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。     

主动电磁轴承失效后转子坠落在备用轴承过程中的非线性动力学

用有限元法建立了任意个由滚动轴承组成的固定间隙备用轴承-主动电磁轴承-多盘多质量转子系统在主动电磁轴承失效前后的动力学方程,以一个多盘转子系统为例分析了主动电磁轴承失效后转子坠落在备用轴承过程中的瞬态非线性动力学特性,讨论了柔性备用轴承的支撑刚度、支撑阻尼和间隙对转子在坠落过程中动力特性的影响。结果表明采用具有较大阻尼柔性结构的备用轴承能够显著地改善转子坠落在备用轴承上的瞬态动力特性,抑制转子在坠落过程中可能出现具有较大振动和冲击力的全间隙区的涡动运动,减小转子坠落对备用轴承寿命和可靠性的影响。柔性结构备用轴承的支撑阻尼越大,支撑刚度越小,间隙越大,转子坠落后出现全间隙区涡动运动的可能性越小。     

Rolling element bearings absolute life prediction using modal analysis

In this paper, the authors introduce an experimental procedure for predicting the fatigue life of each individual rolling element bearing separately using vibration modal analysis. The experimental procedure was developed based on a statistical analysis. A statistical analysis was performed to find an empirical model that correlates the dynamic load capacity of rolling bearings to their dynamic characteristics (Natural frequencies and damping). These dynamic characteristics are obtained from the frequency response function of each individual bearing that results from vibration modal analysis. A modified formula to the already known Lundberg-Palmgren life formula is proposed for rolling element bearings. Given the modified formula, one can predict the fatigue life of each individual rolling element bearing based on its dynamic characteristics. The paper compares the results from the modified formula with those from Lundberg-Palmgren formula. The modified formula provides an accurate prediction for the fatigue life of each individual bearing based on its dynamic characteristics. The experimental validation of the modified formula is considered for future work. Therefore, it can be used in various applications of rolling element bearings in machinery systems.     

柔性转子滚动轴承系统混沌行为研究

研究了滚动轴承支承的柔性转子系统的混沌行为。考虑空间Euler-Bernoulli杆单元、刚性圆盘、圆柱滚子轴承非线性接触力、不平衡力,使用有限单元法建立了柔性转子轴承系统的非线性动力学方程组。根据FPA修正法确定求解周期,采用Runge-Kutta法、Newton-Raphson法求解非线性动力学方程组,用获得的系统最大Lyapunov指数判断系统的混沌行为。以某滚子轴承柔性转子系统为例,研究了该类转子系统在径向间隙、不平衡力、转轴刚度比对柔性转子系统混沌特性的影响规律,发现随着轴承径向间隙的增大,系统的混沌区间逐渐增大、变多。不平衡力的存在使得系统混沌的转速及范围变大。随着刚度比增大,振幅峰值及对应的转速均逐渐增大,系统混沌区间也增多,轴承非线性振动对柔性转子系统非线性行为的影响逐渐增强。     

磁悬浮轴承-转子系统的机电耦合动力学模型

对磁悬浮轴承 -刚性转子系统建立了完整的机电耦合动力学模型 ,其中除了人们通常所考虑的陀螺效应外 ,着重考虑和增加了推力磁轴承对转子横向振动的耦合效应和由于轴颈倾斜所引起的径向磁轴承之间的耦合效应 ,以及控制系统的电学微分方程和传感器与磁轴承非共点安装对系统性能所带来的耦合影响。该模型可用于五自由度磁悬浮轴承 -刚性转子系统的机电耦合动力学性能研究     

带弹性环保护轴承的动力学特性

提出在传统保护轴承外圈加弹性环来提高其在主动磁悬浮轴承(Active magnetic bearing,AMB)系统中的工作性能。为完善转子跌落仿真模型,得到AMB失效前转子准确的运动状态,理论推导得到AMB的支撑动刚度曲线,进而基于有限元分析方法得到转子在其支撑下的模态,并与试验结果进行对比,验证所得刚度曲线的正确性。在刚性转子理论基础上,建立转子在AMB系统中的动力学模型。基于Hertz接触理论,分别建立AMB失效后转子与保护轴承内圈之间的碰撞模型和保护轴承的实时动刚度模型。根据所建立的模型,对不同弹性环支撑刚度阻尼在不同初始转速下跌落后的动力学响应进行仿真计算,并与无弹性环状态下跌落结果进行对比。仿真分析结果表明,选用合适的弹性环有利于降低转子跌落后的振动幅值和碰撞力。分别在不同初始状态下进行跌落试验研究,试验结果与理论分析结果基本相符。     

