Optimum clearance of a gas hydrostatic thrust bearing with maximum load capacity

The optimum design of a gas hydrostatic thrust bearing clearance is obtained using the methods of calculus of variations. The variational problem of determining the clearance shape giving the maximum load capacity is solved for a given external pressurization and various journal speeds. The structure of the optimum solution is found on the basis of the gas lubrication approximation with and without constraints on the height of the bearing pad (pocket). The calculation results embrace all possible values of the parameters. A comparison with optimum liquid bearings is carried out. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–78, July–August, 2000. The work was carried out with support from the Russian Foundation for Basic Research (projects Nos. 99-01-01211 and 96-15-96158).     

Lubrication of a rotating circular thrust bearing with a casson lubricant

Lubricants today are subjected to increasing mechanical shearing forces. This has resulted in an increasing interest in materials having variable viscosity. The problem of rotating circular thrust bearing is investigated with Casson fluid as a shear thinning lubricant. The pressure and load capacity of the thrust bearing is calculated when the feeding is done from the centre of the plates to the periphery. Also, moment of friction acting on the plates is calculated for different values of Casson number and for various values of ratio of inside to outside radius. It has been found that there is a decrease in the value of load capacity of the Casson lubricant. Also, it has been observed that there is an appreciable increase in the values of moment of friction for Casson fluid.     

Analytical studies of temperature and inertia on the performance of hydrostatic porous thrust bearing

In the present analysis an attempt has been made to study the effects of graphite metal which is an alloy of copper, lead and tin on the characteristic of parallel surface porous recessed thrust bearing. In the study interactions of inertia and temperature have been considered. The results obtained for pressure distribution and load capacity have been compared with the results of Ting and Mayer and are illustrated in the graphs.     

A gas thrust bearing with pressurization

The Galerkin method was used to calculate a gas thrust bearing with pressurization. It is shown that, with an appropriate choice of approximating functions, the first approximation already gives satisfactory results. The data obtained are compared with the results of numerical integration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 25–31, January–February, 1973.     

The thermohydrodynamic flow equations for hydrostatic thrust bearings

Summary This paper studies the flow in rotating hydrostatic thrust bearings lubricated with incompressible fluids under pressure. It considers, besides the effects of inertia on the lubricant, its increase in temperature in the film due to fluid friction (thermohydrodynamic flow).From the system of differential equations of Navier-Stokes, continuity and energy, we obtain differential or integro-differential equations that can furnish the values of the temperature and of the components of velocity and pressure of the fluid in the bearing. From these we obtain the values of the load-carrying capacity, of the volume flow rate of the fluid and those of the friction torque.

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Sommario Si studia il regime fluido nei cuscinetti idrostatici di spinta rotanti lubrificati con fluidi incompressibili in pressione, tenendo conto, oltre che degli effetti di inerzia sul lubrificante, anche del suo aumento di temperatura nel meato dovuto alle azioni di attrito fluido (regime termofluidodinamico).Si ricavano dal sistema di equazioni differenziali di Navier-Stokes, di continuità e dell'energia, le equazioni differenziali od integro-differenziali atte a fornire i valori della temperatura, delle componenti della velocità e della pressione del fluido nel cuscinetto e, mediante essi, i valori della capacità di carico, della portata volumetrica di fluido e del momento d'attrito.

     

A tilted pad thrust slider bearing improved by the boundary slippage

The present paper proposes a new type of hydrodynamic lubricated tilted pad thrust slider bearing which is augmented with the boundary slippage at the stationary contact surface in the inlet zone. This design is of purpose to reduce the friction coefficient but increase the load-carrying capacity of the bearing. A theoretical analysis is presented for this bearing. Computational results and design guides for this bearing are given. It is found that the most increase of the carried load of the bearing by the boundary slippage is around 30 %, while the most reduction of the friction coefficient of the bearing by the boundary slippage is more than 40 %. This advantage is reached when the boundary slippage zone occupies 80 % of the bearing lubricated area and the fluid-contact interfacial shear strength at the boundary slippage interface is very low.     

Gas-lubricated sector thrust bearing with maximum load capacity

The problem of the optimization of the microgeometry of a gas-lubricated sector thrust bearing with respect to the maximum lift criterion is considered. The gas lubrication Reynolds equation is used for determining the pressure in the lubricating film. The case of low compressibility numbers is studied. The optimum profile is qualitatively determined on the basis of an analysis of the system of necessary conditions for an extremum. The results are presented for various values of the problem parameters. A comparison is made with the data of a number of gas thrust bearing optimization studies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 35–42, November–December, 1990.     

Effect of angular inertia of lubricant in MHD hydrostatic thrust bearings

Summary Circumferential motion of a conducting lubricant in a hydrostatic thrust bearing is caused either by the angular motion of a rotating disk or by the interaction of a radial electric field and an axial magnetic field. Under the assumption that the fluid inertia due to radial motion is negligibly small in comparison with that due to angular motion, it is found analytically that the rotor causes an increase in flow rate and a decrease in load capacity, while both are increased by the application of an electric field in the presence of an axial magnetic field. The critical angular speed of the rotor at which the bearing can no longer support any load is obtained, and the possibility of flow separation in the lubricant is discussed.Nomenclature a recess radius - b outside disk radius - B ₀ magnetic induction of uniform axial magnetic field - E ₀ radial electric field at r=a - E _r radial electric field - h half of lubricant film thickness - M Hartmann number = (B ₀ ² h ²/)^1/2 - P pressure - P ₀ pressure at r=a - P _e pressure at r=b - Q volume flow rate of lubricant - Q ₀ flow rate of a nonrotating bearing without magnetic field - r radial coordinate - r _s position of flow separation on stationary disk - u, v fluid velocity components in radial and circumferential directions, respectively - W load carrying capacity of bearing - W ₀ load capacity of a nonrotating bearing without magnetic field - z axial coordinate - coefficient of viscosity - _e magnetic permeability - fluid density - electrical conductivity - electric potential - angular speed of rotating disk - _c critical rotor speed at which W=0     

