固有振动

The effect of tribology factors on bearing vibration is studied experimentally. AR model and WPT are used to processing the normal arid abnormal signals. The results are as follows:1. The vibration of ball bearings is caused by the tribology action of contact pairs of ball and ring races and has the essential of tribo-dynamics. Any factors affecting the tribology characteristics of contact pairs will affect vibration and noise of bearings consequently.2. Vibration characteristics of bearing keep almostly unchanged with the increasing of axial load expecting the increasing of nature frequencies. When radial load increasing with axial load unchanged, nature frequencies keep unchanged but some new vibration peaks appears in the spectrum.3. Vibration amplitudes are damped and nature frequency are enhanced with sufficient lubrication. Vibration and noise of bearings increase obviously and roar can happen and the contact surfaces scratch slightly under insufficient and unclean lubrication state. Bearing will be disabled in a few minutes without any lubrication.4. Bearing vibration is unstable under low speed. With the speed increasing, the vibration become stable and natural frequencies increase slightly but the amplitudes increase apparently.5. Bearing vibration can be excited only by some harmonics ofwaviness without lubrication and by all harmonics with lubrication based on the theoretical analysis.6. The nature frequencies of ball bearings decrease with the increasing sizes. When international clearance increasing, nature frequencies decrease in radial and increase in axial and angular and the amplitudes increase in radial and decrease in axial and angular. When the number of balls increasing, nature frequencies increase and amplitudes decrease. When the pitch diameter increasing, axial nature frequency increase and others nearly keep no change. When outer race groove curvature radius increasing, nature frequencies increase in radial and decrease in axial and angular and amplitudes keep no change in radial and increase in axial and angular. When inner race groove curvature radius increasing, nature frequencies decrease and amplitudes increase.7. The distortion in amplitude and frequency components of bearing vibration signals picked up by the present probe measurement method is founded and right conclusions cannot be achieved by the signals. When accelerometer is rigidly screwed with steel stud onto a flat outer surface of a ball bearing, vibration signal can be got without distortion and the reliability of research on bearing vibration is assured.8. AR model is suitable for large samples of bearing vibration signals, square root of length of samples can be used as the upper limitation of order determination and the FPE order selection criterion is effective. Many advantages of AR spectrum are founded over the classical based on FFT.9. Time-Frequency analysis is necessary for abnormal noise of ball bearings. WPT overcomes the principle shortcomings of STFT and proved to be a best tool to process the abnormal signals.

理论分析和试验研究表明： 1球轴承振动是钢球—滚道接触副中的各种摩擦学作用引起的，具有摩擦动力学的本质，任何对接触副的摩擦学特性有影响的因素都将对球轴承的振动和噪声特性产生影响； 2中心轴向载荷作用下，载荷增大使球轴承的固有振动频率升高，载荷越大同样的载荷增幅引起的频率升幅减小，足够大的中心轴向载荷作用下载荷的变化对球轴承振动的频率特性不会产生明显的影响； 3轴向和径向联合载荷作用下，径向载荷不大时球轴承振动的固有频率基本不变，但是可能引起变刚度激励的非线性振动，出现新的频峰，过大的径向载荷将使部分钢球脱离接触，使球轴承的振动和噪声呈现不稳定状态； 4润滑对球轴承的振动和噪声特性有重要的影响，良好的润滑对振动有明显的抑制作用，润滑不充分时，振动和噪声的水平会有明显增高，一定条件下还会激发接触副中的谐振，发出啸声，造成接触表面的伤害，无润滑干接触时，短时的运转就会损伤接触副表面，使振动和噪声迅速增大，并随时可能引发严重的磨损和卡滞失效；接触副润滑良好时，油膜的"刚化效应"使球轴承振动的固有频率有所提高，润滑剂中含有弥散性污浊时，振动的幅度总体升高，但弥散性污浊不会改变球轴承振动的频率特性；浙江大学博士学位论文：球轴承振动的研究 5低速时，球轴承振动的基本特征呈现不稳定状态，随着转速的提高，球轴承振动的频率特性趋于稳定，固有频率频峰升高； 6理论分析表明，干接触时钢球和滚道表面波纹度的某些谐波分量能激励球轴承的振动，振动的幅值与谐波幅值成正比，实际球轴承中钢球的分布不可能完全均匀，波纹度的激励作用会随时发生；润滑接触的分析表明，波纹度的任意谐波分量均能激励球轴承的振动； 7球轴承的几何和结构参数分析表明，球轴承尺寸越大，径向、轴向和角振动的固有频率越低；钢球中心圆直径增大，球轴承的径向和轴向振动的固有频率基本不变，角振动的固有频率有所上升，振动的幅频特性基本不变；径向游隙加大使球轴承的径向振动固有频率降低，轴向和角振动的固有频率有所升高，径向振动幅频特性的幅值升高，而轴向和角向降低；钢球的数量增多使球轴承振动的固有频率上升，幅频特性的幅值下降，径向振动的幅值下降最为明显；外圈沟曲率半径系数增大使球轴承径向振动的固有频率升高，轴向和角振动的固有频率降低，径向幅频特性基本不变，轴向和角向幅频特性幅值升高；内圈沟曲率半径系数增大使径向、轴向和角振动固有频率均下降，振动幅频特性的幅值均有升高； 8试验对比表明，传感器采用探针式安装时，由于探针接触副接触特性的影响，钡(量得到的球轴承振动信号有失真，采用专门设计和制作的试验球轴承，以固定式安装加速度计，首次测量得到了球轴承振动的真实信号，通过对振动信号的分析，验证了球轴承振动的理论模型； 9)基于时间序列分析的AR模型适用于大样本球轴承振动信号的分析，以样本长度的均方根值作定阶上界，FPE做判阶准则，给出的AR谱光滑，频率分辨率高，是球轴承振动分析的简便而可靠的手段； 10以时频域分析的小波包变换分析球轴承异音信号能够比较好地定位和聚焦异音发生的时间，时间间隔，频率范围，同样是球轴承振动分析的可靠的手段，可用作球轴承故障诊断技术。

