Identification of dynamic properties of radial air-foil bearings

Air-foil bearings (AFBs) are self acting hydrodynamic bearings made from sheet metal foils comprised of at least two layers. The innermost “top foil” layer traps a gas pressure film that supports a load while the layer or layers underneath provide an elastic foundation. Air-foil bearings are currently used in many commercial applications, both terrestrial and aerospace. Air-foil bearings provide a means to eliminate the oil system leading to reduce weight and enhanced temperature capability. Regardless of the application of the air-foil bearings, the identification of the dynamic characteristics is important for successful design practice. In the present work, stiffness and damping of radial air-foil bearings are indentified in the light of experimental results. Due to the initial high torque requirement of the air-foil bearing, the experimental setup using single air-foil bearing is proposed instead of standard two-foil bearing setups. Experiments are carried out at maximum speed of 60,000 rpm. Sub-structuring approach is used for identification of stiffness and damping properties of the air-foil bearings. The results have shown that the developed experimental procedure is able to indentify the stiffness and damping properties of radial air-foil bearings accurately.     

Numerical and experimental studies on stability of cryogenic turbo-expander with protuberant foil gas bearings

High speed turbo-expander is an essential refrigerating component in cryogenic systems. In addition to thermodynamic performance, its stability in transient high speed operation is also of great concern for its comprehensive performance. Oil free foil bearing has a great application potential in high speed turbomachinery by virtue of its high stability with no extra external supplying gas. In this paper, finite element model of a 150 Nm³/h cryogenic turbo-expander using foil bearing for air separation is configured for a case study. Influence of bearing structural stiffness and damping characteristics on the rotor-foil bearing system are evaluated for stable operation. Static structural stiffness and damping coefficients of the protuberant foil journal bearing and thrust bearings are obtained from the static loading and deflection tests. With the tested coefficients, rotordynamic performances of the rotor-bearing system is analyzed numerically and compared with the transient experimental results.     

Investigation on Axial Displacement Fault Mechanism Based on Dynamic Characteristic Coefficients Identification of Tilting-Pad Thrust Bearing

To prevent the thrust bearing damage faults, the thrust bearing pad temperature and the static axial displacement variation are usually monitored and cared about, but axial vibration caused by axial dynamic excitation can also result in the severe rubbing. An electric oil pump system with overflow valve is designed on a similar industrial centrifugal compressor test-rig to apply the axial low-frequency excitation from 3 to 7 Hz, and the axial and radial vibration response amplitudes are analyzed. Then, the stiffness and damping coefficients of tilting-pad thrust bearing (TPTB) are identified by instrumental variable filter (IVF) algorithm to reveal the mechanism of TPTB dynamic characteristics affecting axial vibration. Finally, a fault case about surge and the rubbing of thrust bearing is studied. Compared with axial vibration, radial vibration does not directly correlate to axial excitation, and the axial frequency spectrum is an effective method to diagnose axial displacement faults; the static axial load, the dynamic excitation amplitude and the excitation frequency all exert influence on thrust bearing dynamic characteristics and axial vibration response. The research results can guide the design of thrust bearings and help to diagnose the axial displacement faults, while the test device and method can be used to measure the static and dynamic characteristics of thrust bearings.     

采用多自由度转子模型的电磁轴承支承特性测试方法

为描述主动电磁轴承的支承特性,通常是沿袭传统机械轴承支承的刚度阻尼概念,称之为等效刚度和等效阻尼。由于电磁轴承的支承特性与其控制策略有关,因此确定电磁轴承的等效刚度和等效阻尼值相对困难。已有的电磁轴承等效刚度和阻尼测试方法大多是基于单自由度模型的,难以用于实际多自由度电磁轴承-转子系统的刚度阻尼测量,甚至无法实际操作。针对上述问题,首先从理论上分析了采用等效刚度和等效阻尼概念表示电磁轴承支承特性的描述局限性和适用范围,然后提出了一种基于多自由度转子模型的对电磁轴承等效刚度和等效阻尼进行直接测量的方法。实验结果表明该方法能够实时地对电磁轴承-转子系统的等效刚度和阻尼值进行准确识别,其结果可以作为电磁轴承动力学特性研究的依据。     

