Dynamic Characteristics Of Bearing Research Articles

Effect of groove texture on the dynamic characteristics of water-lubricated thrust bearing

In this study, the effects of groove texture on the dynamic characteristics of water-lubricated thrust bearing are theoretically investigated. The turbulent Reynolds equation and its perturbation equations for water-film lubrication are derived and solved by using finite difference method. Dynamic characteristics including the stiffness and damping coefficients of the bearing are calculated. The effects of rotary speed, film clearance and geometrical parameters including groove texture depth and circumferential angle on the dynamic characteristics of the bearing have been investigated.

Study on Dynamic Characteristics of Aerostatic Bearing with Elastic Equalizing Pressure Groove

Microvibration has an important influence on the dynamic performance of aerostatic bearings. Dynamic stiffness and equivalent damping coefficient are the main indexes to evaluate the dynamic characteristics of the aerostatic bearing. In order to study the dynamic characteristics of a new type of aerostatic bearing with the elastic equalizing pressure groove (EEPG), the dynamic characteristics of the new type of bearing are studied by theoretical calculation and experiment. First, the dynamic gas‐solid coupling control equation is established. Then, the steady term and the perturbation term are decomposed by the perturbation method. By solving the coupling model, the dynamic characteristics of the bearing are calculated and analyzed. The calculation results show that the perturbation frequency has a significant effect on the dynamic stiffness and equivalent damping coefficient of the aerostatic bearing with EEPG. The dynamic stiffness increases with the increase of frequency, and the equivalent damping coefficient decreases with the increase of frequency. The experimental results are basically the same with the theoretical results, which effectively verify the correctness of the theoretical analysis.

Analysis of dynamic characteristics and stability prediction of gas bearings

PurposeThe prediction model to estimate the stability of a rotor-bearing system is established, which can predict the stability of gas bearings by applying Routh–Hurwitz stability criterion. This paper aims to provide the theoretical foundation for controlling actively the bearing running stiffness and damping and stemming the instability of a gas film.Design/methodology/approachThe nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established. Perturbation control equation is derived by the partial derivative method. The finite difference method is used to discrete the perturbation control equation in generalized coordinate system, and the difference expression of perturbation pressure is derived. The relational expression which involves the relationship between the dynamic characteristic coefficients of HSGHGB systems and perturbation pressure is deduced. So, the transient perturbation pressure distribution of a three-dimensional micro gas film, nonlinear gas film force, dynamic stiffness and dynamic damping coefficients of bearings are numerically computed using VC++6.0 programs.FindingsThe results show that the influence of supply pressure, speed and eccentricity on the dynamic characteristics of bearings is significant.Originality/valueThe influence law of supply pressure, speed and eccentricity ratio on the dynamic stiffness and damping coefficients of HSGHGB systems is researched. The prediction model to estimate the stability of rotor-bearing system is established, which can predict the stability of gas bearings by applying the Routh–Hurwitz stability criterion.

Study on the Load Distribution and Dynamic Characteristics of a Thin-Walled Integrated Squirrel-Cage Supporting Roller Bearing

Thin-walled integrated flexible support structures are the major trend in the development of current rolling bearing technology. A thin-walled, integrated, squirrel-cage flexible support roller bearing, quasi-dynamic iterative finite element analysis (FEA) model is established in this paper. The FEA model is used to calculate the structural deformation of the thin-wall rings and support structures; the dynamic characteristics of the bearing are analyzed using the noncircular bearing modified quasi-dynamic model. The influence of the integrated flexible support structure on the internal load distribution and the dynamic characteristics of the roller bearing are analyzed. The results indicate that with the support of a flexible squirrel-cage, the maximum contact load is decreased by 14.2%, the loading region is enlarged by 25%, the cage slide ratio is reduced by 24%, and the fatigue life is increased by more than 50%. In addition, as the ring wall thickness increased, the results increasingly approached those under a rigid assumption.

