A study on accuracy of porous journal air bearing

In order to predict error motion of continuous porous journal air bearing, an accuracy model is established to reveal the relationship among error motion, roundness error and structure parameter under quasi-static conditions. Based on the model, averaging coefficient is defined to quantitatively characterize the error averaging ability. The study finds that whether the bush and shaft roundness errors match is the cause of error motion. The trilobal roundness error of shaft has a major impact on accuracy for a porous journal air bearing with an elliptical bush, while the elliptical roundness error of shaft has a major impact on accuracy for that with a trilobal bush. On the two-dimensional plane of bush wave numbers n₂ = 2~7 and shaft wave numbers n₁ = 2~15, the averaging coefficients are symmetrical along the line n₁ = n₂. The shaft wave numbers which equal integer multiples of prime numbers of bush wave number have no impact on accuracy, while the remaining shaft wave numbers have impact. Among them, those at points n₁ = n₂*i ± 1 are with obvious averaging coefficients and have a major impact on accuracy where i is a positive integer. The main peaks of averaging coefficients appear at the points n₁ = n₂ ± 1, which have the most important impact on accuracy. The theory has many potential applications such as prediction of error motion, structural optimization and selection of parts grinding method, which is of significant importance for design and testing of porous journal air bearings used widely in ultra-precision machine tools.     

A stability analysis for a hydrodynamic three-wave journal bearing

The influence of the wave amplitude and oil supply pressure on the dynamic behavior of a hydrodynamic three-wave journal bearing is presented. Both, a transient and a small perturbation technique, were used to predict the threshold to fractional frequency whirl (FFW). In addition, the behavior of the rotor after FFW appeared was determined from the transient analysis. The turbulent effects were also included in the computations.Bearings having a diameter of 30 mm, a length of 27.5 mm, and a clearance of 35 μm were analyzed. Numerical results were compared to experimental results obtained at the NASA GRC. Numerical and experimental results showed that the above-mentioned wave bearing with a wave amplitude ratio of 0.305 operates stably at rotational speeds up to 60,000 rpm, regardless of the oil supply pressure. For smaller wave amplitude ratios, a threshold of stability was found. It was observed that the threshold of stability for lower wave amplitude strongly depends on the oil supply pressure and on the wave amplitude.When the FFW occurs, the journal center maintains its trajectory inside the bearing clearance and therefore the rotor can be run safely without damaging the bearing surfaces.     

A study on compliant layers and its influence on dynamic response of a hydrodynamic journal bearing

For some hydrodynamic bearing applications polymer-lined bearings are chosen over traditional metal alloy bearings due to their better wear and friction properties when operating at very thin films, e.g. in the mixed lubrication region. The introduction of a compliant layer also affects the dynamic behavior of the bearing. The influence of the liner stiffness on the dynamic response of a highly dynamically loaded journal bearing is evaluated by varying the stiffness and comparing the response. The configurations with different liner stiffnesses are evaluated on the parameters that are traditionally used to evaluate hydrodynamic bearing designs: dynamic response, maximum pressure, minimum film thickness, wear, power loss and temperature response. The primary findings are that the maximum pressures are reduced significantly and this comes at the expense of slightly higher eccentricity ratios during operation.     

Rotordynamic modelling of a hydrodynamic pivoted-pad thrust bearing

The rotordynamic characteristics of a hydrodynamic pivoted-pad thrust bearing are investigated in this paper. Firstly, the rotordynamic coefficients of a single pad are defined in the case of small perturbation. The Reynolds equation and its perturbed forms are solved by using the boundary element method (BEM). An iterative procedure is proposed to determine the static positions of the thrust pads when the static tilt of the runner is considered by using the Newton–Raphson method. The characteristics of the thrust bearing are obtained by using an approach based on a coordinate transformation principle.     

A parametric study on design of a microrate-gyroscope with parametric resonance

Parametric excitation for MEMS gyroscopes can provide resonance in both the drive and the sense modes, even with mismatched natural frequencies. In this paper, requirements for such a condition are studied by analyzing the effect of each factor on the steady state amplitudes of the two modes. To develop a general study, the governing equation of the gyroscope is scaled and non-dimensionalized. The resulting governing equation is in the form of a cubic Mathieu equation coupled to a Duffing equation. In the study of the scaled system, for a gyroscope with matched natural frequencies, three sets of optimum designs are obtained. Then, the robustness of parametric excitation for a gyroscope with mismatching modes is shown. As the results indicate, parametric excitation is able to provide high accuracy and robustness for MEMS gyroscopes.     

