A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.

Nonlinear dynamic behaviors of ball bearing rotor system

Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing.Five-DOF dynamic equations of rotor supported by ball bearings were estimated.The Newmark-β method and Newton-Laphson method were used to solve the equations.The dynamic characteristics of rotor system were studied through the time response,the phase portrait,the Poincar?maps and the bifurcation diagrams.The results show that the system goes through the quasi-periodic bifurcation route to chaos as rotate speed increases and there are several quasi-periodic regions and chaos regions.The amplitude decreases and the dynamic behaviors change as the axial load of ball bearing increases;the initial contact angle of ball bearing affects dynamic behaviors of the system obviously.The system can avoid non-periodic vibration by choosing structural parameters and operating parameters reasonably.

NONLINEAR STABILITY OF BALANCED ROTOR DUE TO EFFECT OF BALL BEARING INTERNAL CLEARANCE

Stability and dynamic characteristics of a bail bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Flo- quet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution. The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system.

Bifurcation of Periodic Motion of Rigid Rotor System Supported by Angular Contact Ball Bearings

Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.

滚动球轴承局部故障引起滚珠负载振荡性分析

为深入剖析滚动球轴承局部故障对轴承整体振动特性的影响,利用Hertz接触理论构建了转子偏心力激励下的球轴承-转子系统动力学数字仿真模型,并结合深沟球轴承外圈、内圈、滚珠的局部故障引起的轴承间隙变化,推演了滚珠与各类故障区域间的冲击激励响应方程。在此基础上通过分析单点损伤引起的滚珠内部接触负载变化,揭示了单个滚珠接触应力对相邻滚子负载与系统整体振动特性的影响规律。通过分析轴承转动过程中有效承载滚珠个数的变化情况,建立了的滚珠负载占比时间对故障冲击振荡幅值的影响关系。分析结果表明,滚珠与故障区域的接触分离会使其负载发生振荡,且各故障状态下的振荡频率都为系统共振频率;在2个等效承载滚珠上的运转时间占比越大,故障冲击振荡的强度越大;各类型早期故障状态下的Poincaré映射点的保持在相同幅值附近;当局部故障程度增大到一定程度时,系统振动混沌特性增强,振动幅值相应增大。

吸振器与球平衡器并用控制转子不平衡振动的理论研究

球式自动平衡器(Automatic Ball Balancer,简称ABB)可以在临界转速以上区域完全消除转子未知不平衡量,但其缺点是在临界转速附近会引起大振幅的共振响应和不稳定振荡。为此增加动力吸振器(Dynamic Vibration Absorber,简称DVA)来克服其缺点,改善其抑振性能。以Jeffcott偏心转子模型为研究对象,根据拉格朗日方程建立了吸振器、球平衡器单独使用以及两者结合使用时控制转子不平衡振动的动力学方程,使用谐波平衡法理论求解新耦合系统的振幅表达式,并分析各参数对稳态幅频曲线的影响规律以获得较合适的参数,采用龙格-库塔数值方法计算得到稳态幅频特性图和瞬态振幅时域变化曲线。对比结果表明,两种手段并用的新方案有效降低了转子经过临界共振区时的振动水平,并使转子在临界转速以上区域衰减为零振幅,达到了融合两者优点的目的,具有更优良的抑振效果。

含外圈剥落和不对中的齿轮-转子-轴承系统振动分析

轴承套圈的不对中和剥落是影响齿轮-转子-轴承系统振动特性的典型误差和故障。为了研究外圈不对中和剥落对系统的耦合影响,有必要对含不对中和剥落的齿轮-转子-轴承系统振动特性进行分析。首先,考虑外圈不对中和剥落,计算了轴承的五自由度非线性恢复力。然后,基于轮齿承载接触分析(LTCA)方法,计算了啮合刚度并且建立了直齿轮副的动力学模型。在此基础上,基于切片法建立了花键的等效刚度模型。最后,通过将轴承的恢复力模型、直齿轮副的动力学模型和花键的等效刚度模型与转子系统的有限元模型耦合,建立了齿轮-转子-轴承系统的动力学模型。分析表明,只有剥落位于承载区时,才会对轴承接触力、接触角和系统振动特性产生影响。外圈的不对中导致轴承的承载区范围增大,并使得剥落对系统产生影响的概率增加。

