Lateral Vibration Analysis of Flexible Shafts Supported on Elliptical Journal Bearings

This paper presents the development of a finite element procedure for the dynamic analysis of flexible rotors supported on fluid-film elliptical journal bearings operating under several operating conditions. The rotating shaft is modeled by using Timoshenko beam theory and the coupled rotating components, such as disks and impellers, are modeled by using lumped masses. The modeling of the elliptical journal bearings is performed by solving the lubrication equations generated from the application of a linearized perturbation method on the classical Reynolds equation. The bearing carrying-load capacity and the linearized dynamic force coefficients can be predicted for elliptical bearings with different preloads and journal eccentricities. The rotor transient whirling unbalance response is estimated by performing the time integration of the finite element equations using Newmark method. Experimental whirling unbalance response of a rotating shaft supported at two identical journal bearings is used to validate the finite element procedure. A comparative analysis of the dynamic response of flexible rotors supported on both cylindrical and elliptical journal bearings is performed to show that some elliptical bearings are capable of attenuating the rotor unbalance response more efficiently than cylindrical bearings are.     

波箔片制造误差对径向波箔轴承静刚度的影响

为探究制造误差对径向波箔轴承的影响,基于Timoshenko梁单元建立波箔片变形的简化模型,基于ABAQUS建立波箔片的实体模型,并对比2种模型下波箔片的静刚度。结果显示,Timoshenko梁模型和实体模型的波箔片静刚度曲线较为吻合,且均呈线性变化。建立径向波箔轴承的实体模型,对轴颈进行位移加载,分析轴承的静刚度特性。结果显示,在考虑摩擦时,轴承的静刚度存在明显的滞回特性。设计存在2种不同误差类型的径向波箔轴承,并对其静刚度特性进行分析,发现波高误差对静刚度的影响大于波距误差,且控制起主要支承作用的波纹的波高误差能够有效降低制造误差对径向波箔轴承静刚度的影响。     

Low-friction wear-resistant coatings for high-temperature foil bearings

Compliant foil bearings offer many advantages over rolling element bearings in high-speed and high-temperature applications. However, implementation of foil bearings in these applications requires development of solid lubricant coatings that can survive the severe operating conditions encountered at high speeds and high temperatures. The objective of this paper is to present results on development of an advanced coating system for use with compliant foil bearings that permits higher operating speeds and temperatures. In order to evaluate the coating performance and to select the best coating combination for implementation, tests were conducted using a high-temperature, high-speed tribometer. In these tests, Inconel test substrates, representative of a portion of a foil bearing, were coated with several different Korolon^TM coatings. The counterface disks were coated with a dense chrome, plasma sprayed PS304, hard chrome and Korolon^TM 1350B. Each test was conducted for 500 start–stop cycles up to 810 °C foil pad temperature under 13.8 kPa normal loading.The test results confirmed the excellent tribological behavior of Korolon^TM coatings for high-speed, high-temperature foil bearing applications. While the tribological behavior of Korolon^TM coatings were determined to be a function of temperature, in most cases a minimum coefficient of friction less than 0.1 was observed during startup/shutdown periods. Based on the measured coefficient of friction and post-test visual inspection of the mating surfaces, the hard chrome coating proved unacceptable for high-temperature applications due to extensive surface cracking. The other disk coatings exhibited excellent tribological performance.Following these tests, a foil journal bearing was designed and a composite coating consisting of Korolon^TM 1350A with an overcoat of Korolon^TM 800 was applied to the bearing top foil; and a dense chrome coating was applied to the journal surface. The foil bearing and journal were installed in a 240-lb thrust turbojet engine and operated successfully to 54,000 rpm for over 70 start–stop cycles and 14 h.     

Thermal effects in cylindrical journal bearings of high‐speed gearboxes

The high rotational speeds and loads of gears operating in acceleration gearboxes causes problems related to the correct choice and design of journal or rolling bearings. In the case of journal bearings, these problems are connected with thermoelastohydrodynamic lubrication theory and the dynamics of the bearing system. However, of major importance is the problem of thermal effects in journal bearings. This has been considered for bearings used in a double‐helical gearbox with the pinion and output shaft operating in cylindrical journal bearings. The oil film pressure, temperature, viscosity distributions, and maximum and mean oil film temperatures have been determined. In calculations, laminar adiabatic and turbulent adiabatic models of oil films have been applied. The results of the calculations can be used in the design of cylindrical or other types of journal bearing in rotating machinery, including acceleration or reduction gearboxes.     

