几何分布

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 experimental differential cross section data analysis with thetheory calculation code DWUCK4 using the distorted-wave Bornapproximation and zero-range interaction.

采用逐个事件的方法，用一事先产生的一系列点组成的数据库模拟探测器边界，事件的几何探测效率进行归一化，得到实际的实验室系散射角分布。

Combined the curve theory of differential geometry and the cable model applied distributed load, form analysis and tension analysis of boundary cable, ridge cable and valley cable were performed.

结合微分几何的曲线论和分布荷载作用下索的受力模型，研究了索膜结构中边索、脊索和谷索的受力分析和形状分析。

In this part, the distribution of stable states of a system is worked out under the condition of unbalanced attention parameters on basis of analyzing elementary dynamic equation and synergetic potential function, which improved the discussion of relevant properties of basic synergetic equations. Then, with the analysis of effects of attention parameters in synergetic dynamics, a set of elementary properties are presented to give light how the attention parameters work on pattern recognition process. In the end, in view of geometric sense in synergetic order parameters, some elementary properties are studied, by which a new construction method of order parameters is established so as to provide a general way to constitute new relations of prototype patterns according to practical requirements.

首先在分析了协同模式识别的基本动力学方程及协同势函数的基础上给出了注意参数不平衡情形下系统稳定状态的分布，完善了对协同模式识别基本方程相关性质的讨论；其次，分析了注意参数在协同动力学过程的作用，并给出了注意参数的一些基本性质，指出了注意参数对模式识别过程产生的影响；然后，从协同序参量的几何意义出发，研究了协同序参量的基本性质，并在指出其局限性的同时建立了新序参量的构造方法，从而能够更一般地根据要求建立模式间的新关系，促进识别过程的进行。

According to the theory of wave acoustics and ray acoustics,train is regarded as a moving limited line sound source and the mathematics model of sound field distribution is set up around the elevated railway.

根据波动声学和几何声学原理，将列车看作一运动着的有限长线声源，建立了有声屏障时城市高架轨道交通沿线声场分布计算模型。

By using the matrix geometric solution, we obtain the equilibrium condition of the system, and also derive the stationary probability of the system.

通过使用矩阵几何解的方法，求出了系统的平衡条件，进一步导出了系统的稳态概率分布，并且给出了率阵R的迭代计算程序及j=2时R的精确表达式。

Using the matrix-geometric solution's method,the existing condition of steady-state equilibrium and the steady-state probability vectors are discussed.

利用矩阵几何解的方法讨论了系统的稳态平衡条件和稳态概率分布，并得到了系统的一些稳态性能指标和数值结果。

In this paper, the important indexes of "HT-1" image quality such as noise, image resolving, histogram distribution, the relativity and register error of each band, geometric precision and potential application were pertinently analyzed and evaluated.

对"HT- 1"图像的噪声、地面分辨率、灰度分布与波段相关性、波段间配准误差、图像的几何精度及其初步应用等进行了中肯的分析与评价。

The microfacies and their distributions of fan delta front in Shuanghe oil field are analyzed in detail by using sealed coring data, highly dense well patterns and so on.

储层的微相砂体类型、几何规模特征及分布规律是分析地下油水运动规律和调整注采井网的基础。

By using molecular dynamics simulation, fractal representation and dimension of the interface are obtained.

在研究了界面层中物理量分布的基础上，利用分形理论对界面的几何特征进行了研究。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。