Dynamic characteristics of spindle with water-lubricated hydrostatic bearings for ultra-precision machine tools

A key component of ultra-precision machine tools is the spindle. The motivation for this study was to improve machining accuracies in precision cutting and grinding by pursuing improvements in the spindle characteristics by designing a sophisticated spindle with water-lubricated hydrostatic bearings. The static bearing stiffness of the developed spindle was investigated in previous studies. In addition to the static bearing stiffness, the dynamic characteristics regarding bearing stiffness also affect significantly on the machining results. In this study, dynamic characteristics of the developed spindle with water-lubricated hydrostatic bearings were investigated via simulations and experiments. Not only bearing dynamics but also rotor dynamics were considered in this study.In the simulation studies, the spindle dynamic characteristics were analysed based on the transfer matrix method. A spindle rotor supported with hydrostatic bearings was represented by discrete sections of the rotor. The mathematical model of transverse linear vibrations of the spindle rotor was derived with distributed parameters for these discretized rotor sections. As a result of the analysis on the amplitude-frequency characteristic, radial displacements of the rotor due to bearing displacement and bending deformation were defined. Then, the frequency characteristics were represented with Nyquist plots. Resonant frequencies and amplitudes formation in the transverse vibration of the rotor were determined. The influence of rotor bending deformations on spindle compliance was assessed. Furthermore, the study examined the influences of the supply pressure of the lubricating fluid, radial clearance and journal diameter of the hydrostatic bearings on the amplitude of the rotor vibration, and the resonance frequency of the system.Furthermore, the dynamic characteristics of the spindle were examined experimentally. The simulation results were in good agreement with the actual spindle dynamics obtained experimentally. The influence of the structural parameters of the rotor and the operating parameters of the bearings on the spindle dynamic characteristics was also determined. It was verified that the amplitude of the vibration of the rotor overhang part was dominantly affected not by bearing stiffness but by bending stiffness of the bearing journal of the front bearing and the length of the rotor overhang.Then it was verified that the resultant displacement of the rotor in the radial direction due to the influence of the bearing characteristics and the structural effect of the rotor is significantly small. Practical recommendations to improve the spindle design in terms of the dynamic characteristics of the spindle with water-lubricated hydrostatic bearings were also derived.     

基于频域整形的电磁轴承最优控制

针对电磁轴承刚性转子的不平衡振动，提出基于频域整形最优控制，该控制器的设计，包括保证系统稳定的最优调节器设计，以及频域整形的权函数设计，通过权值函数，改变轴承动特性，从而实现电磁轴承系统不平衡振动的力补偿或位移补偿。实验结果表明，电磁轴承频域整形最优控制可有效抑制主轴不平衡振动。     

高速滚动轴承柔性转子试验机

支承高速柔性转子的滚动轴承的寿命、可靠性及失效形式十分复杂,很难得到准确的理论分析结果。因此新研制了高速滚动轴承柔性转子试验机,可以模拟轴承的载荷、转速、润滑等工况条件,测试支承柔性转子系统的轴承性能,为高速轴承性能分析提供准确的试验数据。对支承柔性转子的滚动轴承进行了试验,验证了试验机的可靠性,发现与刚性转子系统相比,柔性转子系统振幅增大且轴心轨迹复杂,这将影响支承轴承的动力学特性。     

利用弹性支承改善滚动轴承的振动特性

本文研究了弹性支承滚动轴承系统的非线性振动问题，着重分析了利用弹性支承改善滚动轴承振动特性的原理和方法。首先建立了弹性支承滚动轴承的力学模型；然后，根据这一模型对系统进行了振动计算；通过对所得到的最大振幅及轴承动压力的分析，得出了弹性支承可以减小滚动轴承非线性振动的结论；最后，对弹性支承的一个应用实例作了简要说明。     