慣性気体軸受のCFD解析

Hydroinertia gas journal bearings have been used for ultra high-speed rotational machines such as those used in solid state nuclear magnetic resonance (NMR) devices. This type of bearing has inherent orifice restrictors and a large radial clearance compared with conventional externally pressurized gas journal bearings. The large radial clearance makes these bearings suitable for use with a rapidly rotation sample tube (shaft) since instabilities are suppressed by the reduction in hydrodynamic effects. These bearings achieve stable operation for ultra high-speed rotation of spiner shaft at several million rpm. However, solid state NMR devices require a further high speed rotation because of improvement of analysis precision. Therefore, a hydroinertia gas bearing with supply holes inclined in the direction of rotation has been presented. In this bearing, viscous frictional loss is thought to be reduced since this mechanism provides gas flow in the rotational direction. This study reseach practical utillty and the characteristics of this bearings by using a a computational fluid dynamics analysis. This report presents the change of dynamic characteristics of bearings for rotation.

A Comparative Performance Analysis of Gas Lubricated Cylindrical and Elliptical Journal Bearings

The finite element method is employed to perform a comparative analysis of gas lubricated cylindrical and elliptical journal bearings in this work. A finite element procedure, based on the Galerkin weighted residual method, is specially devised to solve the zeroth- and first-order lubrication equations for plain cylindrical and non-cylindrical hydrodynamic journal bearings running on thin gas fluid films. Load-carrying capacity and dynamic force coefficients of gas cylindrical and elliptical journal bearings are computed for some geometric and operating parameters, such as journal eccentricity ratio and rotational speed. Several comparative curves of steady-state and dynamic bearing characteristics depict the differences in the behavior of some gas lubricated fixed-geometry journal bearings.

An Approach to Investigate Dynamic Parameters of Bearings Joint Surfaces Based on the SDOF System

As commonly supporting parts of the spindle and the feed systems on the high-end grade CNC machine tool, the dynamic characteristics of angular contact ball bearings had been a research hot spot in the current. Aiming at solving the problem that obtained dynamic stiffness and damping of angular contact ball bearings, an approach to investigate dynamic parameters of bearings joint surfaces was proposed based on the single degree of freedom (SDOF) system, and several groups of modal testing were carried out. The dynamic characteristics of bearings joint surfaces were viewed as several viscoelastic units of spring and damper. Then, models of bearings dynamic parameters in the axial and radial directions were established, and several groups of modal simulation were carried out. The comparison of experiment and simulation results showed that the proposed approach could accurately identify dynamic stiffness and damping of bearings under different load conditions, and the errors were controlled within 7.6%.

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness, and Different Pad Preloads

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to nonsynchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are compared to a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced nonsynchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two-degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

Centrifugal Expansion of High-speed Spindle and Its Influences on Bearing Dynamic Characteristics

Focusing on a high-speed spindle system,the shaft and the bearing inner ring are modelled as a beam with the same cross-section and a hollow disk,respectively.The radial elastic deformations of the spindle shaft and the bearing inner ring under centrifugal forces are investigated.The changes of the connected state between the shaft and the bearing with speed are analyzed as well.Considering the centrifugal expansion of rotating components,a dynamic model for the high-speed spindle bearing is given with experimental verification.On this basis,the centrifugal influence on the radial preload state of spindle bearings are studied,and then the rules that how dynamic properties of the high-speed rolling bearing change with the speed are revealed.The results show that,the contact angles decrease,while the contact loads increase with the radial expansion deformation.Both the axial stiffness and the radial stiffness of spindle bearings decrease when the rotating speed increases.The radial expansion deformation of bearing inner rings due to the centrifugal force has an ignorable influence on the axial stiffness of bearings,while it can increase the radial stiffness of bearings to a certain extent.

Numerical calculation and experimental verification of static and dynamic characteristics of aerostatic thrust bearings with small feedholes

In this work, aerostatic annular thrust bearings with feedholes of less than 0.05 mm in diameter are considered, and the static and dynamic characteristics of these bearings are investigated experimentally and numerically. In numerical calculations using the finite difference method (FDM), the discharge coefficients of a small feedhole were determined based on computational fluid dynamics (CFD) software and verified experimentally. In addition, the effect of the bearing surface roughness on the bearing characteristics was analyzed experimentally and numerically. It was confirmed that aerostatic thrust bearings with small feedholes could have larger stiffness and damping coefficient than bearings with compound restrictors.

