Spherical Spiral Groove Bearings Research Articles

Thermohydrodynamic Analysis and Thermal Management of Spherical Spiral Groove Gas Bearings

ABSTRACTA thermohydrodynamic model of spherical spiral groove bearings is presented by considering the effect of bearing temperature change on the material property of lubricant, gas flow characteristics in the grooves, and thermal energy transported in the entire bearing system. A gas mixing model in the grooves is introduced as the boundary condition to solve the bearing temperature distribution simultaneously with the heat conduction at the shaft and the housing. The bearing and rotor expansion caused by temperature increases, which is considerable compared to bearing clearance, is also examined. Prediction results show that the thermal expansion determined by actual bearing clearance has a crucial influence on the bearing load capacity. Manufacturing bearings with proper materials has significant effects on controlling thermal expansion effects on the bearing performance. The load capacity, which corresponds to the lubricant gas pressure, and gas suck flow rate have the same variation tendencies as the variation in groove depth and spiral angle. These similar tendencies have an opposite influence on the temperature and result in the temperature increase not being affected by the variation in grooves. However, varying the groove characteristics has a similar effect in carrying away the thermal energy as the variation in heat transfer coefficient, which could significantly control the temperature increase at the same time.

Thermohydrodynamic analysis of micro spherical spiral groove gas bearings under slip flow and surface roughness coupling effect

The effects of gas rarefaction and surface roughness are temperature-related and always neglected in macroscale. These effects were considered in the analysis of the thermohydrodynamic performance of micro spherical spiral groove bearings. The Reynolds equation and the energy equation incorporated with Wu's slip model and the Weierstrass---Mandelbrot function to analysis the coupling effect of slip flow and surface roughness. The effects of spherical grooves on computational accuracy were reduced through parameter transformation and oblique coordinates. To describe the temperature boundary condition at the grooved region, a simple gas-mixing model was presented for the grooves. Prediction results showed that temperature reduced bearing forces and friction torque through the slip flow effect. Surface roughness increased not only temperature significantly but also bearing forces and friction torque through a high eccentricity ratio and a low bearing clearance.

Design of Spherical Spiral Groove Bearings for a High-Speed Air-Lubricated Gyroscope

A spherical spiral groove gas bearing has the ability to not only support radial and axial loads simultaneously but also tolerate extensive misalignment. Thus, this bearing type is considered suitable as a supporting and lubrication component of inertial components such as gyroscopes in the fields of aerospace and navigation. In this study, we propose a numerical method for predicting static and dynamic characteristics and conduct a parametric analysis of an aerodynamic spherical bearing with rotating spiral grooves. The finite difference method and the perturbation method are used to calculate the Reynolds equation to obtain the force coefficients. Given the complicated groove distribution, as well as film discontinuity and compressibility, solving the equations numerically in the spherical coordinates system is difficult. Parameter transformation and oblique coordinate transformation are thus applied in this study to modify the Reynolds equation into the planar oblique coordinate system. An eight-point method is also utilized to deal with film thickness discontinuity. The predictions of this proposed method show good agreement with the available experimental data. Parametric studies on nominal clearance, eccentricity ratio, rotating speed, groove depth, groove angle, and perturbation frequency are then conducted to determine optimum design parameters. The results show that these factors significantly affect bearing characteristics in both the radial and axial directions.

Theoretical analysis of the slip flow effect on gas-lubricated micro spherical spiral groove bearings for machinery gyroscope

The performance of a gas-lubricated micro spherical spiral groove bearing (MSSGB) with slip flow effect is investigated. A modified Reynolds equation incorporated with Barber's first-order slip flow model is proposed to investigate the flow characteristics of gas in MSSGBs. Parameter transformation and oblique coordinate transformation are applied to eliminate the curve effect on the calculation domain. An improved finite difference method (FDM) based on Green's formula is used to solve the Reynolds equation. The perturbation method is adopted to determine the dynamic coefficients. The effects of slip flow and bearing parameters, including the groove depths, rotor speeds, and eccentricity ratios, on the bearing characteristics are investigated and discussed. Prediction results show that the slip flow effect on MSSGB performance is significant. Moreover, the groove depth at micro clearance has a crucial influence on bearing performance.

