挤压油膜阻尼器-滚动轴承-转子耦合系统的非线性响应分析

为了研究转子系统非线性动力学响应,建立了挤压油膜阻尼器-滚动轴承-转子耦合系统动力学模型。在转子系统模型中,考虑了转子、滚动轴承及挤压油膜阻尼器之间的相互耦合作用,并充分考虑了滚动轴承的间隙、非线性赫兹接触和挤压油膜阻尼器非线性油膜力等。运用数值积分方法分析了转子转速、支承刚度以及挤压油膜阻尼器油膜间隙对系统动力响应的影响,并结合分岔图、频谱图、Poincaré映射图和轴心轨迹图分析了转子系统的非线性动力学响应。结果表明:转子系统当转速较高、支承刚度较大或挤压油膜阻尼器油膜间隙较大时,转子系统容易出现拟周期运动。     

Multibody contact dynamics on mechanisms with deep groove ball bearing joints

The dynamics of ball bearings are important to fatigue breakage, dynamic performance and motion precision of mechanisms connected by ball bearings joints with multi-clearances. In this study, a new method is proposed for multibody dynamics analysis on mechanisms under the effects of radial internal clearances and impact of balls/cage pockets interactions of ball bearings. Including balls/rings interactions and balls/cage pockets interactions, the three dimensional dynamics models of the crank slider mechanism are established and calculated by generalized-α algorithms on the basis of Hertzian contact theory and penalty function method. The rules of eccentric trajectories of inner and outer ring center for one ball bearing joint are verified with the results calculated by XU’s references. The results of dynamic errors, motion trajectories, dynamic forces are achieved under different speeds, radial clearances and number of ball bearings. The speeds and radial clearances are critical to the dynamic performances and motion precision of mechanisms, especially the number of ball bearings. The number of ball bearings is important to impact force and motion stability of the mechanism.     

Stability Analysis of Floating Ball Bearing

Conventional disk drive motors supported on ball bearings (BBs) cause nonrepeatable runout (NRRO) due to the surface imperfections on balls and raceways. NRRO is a source of track misregistration between head and disk that inhibits high track density in a hard disk drive. Fluid dynamic bearings with herringbone grooves either on the rotating or stationary surfaces are a suitable replacement for conventional ball bearings. Herringbone grooved bearings have considerably lower noise level than ball bearings and have better stability compared to plain journal bearings at concentric operating position. However, herringbone-grooved patterns are difficult to manufacture because groove depth is of the order of bearing clearance. The major limitation of the BBs is the direct contact between the rotating and stationary parts and also lack of damping effects. This present work attempts to overcome these drawbacks in BBs by eliminating the metal-to-metal contact using a layer of fluid film, and a theoretical analysis of stability characteristics of a floating BB is presented. Results indicate that there is an improvement in the stability of floating BB rotor systems with increase in outer to inner film clearance ratio (β) from 0.7 to 1.3, and with decrease in ratio of outer race radius to inner race radius (δ) from 3.0 to 1.2.     

A Method to Calculate Frictional Effects in Oil-Lubricated Ball Bearings

Friction and heat generation in oil-lubricated ball bearings is mainly the result of sliding in the ball-raceway contacts and agitation of the lubricant in the free space between the balls, cage. and bearing rings. Endurance of a ball bearing is highly dependent on the thicknesses of the oil films which serve to separate the balls from the raceways in a well-lubricated bearing. The film thicknesses, in turn, are dependent upon the lubricant's viscous properties. These are functions of bearing temperatures and are determined by the balance between the rates of frictional heat generation and heat dissipation. Therefore, in the design of a ball bearing application such as the high speed rotor and low speed rotor support bearings in an aircraft gas turbine, it is important to be able to predict the bearing frictional heat generation rates with reasonable accuracy. This paper presents a method to perform the required calculations considering hearing loading and speeds, realistic lubricant rheological properties, and a relatively simple heat transfer system between the hearing rings, halls. And lubricant. The results of the analysis are shown to compare favorably with experimental data.     