Wear identification in rotor-bearing systems by measurements of dynamic bearing characteristics

During operation of rotating machines, journal and bearing mechanisms are progressively worn down. To prevent catastrophic failure of a rotating system, it is necessary both to detect wear precisely, without shutting down and dismantling the machinery and to predict future replacement needs. In this work, Computational Fluid Dynamics (CFD) analysis is used to solve the Navier-Stokes equations. Diagrams of bearing characteristics such as relative eccentricity, attitude angle, lubricant side flow and friction coefficient versus Sommerfeld number are presented for various wear depths and used for online wear identification. A graphical detection method is analytically presented to identify the wear depth associated with the measured dynamic bearing characteristics.

Experimental studies on the dynamic characteristics of rolling element bearings

The effect of varying parameters on the stiffness and damping of an angular contact ball bearing was studied under rotating conditions. Axial and radial preloads have the most significant effect on dynamic characteristics of bearings, as there is a dependence of the characteristics on oil viscosity. The differential heating of the bearing components could also be a very sensitive factor. It was concluded that the joint between the bearing and the housing has a significant effect on the total dynamic characteristics of the bearing assembly.

Vibration Characteristics of Hydrodynamic Fluid Film Pocket Journal Bearings

Theoretical analyses of hydrodynamic fluid film bearings with different bearing profiles rely on solutions of the Reynolds equation. This paper presents an approach used for analysing the so‐called pocket bearings formed from a combination of offset circular bearing profiles. The results show that the variation of the dynamic bearing characteristics with different load inclinations for the pocket bearings is less than that for the elliptic bearing counterpart. It is shown that the natural frequencies as well as the critical speeds, and hence the vibrational behaviour, can also be significantly different for an industrial rotor supported by the different bearings.

Stability of Jeffcott Rotor Operating in Tilting 3-Pad Journal Bearings with Turbulent Oil Film

This paper introduces the results of theoretical investigation on the dynamic characteristics of tilting 3-pad journal bearing that operates with turbulent oil film. The Reynolds, energy, viscosity and geometry equations determine the oil film pressure, temperature distributions, and oil film resultant force that are the grounds for the dynamic characteristics of bearing. These equations were solved simultaneously on the assumption of adiabatic laminar or adiabatic turbulent oil flow in the bearing gap. The stability and system damping of Jeffcott rotor operating in tilting 3-pad journal bearing was determined.

DYNAMIC REYNOLDS EQUATION FOR MICROPOLAR FLUID LUBRICATION OF POROUS SLIDER BEARINGS

182 ABSTRACT In this paper an attempt has been made to study the rheological effects of micropolar fluid lubricants on the steady state and dynamic behavior of porous slider bearings by con- sidering the squeezing action. The general modified Rey- nolds-type equation of porous sliding-squeezing surfaces with micropolar fluids is derived for the assessment of dynamic characteristics of bearings with general film thickness. The detailed analysis is presented for the plane inclined porous slider bearings by using perturbation method. Two Rey- nolds-type equations corresponding to steady performance and perturbed characteristics are obtained. The closed form solution of these equations is obtained. The numerical computations of the results show that, there exists a critical value for profile parameter at which the steady-state load and dynamic stiffness coefficient attains maximum. Further the micropolar fluids provide improved characteristics for both steady-state and the dynamic stiffness and dynamic damping characteristics. It is found that the maximum steady load carrying capacity is func- tion of coupling parameter and the permeability parameter and is achieved at smaller values of profile parameter for larger values of the coupling parameter.

