螺旋槽球形轴承的承载能力

本文运用J·H·Vohr和C·H·T·Pan的理论和方法,建立了广义坐标系下的螺旋槽轴承的压力雷诺方程.然后在球轴承的边界条件下采用参数摄动法导出了动压螺旋槽球轴承润滑油膜的雷诺方程的近似解析解.由此,对各轴承槽型参数关于承载能力的影响作了计算和讨论,给出的最佳槽型参数与实验结果是一致的,与当前已发表的国内外资料相比较也是一致的.由于目前业已发表的文章均为计算机数值解,因此,本文对螺旋槽球轴承的特性研究提供了一个新的方法和途径.本文承中国科学院力学研究所林同骥,付仙罗同志及上海651研究所丁世德,蔡建中同志审阅,并提出了宝贵意见,作者谨在此表示衷心的感谢.     

Application of stabilized term in free boundary problems for optimizing bi-directional-rotation herringbone-grooved journal bearings

In order to deal with the free boundary problems occurred in cavitation region, this work incorporates an artificial term in Reynolds equation to stabilize the solution. The current result shows that adding the extra term gives accurate pressure distribution and benefits the selection of the groove shape and size. In addition, this study utilizes herringbone grooves on a reversible rotating journal bearing (RHGJB) and numerically analyzes the characteristics of miniature journal bearings with an inner diameter of 0.6 mm. Miniature journal bearings are limited in that the load capacity is significantly reduced with decreased bearing size, and therefore, the performances (load capacity and side leakage) of miniature RHGJBs are optimized. The optimum geometrical appearance of miniature RHGJBs is calculated by evaluating several groove parameters. Using the Taguchi parameter design methodology greatly reduces the number of full-factorial experimental design tests required to determine the optimal design parameters of the RHGJB from 5⁹ (1,953,125) to 450 runs.     

Homogenization of Reynolds Equation by Two-Scale Convergence

To increase the hydrodynamic performance in different machine elements, as e.g. journal bearings and thrust bearings, during lubrication it is important to understand the influence of surface roughness. In this connection one encounters homogenization of the incompressible Reynolds equation, where the roughness of the lubricated surface is assumed to be periodic. This problem has recently been studied in more engineering-oriented papers by using the formal method of multiple scale expansion. In this paper, we rigorously prove both homogenization and corrector results by using two-scale convergence, which may be regarded as a justification of the formal multiple scale expansion method described above. Moreover, some numerical illustrations and results are presented.     

A new nonlinear dynamic analysis method of rotor system supported by oil-film journal bearings

The strong nonlinear behavior usually exists in rotor systems supported by oil-film journal bearings. In this paper, the partial derivative method is extended to the second-order approximate extent to predict the nonlinear dynamic stiffness and damping coefficients of finite-long journal bearings. And the nonlinear oil-film forces approximately represented by dynamic coefficients are used to analyze nonlinear dynamic performance of a symmetrical flexible rotor-bearing system via the journal orbit, phase portrait and Poincaré map. The effects of mass eccentricity on dynamic behaviors of rotor system are mainly investigated. Moreover, the computational method of nonlinear dynamic coefficients of infinite-short bearing is presented. The nonlinear oil-film forces model of finite-long bearing is validated by comparing the numerical results with those obtained by an infinite-short bearing-rotor system model. The results show that the representation method of nonlinear oil-film forces by dynamic coefficients has universal applicability and allows one easily to conduct the nonlinear dynamic analysis of rotor systems.     

Nonlinear dynamic analysis for bevel-gear system under nonlinear suspension-bifurcation and chaos

This study aims to analyze the dynamic behavior of bevel-geared rotor system supported on a thrust bearing and journal bearings under nonlinear suspension. The dynamic orbits of the system are observed using bifurcation diagrams plotted with both the dimensionless unbalance coefficient and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents, and fractal dimensions of the gear-bearing system. The numerical results reveal that the system exhibits a diverse range of periodic, sub-harmonic, and chaotic behaviors. The results presented in this study provide an understanding of the operating conditions under which undesirable dynamic motion takes place in a gear-bearing system and therefore serves as a useful source of reference for engineers in designing and controlling such systems.     

