挤压油膜阻尼在储能飞轮转子支承系统中应用研究

在飞轮储能系统实验研究中,利用永磁轴承-螺旋槽流体动压锥轴承的混合支承,并采用了挤压油膜阻尼为转子支承系统提供阻尼。基于流体润滑理论的雷诺方程和长轴承近似理论,推导出一端封闭、一端开口边界的挤压油膜的压力分布近似解析解,得到等效油膜刚度和阻尼系数。最后对比分析了飞轮转子支承系统不平衡响应的计算与试验结果。     

A numerical scheme for solving a periodically forced Reynolds equation

A modified Reynolds equation is used to model the air‐film in a high‐speed squeeze‐film bearing. The axial position of the bearing stator is prescribed as a finite amplitude periodic oscillation. A numerical approach is considered for solving the uncoupled and coupled periodic problems associated with this model. The uncoupled problem requires the computation of the squeeze‐film dynamics when the rotor is held at a fixed axial position and the coupled problem incorporates the additional air–rotor interaction since the rotor position is unknown and modelled as a spring‐mass‐damper system. The details of a Fourier spectral collocation scheme are provided for the reduction of the modified Reynolds equation to a system of non‐linear, first‐order ordinary differential equations in space. Using the Matlab boundary value problem solver bvp4c this system of equations is solved to give the periodic pressure distributions and rotor heights. The high degree of accuracy in the spectral collocation scheme is demonstrated through comparison with an appropriate analytical solution. Further analysis indicates that the direct periodic solver is at least 10 times faster than the equivalent Crank–Nicholson finite‐difference scheme. For changing values of a selected physical parameter the method of arc‐length continuation is employed to track branches of solutions computed using the spectral collocation scheme. A selection of results is presented to demonstrate the range of accessible solutions and the robust nature of the numerical scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

An experimental test of equations predicting the load bearing capacity of squeeze films of elastico-viscous liquid

A form of squeeze film apparatus was recently described in which the movement of one plate towards the other was simulated by the continuous volume generation of liquid over the plate area. The liquid exuded from a large number of holes in the lower plate surface and formed a “continous flow” version of squeeze film apparatus with no moving parts [1]. A later paper gave derivations of equations from which squeeze film load bearing capacity could be evaluated, taking into account viscous, inertial and normal stress effects in the liquid film [2].In order to find the total load in a squeeze film system, it was necessary to obtain the relationship between the first normal stress difference and shear rate for the liquid in use, using an experimental method. At high shear rates, the jet thrust method provided these data [3,4] and from them the load bearing capacity of squeeze films of hot, polymer-thickened oil were predicted [2].A more complete test of the method is possible with a highly elastic liquid because considerable load enhancement due to extra stress is present at moderate deformation rates in squeeze film systems [1,5,6,7]. Thus a 0.1 per cent aqueous polyacrylamide solution gives well-defined load enhancement and (quite independently) the jet thrust method gives the relationship between normal stress and shear rate from which predictions of load enhancement may be made. Furthermore, convergent nozzles may be used in the jet thrust apparatus [3] to measure the stress development in an elastic liquid which is being simulateneously sheared and stretched, a situation which more closely resembles the squeeze film case than that of steady shear.     

Aerodynamic analysis of circular plate-shaped and circular ring-shaped squeeze film bearings

Aerodynamics of circular plate-and circular ring-shaped squeeze film bearings isanalyzed in detail,yielding analytic expressions for the pressure distribution of thesebearings.Several formulae for these bearings are modified using the developed method.Thepaper also gives numerical results of pressure distribution and load-bearing capacities ofthese bearings.     

Inertia effects in hydromagnetic lubrication

Summary A theoretical investigation of inertia effects in a squeeze film bearing with an electrically conducting lubricant in the presence of a uniform transverse magnetic field is presented. The two cases of infinitely long rectangular plates and circular plates as bearing surfaces are considered. It is shown that the load supporting capacity of the bearing increases and the squeeze decreases if the lubricant inertia effects are taken into account. However, the inertia effect becomes smaller when the strength of the magnetic field increases.     

