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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。

According to longitudinal vibration partial differential equation of rod, the longitudinal vibration displacement response of uniform infinite rods by the harmonic point forces was derived.

longitudinal vibration ； wave approach ；从杆纵向振动的偏微分方程出发，推导了无限长杆在简谐点力作用下的纵向振动位移响应，在此基础上，基于结构线性假设和波的叠加原理，得出了有限长梁纵向振动谐响应的波动表达式，列出了常用的边界条件。

In the experimental work, application of proportional controller to active vibration control incorporated with passive vibration isolator to suppress its resonant oscillation of natural frequency is studied in this project. Vibration acceleration acquired from accelerator is inputted to controller as feedback signal. The processed signal from controller is transmitted to voice coil actuator to control vibration. Firstly, based on the theoretical equations which govern the system vibration, the physical mechanism of active control in total system is studied.

在实验部分，则运用比例控制器进行被动式隔振系统自然频率共振抑制之主动控制实验，控制回馈讯号采用加速规量得之振动加速度值，经由控制器计算输出控制讯号驱动音圈致动器进行主动控制。

This text proceed with the theory of the vibration, utilize typical elastic hinge law analyze structure dynamics characteristic when the blade is quivered to instability, and then use relevant knowledge of blade vibration to simplify the model and the aerodynamic force of the vibration. Through the simplification, we can get the equation of the blade, which is dispersed to its instability. Then VISUAL BASIC procedure is utilized to work out thecharacteristic value of vibration and the vibration frequency. At last comparing the result which is calculated by the above-mentioned theory formulae with the result which is calculated by internationally agreed procedure ANSYS to verify the accuracy of the formula of reduction.

本文从振动理论入手，利用最为典型的弹性铰链法分析叶片发生颤振失稳时的结构动力学特性，然后对振动模型及振动时所受的气动力进行简化，利用简化方程得到叶片发生发散失稳时的振动方程，利用编制的VISUAL BASIC程序解出振动的特征值并得到振动频率，最后分别通过上述的理论公式和国际通用的有限元程序ANSYS对风力机叶片模型进行发散失稳时的频率计算，验证简化公式的准确性。

According to structural characteristics of floating slab tracks, a track segment element was taken between two adjacent fasteners. For each element, rails were regarded as Euler beams supported by discrete viscoelastic supports. The fasteners and rubber supports were replaced by a linear spring and damp. So the vibration model of the floating slab track was established. In constructing vibration model of a metro train, each car of the metro train with two suspensions was modeled as a multi-rigid body system, in which rigid bodies were connected with each other by a linear spring and damp. Combining the potential energy of vertical vibration of the track with that of the metro train, the total potential energy of vertical vibration of the train and track was obtained. And then, the matrix equation of vertical vibration of the system was established using the principle of total potential energy with stationary value in elastic system dynamics and the "set-in-right-position" rule for formulating system matrices. The vibration responses of the system can be obtained by solving the matrix equation with the direct time integration such as Wilson-θ method.

摘 要：针对浮置板式轨道结构特点，取相邻2个扣件之间的轨道为1个轨段单元，钢轨视为连续弹性点支承Euler梁，浮置板视为弹性薄板，扣件系统及橡胶支座均模拟为线性弹簧及粘滞阻尼器，建立浮置板式轨道振动模型；将城轨列车中的车辆均离散为多刚体系统，各刚体之间通过线性弹簧及粘滞阻尼器相连，建立列车振动模型；将浮置板式轨道及列车振动势能叠加，得到系统竖向振动总势能；基于弹性系统动力学总势能不变值原理及形成系统矩阵的"对号入座"法则，建立此系统竖向振动矩阵方程；采用Wilson-θ逐步积分法求解此矩阵方程，得出此系统竖向振动响应。

The distribution of gear's contact stress, root stress, and contact engagement line in the engagement situation of gear pairs, were obtained on the base of explicit integration method. 3. Adopting the method of system matrix, the torsional vibration differential equation of general shafting was gained. The simple harmonic forms of excitation torque under the normal combustion or piston flameout of in-line engine and v-type engine were analysed. The decoupled algorithm of free vibration and forced vibration and the solution to the vibration damper's energy of resistance and the off-resonance calculation were studied. The sensitivity formulations of the natural frequency and vibration mode to physical parameters of system were derived by solving the eigenvalue problem. These sensitivity formulations provided the theoretical base for the dynamic modification of structure.

运用系统矩阵法建立了轴系的扭振微分方程，并对直列和V型发动机在正常发火和气缸熄火工况下的激振力矩进行了详细的简谐分析；基于精确方法推导了自由振动和强迫振动的解耦算法，给出了能量法计算中的减振器阻尼功求解和非共振计算方法；并研究了曲轴系扭振非线性分析中的变惯量问题，得到了单缸转动惯量的精确求解公式以及变惯量和固有频率的关系式；最后，从特征方程和振型正交性出发，推导了固有频率和振型对轴系转动惯量和刚度等物理参数的灵敏度，为扭振系统的结构动力学修改提供了理论基础。

The influences of the stiffness and damping of front spring,rear spring and seat cushion were analyzed by orthogonal tests.The seat cushion is the most important for the seat vibration,and the front spring makes a more important effect on seat vibration and hand vibration than the rear spring, the effect of the front spring on seat vibration and hand vibration is not consentaneous.