A Method of Determining the Stability of a Spherical Gasdynamic Bearing Assembly in the Central Position of the Rotor

The stability of a spherical spiral-groove gasdynamic bearing assembly is investigated in the first approximation for small clearances in the central position of the rotor. The gas lubrication equations are discretized by the Bubnov-Galerkin method in order to calculate the stability factor of the bearing.

Dynamic Analysis of a Rotor System Supported by a Spherical Spiral Groove Bearing.

The dynamic characteristics of a rotor system supported by an oil-lubricated spherical spiral groove bearing (SSGB) were analyzed. In the analysis, the characteristics of SSGB were calculated by means of the finite-element method (FEM), and the rotor system had six degrees of freedom. The dynamic stability of the rotor system was analyzed by means of a nonlinear orbit method using the Runge-Kutta-Gill method. The dynamic imbalance response was analyzed and the limiting imbalance was also calculated. Moreover, the effects of sudden elimination of the upper bearing upon stable rotation were also considered. The validity of this analysis was examined by several experiments.

The design of a flat negative pattern to make grooves on a spherical spiral groove bearing

In the present work we describe a procedure to design a Flat Negative Pattern which can be used to photo-etch the spiral grooves on a spherical thrust bearing. The design of the Flat Negative is accomplished in such a way that only one pattern is used for successive exposures resulting in perfect grooves. A groove is taken to be the space bounded by two logarithmic spiral curves separated by a distance equal to the desired width of the groove. The desired Flat pattern is obtained through normal projection of these curves on a plane parallel to the Negative. The projection is accomplished by using three-dimensional (3D) geometric transformations of a large number of points taken on the curves.

Fluid Inertia Effects on the Load Capacity of Spherical Spiral Groove Bearings

The effects of centrifugal force on the load capacity of inwardly and outwardly spherical spiral groove bearings, operated in laminar regime and lubricated with incompressible fluid, have been investigated. The narrow groove theory has been generalized to include the centrifugal effect of lubricant. The analysis demonstrates that the fluid inertia force reduces the load capacity of an inwardly pumping bearing, whereas it increases the load capacity of an outwardly pumping bearing. The theoretical results are compared with the experimental ones.

Stiffness and damping coefficients of spherical spiral grooved bearings: Influences of vertical eccentricity and compressibility of lubricant

The dynamic characteristics of a spherical spiral groove bearing have been analysed using a narrow groove hypothesis for the cases of incompressible fluid film and isothermal gas film. The usefulness of the proposed method is demonstrated by a comparison of results with those obtained using established methods. The method is especially efficient for optimization design and other analysis problems for which other available calculation methods require significant computational effort. The influence of bearing parameters and compressibility of the fluid on dynamic performance and stability are presented.

Fluid Inertia Effects on the Load Capacity of Outwardly Pumping Spherical Spiral Groove Bearings

回転体の高速化に伴い流体によって潤滑された軸受の特性は、流体の慣性力によって影響を受ける。本論文では、ポンプアウト式球面スパイラルグループ軸受の負荷容量などにおよぼあす慣性力の影響について検討している。その結果、ポンプイン式では慣性力によって負荷容量が減少するのに対し、ポンプアウト式では逆に増加すること、またグループ面回転の場合の方が平滑面回転の場合より影響が著しいことを明らかにしている。

Fluid Inertial Effects on the Load Capacity of Spherical Spiral Groove Bearings

回転体の高速化に伴い流体によって潤滑された軸受の特性は,流体の慣性力によって影響を受ける。本論文では,球面スパイラル・グループ軸受の負荷容量に及ぼす慣性力の影響を検討している。その結果,慣性力によって負荷容量が著しく減少すること,また,グループ面回転の場合と平滑面回転の場合では減少量が異なること,そして軸荷重一定の系では浮上量に上限のあることなどを明らかにしている。

Characteristics of Outwardly Pumping Spherical Spiral Groove Bearings : Part 2 Stability

