液体静压主轴油膜滑移现象的分析及试验研究

针对液体静压主轴运动过程中动态特性问题,研究微尺度下油膜滑移对轴承承载力,刚度及动态刚度的影响。把微尺度下发生的速度滑移引入到油膜性能方程中,结合液体静压主轴系统平衡方程推导出了主轴系统承载力、刚度及动态刚度表达式,研究了油膜初期主轴静动态性能及油膜动刚度特性。从仿真结果中得到油膜滑移的发生使得承载力及刚度增大,最大刚度对应油膜厚度减小。最后刚度检测试验间接得出了实际主轴系统油膜流动过程中,存在油膜微滑移现象。本项研究为液体静压主轴微尺度下油膜滑移现象及性能的研究探索了一条新途径。     

Unbalance response of rotor disks supported by fluid film bearings with a negative cross coupled stiffness using influence coefficient methodReponse de desequilibre d'un rotor multidisque sur paliers lisses par a methode des coefficients d'influence

The dynamic response of a multidisk rotor system supported by fluid-film bearing using the method of influence coefficient is presented. The stiffness and the damping coefficients have been considered as speed dependent. The two bearings, which support the rotor shaft, are dissimilar. The dynamic response is calculated by varying parameters such as spacing between the disks, the viscosity ratio of the oil of the bearings, the bearing clearance ratio and the relative mass of the rotor disks. The effect of damping on the rotor response and the critical speed is also presented.     

基于气穴模型的动压轴承动态油膜刚度计算方法

针对雷诺方程很难准确反映动压轴承高速转动过程中引起的周向惯性效应、动态挤压效应等的影响,进而导致油膜动态刚度计算精度难以满足高精度轴承设计的现状,提出用ADINA软件先求解瞬态油膜压力分布和瞬态油膜力,得到轴心轨迹,然后结合差分计算模型计算油膜动态刚度的方法。该计算方法基于流固耦合和气穴模型,定义油膜和轴的流固耦合时,采用任意的拉格朗日-欧拉(ALE)算法有效避免了油膜网格畸变的问题,再现轴心动态平衡过程和三维流场压力分布的动态发展过程,得到瞬态过程中的动态油膜力和动态油膜刚度。试验结果和基于流固耦合和气穴模型的计算结果对比分析发现两者基本吻合,说明该基于流固耦合和气穴模型的数值仿真计算方法是可行和有效的。     

轴质量对用液体油膜轴承支承转子动特性的影响

本文研究了轴质量对支承于液体油膜轴承上的转子的影响.转子假定是位于弹性轴中部的薄盘,它考虑非零弹性轴质量由液体油膜轴承支承.该径向轴承假定为短简易型,用纵向的和相互作用的刚度及阻尼系数表示,这些系数与系统的角速度有关.假定转于由一电机加速,假定电机速度由一两阶传递函数控制.仿真结果表示质量比的小值,它由轴质量对盘质量比...     

Identification of unbalance forces by metaheuristic search algorithms

This paper discusses the identification of parameters in rotary systems, namely, the unbalance magnitude, phase and position in the rotor system. These parameters can be identified using the measured orbits in the hydrodynamic bearings. The oil film forces are evaluated in the different positions of the orbit of the journal and are applied to the model of the shaft. The model, integrated in time domain, allows with an assumed unbalance, to simulate the orbits. The objective function is basically the difference between measured and simulated orbits, and its minimum corresponds to the identified unbalance amount, phase and position along the shaft. With respect to traditional model based identification procedures, this approach using oil film forces instead of oil film linearized stiffness and damping coefficients, and unfiltered orbits instead of 1X vibration components is suitable to deal with non-linear behaviour of the system.     

滑动轴承等效刚度阻尼的计算分析方法

为获得更精确的滑动轴承等效油膜支承,针对滑动轴承沿轴向方向存在不同的刚度阻尼,将滑动轴承沿轴向方向等分为多个截面,探索了滑动轴承多截面等效刚度阻尼的计算分析方法。基于N-S方程,结合FLUENT中的动网格方法,建立了多截面、多工况的滑动轴承仿真分析模型,计算得到沿轴向方向的多截面和不同转速下单一截面的径向等效刚度阻尼的变化规律,为进一步考虑滑动轴承等效结合部参数的转子系统动力学研究提供了参考依据。     

基于高效深切磨床轴承主轴系统的有限元分析

针对实验室研制的高效深切磨床动静压轴承主轴系统,首先利用计算流体力学软件CFX,对动静压轴承的油膜进行稳态分析,得到油膜上的压力分布。通过在不同的小位移和速度扰动的情况下轴承油膜承载力的变化规律,依此来确定轴承油膜的刚度和阻尼系数。在ANSYS中,采用Ma-trix27单元来模拟动静压轴承油膜的刚度和阻尼作用,并对主轴进行模态分析。结果表明,在微小的位移扰动和速度扰动的情况下,油膜的弹性力和阻尼力近似为线性的,主轴模态有限元计算结果与实测结果基本一致,证明了该分析方法的正确性。     