基于AutoCAD VBA的轴承参数化建模方法的研究

标准件在机器或部件中应用极其广泛，有必要实现其三维模型的参数化建模，以减少重复工作，提高设计效率。本文采用Access数据库，建立了球轴承国家标准标准库。以AutoCAD VBA为开发工具，应用ActiveX与ADO对象，完成了球轴承实体模型的参数化建模方法的研究。     

Experiments on thermal effects in a hydrodynamic thrust bearing

The objective of this work is to analyse the characteristics of a fixed-geometry thrust bearing in typical operating conditions and to give experimental results in order to validate future thermohydrodynamic models. The influence of the applied load, the rotational speed and the feeding temperature on the thrust bearing performance is presented and discussed.     

Theoretical and experimental investigations of a variable- impedance hydrodynamic bearing

The aim of the work described in this paper is to develop a hydrodynamic bearing whose oil film dynamic stiffness and damping coefficients could be tuned to take on low values, without upsetting the bearing steady load carrying capacity, in order to obtain an improved dynamic response for machines running in such bearings. It was required that this tuning of the bearing dynamic characteristics could be carried out after assembly of the machine in question, and if necessary while the machine was in operation.A theoretical analysis of the new design of bearing was carried out, based on a finite-difference model of the bearing oil film. This analysis enabled the steady-state load carrying capacity of the bearing to be calculated for any particular running conditions. The oil film stiffness and damping characteristics were then calculated using the finite-displacement technique; these were then used to calculate the unbalance response of a flexible rotor running in such bearings. Experimental measurements of the unbalance response of a model rotor running in the new bearing design were also recorded, and compared with similar measurements obtained when conventional bearings were used.Both theoretical and experimental results show that the proposed new bearing design has a similar steady load carrying capacity to that of conventional hydrodynamic bearings, but that the unbalanced response and force transmissibility of machines running in the new design of bearing are substantially superior to that obtained with conventional bearings.     

Estimation of the performance of a narrow porous journal bearing with hydrodynamic turbulent lubrication considering slip velocity and arbitrary wall thickness

A closed-form mathematical analysis is presented for the hydrodynamic lubrication of a 360° short porous metal journal bearing with arbitrary wall thickness which is press fitted in a solid housing and works with a turbulent film of newtonian lubricant. A new pressure equation is used. The bearing is assumed to be narrow, and therefore circumferential flow of the lubricant in the clearance region is negligible in comparison with that in the axial direction which makes the governing differential equation simpler to solve. However, this simplification is not applicable to darcian flow in the porous matrix so that a three-dimensional Laplace equation is required to describe the continuity of flow in the pores. The film curvature is included by retaining terms containing $\text{C}\text{R}{}_1$ in the expression for film thickness. The curvature of the permeable bearing matrix, which allows it to have an arbitrary wall thickness, is taken into account by a direct approach. Infinite Fourier series and their orthogonal properties are utilized for the determination of the turbulent hydrodynamic pressure distribution from which the load-carrying capacity and attitude angle are calculated. All the results of interest are simple and fully analytical in nature permitting easy and economical calculation of numerical data over a very wide range of parameters.     

Integral characteristics of a porous gas axial bearing

A flat axial bearing with pressurized gas supply through an annular flow valve made from anisotropic porous material is considered. The differential equation for the pressure in the lubricant layer adjacent to the porous wall is numerically solved using the Runge-Kutta method, with two boundary conditions taken into account. One of these, which is integral, has remained out of sight in the porous support analysis until recently. An algorithm for calculating the lifting force and rigidity of support as well as mass rate of gas flow through this support is presented. The optimization of support is performed, and conclusions are drawn as to its influence on different factors.     

Thermal modelling of the lemon-bore hydrodynamic bearing

The lemon-bore hydrodynamic lubricated journal bearing is a bearing type which is commonly used in high-speed machinery. This is because the lemon-bore bearing is less susceptible to self-excited vibrations or instability than the plain cylindrical bearing at high speeds, while remaining easy to manufacture. However, the increased viscous shear will result in a higher increase in the temperature in the lubricating film.In this paper a finite element analysis is presented which has been used to calculate the pressure and temperature distribution in the lubricating film of a lemon-bore journal bearing. This thermo-hydrodynamic (THD) model is an inverse model, that is, a model in which the shaft eccentricity and attitude angle are calculated given a certain known and prescribed load and load angle. A novel, simple and fast mass-conserving cavitation algorithm has been used in order to calculate the pressure and mass fraction distribution in the lubricating film, and consequently accurately describes the heat flow in the cavitated areas. Furthermore, care has been taken to accurately model the heat to and from the oil supplies.This model has been used to check the design of the lemon bearings in a specific naval application. The results of this model are compared with those obtained using the bearing manufacturer's design code. The influence of several operating and design parameters is studied, particularly with respect to the maximum temperature. The results of this parameter study have been used to suggest design improvements for this particular application.     