Effect of lubricant inertia in bearings with a non-Newtonian lubricant

Summary The inertia effects in externally pressurized and squeeze film bearings with lubricants obeying a power law are considered. It is found that the inertia forces decrease the load capacity of the externally pressurized bearing with a given flow rate and the inertia effect increases with the flow behaviour index. At a given feeding pressure, on the other hand, the inertia increases or decreases the load capacity when the flow behaviour index is smaller than or greater than 3, respectively. For squeeze films between circular plates and rectangular plates, the rate of squeeze is slowed down by the inertia and the inertia effect is larger in dilatant lubricants than in pseudoplastic lubricants.Nomenclature 2a diameter of the bearing, width of rectangular plates - 2b diameter of the recess - 2h film thickness - 2h ₀ initial thickness of squeeze films - l length of the rectangular plates - m consistency index - n flow behaviour index - p pressure - p _e external pressure - p _i feeding pressure - q flow rate - r radial distance - t time - u velocity of the lubricant - v squeeze velocity - w load capacity - W dimensionless load capacity - axial distance - viscosity of the lubricant - density of the lubricant     

Combined effects of non-Newtonian couple stresses and fluid inertia on the squeeze film characteristics between a long cylinder and an infinite plate

On the basis of the Stokes micro-continuum theory together with the averaged inertia principle, the combined effects of non-Newtonian couple stresses and convective fluid inertia forces on the squeeze film motion between a long cylinder and an infinite plate are presented. A closed-form solution has been derived for squeeze film characteristics including the film pressure, the load capacity and the response time. Comparing with the Newtonian-lubricant non-inertia case, the combined effects of couple stresses and convective inertia forces provide an increase in the film pressure, the load capacity and the response time. In addition, the quantitative effects of couple stresses and convective inertia forces are more pronounced for cylinder–plate system operating at a larger couple stress parameter and film Reynolds number, as well as a smaller squeeze film height. To guide the use of the present study, a numerical example is also illustrated for engineers when considering both the effects of non-Newtonian couple stresses and fluid convective inertia forces.     

有限长滑动轴承非线性油膜力的近似解法

本文中提出了一种求解有限长径向滑动轴承非线性油膜力的近似解析方法.在滑动轴承-转子系统非线性动力行为分析中,油膜力计算模型通常采用"π"油膜假设,但是,实际工况中油膜的存在区域并非是"π"区域,运行时油膜中出现气穴,破裂成条纹状(即具有Reynolds边界条件).本文中的近似解析方法采用Reynolds边界条件,基于变分原理,运用分离变量法求解油膜的压力分布,其中油膜压力的周向分离函数通过无限长轴承的油膜压力分布获得,油膜的破裂终止位置角通过连续条件确定,轴向分离函数运用变分原理并结合周向函数求得.计算结果表明:本文中提出的方法和有限元方法的结果吻合得很好.在此基础上,分析了一些轴承参数对油膜压力分布的影响.     

Nonlinear vibration response of a complex aeroengine under the rubbing fault

Nonlinear Dynamics - Rolling bearing and squeeze film damper will introduce structural nonlinearity into the dynamic model of aeroengine. Rubbing will occur due to the clearance reduction design of...     

基于发动机主轴轴承异常油膜噪声特征的模拟试验研究

由发动机主轴轴承油膜空穴造成的不规则打字机敲击噪声一直是汽车领域未解决的难题. 为了探究发动机主轴轴承动态载荷性能耦合作用下产生的异常空穴噪声，本文作者利用自行设计的平行板挤压油膜试验机进行模拟噪声试验并探究空穴噪声的特征. 该试验机可同时采集振动、位移、声压、力和空穴图像等五种信号，通过试验探究了不同激励信号、挤压振幅、挤压频率、润滑油黏度等因素对空穴噪声的影响，结果表明在方波、大振幅、使用高黏度润滑剂以及挤压频率为12 Hz的状况下容易产生空穴噪声.      