利用正交优化法分析了悬架、坐垫参数对平顺性的影响，结果表明：坐垫参数对座位处振动影响最大，相比后悬架，前悬架参数对座位处和手把处振动的影响大，前悬架小刚度大阻尼对座位处振动有利，前悬架大刚度小阻尼对手把处振动有利。

Armour rods (to be installed in suspension clamps) Parallel clamps Sub-Total, items 4.1-4.7 OTHER HARDWARE Counterweights for jumper or suspension insulator strings, including necessary device for attachement 50 kg 100 kg Sub-total, item 5.1 – 5.3 SPARES Insulator Units Type U160 Type U210BS Hardware for Conductor ACSR-BISON Complete set of hardware and fittings for suspension string Complete set of hardware and fittings for tension string Complete set of hardware and fittings for jumper string Complete set of hardware and fittings for transposition string Extra suspension clamps Extra tension clamps Extra tension joints Extra repair sleeves Extra vibration dampers Extra armour rods Extra spacers: for span for jumper alternatively spacer dampers Hardware for Earthwire 7 No. 6 AWG Complete suspension set Complete tension set Vibration dampers, Stockbridge type Extra tension clamps Extra tension joints Extra vibration dampers Extra parallel clamps Extra armour rods Hardware for Earthwire 7 No. 6 AWG Complete suspension set Complete tension set Vibration dampers, Stockbridge type Extra tension clamps Extra tension joints Extra vibration dampers Extra parallel clamps Extra armour rods Sub-Total, items 6.1-6.4 Sub-total, Items 1.4, 2.7, 3.8, 4.8, 5.4 and 6.5 Transfer to Summary, Schedule AS-1

装甲棒 平行夹具小计，项目4月1号至4月7号其他硬件重物跳线或中止绝缘子串，包括必要的设备attachement 50公斤 100公斤小计，项目5月1号至5月3号备件绝缘子单位型U160 类型U210BS 硬件导体钢芯铝绞线，拜森一套完整的硬件和配件的暂停字符串一套完整的硬件和配件的紧张字符串一套完整的硬件和配件的跳投字符串一套完整的硬件和配件的转字符串额外的悬浮夹额外的紧张局势夹额外的紧张关节额外的修理袖子额外的振动阻尼器额外的装甲棒额外的间隔：为跨度跳线或者间隔减震器硬件Earthwire 7特设工作组第6号完整的悬挂设定一套完整的紧张局势振动阻尼器，斯托克型额外的紧张局势夹额外的紧张关节额外的振动阻尼器额外的平行夹具额外的装甲棒硬件Earthwire 7特设工作组第6号完整的悬挂设定一套完整的紧张局势振动阻尼器，斯托克型额外的紧张局势夹额外的紧张关节额外的振动阻尼器额外的平行夹具额外的装甲棒小计，项目6月1号至6月4号小计，项目1.4 ， 2.7 ， 3.8 ， 4.8 ， 5.4和6.5 （换乘摘要，附表1 仅供参考

From the analysis of automobile vibration sources and the human responses to vibration, a mechanic model of man-chair-vehicle system with 13 degrees of freedom is built by vibration pattern analyzing technology. Using the random vibration theory, the calculating methods are developed for parameters, including vibration pattern, transfer function, wheel transient load, and acceleration of seat, automobile ride quality simulation software is developed.

通过分析汽车振动源和人体对振动的反应，用模态综合技术，建立了十三自由度人－椅－车系统的动力学模型，运用随机振动理论，给出了振动形态、传递函数、悬架动挠度、车轮动载荷、座椅加速度等参量的计算方法，开发了一套&汽车平顺性仿真软件&并利用已有的汽车数据，对汽车行驶时的振动特性进行了仿真，得到了重要结论：发动机与轮胎刚度、阻尼，后桥阻尼对驾驶员座椅处的振动影响不大；驾驶员座椅的垂直刚度增加很大时，对垂直方向振动响应比较大；前桥刚度、阻尼对驾驶员座椅处的振动影响较大；前轮胎刚度对前桥振动影响较大，前轮胎刚度增加，则振动加强；后桥刚度对汽车平顺性有一定影响，后桥刚度减小，则座椅处垂直加速度减小。

Vibration-proof materials are arranged at the connection of the impacting object and the support to judge whether the impact point is right, avoiding misoperations.

Vibration-proof材料被安排在冲击的对象和支持的连接判断命中点是否是不错，避免misoperations。

Graf, without question, is the greatest women's player in history.

格拉芙，现在，毫无疑问是女子网坛历史上最伟大的选手。

If not, you will have to look around at all your important data.

如果没有，您将需要检查所有的重要数据。