The effect of speed of balanced rotor on nonlinear vibrations associated with ball bearings

The paper deals with the structural dynamic response of rotor supported by ball bearings. The mathematical model takes into account the sources of nonlinearity such as Hertzian contact force, surface waviness, varying compliance and internal radial clearance resulting transition from no contact to contact state between rolling elements and races. In terms of the feature that the nonlinear bearing forces act on the system, a new reduction method and corresponding integration technique is used to increase the numerical stability and decrease computer time for system analysis. The effects of speed of balanced rotor in which ball bearings show periodic, quasi-periodic and chaotic behavior are analyzed. The results are presented in the form of time displacement responses, frequency spectra and Poincarè maps. It is implied from the frequency spectra that peak amplitude of vibrations appear at the varying compliance frequency.     

Reduction of NRRO in ball bearings for HDD spindle motors

In this paper, it is theoretically and experimentally analyzed that the non-repetitive run-out (NRRO) of a ball bearing is caused by geometrical errors of the inner and outer races and the balls, and the number of balls.

The results are summarized as follows:

(1) As for the geometrical errors of the inner and outer races, it is possible to reduce the NRRO to be less than 1 nm by choosing 12 or 18 number of balls, even if the inner and outer races have a harmonic undulation of less than the 11th order.

(2) The NRRO of a ball bearing with 12 balls is very small even if the geometrical errors of ball bearing parts are large. It was confirmed that 12 was an optimal number of balls for ball bearings used for HDD spindle motors.

     

滚动轴承支承下的不平衡转子系统非线性动力响应分析

建立了滚动轴承支承下的转子系统非线性动力学模型。在滚动轴承模型中,充分考虑了滚动轴承的间隙、滚动轴承的滚珠与滚道的非线性赫兹接触力及由滚动轴承支撑刚度变化而产生的VC（varying compliance）振动,在转子系统中考虑了由于转子质量偏心而产生的不平衡力。运用数值积分方法获取了系统的非线性动力响应,分析了转子旋转速度、滚动轴承间隙对系统动力响应的影响,并运用分叉图、相平面图、频谱图及Poincaré映射进行了系统分叉与混沌特征分析,发现了通往混沌的倍周期分叉、拟周期环面破裂和阵发性分叉途径。     

基于ROMAX的球轴承转子系统动态性能分析

滚动轴承转子系统在旋转机械系统中得到广泛应用,其动态性能对旋转机械有着重要的影响。基于Romax软件建立球轴承转子系统的动力学分析模型,通过算例分析了工况参数和结构参数对球轴承转子系统动态特性的影响规律,并通过实验结果验证了Romax对轴承性能预测的准确性。研究发现球轴承的接触角、内外圈沟曲率系数与安装位置对轴承的刚度、寿命与转子系统临界转速等动态性能有较大影响。工程中需要选择合适的结构与工况参数以满足转子系统的性能要求。     

RV减速器主轴承拟静力学模型简化分析方法

针对RV减速器主轴承球数较多导致求解受力和变形的非线性方程组数量成倍增加,求解速度慢的问题,建立了径向载荷、轴向载荷及力矩载荷联合作用下的五自由度角接触球轴承拟静力学模型,在牛顿-拉弗森算法的基础上,提出了假设相邻几个球的接触角、接触载荷与接触变形一致,计算中将其作为相同零件处理的简化分析方法.并以某减速器用主轴承H7...     

滚动轴承支承的柔性转子系统的非线性动力学分析

研究滚动轴承支承的柔性转子系统的非线性动力学特性。建立柔性转子系统的有限元模型,研究不同轴承间隙系统的稳定性及分岔行为。在转子系统中考虑Hertz接触力,以及由转子质量偏心引起的不平衡力,用数值积分的方法得出系统间隙量在不同区域内的轴心轨迹、Poincaré映射图以及时域图。研究结果表明:在间隙较小时,系统表现出丰富的非线性现象,随着间隙的增大,系统的失稳区域也随之增大。     