深沟球轴承中球的自转规律研究

建立航空发动机高低压转子系统中深沟球轴承的拟静力学模型,运用Newton-Raphson法进行求解,分析载荷和转速对深沟球轴承内部载荷分布和球自转规律的影响。结果表明:深沟球轴承在转速不高时,径向力的改变对钢球自转角速度的影响不明显,而在转速较高时,随着径向力的增加,钢球自转速度逐渐增大;随着径向力的增加,承载区最外侧钢球的自转角速度比承载区内侧钢球的自转角速度增幅大;随着转速的增加,钢球的自转角速度增加。

Research on the Critical Speed of a Mixed-Flow Turbocharger with Hybrid Ceramic Ball Bearing

The critical speeds for a vehicle turbocharger with hybrid ceramic ball bearing are researched. The ball bearing-rotor system produces resonance when it working in critical speed and that makes the turbocharger injury working for a long time. The calculation and analysis methods of the critical speed for the vehicle turbocharger are described. The critical speed is computed by two methods including Riccati transfer matrix and DyRoBeS finite element method for a vehicle turbocharger with hybrid ceramic ball bearing. The vibration experiment had been taken to validate the calculating result, Comparison between the results by two calculation methods and the test results show that the first critical speed differences are 6.47 % and 5.66 %, the second critical speed differences are 2.87 % and 2.94 % respectively. And then, the primary factors which influence the critical speed are analyzed, the conclusions will be helpful for the vehicle turbocharger bearing-rotor system design.

Analysis on Nonlinear Dynamic Properties of Dual-Rotor System

In order to clarify the effects of support structure on a dual-rotor machine,a dynamic model is established which takes into consideration the contact force of ball bearing and the cubic stiffness of elastic support. Bearing clearance,Hertz contact between the ball and race and the varying compliance effect are included in the model of ball bearing. The system response is obtained through numerical integration method,and the vibration due to the periodic change of bearing stiffness is investigated. The motions of periodic,quasiperiodic and even chaotic are found when bearing clearance is used as control parameter to simulate the response of rotor system. The results reveal two typical routes to chaos: quasi-periodic bifurcation and intermittent bifurcation. Large cubic stiffness of elastic support may cause jump and hysteresis phenomena in resonance curve when rotors run at the critical-speed region. The modeling results acquired by numerical simulation will contribute to understanding and controlling of the nonlinear behaviors of the dual-rotor system.

重力场作用下的引信球转子动力学特性数值模拟

针对低速旋转弹引信球转子机构解除保险运动过程中的动力学问题,应用刚体动力学理论、欧拉动力学以及外弹道学理论,研究在重力场作用下的引信球转子动力学特性。通过分析引信球转子的力学环境,建立在重力场作用下的引信球转子动力学模型,并采用Matlab软件编制数值模拟程序;以典型引信球转子为例,通过吉尔算法进行数值模拟,得到有无重力作用下的球转子解除保险距离、动态平衡角和章动角随时间的变化规律。结果表明:在重力场作用下的低速旋转弹引信球转子的解除保险距离至少缩短14.00%,动态平衡角散布至少减小18.60%。低速旋转弹引信球转子机构的重力效应可以提高引信发火的可靠性,同时可以使球转子发生反转,但对解除保险可靠性的影响较小。

磁悬浮轴系保护轴承抗冲击特性及试验方法

为评估磁悬浮保护轴承的抗冲击能力,结合保护轴承特有的跌落工况,建立转子动力学模型,对磁悬浮轴承失效前后转子响应进行分析,同时建立保护轴承可靠性试验平台和试验方法,对保护轴承抗冲击特性分析方法进行验证。结果表明:保护轴承可靠性试验平台可实现碰撞力的直接测量;通过有、无安装冲击力传感器对比试验和应力-冲击力标定试验可知碰撞力测量误差在7%以内,验证了试验方法的准确性;且碰撞力的理论分析与实测误差为8.4%,可满足保护轴承抗冲击特性分析要求,指导保护轴承可靠性评估。

轴承安装配合方式对电主轴轴承-转子系统振动的影响

轴承-转子系统是决定电主轴单元工作性能的核心部件,而轴承的安装配合关系会直接影响系统的运行精度。考虑热膨胀和轴承内、外圈配合方式,建立了电主轴轴承-转子系统动力学模型,分析了内圈过盈配合和外圈间隙配合对转子振动特性的影响,并通过试验验证了模型的正确性。结果表明:转子振幅随内圈配合过盈量增大而减小,随外圈配合间隙量增大而增大,且外圈配合间隙量对转子振动影响更大;考虑热膨胀时的转子振幅小于不考虑热膨胀时的转子振幅。