The stability characteristics of outwardly pumping spherical spiral groove bearings lubricated with incompressible liquid are investigated. The resultant bearing forces induced by small vibrations of a rotor under radially unloaded conditions are obtained. The bearing parameters have been optimized in search of the maximum axial load capacity, and then in search of the maximum radial stiffness. The stability characteristics of outwardly pumping spherical spiral groove bearings are compared with those of inwardly pumping ones. Experimental results are in good agreement with the theoretical ones. The conclusions are as follows. Although the maximum axial load capacity of outwardly pumping bearings is a fraction of that of inwardly pumping ones, outwardly pumping bearings are as stable as inwardly pumping ones. Generally, the stability threshold when a grooved member is rotating is higher than when a smoothed member is rotating.

Characteristics of Outwardly Pumping Spherical Spiral Groove Bearings : 2nd Report, Stability

Characteristics of Outwardly Pumping Spherical Spiral Groove Bearings : 2nd Report, Stability

Exact Two-Dimensional Theory of Spherical Spiral Groove Bearings

This paper is concerned with a method of obtaining exact solution for the flow of fluid film of spherical spiral groove bearing. The problem is analyzed for three cases where the centers of two elements of a bearing coincide, slightly offset vertically and arbitrarily offset vertically. Effects of bearing parameters on the load capacity are examined. A perturbation technique is applied for the case of slight offset of centers of two spheres, and the stiffness is calculated. For the case of large offset, a new iterative method is developed in this paper.

Dynamic Stability of Rotor System Supported by Spherical Spiral Groove Bearing

油潤滑の球面スパイラルみぞ軸受(SSGB)と静圧空気軸受によって支持されたたて形回転軸系の動的安定性を線形安定判別法によって解析した.解析では,回転軸系は6自由度を持つものとし,つぎのパラメータの影響を求めた.すなわち,SSGB油膜,SSGB支持ダンパおよび上部軸受の弾性係数と減衰係数,回転軸とSSGBの質量および回転軸のジャイロモーメントである.

Stability Characteristics of Spherical Spiral Groove Bearings : 1st Report, Theoretical Analysis

The stability characteristics of spherical spiral groove bearings lubricated with incompressible liquid are investigated theoretically. Solving a differential equation for a bearing which have an infinite number of grooves, we obtain the pressure distribution induced by small vibrations of a rigid rotor about a static equilibrium position. From the pressure distribution we derive a stability criterion for radially unloaded bearings, and clarify the dependence of the stability on bearing parameters and on axial displacements of a rotor. The bearing parameters considered are the spiral groove angle α, the relative groove depth Hg, the groove ratio δ, and rotational speeds of grooved member ω1 and smoothed member w2.

Performance of Spherical Spiral Groove Bearings

Performance of Spherical Spiral Groove Bearings

Stability Characteristics of Spherical Spiral Groove Bearings : 3rd Report, The Effects of Ungrooved Region at the Bottom of a Bearing

Stability Characteristics of Spherical Spiral Groove Bearings : 3rd Report, The Effects of Ungrooved Region at the Bottom of a Bearing

Characteristics of Outwardly Pumping Spherical Spiral Groove Bearings : 1st Report, Load Capacity

Characteristics of Outwardly Pumping Spherical Spiral Groove Bearings : 1st Report, Load Capacity

Stability Characteristics of Spherical Spiral Groove Bearings : 3rd Report. Effects of the Ungrooved Region on Load Capacity and Stability

The characteristics of spherical spiral groove bearings, having ungrooved regions at their bottoms, are investigated. The radial bearing forces and the load capacity are found approximately valid for small radial eccentricities, and then the effects of the ungrooved region on the load capacity and the stability are examined. The existence of the ungrooved region alters the characteristics of the bearing. With an increase in the central angle 2θ1 of the ungrooved region, the load capacity diminishes to zero when θ1=90°, while the radial stiffness increases to a maximum value when θ1≒60° and then diminishes to zero when θ1=90°. When a grooved member is rotating and the proper magnitude of the angle θ1 is selected, the bearing has a very high degree of stability without much loss of the load capacity.