Analytical solution for squeeze film damping of MEMS perforated circular plates using Green’s function

Squeezed air film between two closely spaced vibrating microstructures is the important source of energy dissipation and has profound effects on the dynamics of microelectromechanical systems (MEMS). Perforations in the design are one of the methods to model these damping effects. The literature reveals that the analytical modeling of squeeze film damping of perforated circular microplates is less explored; however, these microplates are also an imperative part of the numerous MEMS devices. Here, we derive an analytical model of transverse and rocking motions of a perforated circular microplate. A modified Reynolds equation that incorporates compressibility and rarefaction effects is utilized in the analysis. Pressure distribution under the vibrating microplate is derived by using Green’s function and also derived by finite element method (FEM) to visualize the pressure distribution under perforated and non-perforated areas of the microplate. The analytical damping results are validated with previous renowned analytical models and also with the FEM results. The outcomes confirm the potential of the present analytical model to accurately predict the squeeze film damping parameters.     

圆平板挤压膜实验及其参数识别

完成了简谐激励下水中平行圆板的挤压膜振动实验．用最小二乘法识别出非线性粘性挤压膜力模型中的４个系数．不同挤压膜厚、不同频率和不同振幅情况的数值模拟结果与实验值吻合较好．研究结果表明，所用模型可较好地描述粘性挤压膜运动，识别出的系数在一定范围内给出良好精度的数值模拟．     

球轴承启停过程的瞬态热混合润滑分析

建立了角接触球轴承的几何和数学模型,通过求解考虑了热效应和时变效应的Reynolds方程,对启动和制动过程中的球轴承瞬态热混合润滑问题进行了分析,考虑了不同加速度启动工况下的瞬态热混合润滑情况.结果表明:启动过程中,随转动速度的增大,最小膜厚增大,轴承逐渐由边界润滑进入弹流润滑状态;不同滑滚比下进入弹流润滑状态的时间有所不同,随着滑滚比的增大,进入弹流润滑的时刻有所推迟,轴承处于同一转速条件下的油膜厚度变小;随着转速的增大,油膜温度升高,最高油膜温度增长幅度减小;加速度的增大使边界润滑消失的时间提前,随着转速的增加,油膜温度增大,且在同一时刻加速度越大油膜温度越高;油膜减小过程中的挤压膜作用导致轴承制动过程中的油膜厚度大于启动过程中的油膜厚度;由于在相同转速下轴承在启动时处于边界润滑状态,而在制动时处于弹流润滑状态,润滑状态的不同导致制动过程中的最高油膜温度较启动过程较小.     

Performance of hydromagnetic squeeze films between conducting porous rough conical plates

An endeavor has been made to discuss the behavior of hydromagnetic squeeze film between two conducting rough porous conical plates. The plates are considered to be electrically conducting and the clearance space between them is filled by an electrically conducting lubricant. A transverse magnetic field is applied between the plates. Efforts have been made to solve the concerned Reynolds’ equation with the associated boundary conditions to get the pressure distribution. This in turn, is used to obtain the expression for load carrying capacity leading to the calculation of the response time. The results are presented graphically as well as in tabular form. It is suggested by the results that the bearing system records an enhanced performance as compared to that of a bearing system working with a conventional lubricant. It is noticed that the pressure, load carrying capacity and the response time increase steadily with increasing values of the magnetization parameter. In general, the bearing suffers owing to transverse surface roughness. However, the negatively skewed roughness tends to better the performance of the bearing system marginally. This performance gets further improved especially, when the negative variance is involved. It is observed that the semi-vertical angle increases the load carrying capacity. Besides, the conductivity also increases the load carrying capacity significantly. In addition, it is revealed that the negative effect induced by the porosity can be neutralized to a nominal extent by the positive effect of the magnetization parameter in the case of negatively skewed roughness in the presence of negative variance. Thus, this study provides ample scopes for improving the performance of the bearing system considerably by choosing a suitable combination of magnetization parameter, semi-vertical angle and the conductivities of the plates.     

