition, the thermohydrodynamic (THD) lubrication was numerically solved by a finite volume method, considering an approach for a 3D THD model and the pivot flexibility.

Effect of clearances in rolling element bearings on their dynamic performance, quality and operating life

The performance of rolling element bearings is one of the machine quality measures in industry. The fatigue life and performance of rolling element bearings depends mainly on the dynamic characteristics of those bearings. This paper studied the effect of the internal radial clearance on the damping characteristics, natural modes of vibration, and fatigue life of rolling element bearings. Vibration modal analysis was performed on rolling bearings of the same size and type to measure their dynamic characteristics. These dynamic characteristics include the natural frequency of the first mode of vibration, damping, and amplitude of frequency response function at resonance. The internal radial clearances of these bearings were measured. A statistical analysis was performed to study the correlation between the internal radial clearance and the dynamic characteristics of rolling bearings. It was found that the damping ratio of the bearing assembly increased by reducing the internal radial clearance of the bearing. Similarly, rolling bearings that have large internal clearances showed short predicted fatigue life. It is concluded that the dynamic characteristics, and consequently the dynamic performance, of rolling bearings are significantly affected by the internal radial clearance.

Influences of wear on dynamic characteristics of angular contact ball bearings

Wear between balls and races has significant effects on the dynamic characteristics of bearing, which is the main reason to cause bearing failure. Some existing contact stiffness models were established to study the dynamic characteristics of bearing. However, the wear of bearing has been rarely investigated due to the complexities of contact load and wear mechanism. This paper presents a new dynamic wear simulation model of angular contact ball bearings mounted in pairs to solve this problem. A final contact stiffness model is established based on the wear model. The effects of running distance, horizontal load, preload, initial contact angle, number and diameter of balls on wear performances are analyzed. A generalized time-varying and piecewise-nonlinear dynamic model of angular contact ball bearings is established to perform an accurate investigation on its dynamic characteristics, especially considering the coupling effects of wear and rolling contact. The effects of wear on the contact stiffness and nonlinear dynamic characteristics are analyzed according to the dynamic model. Additionally, the variations of the contact stiffnesses and frequency responses with different preloads are discussed and the results indicate that parameter selection has significant effects on the wear and nonlinear response.

Assessment of Bearing Dynamic Characteristics by Numerical Modeling with Effects of Oil Film and Centrifugal Deformation

This paper developed a modified quasi-static model (MQSM), considering the oil film thickness between the bearing parts and the centrifugal deformation of the inner ring, and contrasting with traditional quasi-static model (TQSM), to analyze the dynamic characteristics of spindle bearing. The model was verified with the experimental results. A systematic parametric analysis was made to investigate the influence of applied load, inner ring rotation speed (ni), and the radius coefficient of groove curvature (RCR) on the contact load, contact angle, and heat generating rate. The results show that there is a smaller influence on the contact load, contact angle, and heat generation of bearing with the changes of ni and axial load (Fa) of bearing in the case of MQSM and TQSM. But the radial load (Fr) and RCR have great influence on this.

Effect of surface texturing on the dynamic characteristics of hydrodynamic journal bearing comprising concepts of green tribology

Surface texturing has emerged as a viable option for enhancing the surface properties. The present study analyzes the effect of full and partial micro-textured surface, at different locations and different kinds of dimple geometries, on the dynamic characteristics of hydrodynamic journal bearings and made a comparative study with the non-textured bearings. Three different kinds of dimple geometries, namely, circular texture, square texture, and densely distributed square texture have been adopted for study. The important dynamic characteristics of bearings were evaluated and stability charts were plotted. Location of the texture was found as an important parameter for improved dynamic characteristics though the extent of improvement depends largely on the geometry of texture. The partial textured bearing with proper geometry and location was found to be more stable. Stability margin of such bearings was more in comparison to the plain journal bearings and the relative improvement was found to be the maximum for circular texture and minimum for square texture. The study also shows the potential of surface texturing to make contribution in the accomplishment of the objectives of green tribology.