Study on dynamic characteristics of angular ball bearing with non-linear vibration of rotor system

A rotor system supported by an angular ball bearing displays very complicated non-linear behaviour due to non-linear Hertzian contact force. The non-linear force and moment caused by the ball bearing are calculated on the basis of the relationship between deflection, and five-degree-of-freedom dynamic equations of the rotor ball bearing system are established. The Newmark-β method and the Newton—Raphson method are used to solve the non-linear equations. The dynamic characteristics of angular ball bearings are computed, considering the non-linear vibration of the rotor system. Taking angular ball bearing QJS208ACQ4C1/HNP4 as an example, the effects of the vibration of the rotor system on bearing dynamic characteristics are analysed. The results show that the spin-to-roll ratio of balls, the slide ratio of the cage, and stiffness of the bearing all vary obviously with the non-periodic vibration range of the rotor; initial contact angle and axial load of the ball bearing change the non-linear dynamic nature of the rotor system and dynamic characteristics of the bearing. The rotor ball bearing system can work stably by choosing the structural and operation parameters reasonably.

Dynamic Reynolds equation for micropolar fluids and the analysis of plane inclined slider bearings with squeezing effect

The general dynamic Reynolds equation of sliding-squeezing surfaces with micro-polar fluids is derived for the assessment of dynamic characteristics of bearings with general film thickness. The detailed analysis is presented for the plane inclined slider bearings by using perturbation method. Two Reynolds-type equations corresponding to steady performance and perturbed characteristics are obtained. The closed form solution of these equations is obtained. The numerical computations of the results show that, the micropolar fluids provide an improved characteristics for both steady-state and the dynamic stiffness and damping characteristics. It is found that the maximum steady-load-carrying capacity is function of coupling parameter and is achieved at smaller values of profile parameter for larger values of the coupling parameter.

Analysis of Dynamic Characteristics of Spiral-Grooved Journal Bearing with Considering Cavitation Occurrence

Dynamic characteristics of an oil-lubricated spiral-grooved journal bearing are theoretically investigated in this paper with considering the effect of cavitation occurrence in the bearing clearance. The Reynolds equation by cooperating with a cavitation theory called ‘equivalent flow model’ as a formulation for cavitation occurrence is expanded by perturbation scheme with respect to the journal eccentricity, so that the dynamic bearing characteristics, such as bearing stiffnesses and damping coefficients, are calculated from the obtained results of perturbed pressure distributions. It is shown that, when the cavitation occurrence is considered, the value of the direct bearing stiffness becomes larger, while those of the cross-coupling bearing stiffness and damping coefficients become smaller, compared with those with neglecting the contribution of the cavitation occurrence. Stable operating limits against ‘half-frequency whirl’ are discussed as well, showing that the critical mass values become larger when considering the cavitation occurrence than those with neglecting it.

Estimating the static load on the fluid bearings of a flexible machine from run-down data

A series of recent papers has discussed the problem of parameter identification for rotating machinery. Two techniques have been developed to identify the foundation parameters, the unbalance distribution and the state of bend. In this paper, the method based on the non-linear optimisation of the fit between the measured and model behaviour is extended to evaluate the steady load in oil film bearings. This is an important practical problem since these steady loads have a strong influence on the bearing's dynamic characteristics. After developing the theory, two distinct examples are simulated and corrupted with noise. In simulation it is shown that the technique is capable of yielding accurate results. It is demonstrated that a measurement of absolute shaft motion is required to give predictions that are sufficiently accurate to be useful. This is not an undue restriction since most modern machines are equipped with proximity probes. The experimental verification of the method is planned on a new rig, currently under construction.

Calculation of Journal Bearing Dynamic Characteristics Including Journal Misalignment and Bearing Structural Deformation©

A detailed journal bearing analysis for accurate evaluation of film dynamic characteristics is presented. The new formulation is based on a local perturbation of the oil film at each computational node that captures the important effects of journal misalignment and bearing structural deformation in rotor dynamics and engine NVH applications. The new algorithm is an extension to the classical approach of evaluating film dynamic characteristics based on journal eccentricity perturbation. The governing equations for the oil film pressure, stiffness, and damping are solved using a finite difference approach and their output is validated with numerical results from the literature.