Gas-dynamic Bearing Research Articles

Fractional-order model and nonlinear vibration analyses of hybrid gas journal bearing–rotor system

It is important to propose a reasonable nonlinear dynamic model of gas dynamic bearing–rotor system for the stable operation of turbocharger. This paper presents a hybrid gas journal bearing (HGJBs)–rotor system with flexible supporting structure. A fractional-order dynamic model of the symmetrical flexible HGJB–rotor system is established. A tracking–alarming method is proposed to obtain the rotational speed ratio at the bifurcation point. The stable and unstable regions of the rotational speed ratio Ωω for both the rigid bearing–rotor system and flexible HGJB–rotor system are analyzed. The nonlinear dynamic behaviors of HGJB–rotor system versus the fractional order αd and rotational speed ratio Ωω are studied. Results show the fractional-order dynamic model can realize the reasonable prediction of nonlinear dynamic behaviors. An increase in the rotational speed ratio Ωω and the decrease of fractional order αd result in a growth of the vibration amplitude. The adoption of flexible supporting structure is a good strategy to increase the size of stable region.

The Effect of Manufacturing Errors on the Performance of a Gas-Dynamic Bearing Gyroscope

The purpose of this paper is to investigate the effect of manufacturing errors on the performance of a gas-dynamic bearing gyroscope. Five kinds of manufacturing errors including bearing taper error, oval error, trigone error, eccentricity of the axis, and angular deviation of the axis are studied. A mathematic model of these errors is established to describe the variation of gas film thickness. The Reynolds equation is solved, and the perturbation method is applied to analyze the performance of the gas-dynamic bearing with the manufacturing errors. Based on the analysis, the interference torque and overload limit are investigated to assess the effects of manufacturing errors. Results show that taper error will cause interference torque. Oval error or trigone error will cause interference torque with a radial specific force. The eccentricity or angular deviation of the axis will cause interference torque with any specific force. In general, the interference torque is small, which is 10–1000 times smaller than that under the condition of both radial and axial specific forces. The manufacturing errors also reduce the ultimate overload significantly. The taper error has the greatest influence on the gas-dynamic bearing gyroscope among the manufacturing errors studied in this paper.

Design of a Combined Magnetic and Gas Dynamic Bearing for High-Speed Micro-Gas Turbine Power Plants with an Axial Gap Brushless Generator

The development of modern energy is moving towards distributed generation, in which numerous sources of different capacities are connected into a single network. This makes it possible to increase the reliability of the entire system, since the probability of the failure of several energy sources at the same time is small. One of the major possibilities of distributed generation is the generation of electric energy based on high-speed gas turbines. The main advantage of these sources are high specific energy indicators, which improve with increasing rotation speed. However, it is technically difficult to realize the advantages of high-speed devices. It is necessary to abandon the step-down gearbox for the generator and directly connect it to a high-speed turbine, use high-strength materials that can withstand the load from centrifugal forces, abandon traditional plain bearings, and use special supports. Installations with generators that have a radial rotor design are the most widespread. The main problem with generators of this type is that the rotor diameter is limited by the mechanical strength from centrifugal forces and the power can be increased only by increasing the axial length. At the same time, only two supports can be used for a radial structure; this leads to a decrease in the rigidity of the shaft and the occurrence of resonant frequencies during acceleration. In addition, radial generators have unreasonably large losses in the stator magnetic circuit, which increase with increasing speed and are difficult to remove from a limited volume. For this reason, radial structures have exhausted their reserves and cannot develop further in the direction of increasing the speed of rotation. This article proposes the design of a high-speed gas turbine installation based on a generator of a fundamentally different design. This is a multi-section generator with an axial air gap. The electric machine has a diamagnetic armature, which eliminates magnetic losses and allows for increased efficiency and simplification of the design. A large number of rotor sections can be used as supports for a gas-dynamic bearing, which greatly increases the rigidity of the structure and eliminates resonant frequencies during acceleration. The main structural difference from existing designs is the use of two types of bearings at the same time: magnetic bearings and gas-dynamic bearings. Magnetic bearings ensure operation at low speeds during acceleration, and gas-dynamic bearings ensure the rotation of the rotor and its rigidity at high speeds. Analysis of developments in this area shows that this solution is innovative. The proposed design required study of both the power part, including the axial inductor and the diamagnetic armature, and the combined support. This article shows the results of the development of a combined suspension and provides calculations of magnetic and gas-dynamic bearings for a gas turbine installation of 100 kW and 70,000 rpm. The results of the study can be applied to a number of gas turbine installations from 10 kW to 500 kW. The authors consider this concept to be competitive with modern analogues that have a radial generator design.