Three-dimensional hydrodynamic analysis of a journal bearing with a two-component surface layer

The article presents a three-dimensional hydrodynamic analysis of a bearing with a two-component surface layer journal. This kind of bearing is characterized by an experimentally proved susceptibility to oil contaminants which is five times lower than that of a typical bearing. The oil flow was described with the Navier–Stokes and energy equations. The equation system was solved by the finite element method. The distributions of pressure, temperature and oil flow velocity were determined. The computation results made it clear that a journal with a two-component surface layer causes a reduction in the bearing load capacity for high eccentricity ratio values (0.7–0.9). Besides, contrary to a typical bearing, considerable velocity changes in oil flow in all directions (circumferential, radial and axial) were observed in the bearing under consideration. Particularly great velocity changes occurred in the radial direction. However, no essential changes were found in the temperature of the oil film and in the attitude angle.     

The optimum profile for a porous slider bearing

The load capacity of a porous slider bearing was investigated. The optimum profile was found to be a step form with the riser location and step height ratio depending on the porosity. Porosity decreases the load capacity of a slider bearing. A porous slider bearing of optimum profile supports more load than a porous inclined slider bearing     

新型可逆式动压推力轴承的承载能力计算

根据流体力学有限元理论,对新型可逆式动压推力轴承承载能力作用计算。同时考虑了轴瓦的热变形的影响。建立了最小油膜厚度、油楔角与承载力的关系曲线。并与未考虑热变开遥曲线作了比较。建议在实际调整最小油膜厚度时需增加该值的１３％左右,用来补偿热变形。     

Effect of textured area on the performances of a hydrodynamic journal bearing

A growing interest is given to the textured hydrodynamic lubricated contacts. The use of textured surfaces with different shapes of microcavities (textures) and at different locations of the texture zone can be an effective approach to improve the performance of bearings. The present study examines the texture location influence on the hydrodynamic journal bearing performance. A numerical modelling is used to analyze the cylindrical texture shape effect on the characteristics of a hydrodynamic journal bearing. The theoretical results show that the most important characteristics can be improved through an appropriate arrangement of the textured area on the contact surface.     

Investigations on a permanent magnetic–hydrodynamic hybrid journal bearing

In the present work, a permanent magnetic–hydrodynamic hybrid journal bearing is developed. The force of the journal bearing comes from the hydrodynamic film and the permanent magnetic field. When a hydrodynamic film does not form, such as during starting and stopping a machine, the journal bearing relies on the magnetic force to support the rotor system. This paper studies a model of the permanent magnetic force and develops an experimental rig of the journal bearing. Experiments show that the hydrodynamic film force uncouples with the magnetic force in the journal bearing. Predictions from the model are compared with experimental data.     

Roughness effects in a narrow porous journal bearing with arbitrary porous wall thickness

The paper uses Christensen's stochastic theory to study the effects of surface roughness in a narrow porous journal bearing. An exact solution, valid for arbitrary wall thickness, is given for the film pressure and pressure in the bearing material. The results are compared with the approximate solutions, and the range of various influencing parameters, for which the approximate analysis is satisfactory from a practical point of view is determined.     

Magnetic-fluid-based porous inclined slider bearing

A porous inclined slider bearing, lubricated with a magnetic fluid, in the presence of an externally applied magnetic field which is oblique to the lower surface of the bearing is discussed. The load capacity of the magnetic-fluid-based porous inclined slider bearing is found to be greater than that of a viscous porous inclined slider bearing. It is shown that the magnetic-fluid-based porous inclined slider bearing has a performance superior to that of the viscous porous inclined slider bearing.     

Abnormal behavior of a hydrodynamic lubrication journal bearing caused by wall slip

Reynolds lubrication theory assumes that there is no wall slip on the interfaces between the solids and lubricant. During recent years, however, it is found that wall slip often happens. The present paper analyzes the wall slip occurring in a hydrodynamic lubrication journal bearing. If the two surfaces have the same adhesion property wall slip always decreases the oil film load support capacity. If there is wall slip over all of the lubricated surfaces, the hydrodynamic effect of the journal bearing vanishes, and no load support exists. If the two lubricated surfaces have different adhesion properties, the wall slip effect is more complex and may cause the journal bearing to operate in an instable manner. In order to avoid the wall slip, the limiting shear stress at the bearing surface should be higher than that at the journal surface.