计及套圈变形的电主轴角接触球轴承动刚度分析

针对高速电主轴结构特点,应用弹性力学和滚动轴承动力学理论,建立考虑内圈弯曲变形影响的角接触球轴承动刚度分析模型,探讨不同工况下内圈的径向挠度及其对轴承动刚度的影响,最后在12MD60Y6型号电主轴上进行轴承动刚度测试。理论和实验结果表明,内圈径向挠度和轴承的轴向载荷成正比、与转速成反比,在重载条件下其值不容忽视。考虑内圈径向挠度的轴承动刚度计算结果更接近实验结果。     

交替层合阻尼结构主控各向异性层参数对结构阻尼的影响

借助动态热机械分析仪(DMA Q800) 对交替层合各向异性阻尼结构阻尼性能的影响权重最大层的各参数进行优化实验研究。探讨了该主控约束层的不同铺设角度、不同厚度和不同多子层替代对层合阻尼结构刚度、阻尼的温频特性的影响规律。实验结果表明, 结构阻尼性能的影响权重最大层纤维铺设角度越接近90°(包括两个90°约束层层合) 时, 结构阻尼性能越好; 结构不同, 影响权重最大层较优厚度有所差异, 当阻尼层总厚度与结构阻尼性能影响最大层厚度比约为10 时, 结构阻尼性能较好。      

基于不平衡响应的磁悬浮轴承刚度阻尼辨识方法研究

磁悬浮轴承的支承特性对转子轴承系统的临界转速、不平衡响应、稳定性有着非常重要的影响。研究一种基于不平衡响应辨识磁悬浮轴承刚度和阻尼的方法。首先使用MSC.Patran建立磁悬浮轴承转子有限元模型;使用Matlab软件实现基于不平衡响应辨识磁悬浮轴承刚度阻尼的基本原理;然后用有限元模型进行仿真辨识来验证该方法的可行性;并对一个五自由度的磁悬浮轴承试验台进行基于不平衡响应的磁悬浮轴承刚度阻尼的辨识试验研究。最后,为了检验辨识结果的正确性,赋予转子有限元模型试验辨识的磁悬浮轴承的刚度和阻尼,进行仿真与试验的系统不平衡响应对比,结果两者基本一致,表明该方法可以有效地辨识磁悬浮轴承的刚度和阻尼。     

Dynamic analysis and damping of composite structures embedded with viscoelastic layers

In recent years, it has been found that composites co-cured with viscoelastic materials can enhance the damping capacity of a composite structural system with little reduction in stiffness and strength. Because of the anisotropy of the constraining layers, the damping mechanism of co-cured composites is quite different from that of conventional structures with metal constraining layers. This paper presents an analysis of the dynamic properties of multiple damping layer, laminated composite beams with anisotropic stiffness layers, by means of the finite element-based modal strain energy method. ANSYS 4.4A finite element software has been used for this study. The variation of resonance frequencies and modal loss factors of various beam samples with temperature is studied. Some of these results are compared with the closed-form theoretical results of an earlier published work. For obtaining optimium dynamic properties, the effects of different parameters, such as layer orientation angle and compliant layering, are studied. Also, the effect of using a combination of different damping materials in the system for obtaining stable damping properties over a wide temperature range is studied.     

Deformation of extreme viscoelastic metals and composites

The figure of merit for structural damping and damping layer applications is the product of stiffness E and damping tan δ. For most materials, even practical polymer damping layers, E tan δ is less than 0.6 GPa. We consider several methods to achieve high values of this figure of merit: high damping metals, metal matrix composites and composites containing constituents of negative stiffness. As for high damping metals, damping of polycrystalline zinc was determined and compared with InSn studied earlier. Damping of Zn is less dependent on frequency than that of InSn, so Zn is superior at high frequency. High damping and large stiffness anomalies are possible in viscoelastic composites with inclusions of negative stiffness. Negative stiffness entails a reversal of the usual directional relationship between force and displacement in deformed objects. An isolated object with negative stiffness is unstable, but an inclusion embedded in a composite matrix can be stabilized under some circumstances. Ferroelastic domains in the vicinity of a phase transition can exhibit a region of negative stiffness. Metal matrix composites containing vanadium dioxide were prepared and studied. The concentration of embedded particles was sensitive to the processing method.     