Experimental Study of Destruction of a Foil Gas-Dynamic Bearing

The paper describes the results of the experimental study of destruction of the foil gas dynamic bearing for a rotor of the gas turbine power plant. An analysis of temperature field, displacement and torque in the bearing was performed depending on the load and at the moment of destruction. The ultimate bearing capacity and the range of stable operation were determined.

Interference Torque of a Gas-Dynamic Bearing Gyroscope Subject to a Uniform Change of the Specific Force and the Carrier Angular Velocity.

The work is devoted to an analysis of interference torque of a gas-dynamic bearing gyroscope, while a condition with uniformly changed specific force and carrier angular velocity are taken into account. A five-degrees-of-freedom (5-DOF) model is established considering the translation and tilt of the rotor, which solves dynamic rotor equations and the Reynolds equation simultaneously. The model makes it possible to obtain the rotor trajectory under time-transient specific force and carrier angular velocity. The interference torque of the gyroscope is analyzed based on the rotor trajectory. Results indicate that the gas-dynamic bearings show a significant hysteresis effect with a perturbation of bearing force or bearing moment, which indicates the necessity of transient research. Interference torque is large when the carrier angular velocity starts to change or stops to change, and when the specific force stops to change. When the specific force change rate is less than 8.4 km/s3 with no change of the carrier angular velocity, the condition could be simplified as a steady state, which is consistent with the previous study.

Податливость газодинамического подшипника с эластичным компенсатором перемещения

Податливость газодинамического подшипника с эластичным компенсатором перемещения

Physico-mathematical modeling methods for the pressure distribution determination in the gas-dynamic bearing gap of the ball gyroscope

The considering problem in the article connects with solution methods of the specific questions in gas-dynamic lubrication theory. The comparative analysis of analytical and numerical methods for the calculating gas-dynamic bearing characteristics is provided. The main applying aspects of them for the solving of specific gas lubrication theory points are presented. This research is carried out for the investigated gap bearing geometry for the designed ball gyroscope construction. The main mathematical equation and results of developed numerical simulation for the pressure distribution determination are shown.

Experimental Study of Foil Gas-Dynamic Bearing Elastic Elements Deformation

The paper considers the questions of experimental research of deformation of elastic elements regarding the foil gas dynamic bearings. This research is required to check the adequacy of developed theoretical basics and the applicability to the real operation of a high-speed rotor. The paper presents the description of a test rig, the choice of the controlled and measured parameters, the experimental set up of the systems of control and measurement; and identifies the range of controlled parameters deviation. The paper also features schemes and photos of original measurement system, which include a mechanical part and the data acquisition system. The data acquisition system is based on an ADC by National Instruments and inductive proximity sensors. The software developed in LabVIEW is used as an instrument of experimental data registration. The test results have been compared to the numerical results of the mathematical modeling.

Determination of Rotor Surfacing Time for the Vertical Microturbine with Axial Gas-Dynamic Bearings

The rotor surfacing time of a vertical microturbine with the axial gas-dynamic bearings is estimated in this article. The problem of providing low coefficient of friction in vertical turbomachines can be solved by using various types of bearings. The earlier research showed the efficiency of the gas-dynamic bearings at nominal regimes of vertical power installations. However, the rotor does not immediately pop up in the axial gas-dynamic bearing. At the initial speed of the rotor, i.e., in the start mode, the active friction of the shaft and the bearing-rotor petals occurs. Thus, the article presents an estimation of the rotor surfacing time in locally produced gas-dynamic lobe bearings made by means of mathematical modeling method.

Numerical computation of the main gas-dynamic bearing static characteristics for the ball gyroscope

The numerical computation questions and analysis of the engineering calculation of the main gas-dynamic bearing static characteristics for the ball gyroscope experimental model are considered. The developed gyroscopic device construction is provided. These investigations for evaluation of the possibility to realize a sensitive element, which base on the developed device were provided. It is supposed, that this sensitive element can be used in information measuring systems of various applications. The main calculation data, such as load-bearing capacity and other characteristics of the hemispherical gas-dynamic bearing is carried out. According to the attained results, preliminary implications are stated. The basic problems for the further research are determined.