Gas-dynamic foil bearing model

A method is developed to calculate the characteristics of gas-dynamic bearings of rotors of gas-turbine engines and gas-turbine units. The method takes into account the contact interactions between the shaft journal, the fluid film, and the elastic bearing elements. The problem of multidisciplinary mathematical simulation of the elastic gas-dynamic contact is formulated and solved to determine the parameters of lubrication and deformations of the shaft and bearing. The considerable nonlinearity of the problem is governed by the equations describing the fluid flow in the bearing and the features of the elastic contact during deformation of the bearing elements. The calculation of the fluid-film flow in the bearing is based on the solution of the nonlinear two-dimensional Reynolds equation for a compressible fluid. The method of consecutive loading with error correction that within the interval prompts to the linearized Reynolds equation solution for fluid film pressure increment is used. The results of calculation of the fluid-flow parameters in the clearance between the shaft and the bearing are compared with the results obtained by solving the fluid-flow problem in a bearing modeled with the Navier-Stokes equations with the STAR-CD software. The stress-strain state of the elastic bearing elements is studied with the finite element model taking into account the contact interaction between the foils themselves and with the bearing race. The pressure distribution and the clearance in the shaft are determined iteratively by the coupled solution of the fluid flow and bearing foil deformation problems. Bearing stiffness characteristics, its carrying force and attitude angle are determined versus shaft journal displacement value and direction. It is shown that the stiffness characteristics of the bearing depend on the direction of displacement of the shaft journal in the bearing. The influence of the bearing elastic element deformations on the support load carrying capacity and the stiffness characteristics are studied. The results yielded by the calculations with the developed method are compared with those when the fluid-layer thickness in the bearing was calculated using the analytical model proposed by H. Heshmat and co-authors.     

The Role of Radial Clearance on the Performance of Foil Air Bearings

Load capacity tests were conducted to determine how radial clearance variations affect the load capacity coefficient of foil air bearings. Two Generation III foil air bearings with the same design but possessing different initial radial clearances were tested at room temperature against an as-ground PS304 coated journal operating at 30000 rpm. Increases in radial clearance were accomplished by reducing the journal's outside diameter via an in-place grinding system. From each load capacity test the bearing load capacity coefficient was calculated from the rule-of-thumb (ROT) model developed for foil air bearings.

The test results indicate that, in terms of the load capacity coefficient, radial clearance has a direct impact on the performance of the foil air bearing. Each test bearing exhibited an optimum radial clearance that resulted in a maximum load capacity coefficient. Relative to this optimum value are two separate operating regimes that are governed by different modes of failure. Bearings operating with radial clearances less than the optimum exhibit load capacity coefficients that are a strong function of radial clearance and are prone to a thermal runaway failure mechanism and bearing seizure. Conversely, a bearing operating with a radial clearance twice the optimum suffered only a 20% decline in its maximum load capacity coefficient and did not experience any thermal management problems. However, it is unknown to what degree these changes in radial clearance had on other performance parameters, such as the stiffness and damping properties of the bearings.     

Thermal Structural Effects in a Gas-Lubricated Foil Journal Bearing

A theoretical model for gas-lubricated foil journal bearings that incorporates thermal structural effects is presented. Bending and membrane effects in the top foil resulting from temperature are included along with thermal expansion of the journal, subfoil, and bearing housing. The model includes thermal transport through the journal, foils, and bearing housing. Pressure in the gas film is predicted using the Reynolds equation, and a thermal bulk flow model is used to predict temperature. The results demonstrate that models will overpredict film thickness along the side edge of a bearing if thermal strain in the top foil is not included. In addition, the results show the need for a three-dimensional thermal flow model at the trailing edge of a bearing when backflow occurs.     

Structural Stiffness and Coulomb Damping in Compliant Foil Journal Bearings: Theoretical Considerations

Compliant foil bearings operate on either gas or liquid, which makes them very attractive for use in extreme environments such as in high-temperature aircraft turbine engines and cryogenic turbopumps. However, a lack of analytical models to predict the dynamic characteristics of foil bearings forces the bearing designer to rely on prototype testing, which is time-consuming and expensive. In this paper, the authors present a theoretical model to predict the structural stiffness and damping coefficients of the bump foil strip in a journal bearing or damper. Stiffness is calculated based on the perturbation of the journal center with respect to its static equilibrium position. The equivalent viscous damping coefficients are determined based on the area of a closed hysteresis loop of the journal center motion. The authors found, theoretically, that the energy dissipated from this loop was mostly contributed by the frictional motion between contact surfaces. In addition, the source and mechanism of the nonlinear behavior of the bump foil strips were examined. With the introduction of this enhanced model, the analytical tools are now available for the design of compliant foil bearings.     