轴承载荷对转子系统各支承的耦合振动分析

以多支承转子 轴承 弹性基础系统为研究对象,对多支承转子系统某支承处轴承载荷变化引起不同支承点处轴及轴承的耦合振动响应进行了研究。首先,建立了多支承转子系统支承间的耦合振动模型,并进行了仿真和试验,耦合振动模型考虑了每个支承处的油膜耦合效应,通过轴承载荷敏感度矩阵得到各支承耦合力;然后,利用龙格库塔法对油膜刚度为定刚度和动刚度两种情况下的转子系统进行了数值分析及仿真;最后,在8支承转子试验台上进行试验,采取改变某一支承处的位移来得到轴承载荷的变化,并提取各支承处的振动信号。结果表明,轴承位置在稳态和瞬态两种情况下改变时振动响应明显不同,油膜刚度为动刚度的分析结果更为合理。     

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.     

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.     

舰船尾轴承变形对其阻尼特性的影响研究

舰船推进轴系受多个载荷的作用，导致船体、螺旋桨轴和尾轴承发生变形，并在尾轴承中心线与螺旋桨轴颈中心线之间形成一个变形角。研究了变形夹角对轴承油膜动态阻尼参数的影响关系，用数值计算的方法计算得到了轴承油膜阻尼参数与变形角之间的变化关系。结果表明：轴承中线与轴颈轴线之间的变形夹角对轴承润滑阻尼参数的影响关系为强的非线性关系；变形角对轴承阻尼特性影响较大，随着变形角的增大，油膜阻尼Dxx和Dyy会增大，而阻尼Dyz和Dxy会减小；轴颈中线与轴承中线之间夹角对油膜阻尼参数的影响局限在一定的弯曲变形范围内，当变形继续增大时，螺旋桨轴与尾轴承发生刚性接触，此时轴与轴承的刚性接触摩擦作用增大，阻尼作用急剧改变。     

有限长轴承支撑的转子系统非线性动力学分析

基于π油膜假设,运用变分约束原理和分离变量法求得了有限长动压轴承非线性油膜力的近似解析表达式。通过计算比较可知,该方法和有限元法的计算结果非常接近,而且可以节约大量计算时间。在此基础上,以转子的角速度、圆盘处的偏心量及转轴的刚度为控制参数,运用Newmark法分析了轴承-转子系统的非线性动力学行为。数值结果揭示系统具有周期运动、倍周期运动、准周期运动、六周期运动、十周期运动等复杂丰富的非线性动力学特征。     

Rotational Stiffness and Damping Coefficients of Fluid Film in a Finite Cylindrical Bearing

The dynamic behavior of flexible rotors supported on fluid-film bearings are studied including the rotational stiffness and damping coefficients of the oil film. The rotational stiffness and damping coefficients have been evaluated for a finite cylindrical fluid-film bearing by solving the appropriate Reynolds equation for the oil film, using finite difference method. The resulting critical speeds and the unbalance response for a single-disk flexible-rotor system modelled by finite element method are compared with those which were obtained using a short bearing approximation.     

Identification of the dynamic parameters of active magnetic bearings based on the transfer matrix model updating method

The stiffness and damping coefficients of Active magnetic bearings (AMBs) have a great impact on the dynamics of a high-speed rotor AMB system, from its bending critical speed to the modes of its vibration and stability. To accurately obtain the stiffness and damping coefficients of AMBs, this study proposes a new identification approach based on the transfer matrix model updating method. By minimizing the error between the unbalance response calculated through the transfer matrix approach and the experimental measurements, the stiffness and damping coefficients are obtained using the simplex optimization algorithm based on the updating method of the model. According to the experimental data, we identify the parameters from 20 Hz to 260 Hz (1200 rpm to 15600 rpm). To verify the identified results, a finite element rotor AMBs model is created, and the theoretical unbalance response is predicted using the identified parameters. The theoretical unbalance responses closely coincide with the experimental measurements, indicating the effectiveness of the proposed method.     

A Method for Identification of Bearing Force Coefficients and Its Application to a Squeeze Film Damper with a Bubbly Lubricant

A general formulation of the instrumental variable filter (IVF) method for parameter identification of a n-DOF (Degrees Of Freedom) mechanical linear system is presented. The IVF is a frequency domain method and an iterative variation of the least-squares approximation to the system flexibilities. Weight functions constructed with the estimated flexibilities are introduced to reduce the effect of noise in the measurements, thus improving the estimation of dynamic force coefficients. The IVF method is applied in conjunction to impact force excitations to estimate the mass, stiffness, and damping coefficients of a test rotor supported on a squeeze film damper (SFD) operating with a bubbly lubricant. The amount of air in the lubricant is varied from nil to 100 percent to simulate increasing degrees of severity of air entrainment into the damper film lands. The experimental results and parameter estimation technique show that the SFD damping force coefficients increase as the air volume fraction in the mixture increases to about 50 percent in volume content. The damping coefficients decrease rapidly for mixtures with larger air concentrations. The unexpected increase in direct damping coefficients indicates the complexity of the SFD bubbly flow field and warrants further experimental verification.     