考虑三维运动和相对滑动的滚动球轴承局部表面损伤动力学建模研究

滚动体通过局部表面损伤时轴承的运动参数及动力学响应是轴承疲劳损伤分析和故障诊断的有效输入和重要依据。基于GUPTA轴承模型构建具有局部表面损伤的滚动球轴承的完整动力学模型。该模型中每个轴承元件(滚球、内圈及外圈)具有6个自由度,并且考虑了元件之间的相对滑动和润滑牵引特性。在对局部表面损伤进行建模时,完整考虑了损伤出现后由于材料缺失而引入的额外间隙,以及损伤对赫兹接触刚度及接触载荷作用方向的影响。研究滚球在通过局部表面损伤时轴承的加速度与滚球/损伤之间冲击力的对应关系,以及轴承转速和损伤宽度对轴承振动响应的影响规律。仿真结果表明,由于考虑了相对滑动和滚球/损伤之间冲击力的影响,本模型能够对具有局部表面损伤的球轴承进行更为合理的动力学特性分析,可为滚动球轴承的疲劳损伤分析和故障定量诊断提供一定的理论依据。     

Effect of rotational speed fluctuations on the dynamic behaviour of rolling element bearings with radial clearances

The behaviour of rolling element bearings is of major importance to the vast majority of rotating machines. Due to the varying assembly compliance and the internal clearance existing in the bearing in most cases, a highly non-linear behaviour of the rotor bearing system appears. Thus, a dynamic model of a horizontal rotor supported on ball bearings with radial internal clearance is considered, taking into account contact forces between the balls and the races, as well as the effect of varying compliance and of the internal radial clearance. However, since rotational speed fluctuations of various levels practically appear in all rotating equipment, their effect is now additionally considered. Their effect is examined in two characteristic rotor bearing cases. The analysis includes all the characteristic states of the dynamic behaviour of the rotor, such as periodic, unstable periodic and chaotic responses, using methods like frequency spectra, phase spaces, higher-order Poincare maps and Lyapunov exponents. All results presented show a dominant stabilization effect of the speed fluctuations with respect to the system behaviour. From the analysis performed, it is concluded that even a minimum fluctuation of the rotor speed may result in major changes of the system dynamics, indicating that speed fluctuations of the rotor are a governing parameter for the dynamic behaviour of the system.     

Bifurcation and chaos analysis of nonlinear rotor system with axial-grooved gas-lubricated journal bearing support

Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson-0-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincar6 map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.     

Fluid Flow Analysis for Friction Torque around Rolling Element in Ball Bearings

Ball bearings (e.g., deep-groove, angular-contact, and roller bearings) support loads in a rotor system and provide lubrication between the shaft and housing. The deep-groove ball bearings used in a turbopump do not differ significantly from angular-contact ball bearings or the bearings found in other applications. Deep-groove ball bearings consist of rolling elements, an inner raceway, an outer raceway, and a retainer to guide the rolling elements. In ball bearings, the resistive (churning or drag) forces and torques acting on the rolling elements and raceways are affected by the fluid flow rate and direction, as well as the rotational speed. These churning and drag forces and torques affect the internal dissipation or power losses into the bearing, which become very significant for high-speed applications. This study numerically investigated the characteristics of the flow conditions for deep-groove ball bearings, with a particular focus on the friction distribution on the rolling elements. A simple analytical model of the fluid flow inside a ball bearing was developed using a computational analysis, and the flow characteristics at high rotational speeds are presented.     

The nonlinear and ball pass effects of a ball bearing on rotor vibration

A ball bearing is generally assumed as a linear spring in rotor dynamic analysis. In real case, the force equilibrium of the bearing is changed as the relative position, of each ball with respect to the direction of radial force. So, the stiffness of the bearing is also changed and is a function of time and position. In this study, the nonlinear characteristics of a ball bearing are considered in analyzing the vibration response of a rotating shaft due to an unbalance force. A finite element method is used to analyze the vibration characteristics of a rotor-bearing system and a direct numerical integration is performed to calculate the transient response of the rotor system. The responses are converted to the frequency domain and the effects of the parametric excitation due to a ball bearing are examined. The test rig for the investigation of the effect of a ball bearing on the rotor vibration is set up and the results are compared with those of numerical calculation. The calculation results show that the amplitudes of the nonlinear model are larger than those of the linear one. The frequencies of the calculations can be matched to the measured frequencies.     

