固有频率

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。

After knowing the structure nature frequency, optimize the structure, such as disposal the point of support, reduce the number of elbow, change the thickness of pipe, setting the dilatant and so on, which offer a basic to avoid resonance.

当知道结构固有频率后，便可以通过优化结构，例如重新布置支点、减少弯头数、改变管的厚度、设置膨胀圈等方法，改变结构的固有频率，为避开共振频率打下基础。

The paper introduced the basic concept and theory of model analysis and structure dynamic analysis;performed the model analysis of the whole framework of hydraulic pressure and calculated the first ten-rank inherency frequency and corresponding vibratory-type;analyzed and estimated the first three-rank inherency frequency and corresponding vibratory-type of hydraulic pressure.

对液压机的整体机架进行有限元模态分析，得到了机架的前十阶固有频率和相应的固有振型，并对前三阶固有频率和振型进行了详尽的分析和评价。

The equations of dynamics for the balance are established by Kane's method, from which derives the characteristic equation of natural frequency by means of linearization of dynamic equations, and the six natural frequencies being developed according to the theory of vibration. The law of the six natural frequencies varying with mass of the upper platform and the stiffness of the elastic element are presented,and the Finite Element Method is employed to testify the validity of theoretical results.

基于 Kane 方法研究天平的动力学及模态，通过线性化动力学方程建立天平的固有频率方程，依据振动理论推导出并联天平的六阶固有频率及其对应的振型，同时研究了天平的六阶固有频率随敏感单元刚度系数及上平台质量的变化规律，并用有限元法验证理论计算结果的正确性。

In study of the truss structural dynamic characteristics analysis, randomness of the structural physical parameters and geomtric ones are all considered. The finite element model of the stochastic truss is built and the random functions of its natural frequencies are obtained by use of the Rayleigh quotient. Employing probabilistic distribution function expression for the random functions, through a series of mathematical processing including determination of limits of integrals, variable substitution etc., the probaabilistic density function for the truss natural frequencies are gained to realige accurate calculation for the reliability of the truss natural frequencies.

考虑结构物理参数和几何参数的随机性，通过构建随机参数桁架结构的有限元模型，利用瑞利商公式获得了结构固有频率随机函数的计算表达式，应用随机函数的概率分布函数表达式，通过确定积分区间、变量替换、积分顺序变换等一系列数学上的处理，获得结构固有频率的概率密度函数，进而实现对结构固有频率可靠度的精确计算。

The method is as follows that the two ends of a nanometer are fixed on two pivots and an axial micro-pulling force T is applied on the nanometer; an electrode is arranged on the middle part of the side of the nanometer and an alternate voltage is applied on the electrode to motivate the nanometer to generate resonance, and therefore, the natural frequency f of the nanometer is measured and acquired; according to the material characteristics and the geometry characteristics of the nanometer as well as the boundary condition of the nanometer material, the relation between the natural frequency and the axial pulling force of the nanometer, namely the f-t curves of the nanometer, can be calculated by a vibration equation; according to the measured natural frequency f, the size of the micro-pulling force T can be acquired.

该方法将一根纳米材料的两端固定在两个支点上，给纳米材料施加一个轴向的微小拉力T；在纳米材料的侧面，位于该纳米材料的中部放置一个电极，在电极上施加一个交变的电压激励纳米材料使其发生共振，测得纳米材料的固有频率f；根据纳米材料的材料特性和几何特征以及纳米材料的边界条件，由振动方程计算出该纳米材料的固有频率与所受的轴向拉力的关系，即纳米材料的f-T曲线；根据上述测得的固有频率f，得到微小拉力T的大小。

The formula put together the natural frequency f s of shearing bending vibration of superstructure rigidly fixed on the hull and the natural frequency f r of rigid rotating vibration of superstructure elastically fixed on the hull, in which t...

推导中 ，仍将上层建筑整体纵向固有频率视为由下述两部分串联合成：上层建筑根部刚性固定在主船体上的剪弯振动固有频率 fs；上层建筑根部弹性固定在主船体上的刚体转动固有频率 fr。

The results show that the effect of small-sized hole and delaminations is not great . On the natural frequencies , the effect of t ransverse elliptical multiple delaminations around an elliptical cent ral hole is more serious than that of lengthways elliptical multiple delaminations around an elliptical cent ral hole ; the natural f requencies are very sensitive to damages location , and less sensitive to multiple delaminations' size and the holes'size.

结果表明：当穿孔和分层的尺寸较小时，其对层合板固有频率的影响很小；横向穿孔-多分层损伤对层合板固有频率的影响较纵向穿孔-多分层损伤更显著；平面编织层合板固有频率对损伤位置最为敏感，分层尺寸次之，穿孔尺寸的影响最弱。

Numerical simulations and analytical results show: in longitudinal and oblique seas, ship may be subjected to primary parametric resonance with large roll amplitude and even capsizing, when encounter frequency is near the twice of roll natural frequency, wave length and ship length are of the same order and the wave height is larger than a certain value; in oblique seas, ship roll motion is a forcedly-parametrically excited oscillation, primary resonance occur as the encounter frequency is near the roll natural frequency, which may lead to large rolling and capsizing too.

数值仿真和解析分析结果表明：在纵浪和斜浪中，当遭遇频率接近船舶横摇固有频率的两倍，波长和船长接近，波高超过某一阈值的时候，船舶会发生主参数共振，产生大幅横摇甚至倾覆；在斜浪中，船舶发生的是参强激励横摇运动，遭遇频率接近横摇固有频率时，还会激起横摇主共振，同样会产生大幅横摇甚至倾覆。

The effect of the thickness on the buckling critical pressure is calculated first.

本文还对减压转油线进行了振动特性分析，研究了总体管道系统在刚性支撑和弹性支撑下的固有频率及振动模态，得出了支撑刚度对固有频率和振动模态的影响；计算了进口端竖直管两种不同的约束方式对减压转油线整体固有频率及振动模态的影响，为以后对转油线进行进一步的振动分析提供了宝贵的数据。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。