Generalization of the continuous and discrete structural approaches to the solution of problems of the dynamics of laminated composite plates and structures with stratification. Part 1. Applied mathematical model of the dynamic deformation of laminated composite structures

We construct an applied mathematical model of dynamic deformation of laminated structures. The proposed model can be regarded as a generalization of continous and discrete structural approaches to the analysis of laminated structures. This model enables one either to consider a structure as a single layer with reduced stiffness characteristics or split it across its thickness into a set of components each of which may include several layers and/or parts of layers. It is also possible to simulate various conditions of contact of layers (rigid or sliding). The differential operators appearing in the proposed model are similar to the operators used in the classical theory of shells, which simplifies the numerical realization of the model. Ukrainian Transport University, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 86–91, July–August, 1999.     

不同边界条件和应变振幅对各向异性层合阻尼结构内耗的影响

制备了由纤维增强树脂复合材料层与黏弹阻尼材料层交替层合的7层各向异性层合阻尼结构, 借助动态热机械分析仪(DMA Q800)首次考察了不同的结构应变振幅和不同的边界条件对该结构内耗温度频率特性的影响, 为新型减振降噪阻尼结构的理论分析与应用提供相应的实验研究依据。结果表明: 在不同的边界条件和常温(25℃)下, 各向异性层合阻尼结构的内耗都随着结构应变振幅的增加而减少, 且结构内耗峰所对应的温度随应变振幅的增加而向低温方向移动; 当结构应变振幅相同时, 单悬臂梁模式下的结构内耗最高, 双悬臂梁模式下次之, 三点弯曲模式下最低。      

High‐order layerwise finite element for the damped free‐vibration response of thick composite and sandwich composite plates

A high‐order layerwise finite element methodology is presented, which enables prediction of the damped dynamic characteristics of thick composite and sandwich composite plates. The through‐thickness displacement field in each discrete layer of the laminate includes quadratic and cubic polynomial distributions of the in‐plane displacements, in addition to the linear approximations assumed by linear layerwise theories. Stiffness, mass and damping matrices are formulated from ply to structural level. Interlaminar shear stress compatibility conditions are imposed on the discrete layer matrices, leading to both size reduction and prediction of interlaminar shear stresses at the laminate interfaces. The C¹ continuous finite element implemented yields an element damping matrix in addition to element stiffness and mass matrices. Application cases include thick [0/90/0], [±θ]_S and [±θ] composite plates with interlaminar damping layers and sandwich plates with composite faces and foam core. In the latter case, modal frequencies and damping were also experimentally determined and compared with the finite element predictions. Copyright © 2008 John Wiley & Sons, Ltd.     

Prediction of material coupling effect on structural damping of composite beams and blades

The present paper investigates the effect of material coupling on static and modal characteristics of composite structures. Incorporation of stiffness and damping coupling terms into a beam formulation yields equivalent section stiffness and damping properties. Building upon the damping mechanics, an extended beam finite element is developed capable of providing the stiffness and damping matrices of the structure. Validation cases on beams and blades demonstrate the importance of all stiffness and damping terms. Numerical results validate the predicted effect of material coupling on static characteristics of composite box-section beams. The effect of the full coupling damping matrices on modal frequencies and structural modal damping of composite beams is investigated. Box-section beams and small blade models with various ply angle laminations at the girder segments are considered. Finally, the developed finite element is applied to the prediction of the modal characteristics of a 19 m realistic wind-turbine model blade.     

Dynamic characteristics of a double‐row multirecess externally pressurized journal bearing

Abstract

A numerical method is used to compute the characteristics of an externally pressurized journal bearing. Results indicate that the squeeze term due to the oil pocket has very small effect on the bearing characteristics. At lower rotational speeds, double‐row hydrostatic journal bearings have higher damping coefficients than the single‐row bearings and, therefore, have a better stability. However, the stiffness coefficient and the loading capacity are lowered when using double‐row bearings.     

喷涂阻尼厚度对车轮振动声辐射的影响

在列车车轮表面喷涂阻尼材料可以降低车轮振动声辐射,通过试验调查喷涂阻尼厚度对其减振降噪性能的影响。在半消声室进行对比试验,测试了斜曲型辐板车轮在无阻尼、喷涂1 mm和2 mm情况下的振动声辐射,和双S型辐板车轮在无阻尼、喷涂1 mm和4 mm阻尼下的声辐射。测试结果表明：对于斜曲型辐板车轮,2 mm阻尼层对车轮的减振区域和减振量均优于1 mm阻尼层,在径向和轴向激励下,1mm阻尼层降噪量分别为2.0 dB(A)和1.0 dB(A);对于双S型辐板车轮,在径向和轴向激励下,1 mm阻尼层降噪量分别为1.9 dB(A)和1.1 dB(A)。对于这两种辐板形式车轮,阻尼层增厚,降噪效果均增加。对于斜曲型车轮,在径向激励下阻尼具有更好的降噪效果,对于双S型车轮,在径向激励和轴向激励下阻尼降噪效果近似相同。     