The Statement of Design and Application Questions for the Gyroscope with a Gas-dynamic Suspension of Ball Rotor in the Navigation Support Drilling System

The general issues of creation the inertial navigation system are considered. Analysis of the possible implementation of the gyroscope with a gas-dynamic suspension of ball rotor for using it as a sensor in the information and measuring complex is provided. The permissible layout construction is proposed. The software system variants for the mathematical modelling of the main gas-dynamic bearing characteristics are considered. Mathematical modelling is essential to extend and optimize the design parameters of the developed gyroscopic construction. Some results of modelling, theoretical evaluation and preliminary experimental studies are summarized.

Application of flap gas-dynamic bearing in turbine-generator units of low power

The article provides an overview of bearings used in high-speed turbomachines. It is shown that for low-power turbine-generator units in stationary or transport variant the most promising is use of flap gas-dynamic bearing, it is shown a comparison of different designs of flap gas dynamic bearings. The most detailed characteristics were given for flap gas-dynamic bearing with overlapping flaps developed in National Research University Moscow Power Engineering Institute, there are described the methods of their experimental study, shown operating and dynamic characteristics, as well as the range of products.

Study of the gasdynamic cell-type bearing

The paper studies the possibility of the cell gasdynamic thrust bearing in various modes of operation. The differential equation for the gas pressure in the operating clearance of the thrust bearing is obtained. The graphs of dependencies of the lifting force, hardness, and the flow rate on the compressibility parameter are presented.

Analysis and design of hydrodynamic journal air bearings for high performance HDD spindle

In this paper, we proposed the design concept of NRRO-free non-contact bearings for a high performance hard disk drive (HDD) spindle. We numerically analyzed three types of hydrodynamic journal air bearings [gas dynamic bearing (GDB)], such as a partial herringbone groove, a sinusoidal wave, and a taper-flat type. And we compared their performances in terms of pressure distribution, load capacity, radial stiffness, unbalance response, and stability threshold. For the design examples, we examined the Case 1 with 2.0 μm bearing clearance and 10000 rpm, and the Case 2 with 1.0 μm clearance and 15000 rpm. As a result of numerical analysis, we found that the taper-flat type was the most promising for high performance HDD spindle compared with the other types. It can have the bearing stiffness of about 3.0 × 106 N/m in Case 1 and of about 2.0 × 107 N/m in Case 2. We also discussed the allowance of parameters for the optimal design of the taper-flat type journal bearing.

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.

On the Translatory Whirl Motion of a Vertical Rotor in Plain Cylindrical Gas-Dynamic Journal Bearings

For the theoretical prediction of the dynamical characteristics of a rotor system, it is necessary to have an accurate knowledge of the bearing fluid film forces under dynamical conditions. With a small clearance ratio and at a moderate speed, the motion of the lubricant is governed by the generalized Reynolds equation. If the lubricant is a gaseous medium, the Reynolds equation is complicated by the compressibility effects, which include nonlinearity and time-dependence under dynamic conditions [1]. In the case of a vertical rotor operating in plain cylindrical journal bearings, the steady whirl approximation is appropriate and time-dependence in the Reynolds equation can be removed by a co-ordinate transformation. The form of the transformed equation is identical to the static Reynolds equation except that the compressibility number is modified by a factor which depends on the angular speed of the whirl motion [2, 3]. The altitude angle, in the presence of the whirling motion, is quite different from the static attitude angle. On the other hand, the magnitudes of the forces are not very different. The steady whirl analysis may be used to determine the synchronous whirl motion of an unbalanced rotor. The phase angle between the fluid film force and the maximum film thickness plane is the complement of the attitude angle according to the quasi-static analysis. Experimental data are in excellent agreement with the results of the steady whirl analysis. Also, the modified compressibility number is reduced to zero at half-frequency whirl, and the Reynolds equation, for an isothermal gaseous film with the small eccentricity ratio approximation, becomes identical to that of the liquid film. Since it has been established that the threshold of half-frequency whirl for vertical rotors operating in plain cylindrical journal bearings is at zero speed in [4], the same conclusion applies to the corresponding gas-dynamic bearing.