The main research contents are stated asfollow: 1. Simplified analysis method of space grids structuresDouble-layer space grids have been assumed as sandwich plate, and are analyzed bythe nontraditional theory of plate with consideration of shear deformation and threegeneralized displacements. Using the theory of energy variation, simplified methodsfor bending, stability and vibration analysis of double-layer space grids have been putforward based upon the idea of split rigidity. The formulas for calculating internalforces, displacements, critical load and natural frequency have been given out. Set thestable cables and bearing cables in hyperbolic paraboloid cable nets are all replaced bytruss-cable to form truss-cable nets structures. Natural vibration analysis method fortruss-cable nets structures has been put forward using the energy variation method andRayleigh method.

主要内容包括： 1、空间网格结构静动力简化分析方法把网架结构简化为夹层板，采用考虑剪切变形的具有三个广义位移的平板弯曲理论进行分析，基于分解刚度思想利用能量变分原理提出了网架结构弯曲、稳定与振动分析的简化计算方法，给出了位移、内力、屈曲临界荷载和固有频率的计算公式；将双曲抛物面索网中的稳定索与承重索均用劲性索代替形成劲性索网结构，基于能量变分法和Rayleigh法给出了劲性索网结构固有振动分析的简化计算公式。

This paper gives a method of combining experiment with theoretical calculus, which can be used to obtain the precious vibration mode functions of disk bladed of turbine machinery.

对透平机械常用的叶轮的固有振动问题给出了一种试验与计算相结合求取其精确振动模态函数的方法。

The natural twist vibration equation is set up by making use of the constitutive relation of nonlinear material.

利用非线性材料的本构关系，建立了非线性材料圆杆的扭转固有振动方程，然后采用傅立叶级数法求得了圆杆扭转固有振动的所似解，通过实例计算讨论分析了非线性材料圆杆的扭转固有振动特性。

Based on the generalized potential energy variational principal of nonlinear elasticity theory with large deflection, the incomplete generalized potential energy functional with large deflection is established on the space coupling free vibration of three-span self-anchored suspension bridge by considering the effect of axial compressive and shearing strain energy of stiffening girder.

摘 要：摘要：基于大位移非线性弹性理论的广义变分原理，考虑了加劲梁轴向压缩应变能和剪切应变能的影响，建立了三跨自锚式悬索桥空间耦合自由振动的大位移不完全广义势能泛函，通过约束变分导出了自锚式悬索桥的竖向挠曲振动、横向挠曲振动、纵向振动及扭转振动的基础微分方程，为自锚式悬索桥的固有振动性状分析提供可靠的理论依据。

Taken example for solving real engineering problem, the methods and steps for the analysis of the steering-wheel vibration is discussed.

为了解决某型轿车的转向盘振动问题，本文通过对影响转向盘振动的诸多因素逐一进行分析，结合先进的试验手段和CAE分析技术，找出了引发该轿车转向盘振动的主要原因是车轮动平衡质量不合格及固定转向柱管的仪表板横梁刚度不足，通过提高车轮动平衡质量，改进仪表板横梁设计，提高仪表板横梁的刚度和固有振动频率，结合道路试验进行主观评价，改进后的转向盘振动达到了平顺性要求。

Period of processing of the multi-input nonblocking series production lines

又称&本征频率&。振动系统作固有振动时的频率。

According to the structural properties of tuning blade-disk assemblies, the matrix perturbation method is used to analyze the influence of mistuning on the natural vibration characteristics. The formulas for perturbation values of first and second order are derived.

根据谐调叶盘的结构特点，用矩阵摄动法分析了失调对叶盘固有振动特性的影响，推导了孤立特征值和密集模态组二种情况下固有频率和振型的一阶、二阶摄动计算公式。

ChapterⅢ,system model of chapter II was simplified as the free vibrationmodel of the system to solve the inherent vibration frequency and vibration mode.The inherent vibration modes are divided into three categories:torsional vibrationmode of central component,translational and torsion pendulum vibration mode of thecenter component and planetary gear vibration mode.

第三章对第二章建立的系统模型简化为自由振动模型，求解了系统的固有振动频率及振型，将各工况下的固有振型分为三类：中心构件扭转振动模式、中心构件平移扭摆振动模式和行星轮振动模式。

The vibration velocity and sound radiation power curves of submerged cylindrical shell, has strong resonant characteristics. It can be described by resonance radiation formulas, which include superposition of inherence vibration modes, by using resonance radiation theory .

本文为验证共振辐射理论，对无限长和有限长圆柱壳体，首先计算了复共振频率并分析其固有振动特性，然后结合共振辐射理论讨论壳体振动和声辐射中各振动模式的贡献及其作用特性。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。