An analytical method for calculating stiffness of two-dimensional tri-axial braided composites

This paper presents a new analytical method for calculation of the stiffness of two-dimensional tri-axial braided composites. A unit cell has been introduced as a representative cell of a braided composite and its components. The braided composite is considered as consisting of three layers. The first two layers represent braided tows and the third layer is the axial tow. Then, using rule of mixtures, mechanical properties of each layer are calculated. Next, using analytical relations, the undulation of representative layers of braided tows is calculated. Finally, using a volume averaging method, the total stiffness of the braided composite is calculated. The results are compared with those obtained from experimental methods and the effect of braided tows crimp on the stiffness of braided composites is examined.     

Sandwich-fabric panels as spacers in a constrained layer structural damping application

Sandwich-fabric panels can provide for an alternative spacer material in a constrained layer damping configuration. Constraining layer configurations with sandwich-fabric spacers can be a weight efficient replacement for full composite constraining layers, if the shear stiffness of the rubber used is not too high. It seems that in any case the use of sandwich-fabric spacers can lead to a more cost-effective damping treatment. To predict the damping of multilayer materials a strain energy method was used. The damping of multilayer beams could be accurately modelled by calculating the distribution of strain energies in the structure with the help of finite elements and knowledge of the loss factors of the individual layers (as a function of frequency).     

固体火箭发动机复合材料壳体承载力分析

为了提高固体火箭发动机(SRM)的外载荷承载能力,研究了其复合材料壳体的失效机制,提出了复合材料壳体的增强改进结构形式。通过提高复合材料外缠绕层的轴向刚度和横向弯曲刚度,使得连接区域内的内、外缠绕层的轴向变形相协调,改善了内、外缠绕层的轴向承载分配,使增强改进后的复合材料壳体结构的承载能力提高了124%,而结构质量增加低于10%。研究结果表明: SRM复合材料壳体承载能力的关键因素是连接区域内复合材料内、外缠绕层的刚度匹配设计,只有保证连接区域内的刚度匹配和位移变形相协调,才能充分发挥复合材料壳体的承载能力。     

Identification of the Damping Properties of Orthotropic Composite Materials Using a Mixed Numerical Experimental Method

A mixed numerical experimental approach is the basis of a new method for the identification of the material damping properties of fibre reinforced polymers, which provides an answer to many problems encountered in experimental damping characterization. Experimental modal parameters, measured on a plate specimen, are compared with corresponding results from a numerical calculation, thus allowing to determine the stiffness and damping properties of the material. The relation between the modal parameters (structural parameters) and the material parameters, is obtained by using a numerical model of the specimen in combination with the modal strain energy method. In the first part of this paper, the complex moduli are introduced as measures for both material stiffness and damping and the relation between these complex moduli and the modal parameters of a thin plate specimen is derived. Next, the practical procedure of the mixed numerical experimental method is presented, followed by a procedure for estimating the reliability of the obtained results. Finally, two examples are discussed in which all the independent material damping properties are identified as functions of frequency.     

Characterization and numerical evaluation of vibration on elastic–viscoelastic sandwich structures

The objective of this paper is to study the vibration characteristic for a sandwich beam with silica/polymer blend as principal material, and pure polymer matrix as surface laminate. It is anticipated that high stiffness and structure damping of viscoelastic layer can be obtained by taking advantage of fascinating network of densely packed between silica and polymer matrix. Spherical particles of size 12–235 nm at various filler fraction (10–50 wt.%) and three different polymer matrices, polyacrylate, polyimide and polypropylene, were selected as the matrix materials. The mechanical damping and stiffness of the sandwich cantilever beam are recorded by using a Dynamic Mechanical Thermal Analyzer (DMTA). The silica’s small particle size feature and strain difference between principal and surface layers could highly enhance the energy dissipation ability of the beam structure. A numerical model is then developed and validated for the vibration of a symmetric elastic–viscoelastic sandwich beam. Experimental results show that the structure deformation for these sandwich beams with contiguous and constraining layers are in reasonable agreement with the prediction of the model. Both higher resonant vibrations are well damped in accordance with the symmetric motion of the elastic layers and relative little motion of the constraining layer.