On the Fluid Flow and Thermal Analysis of a Compliant Surface Foil Bearing and Seal

Foil gas bearings have been applied successfully to a wide range of high-speed rotating machinery such as air cycle machines (ACMs) and auxiliary power units (APUs). The performance of these bearings are based on the high pressure gas in a very thin layer between the journal and the bearing governed by the Reynolds equations. Generation of heat in these bearings especially at high journal rotating speed and high loads or at high ambient temperature directly affect their performance. Thermal and fluid flow analysis of an advanced compliant foil journal bearing/seal are presented. The side flow (known as leakage) and the approximate temperatures are the results of this analysis. The result of preliminary analysis shows that the major portion of the heat is carried through conduction and using the modified Couette flow approximation for the present working fluid, air, helped in analysis of the temperature magnitude, which can be related to the gas viscosity behavior and thin gas film thicknesses.     

Performance and Durability of High Temperature Foil Air Bearings for Oil-Free Turbomachinery

The performance and durability of advanced, high temperature foil air bearings are evaluated under a wide range (10 to 50 kPa) of loads at temperatures from 25° to 650 °C. The bearings are made from uncoated nickel based superalloy foils. The foil surface experiences sliding contact with the shaft during initial start/stop operation. To reduce friction and wear, the solid lubricant coating, PS304, is applied to the shaft by plasma spraying. PS304 is a NiCr based Cr₂O₃ coating with silver and barium fluoride/calcium fluoride solid lubricant additions.

The results show that the bearings provide lives well in excess of 30,000 cycles under all of the conditions tested. Several bearings exhibited lives in excess of 100,000 cycles. Wear is a linear function of the bearing load. The excellent performance measured in this study suggests that these bearings and the PS304 coating are well suited for advanced high temperature, oil-free turbomachinery applications.     

基于弹性壳体模型的波箔型气体动压径向轴承静特性分析

采用有限单元法,对波箔型气体动压径向轴承的箔片建立了弹性壳体单元模型。该模型综合考虑了箔片膜效应与弯曲效应之间的耦合,更能真实地反映出波箔和平箔的变形。运用有限差分法及Newton-Raphson迭代法耦合求解Reynolds方程和气膜厚度方程,分析了轴承气膜厚度分布、压力分布、箔片变形量分布以及承载能力,并与实验结果进行了比较,证明了该方法的可行性和精确性。分析了转速、箔片厚度对轴承特性的影响,结果表明:转速上升,承载能力增大;箔片厚度小于0.2mm时,厚度的改变对轴承的影响较大。     

考虑摩擦的弹性支承箔片径向轴承的结构刚度分析

结构刚度是对箔片轴承进行理论分析的基础。对箔片轴承运行时存在的库伦摩擦力进行受力分析,建立弹性支承箔片径向轴承的有摩擦均匀结构刚度模型,并计算该箔片轴承的结构刚度。结果表明,弹性支承箔片径向轴承的结构刚度与弹性基础的材料性质以及箔片元件和轴承座的几何尺寸有关;考虑摩擦下的结构刚度大于不考虑摩擦的结构刚度,且2种结构刚度都是随着厚度的增加而逐渐减小,并且考虑摩擦下的结构刚度减小的趋势更明显。     

圆轴承温粘热效应有限元方法分析

构筑了有限宽圆轴承温粘热效应二维有限元模型。依据圆轴承温粘热效应的三维模型计算结果，油膜温度场变化沿轴向可以忽略，在轴瓦和轴颈与油膜界面使用绝热边界条件，用有限元方法联立求解周向和径向二雏能量方程、双雷诺边界条件广义雷诺方程、周向速度方程和温粘方程，给出中心对称面上油膜温度和速度分布，轴承特性系数与工程上应用数据吻合。研究结果表明，不考虑轴瓦的导热使油膜力计算结果偏高，同时，将进油槽处温度作为油膜的始温叉使油膜力的计算结果偏低，这一高一低相互抵消，证实该模型合理，符合工程应用。     

弹性转子的轴心轨迹

研究了非线性弹性转子 -轴承系统的轴心轨迹 ,认为对称不平衡转子是连续弹性轴 ,它两端支撑在滑动轴承上 ,油膜反力采用非线性短轴承模型。推导出了系统的非线性运动方程 ,所求方程的近似周期解即为轴心轨迹。给出在某些参数下轴迹的数值计算结果     

Numerical study on foil journal bearings with protuberant foil structure

A numerical model coupling the hydrodynamic pressure of lubricant film with the deformation of foil structure was developed for a type of foil journal bearing with protuberant foil structure. An isothermal and isoviscous lubricant was used in the fluid model, and a perturbation method was applied to linearize the Reynolds equation. The top foil was modeled as a strip of rectangular thin plate supported at a rigid point. The distributions of film pressure, film thickness, and foil deformation were solved by the finite element method (FEM). The effects of eccentricity ratio, bearing number, and number of protuberances on the characteristics of bearings were analyzed.     