Influence of orifices on stability of rotor-aerostatic bearing system

This paper has studied the influences of both the number and locations of entry holes on the stability of a rigid rotational rotor supported by two double-row, orifice compensated aerostatic bearings. The air is assumed to be perfect gas, undergoing the adiabatic process and passing through entry holes into the bearing clearance, is governed by Reynolds equation including the coupled effects of wedge due to rotor rotation and squeezed film due to rotor oscillation. The Ph-method is used to analyze Reynolds equation which is then solved by the finite difference method and numerical integration to yield static and dynamic characteristics of air film. The equation of motion of the rotor-bearing system is obtained by using the perturbation method and the eigen-solution method is used to determine the stability threshold and critical whirl ratio. The eccentricity, rotor speed, and restriction parameter are considered in the analysis of the whirl instability of the rotor-aerostatic bearing system for the comparisons between various designs in the number and locations of entry holes of aerostatic bearings.     

球轴承涡轮增压器轴承-转子系统动力学分析与应用

相比于普遍使用的浮动轴承,在涡轮增压器中使用球轴承具有机械效率高和加速响应快的优势。以车用球轴承涡轮增压器为研究对象,用有限元法对轴承-转子系统进行了转子动力学特性的研究,对轴承-转子系统的临界转速进行了计算与分析,这是判断转子工作转速是否稳定和涡轮增压器工作是否可靠的重要依据;建立了增压器模型,并对比了计算结果和试验结果,证明了方法的可行性。通过整机试验表明,球轴承涡轮增压器能够满足当前车用发动机的需求,能够提高发动机的工作性能。     

滚动轴承动力特性测试方法

轴承的动力特性对转子－轴承系统的动力特性有重要的影响。但至今，滚动轴承的动力特性仍缺乏系统的资料，在许多情况下，将滚动轴承简化为无阻尼的定常弹性元件。本文分析了滚动轴承动力特性的主要影响因素，介绍了滚动轴承动力特性的两种测试方法，并以某航空轴承为例作了具体测试，取得了比较一致的结果。本文提出的方法可作为建立滚动轴承动力特性数据库的基本手段。     

不同轴承支撑下碰摩转子系统的动力学特性

研究了不同类型轴承支撑下的转子碰摩故障振动特征。首先,采用了计及回转效应、剪切效应及横向扭转的梁单元建立了实验装置转子的有限元分析模型;然后,通过二维计算流体力学方法得到不同类型轴承的动力学参数;最后,在此基础上,结合非线性动力学理论,分析比较了转子在圆柱轴承、可倾瓦轴承等5种轴承支撑下的碰摩非线性动力学行为。研究结果表明：在椭圆轴承、五瓦轴承和四瓦可倾瓦轴承支撑下,系统主要表现为同频周期运动;而对于圆柱轴承和四油叶轴承支撑,系统会出现较复杂的运动。本研究工作是对之前转子碰摩非线性动力学研究的扩展,所得计算结果可为大型高速旋转机械系统动态设计制造和碰摩故障的诊断和控制提供理论参考。     

配对角接触球轴承静态力学特性

根据角接触球轴承实际的工作状态,建立背靠背配对安装形式的角接触球轴承接触模型,计算配对轴承在径向、轴向和力矩载荷联合作用下的载荷分布以及接触应力,并将理论值与Ansys有限元法得出的结果进行对比,验证计算结果的准确性。详细研究了在联合载荷的作用下,配对轴承静态载荷分布以及接触特性的变化规律。研究结果表明:配对角接触球轴承的内圈在联合载荷作用下发生位移,使载荷分布不均匀,接触应力主要集中在载荷对称线附近的部分钢球上,改变联合载荷会使两列轴承载荷分布规律以及接触特性发生变化。