Combined effect of viscosity variation and non-Newtonian Rabinowitsch fluid in wide parallel rectangular-porous plate with squeeze-film characteristics

The present article carries out the study of viscosity variation of non-Newtonian fluid with the homogeneous porous wall on wide parallel rectangular-plate based on the Rabinowitsch fluid model. The non-linear modified Reynolds equation is derived for the lubrication of rectangular squeeze film bearing with viscosity variation and porous parameter. Using the Morgan–Cameron approximation, the nonlinear Reynolds-type equation for squeeze-film which governs the film pressure is solved within the fundamentals of small perturbation technique. The characteristic of the wide parallel rectangular-porous plate is numerically computed for different physical quantities such as film pressure, load carrying capacity and response time. Moreover, as limiting cases some of the results from the available literature are recovered also. Further, the findings reveal that the viscosity variation of non-Newtonian fluid and the presence of porous wall lead to reduction in the load capacity and the response time respectively. Here, the porous matrix consists of a system of capillaries of very small radii with the homogeneous porous wall. The impact of porosity is incorporated as a result it acts as self-lubrication on bearing surface. Also, the effect of viscosity variation is one of the most important characteristics of fluid which helps in the design of bearings for lubrication in engineering and industrial applications.

     

The flow of a power-law liquid in a continuous-flow squeeze film

Consideration is given to the flow of an inelastic ‘power-law’ liquid in a continuous flow squeeze film. This simulates the flow in a conventional squeeze film by continuously injecting fluid into the narrow gap between two plates through the lower plate (Oliver et al. [6]). To zero order in the usual lubrication approximation the results are identical with those for the conventional squeeze film. To first order, useful corrections to the normal force due to the effects of inertia are obtained.     

碟形弹簧支承圆形瓦推力轴承热动力润滑性能分析

对碟形弹簧支承圆形瓦推力轴承在稳态运行时的热动力润滑性能进行了分析研究,考察了弹簧弯曲刚度,载荷和转速对轴承的油膜厚度为分布,压力分布,温度分布,功耗及油膜压力中心位置的影响,并提出了温度因子概念,研究表明,较小的弹簧弯曲刚度和载荷有利提高轴承的热动力润滑性能,油膜温度随温度因子的增大而增大,当轴承转速在较大的范围内变化时,温度因子基本为常母,油膜温度敢基本不变,油膜压力中心位于瓦几何中心的上游区     

Comparing numerical and analytical solutions for squeeze-film levitation force

In this paper, a two-dimensional numerical study on the levitation force induced by pressure radiation in a gas squeeze film is carried out. In particular, the validity of the pressure release boundary condition and the isothermal assumptions are examined by a CFD scheme. The results are compared to a one-dimensional analytical solution, leading to findings on the role and accuracy of commonly used boundary conditions. It appears that when taking into consideration the energy leakage near the edges of the levitated object, the levitation force due to the squeeze film could be smaller by up to 50% in comparison with the analytical, one-dimensional solution that assumes pressure release conditions.     

挤压油膜阻尼器的非线性特性研究

首先借助Reynolds方程导出挤压油膜的压力分布，然后采用二系数法分析挤压油膜阻尼器的非线性特性．理论分析和实例计算的结果都表明：它的刚度系数和阻尼系数都是非线性变化的，是一个高度非线性的元件，用二系数法对其进行线性化会产生很大的误差．     

双盘悬臂柔性转子--同心型挤压油膜阻尼器系统关于稳态圆响应的参数优选

获得了双盘悬臂柔性转子－同心型挤压油膜阻尼器（ＳＦＤ）系统在ＳＦＤ轴承处的稳态响应的频响特性曲线、盘的频响曲线及传递率曲线。通过求解各方程和分析响应曲线图优选出可以避免出现双稳态和不稳态的参数组合。在给定的参数范围内分析了参数对于各项系统特性的影响,保证了所选能较好地满足各项性能要求,使系统具有优良的稳定性和动态特性。