Vibration analysis on the rolling element bearing-rotor system of an air blower

Air blowers are widely used in industry. The vibration of the rolling bearing-rotor is a key factor in the blower’s performance because it significantly influences the security and working life of the whole system. In previous research on the vibration characteristics of the air blower, the supporting rolling element bearing was always simplified as a particle on a shaft with radial stiffness and damping coefficient. Such simplification neglects the effects of the bearing structure on the vibration performance of the rotor system. In this paper, a numerical model of the bending stiffness of the tapered roller bearing was established through mechanics and deformation analysis. On the base of the model, a new TMM (transfer matrix method) for bearing-rotor system was established; the new TMM considers the influences of the bearing structure on the vibration of the rotor system. Furthermore, modal analysis on an air blower rotor system was carried out by using the new TMM, and the mode shape, critical speed and unbalance response of the air blower system were obtained. The same blower rotor was also analyzed by FEM to verify the validation of the new TMM, showing that the new method proposed in this paper for vibration characteristics calculation of an air blower is credible.     

Influence of the Mechanical Seals on the Dynamic Performance of Rotor–Bearing Systems

In this paper, to consider the effects of mechanical seals, a lumped-mass model and the transfer matrix method are used to establish the equations for the dynamics performance of rotor bearing system. The general inverted iteration method is also used to solve the eigenvalue problem of these equations. To check the response of the rotor bearing system under unbalance motivation, the Gauss method is used to calculate the dynamic response of the constrained vibration. The results, based on the dynamic properties calculation of a typical mechanical spiral seal, such as stiffness coefficients and damping coefficients, exert the influence of the mechanical seal on the rotor bearing system of the high-speed machinery. Meanwhile, some structure parameters that may affect the dynamic performance and forced vibration under unbalance motivation of the rotor bearing system considering mechanical seals are analyzed in the paper. The analysis results show that the mechanical seal more or less has effects on the rotor bearing system. The mechanical seal has much more effects on the flexible rotor bearing system than on the rigid one. For instance, in a certain case, if the effects of the mechanical seal were taken into account, the system s critical speed may increase by 70 80%.     

Effect of fluid film wave bearings on attenuation of gear mesh noise and vibration

The attenuation of the gear mesh noise/vibration by fluid film wave bearings relative to rolling element bearings was experimentally investigated. Tests were performed on a gearbox that can accommodate both rolling element bearings and wave bearings. It was found that at specific speeds and torques, the wave bearings could significantly reduce the noise/vibration compared to rolling element bearings. Because the gear noise is accompanied by noise from other sources, a method was developed to extract from the original signal only the mesh harmonic components.The wave bearing dynamic coefficients were also predicted. It was found that adjusting the wave bearing parameters could considerably increase the capacity of the wave bearings to attenuate the gear mesh noise and vibration.     

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。     

Simulation and analysis of vibration signals generated by rolling element bearing with defects

Dynamic loading of a rolling element bearing structure is modeled by a computer program developed in Visual Basic programming language. The vibration response of the structure to the dynamic loading is obtained using a standard finite element package I-DEAS. A force model is proposed to model the localized rolling element bearing defects. Time and frequency domain analyses are performed for diagnostics of rolling element bearing structures. Statistical properties of the vibration signals for healthy and defected structures are compared. The envelope (HFRT) method is employed in the frequency domain analysis. The effect of the rotational speed on the diagnostics of rolling element bearing defects is investigated. An optimum sensor location on the structure is sought. Effect of the structure geometry on the monitoring techniques is studied. An optimum monitoring method can be employed by analyzing the rolling element bearing structure following the procedure proposed in this study. The present commercial computer aided engineering packages can be used in special engineering applications such as condition monitoring of rolling element bearings.     