Dynamic stiffness and damping coefficients of aerodynamic tilting-pad journal bearings

The dynamic gas–film forces of aerodynamic bearing often can be characterized by eight linear stiffness and damping coefficients. How to theoretically predict these coefficients is a very difficult issue for tilting-pad gas bearing design because of its structural complexity. The current study presents a novel and universal theoretical analysis method for calculating the dynamic stiffness and damping coefficients of aerodynamic tilting-pad bearing. The gas–film pressure within the bearing is expressed in the form of dimensionless compressible gas-lubricated Reynolds equation, which is solved by means of the finite element method. With the assumption that the journal and the pads are disturbed with the same frequency, the dynamic coefficients of tilting-pad gas bearing are computed by using the partial derivative method and the equivalent coefficient method. Finally, the investigations are conducted about the effects of bearing number, perturbation frequency of the journal and the pads, eccentricity ratios, preload and length-to-diameter ratio of the bearing on the dynamic coefficients of aerodynamic tilting-pad journal bearing. The numerical results indicate that the dynamic stiffness and damping coefficients of tilting-pad gas bearing are closely related with these factors. The proposed analytical method provides a valuable means of predicting dynamic performances of tilting-pad gas bearing. The solution can be used for the purpose of prediction of dynamic behavior of the rotor systems supported by aerodynamic tilting-pad bearings.     

Stability of Rotors Under the Combined Influence of Fluid Film Bearing Characteristics and Shaft Material Damping

Fluid film characteristics and shaft material damping form an interesting combination in rotor dynamic applications. Under certain conditions, a rotor which is unstable due to the damping, can be stabilized with the proper choice of fluid film bearings as supports. On the other hand, increasing the material damping in the rotor shaft can attenuate stress fluctuations in the rotors supported by fluid film bearings. The influence of the above combination on the stability of rotor bearing systems is investigated using a Jeff cot rotor with significant material damping and supported by fluid film bearings in the rotor dynamic model. The results indicate that under certain conditions, the interaction of the above two factors can be gainfully utilized in the design of rotor bearing systems.     

多因素影响下空气静压轴承静态特性分析及实验研究

由于空气静压主轴气膜厚度处于微米级别,而主轴中的不平衡现象会影响轴承内的气膜厚度变化,因而需要对各微尺度影响因素综合考虑,并对影响主轴不平衡的各因素进行充分考虑才能真实反映主轴内的气膜流动状态,仿真出轴承的静态性能。充分考虑影响主轴不平衡的各因素并对传统雷诺方程进行修正,研究黏度、流量因子、速度滑移3个微尺度因子及转子偏心和制造误差对轴承静态性能的影响,并通过实验验证从而实现对空气静压主轴静态特性的真实预测和分析。结果表明：3个微尺度因子中,速度滑移对轴承气体压力分布影响最大,同时考虑3个微尺度因子时更能反映轴承气膜流动真实状态;转子偏心与制造误差耦合时,随转子偏心率增大,轴承中各节流孔附近的气膜压力分布与气膜刚度差异越来越大,将严重影响轴承气膜刚度。     

Oil film stiffness and damping in an elastohydrodynamic lubrication line contact-vibration

An elastohydrodynamic lubrication line contact-vibration model is proposed to study the stiffness and damping of the oil film existed in the EHL contact region. An initial mutual approach between interacting surfaces, which deviates from the steady-state balanced position, is assumed under the free contact-vibration to predict the response of the mutual approach. An inertia term, which represents the acceleration of the gap motion, is added to the classical force balance equation to form the equation of motion of the mutual approach. Response of the mutual approach is solved based upon the solving of the contact-dynamic model. The oil stiffness is calculated according to the natural frequency of the response under damped and non-damped conditions, the latter of which represents dry contact conditions. The oil film damping is calculated in terms of the principle of the energy conservation which utilizes the whole history of response compared with the log decrement method. Effect of the normal load, the rolling speed and the amplitude of the regular sinusoidal surface waviness on the oil film stiffness, the contact stiffness and the oil film damping are studied. The study provides an insight on the oil film dynamic characteristics of lubricated contact-vibration problems which appear in gears, bearings, etc. The results show that the oil film damping factor decreases with the increasing normal load as well as the increasing rolling speed. The oil film stiffness increases with the normal load and decreases with the rolling speed. Also, compared to the contact stiffness, the oil film stiffness makes less contribution to the total stiffness. The surface waviness amplitude has little effect on the oil film stiffness and the oil film damping.