滚动轴承转子系统的非线性动力学特性分析

接触非线性和间隙非线性耦合导致滚动轴承 转子系统表现出复杂的动力学特性 ,在工作转速范围内系统会产生分岔混沌振动 ,从而影响系统工作的稳定性和可靠性 ;在计及轴承接触非线性和径向间隙的条件下 ,建立了滚动轴承支承的水平刚性转子系统的非线性动力学模型 ,用数值积分方法得到系统在不同参数域中的相图、轴心轨迹、频谱图及Poincar啨映射图 ,研究了系统响应随转子转速的变化趋势。结果表明 :轴承的径向间隙是决定轴承 转子系统动态响应的一个重要参数。随着间隙的增大 ,混沌响应区变宽 ,轴承的动态刚度减小 ,故在设计滚动轴承 转子系统时 ,应对径向间隙进行优选。

滚动轴承-火箭发动机液氢涡轮泵转子系统的动力特性分析

用有限元方法建立火箭发动机液氢涡轮泵转子的离散化模型,并提出考虑滚动轴承内间隙、运行表面波纹度和滚动体离心力等因素的二自由度滚动轴承模型,从而建立了滚动轴承-液氢涡轮泵转子系统的非线性动力学模型。通过数值仿真研究了液氢涡轮泵转子系统动力学问题集中的启动阶段的非线性动力特性。发现在启动阶段不但有同步共振,而且会发生亚谐共振。径向载荷的大小会显著影响同步及亚谐共振的起始时间。滚动体的离心力和滚动轴承的波纹度对转子系统的动力特性有明显影响。

考虑径向内间隙的滚动轴承平衡转子系统的非线性动力稳定性

研究滚动轴承平衡转子系统在不同轴承内间隙量,不同转速下系统的稳定性及其分岔特性和混沌.考虑Hertz接触力、滚动体通过振动和轴承径向内间隙等非线性因素建立数学模型,根据Floquet理论分析不同间隙量下滚动轴承转子系统的周期解稳定性,找到了3种导致周期解失稳的方式:倍周期分岔失稳、拟周期分岔失稳和边界激变导致混沌失稳.通过对各间隙量下转子系统拓扑特性变化和失稳区域的研究,表明滚动轴承间隙量是影响转子系统动力稳定性的一个重要因素.

航空发动机转子-滚动轴承-支承-机匣耦合系统的碰摩故障分析与验证

针对实际的航空发动机转子系统,建立了含碰摩故障的转子-滚动轴承-支承-机匣耦合动力学模型.在模型中,考虑了机匣运动,弹性支承、挤压油膜阻尼,充分考虑了轴承间隙、滚珠与滚道的非线性赫兹接触力以及由滚动轴承支撑刚度变化而产生的变柔性(Varying compliance VC)振动.运用数值积分方法获取了系统响应,并建立带机匣的航空发动机转子实验器进行碰摩故障实验,仿真结果与实验结果比较分析表明了模型的有效性.

引信球转子动力学分析

球转子机构是旋转弹药引信典型的保险与解除保险机构之一,除主要用于满足引信隔爆安全性要求外,同时也可兼作延期解除保险。应用欧拉刚体动力学理论,分析了球心、质心及弹丸旋转轴均不重合时的球转子动力学问题,给出了描述球转子在其腔室内转正运动的微分方程组,为引信球转子的工程设计提供了理论支持。

气浮球形陀螺转子的控制

球形陀螺转子由球形静压气体轴承、转子、定子绕组、电动机负载和转子平衡配重等组成,以三相Y接半控电路为例,给出了其运行特性和传递函数,并介绍了转子稳速旋转电路及典型芯片的使用。

引信机构旋转偏心的蒙特卡罗模拟

旋转偏心是旋转弹引信机构工作特性分析与计算的重要参数。为了得出引信机构旋转偏心的具体数值,以某引信球转子机构为例,对其旋转偏心所涉及的方向随机的矢量尺寸链进行了详细分析,应用蒙特卡罗法对旋转偏心进行了模拟计算,计算过程中涉及了作为组成环之一的采用相关原则标注的同轴度,并将模拟结果与极值法和概率统计法所得结果进行了对比分析。模拟结果表明:引信机构旋转偏心数值为近似于瑞利分布的偏态分布,最小值大于零,而其方向角为关于0°的对称分布,但并非均匀分布,也非正态分布。