固有振动频率

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。

Equation (4-198) yields a first approximation for the change in the natural frequency of vibration.

方程（4－198）给出了一级近似下的固有振动频率的改变量。

Equation(4-198) yields a first approximation for the change in the natural frequency of vibration.

方程（－98）出了一级近似下的固有振动频率的改变量。

On that basis, the corresponding linerized model is built, and the dynamic properties are analyzed while the configuration or end-point load is greatly changed, the predictable equation of the built-in frequency is established by virtue of perturbation method for the application of variable parameter control in that case.

利用拉格朗日方法推导了双杆柔性机械手的动力学方程，在此基础上了建立相应的线性化模型，分析柔性机械手当位形和负载发生较大改变所表现出的的动力学特性，用摄动方法建立了固有振动频率的预示表达式，以应用于位形和负载有较大改变情形的变参数控制。

Then according to the free-vibration characteristics of monorail beam, the limit safety values were discussed.

此外针对轨道梁的固有振动频率讨论其安全限值问题。

By means of the RITZ method,the free frequencies of the first and the second mode of the cables were given.

引用压杆屈曲函数构造两固端刚性拉索的一阶和二阶振型函数，由 RITZ法原理求得其相应的一阶和二阶固有振动频率。

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。

Since the human body and organs in the body can be seen as more focused, more flexible point of vibration whose vibration inherent in the frequency infrasound vibrations, so infrasound have a stronger effect on the human body.

人体和体内器官固有振动频率均在次声震动范围内，次声波对人体有较强的作用效果。

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 Major Planet Carriers Topology Optimization needs to submit to the intensity conditions when its Structure Stiffness and Nature Frequency change as little as it can.

大行星架结构拓扑优化需要在满足强度条件的前提下，使得结构的刚度、固有振动频率改变最小。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