Reduction Approaches for Thermogasdynamic Lubrication Problems

Gas thrust bearings are often used in low-load applications, e.g. in air cycle machines, in micro gas turbines or in rotor systems for fuel cell applications, to support a shaft in axial direction. The pressure and temperature distribution in a gas thrust bearing pad are described by the generalized Reynolds equation according to Dowson and the 3D energy equation. In this paper, two different approaches are presented in order to reduce the dimension of the governing nonlinear integro-differential equation system and in order to stabilize the solution process. In the first reduction approach, the temperature in the fluid is averaged across the fluid film according to Lee and Kim. In the second approach, Legendre polynomials are used to approximate temperature, density and fluidity across the fluid film according to Elrod, Brewe and Moraru. The reduction techniques are compared with respect to numerical efficiency, accuracy and convergence behavior. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two classes of sub-optimal shapes for one dimensional slider bearings with couple stress lubricants

Shape optimization of slider bearings operating with couple stress lubricants is performed here for the first time by using a novel direct optimal control approach, which defines the gradient of the film height as a control. The bearing load is maximized. One dimensional Reynolds and energy equations are used. Several constraints are taken into consideration. They avoid the occurrence of cavitation and ensure the validity of the Reynolds equation. The model is validated against a known analytical solution (the Rayleigh step bearing). Two simple design rules are inferred, which yield two different classes of sub-optimal shapes: the multi-stepped bearings and the multi-sloped bearings, respectively. Multi-stepped bearings consist of several steps and the couple stress parameter may affect the constant value of the film height between steps. Multi-sloped bearings consist of several inclined regions and the couple stress fluid parameter may affect the constant value of the film height between regions. The slider bearings operation under variable load is stable. A sensitivity analysis identified the design parameters which have the highest impact on bearing performance. The optimal slider bearing shapes obtained for Newtonian lubricants do not change when most common couple stress fluids are used. Isothermal models may be used successfully at lower values of the couple stress parameter.     

On the dynamics of a nonlinear rotor-floating ring bearing system

Today, in high speed applications the rotors are commonly supported by hydrodynamic journal bearings. One typical configuration of journal bearings incorporated in automotive turbochargers is the floating ring bearing. Rotors supported by floating ring bearings have many advantages, regarding costs and power consumption for example. However, they might become unstable with increasing speed of rotation. At the onset of instability both the perfectly balanced and unbalanced rotor undergo self-excited vibrations which could cause the mechanical breakdown of the system. The “oil whip”-phenomenon, very well known from the investigations of the plain journal bearing occurs here in a different form. At the stability limit the rotor begins either oscillating with about the half of the ring speed or the half of the ring speed plus the half of the journal speed depending on the system parameters. For this reason a rotor-floating ring bearing model is presented showing the mentioned characteristics. By applying the nonlinear equations of motion the limit cycles of the system are determined and its loss of stability is investigated. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chaotic response and bifurcation analysis of a flexible rotor supported by porous and non-porous bearings with nonlinear suspension

This study presents numerical work investigating the dynamic responses of a flexible rotor supported by porous journal bearings. Both porous and non-porous bearing types are taken into consideration in this study. The rotating speed ratios and imbalance parameters are also presented and proved to be important control parameters. Many non-periodic responses to chaotic and quasi-periodic motions are found, too. From the bifurcation diagrams in this paper, it is also evidenced that the vibration behaviors would be improved by porous bearings. The modeling result obtained here can be employed to predict the dynamics of bearing–rotor systems, and undesirable behavior of the rotor and bearing orbits can be avoided. Also, this could help engineers and researchers in designing and studying bearing–rotor systems or some turbo-machinery in the future.     