On the Dynamics of Lubricated Cylindrical Roller Bearings,Part II: Linear and Nonlinear Vibration Analysis

This article is the second part of two companion papers. In the first article, curve-fitted relations of stiffness and damping coefficients of a single roller-to-race contact of lubricated roller bearings were developed. In the present work, these relations are applied to a rotor–bearing system. Two cases are studied to investigate the influence of lubricated cylindrical roller bearings on the vibration characteristics of the rotor system. In the first case, lubricated contacts are simulated as a linear spring–damper model. The overall stiffness and damping matrices are calculated by using the dynamic coefficients of individual load sharing rollers. These matrices are used in the finite element analysis of flexible rotor. In the second case, the nonlinear structural vibration of a lubricated cylindrical roller bearing is studied. Equations of motion of bearing elements are derived using the Lagrange equation. A nonlinear load–deflection contact model developed through the derived curve-fitted relations of dynamic coefficients is used in the equations of motion. Equations of motion are solved by a fourth-order Runge-Kutta integration method. The response of bearing elements under free vibration and due to rotating unbalance is studied for damped and undamped cases. Furthermore, results obtained using elastohydrodynamic finite and infinite contact theories are compared.     

Stability analysis of a rotor bearing system due to surface waviness and number of balls

In the paper, the stability analysis of a rigid rotor supported by ball bearings has been studied. In the analytical formulation, the contacts between balls and races are considered as nonlinear springs, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The implicit type numerical integration technique Newmark-β with Newton–Raphson method is used to solve the nonlinear differential equations iteratively. The effects of surface waviness and the varying number of balls on stability of rotor bearing system are observed. All results presented in form of fast fourier transformations show that the vibration characteristics of the rotor and its bearings change, when the bearings operate in different regions of their nonlinear load deflection characteristics. From the analysis, it is implied that the number of balls and number of waves in the ball bearing are two important governing parameters affecting its dynamic behavior.     

发动机转子-滚动轴承系统的振动性能研究

针对发动机转子 滚动轴承系统建立了有限元模型,将弹性轴段、刚性圆盘和弹性支承的动力方程集结后得到系统振动方程,分析计算了支承刚度对系统固有频率的影响。将转子不平衡惯性力和轴承支反力作为激励,求解了系统的稳定响应,得出了合理设计支承刚度和阻尼,可以改善转子系统的振动特性的结论。通过转子系统模拟实验,对该结论进行了验证。     

Simulating gear and bearing interactions in the presence of faults: Part II: Simulation of the vibrations produced by extended bearing faults

This paper presents a combined dynamic model for gears and bearings, in which an extended fault in the inner/outer race of rolling element bearings can be studied in the presence of gear interaction. A combined gear/bearing model has been made to obtain a better understanding of the interaction of the two components. The essentials of the gear/bearing model and the results of simulating the vibration of localized faults in rolling element bearings in a gearbox environment have been discussed and illustrated in the first part of this paper (part I). The simulation model has now been modified to model extended faults of the type that do not necessarily produce high frequency impact responses, but do modulate the gearmesh signals. The paper compares the simulated and actual signals from the gear/bearing test rig for inner and outer race extended faults, and in particular demonstrates that they react similarly to existing diagnostic techniques.     

Vibration analysis of rolling element bearings with various defects under the action of an unbalanced force

In this paper, a method based on the finite element vibration analysis is presented for defect detection in rolling element bearings with single or multiple defects on different components of the bearing structure using the time and frequency domain parameters. A dynamic loading model is proposed in order to create the nodal excitation functions used in the finite element vibration analysis as external loading. A computer code written in Visual Basic programming language with a graphical user interface is developed to create the nodal excitations for different cases including the outer ring, inner ring or rolling element defects. Forced vibration analysis of a bearing structure is performed using the commercial finite element package I-DEAS under the action of an unbalanced force transferred to the structure via a ball bearing. Time and frequency domain parameters such as rms, crest factor, kurtosis and band energy ratio for the frequency spectrum of the enveloped signals are used to analyse the effect of the defect location and the number of defects on the time and frequency domain parameters. The role of the receiving point for vibration measurements is also investigated. The vibration data for various defect cases including the housing structure effect can be obtained using the finite element vibration analysis in order to develop an optimum monitoring method in condition monitoring studies.