A Three-Dimensional Foil Bearing Performance Map Applied to Oil-Free Turbomachinery

To effectively apply compliant foil gas bearings to increasingly larger and more challenging turbomachinery, a comprehensive method that compares a foil bearing's capabilities with the application's operating requirements is needed. Extensive laboratory and field experience suggests that foil bearing failure is generally due to thermal stress brought on by excessive viscous power loss; therefore, a map that graphically relates component- and system-level parameters (bearing size, applied loads, and shaft rotational speeds) directly to bearing power loss is more elucidating than a map based on a lumped speed/load parameter like the Sommerfeld number. In this article we describe a performance map featuring a three-dimensional contour plot that illustrates the expected power loss in a foil bearing as a function of applied load and shaft speed. Using this performance map, bearing capabilities can be examined at the anticipated system operating conditions and safety margins between an operating point and incipient bearing failure can be ascertained. To demonstrate the concept's features and usefulness, we present a performance map generated from foil bearing power loss test data. We expect that these maps, combined with other predictive tools, will help evaluate a foil bearing's general suitability for a candidate rotor system and will lead to more robust and successful oil-free turbomachinery designs.     

牙轮钻头滑动轴承失效分析

收集了近几年20只现场失效牙轮钻头,对其轴承表面金相组织和硬度以及影响牙轮钻头滑动轴承失效的主要因素进行了分析。结果表明,牙轮钻头在工作过程中温度升高引起的轴承表面金相组织发生改变、硬度降低、抗磨性能减弱,是导致牙轮钻头轴承在高转速下快速失效的根本原因;牙轮钻头轴承的主要失效形式就是粘着磨损,其中载荷工况、相对滑动速度和表面涂层是影响牙轮钻头滑动轴承摩擦学性能的主要因素;采用在原轴承基础上加入浮动套的方法降低原轴承的相对滑动速度,是目前提高牙轮钻头滑动轴承摩擦学性能,延长轴承在高速钻井下使用寿命的有效途径。     

Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications

This paper introduces a simple “Rule of Thumb” (ROT) method to estimate the load capacity of foil air journal bearings, which are self-acting compliant-surface hydrodynamic bearings being considered for Oil-Free turbomachinery applications such as gas turbine engines. The ROT is based on first principles and data available in the literature and it relates bearing load capacity to the bearing size and speed through an empirically based load capacity coefficient, D. It is shown that load capacity is a linear function of bearing surface velocity and bearing projected area. Furthermore, it was found that the load capacity coefficient, D, is related to the design features of the bearing compliant members and operating conditions (speed and ambient temperature). Early bearing designs with basic or “first generation” compliant support elements have relatively low load capacity. More advanced bearings, in which the compliance of the support structure is tailored, have load capacities up to five times those of simpler designs. The ROT enables simplified load capacity estimation for foil air journal bearings and can guide development of new Oil-Free turbomachinery systems.     

计入能量和状态方程时有限长滑动轴承的完全Navier－Stokes解

应用ＦＩＤＡＰ程序，直接对完全的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组，能量方程（包括耗散项），和状态方程联立求解，得到了有限长径向滑动轴承的三维速度场，压力场和温度场。给出了以真实油膜形状作为基底的压力，温度三维等值线。从理论上完全证实了滑动轴承润滑理论中几个著名的物理现象。为全面讨论润滑油膜的物理特性和各种参数对轴承性能的影响奠定了基础。     

Severity Estimation of Cracked Shaft Vibrations within Fluid Film Bearings

The equations of motion, with four degrees of freedom, taking into consideration the flexibility, damping and cross coupling of the fluid film bearings are derived for a cracked Jeffcott rotor supported on fluid film bearings.

Dimensionless equations are developed for dynamic radial load, dynamic pressure developed in the fluid film bearings and coefficient of dissipation considering the journal vibrations in two harmonics; bearing fluid film stiffness and damping coefficients. These are applied to a cracked Jeffcott rotor supported on different types of bearings, i.e., cylindrical journal bearings, offset cylindrical bearings, tilting pad journal bearings and three-lobe bearings. Based on the allowable dynamic pressure developed in the fluid bearings, the severity of cracked shaft and allowable crack depths are estimated in this study. Measurement of dynamic pressure and dissipation for monitoring the crack growth is suggested. However, 2x vibration is the best indicator of cracks in the shafts.