A study of pressure distribution for a slider bearing lubricated with a second‐grade fluid

An infinitely wide lubricated bearing consisting of connected surfaces of second‐grade fluid is analyzed in the present study. The velocity and pressure fields are obtained by a homotopy analysis method (HAM). Two cases, namely, inclined and parabolic slider bearings are considered. The viscoelastic effects play an important role even under the assumption of the order of the magnitude of the variable. However, inertial term does not contribute. Graphical results are interpreted. Comparison between the numerical values for the inclined and parabolic slider bearing is also presented. In addition to that for a meaningful solution, the graphs of convergence parameter, residual error, and numerical comparison are also presented. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1231–1241, 2011     

On the optimization of surface textures for lubricated contacts

The pressure field that develops inside a lubricated contact obeys an elliptic equation known as Reynolds equation, with coefficients that depend on the shape of the contacting surfaces. The load-carrying capacity of a contact, defined as the integral of the pressure field, is an important performance indicator that should be as high as possible to avoid wear and damage of the surfaces. In this article, the effect of arbitrary uniform periodic textures on the load-carrying capacity of lubricated devices known as thrust bearings is investigated theoretically by means of homogenization techniques and first-order perturbation analysis. It is shown that the untextured shape is a local optimum for the load-carrying capacity of the homogenized pressure field. This is proved for bearings of general shape and considering both incompressible and compressible models for the lubricant. The homogenization technique however implies an error. Suitable bounds for the effect of this error are provided in a simplified case.     

Vibrations of Rotors Supported on Nonlinear Bearings

Rotors in electrical machines are supported by various types of bearings. In general, the rotor bearings have nonlinear stiffness properties and they influence the rotor vibrations significantly. In this work, this influence of these nonlinearities is investigated. A simplified finite element model using Timoshenko beam elements is set up for the heterogeneous structure of the rotor. A transversally isotropic material model is adopted for the rotor core stack. Imposing the nonlinear bearing stiffnesses on the model, the Newton-Raphson procedure is used to carry out a run up simulation. The spectral content of these results shows nonlinear effects due to the bearings. The rotor vibrations are further investigated in detail for various constant speeds. These results show non-harmonic vibrations of the rotor in a section of the investigated speed range. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal Planetary Orbital Transfers via Chemical Engines and Electrical Engines

Because the orbital periods for planetary orbital transfers are of order hour, the primary objective of an optimal trajectory is to minimize the propellant consumption. In this paper, we present a systematic investigation of optimal trajectories for planetary orbital transfer. Major results on thrust control, propellant consumption, and flight time are presented with particular reference to LEO-to-GEO transfer. The following results were obtained with the sequential gradient-restoration algorithm in either single-subarc form or multiple-subarc form:

Wear and fluid-solid-thermal transient coupled model for journal bearings

In this study, the transient interactions between the sliding wear behaviour and fluid–solid–thermal (FST) characteristics of journal bearings are revealed using an established mathematical model. The calculated temperature distribution is validated by a comparison with experimental results from the literature. Furthermore, a wear test for lubricated journal bearings is conducted to verify the predicted wear rate. The time-varying wear and FST performances of the journal bearing, including the wear rate, wear depth, fluid pressure, contact pressure, and maximum temperature are calculated numerically. Through numerical simulations, the effects of the boundary friction coefficient and surface roughness on the wear and FST performances are evaluated. To demonstrate the importance of considering the three-dimensional (3D) thermal effect during the wear analysis of lubricated journal bearings, the numerical results predicted by the isothermal model and the thermal model are compared systematically within a wide range of operating conditions. The numerical results reveal that the worn surface profile slightly decreases the maximum temperature. Additionally, the worn region is primarily located at both edges of the bearing, and the time-varying worn surface profile may be beneficial for improving the hydrodynamic effect. Furthermore, the effect of the 3D thermal characteristics on the wear prediction of journal bearings cannot be ignored when the external load, boundary friction coefficient, surface roughness are relatively large.     

Active magnetic damper in a power transmission system

In rotor dynamics, the bearing characteristics exerts a decisive influence on dynamics of the rotating shaft. The research and application experience have led to active magnetic bearings (AMBs), which allow for unique applications in rotating systems. The paper presents the investigations concerning optimization of the magnetic bearing construction. An active magnetic bearing operates as a radial, auxiliary damper, which cooperates with the long, flexible shaft line (aircraft industry applications) and modifies its dynamic properties. In the developed concept of AMBs for aviation purposes, a necessity of increasing its bearing load capacity and damping has occurred. The second important criterion is a weight reduction. This advanced problem leads to specific requirements on the design and materials for the AMB. To achieve these goals, some simulations have been performed. The experimental results are presented as well.     