亚微米级颗粒物在气体动压轴承内运动与沉积分析

气体轴承中的多余颗粒物是导致陀螺电机不起动的主要原因。研究颗粒物的吸入、运动沉降以及排出规律,对解决陀螺电机不启动问题具有重要意义。以螺旋槽气体动压止推轴承为研究对象,将气体流场作为连续相,颗粒物作为离散相,通过联立求解气体N-S方程和颗粒物力平衡方程,得到了亚微米级颗粒物在轴承中的运动与沉积规律。分析发现气膜中速度场分布与颗粒物沉积之间的相关性,且与实验结果有较好的一致性;同时,发现槽数为12或13、螺旋角为α=20°左右时颗粒物最容易从轴承中排除,增加槽深和较小槽长也有相同效果。为在生产实践中优化陀螺电机轴承结构参数,降低不启动率提供了理论依据。     

A two-temperature generalized magneto-thermoelastic formulation for a rotating medium with thermal shock under hydrostatic initial stress

Continuum Mechanics and Thermodynamics - The interaction between magnetic field and thermal field in an elastic half-space, homogeneous and isotropic under two temperature and initial stress are...     

Influence of rotation speed on motion accuracy of hydrostatic journal bearing

Nonlinear Dynamics - In order to study the influence of the rotation speed on the motion accuracy of the hydrostatic journal bearing, a new dynamic accuracy model is built to predict the error...     

Dynamics of rotating conveying mud drill string subjected to torque and longitudinal thrust

In the view of fluid-structure interactions and rotor dynamics, this paper models the lateral vibration of a vertical downward rotating elastic drill string conveying mud subjected to supporting stabilizers, bit torque and longitudinal thrust. The dynamic model involves the rotational inertia of the drill string tube cross section, the gyroscopic effect caused by rotation, the damping due to friction with the surrounding fluid, the gravity force and mud buoyancy. Damped natural frequency, stability and resonance of the drill string system are determined by quadratic eigenvalue problem and investigated at influences of the stabilizer, rotational angular speed, mud flowing velocity, bit torque and thrust. As a result, the drill string can lose stability both at simultaneous and separate influences of the mud conveying, bit torque and thrust, whereas the rotation, stabilizer and gravity of the drill string can improve system stability; the rotational angular speed causing system resonance decreases with the increase of the mud flowing velocity, bit torque and thrust.     

Actively compensated aerostatic thrust bearing: design,modelling and experimental validation

Active compensation is an effective method for increasing air bearing static and dynamic performance. This paper describes the design, modelling and experimental validation of an actively compensated externally pressurized gas bearing. The active compensation is obtained through the support compensation strategy. With this strategy, the system’s initial working position is restored by compensating for air gap variations through adjustments to the bearing vertical dimension. The described bearing consists in a conventional thrust bearing which is integrated with a multilayer piezoelectric actuator, a compliant mechanism and a digital controller. Nevertheless the non-linear nature of the air system, a simple linear model results to be an effective choice for neighbour of equilibrium conditions. Results demonstrate the good accuracy of the model and the system’s good capacity of rejecting external force disturbances.     

Flow transitions in a rotating magnetic field

Critical Rayleigh numbers have been measured in a liquid metal cylinder of finite height in the presence of a rotating magnetic field. Several different stability regimes were observed, which were determined by the values of the Rayleigh and Hartmann numbers. For weak rotating magnetic fields and small Rayleigh numbers, the experimental observations can be explained by the existence of a single non-axisymmetric meridional roll rotating around the cylinder, driven by the azimuthal component of the magnetic field. The measured dependence of rotational velocity on magnetic field strength is consistent with the existence of laminar flow in this regime.List of symbols B ₀ magnitude of magnetic induction - B_r, B radial and azimuthal magnetic induction components - C wall admittance - d cell diameter - d _w wall thickness - g gravity at earth's surface - Ha Hartmann number - h cell height - k _f thermal conductivity of fluid - k _w thermal conductivity of wall - L1, L2, L3, L4 thermistor temperatures - Ra Rayleigh number - Ra ^c critical Rayleigh number for the transition from no flow to laminar flow - Ra ^t critical Rayleigh number for the transition from time-independent to time-dependent flow - r radial coordinate - T _a temperature at top of cell - T _b temperature at bottom of cell - T temperature difference between cell bottom and cell top - T_c critical temperature difference between cell bottom and top time - t time - U1, U2, U3, U4 thermistor temperatures - z vertical coordinate - volumetric thermal expansion coefficient - skin depth - k thermal diffusivity - magnetic permeability - kinematic viscosity - density - electrical conductivity - azimuthal coordinate - angular frequency of magnetic induction This work was supported by the Microgravity Science and Applications Division of the National Aeronautics and Space Administration.     

Electromagnetic field in rotating frame of reference

The problem of transformation of electromagnetic field from inertial frame of reference to non-inertial rotating frame of reference and vice versa is discussed. By the use of the tetrad method (moving reper method) it is shown that in cylindrical coordinates the usual Lorentz formulas can be applied. It is also shown that in cylindrical coordinates the form of Maxwell equations in rotating frame of reference is the same as in inertial one.