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Week 5 Angular momentum of particle and conservation law of angular momentum, angular momentum of rigid body, theorem of angular momentum, conservation law of angular momentum.

第5周 质点的角动量和角动量守恒定律，刚体的角动量、角动量定理、角动量守恒定律。

And the concept of angular dispersion of diffractive polar angle(the first kind angular dispersion) and angular dispersion of diffractive azimuthal angle (the second kind angular dispersion) are established.

确立了二维平面光栅衍射极角角色散和衍射方位角角色散的概念。

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。

Because the body inertia in ball hitting moment was very small, the angular momentum was mainly affected by angular velocity. In the phase, the average value, largest value and hitting moment value of angular momentum with kick hitting are larger than those with glide hitting. Therefore, the kick hitting could get larger linear and angular momentum.

此阶段平均身体角动量、最大值与击中球瞬间，抬腿击球法三者平均角动量均大於滑步击球法，因此抬腿击球法技术的旋转特质与优势在这可以清楚的看出到，意谓著抬腿击球法打击技术可以使球获得较大的动量与角动量。

B Angular momentum is a vector quantity as are also angular velocity, angular acceleration and torque.

角动量是个矢量，角速度和角加速和转矩也都是矢量。

Angular momentum is a vector quantity as are also angular velocity, angular acceleration and torque.

角动量是个矢量，角速度和角加速和转矩也都是矢量。

The positions of cam and dial were analyzed accompanied with their angular position, angular velocity and angular acceleration.

分析了凸轮和转盘的位置、角速度、角加速度的变化规律，给出了直角式精密分度凸轮的设计算法，同时计算了数控加工的刀位轨迹，并给出了四坐标联动数控加工和编程方法。

First, a program which can be used to obtain the encoder values of each joint D. C. servomotor and then change them into angular position is developed. By means of cubic spline, the angular velocity and angular acceleration are calculated.

本文开发了实时采集和转换机器人各关节的码盘值为角位移的程序，并提出了以三次样条函数求各关节角速度和角加速度的方法，提高了计算精度。

The Von Mises angular function is used to describe the angular correlation for the distributed source and derive a novel distributed source model from the quantitative angular correlation.

利用阵列接收信号协方差阵的特征值分析了源内角度相关程度对有效信号子空间的影响。

Correlation between spin angular momentum s and background angular momentums of planets;2. In the paper the principle of optical rotation due to the transfer of spin angular momentum from light to particles was discussed by analyzing the interaction between the beam of light and birefringent crystal particles, and then an optical tweezers was formed on nanometer optical tweezers system with a linearly polarized light beam (He-Ne laser 633 nm, 10 mW).

从理论上分析了偏振光束与双折射晶体粒子的相互作用过程，讨论了由于光束自旋角动量向晶体粒子的传递所导致的光致旋转效应的原理，并在纳米光镊装置上利用线偏振He Ne激光器(633 nm，10 mW)形成了光镊光阱，利用1/4波片来改变光镊光束的偏振状态，在不同的椭圆偏振状态下实现了直径约为几微米的CaCO3 晶体微粒的捕获和光致转动。

"Yes, now you can give yourself airs," she said, you have got what you wanted.

"对了，您现在高兴了，"她说道，这是您所期待的。

Then the LORD said to me: Rebel Israel is inwardly more just than traitorous Judah.

上主于是对我说：＂失节的以色列比失信的犹大，更显得正义。