Coupling of the Reynolds Fluid-Film Equation with the 2D Navier-Stokes Equations

The pressure field in thin fluid films can quite precisely be calculated by Reynolds fluid-film equation. In some problems, it may be useful to couple thin fluid-films with general 2D or 3D fluid flows. In the current work, we analyze the fluid flow, pressure and temperature field in a hydrodynamic journal bearing with a rectangular oil groove. Pressure and temperature in the fluid gap are calculated by means of the Reynolds equation and the 2D energy equation. Cavitation effects are taken into account by incorporating a 2-phase cavitation approach. In order to calculate the velocity and pressure field in the oil groove, the 2D Navier-Stokes equations are used; the temperature distribution in the oil groove is computed by means of the 2D energy equation. Appropriate coupling conditions for velocity, pressure and temperature are formulated in order to couple the flow in the fluid gap with the flow in the oil groove. Thermal expansion of journal shaft and bearing housing are also taken into account, since the bearing clearance changes with increasing temperature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inertia effects in circular squeeze film bearing using Herschel–Bulkley lubricants

Recent engineering trends in lubrication emphasize that in order to analyze the performance of bearings adequately, it is necessary to take into account the combined effects of fluid inertia forces and non-Newtonian characteristics of lubricants. In the present work, the effects of fluid inertia forces in the circular squeeze film bearing lubricated with Herschel–Bulkley fluids with constant squeeze motion have been investigated. Herschel–Bulkley fluids are characterized by an yield value which leads to the formation of a rigid core in the flow region. The shape and extent of the core formation along the radial direction is determined numerically for various values of Herschel–Bulkley number and power-law index. The bearing performances such as pressure distribution and load capacity for different values of Herschel–Bulkley number, Reynolds number, power-law index have been computed. The effects of fluid inertia and non-Newtonian characteristics on the bearing performances have been discussed.     

Modelling and system identification of active magnetic bearing systems

Active magnetic bearing (AMB) systems have recently attracted much attention in the rotating machinery industry due to their advantages over traditional bearings such as fluid film and rolling element bearings. The AMB control system must provide robust performance over a wide range of machine operating conditions and over the machine lifetime in order to make this technology commercially viable. An accurate plant model for AMB systems is essential for the aggressive design of control systems. In this paper, we propose two approaches to obtain accurate AMB plant models for the purpose of control design: physical modelling and system identification. The former derives a model based upon the underlying physical principles. The latter uses input – output data without explicitly resorting to physical principles. For each problem, a brief summary of the theoretical derivation and assumptions is given. Experimental results based on data collected from an AMB test facility at the United Technologies Research Center provide a vehicle for a comparison of the two approaches.     

Finite element analysis of orifice-compensated multiple hole-entry worn hybrid journal bearing

This paper presents the analysis of a non-recessed worn hybrid journal bearing with orifice restrictors. Using Newton–Raphson method, FEM is used for solving Reynolds equation governing the flow of lubricant in the bearing clearance space. The bearing performance characteristics are presented for a wide range of wear depth. The results are computed for an orifice-compensated hole-entry configuration with uniform distribution of holes in the circumferential direction. The results show that the wear affects the bearing performance significantly and therefore, a due consideration of wear defect should be given for an accurate prediction of the bearing performance over a number of cycles.     

Natural oscillations of yarn balloons in ring spinning

Ring spinning is the most relevant production process for high quality short staple yarn. Recent technological advances using a twisting system involving frictionless superconducting magnetic bearings motivate a renewed interest in the dynamics of the process.A new deduction of the equations of motion for stationary and oscillatory movement is presented using Hamilton’s Principle of Least Action, taking into account axial transport, air drag and boundary conditions at the bearing. By application of Ritz’s method, system matrices are defined to enable the study of natural frequencies and mode shapes. These are validated by comparing to experimental results from literature, and case studies for industrially relevant parameter variations are performed.