均方根值

In this paper the influence of coma and spherical aberration on the far-field distribution and antenna receiving power is analyzed, in which aberration attenuation factor is introduced and the relation of it to root mean square of wavefront aberration is given.

分析了球差和彗差对信号光远场分布、天线接收光功率的影响，引入了畸变衰减因子，给出了畸变衰减因子与波前畸变均方根值的关系。

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。

Under the condition of running on the hard soil pavement with the total train mass, the riding comfort tests of the tractor-trailer combinations with the stiff and the flexible drawgear have been performed, and the dynamics longitudinal force has been studied. When the flexible drawgear was used, the theoretical results and the experimental data showed that the peak value of the dynamics longitudinal force, the peak value of the RMS of the dynamics longitudinal force, and the PSD both of the dynamics longitudinal force and of the longitudinal acceleration decreased largely.

以平稳随机路面激励状况下满载行驶作为挂接车辆的经常行驶工况，进行了挂接车辆以刚性牵引架及不同柔性牵引参数的柔性牵引装置牵引运行时的平顺性试验，柔性牵引理论分析结果与试验结果均表明，使用柔性牵引参数值接近优化值的柔性牵引装置后，动态纵向牵引力的峰值、功率谱密度峰值及均方根值均有了大幅度的降低；主车和挂车的纵向振动加速度功率谱峰值也有了很大的降低。

The traditional method is that sampling 20 equidistance discrete voltages to calculate the virtual value. To gain the virtual value, we firstly average their square values, and then extract it.

传统的计算有效值的方法是利用一个周期内等距离散的20个采样点的瞬时值进行求解，通过计算它们的均方根值来得到有效值。

Through simulation,the maximum root mean square value of weighted acceleration and the root mean square value of total weighted acceleration of given points are obtained directly.

通过仿真可直接获得给定测点的加权加速度均方根值分量的最大镇和总加权加速度均方根值。

The results show that there will be slight decrease of the control efforts when the mean absolute value or the root mean square value of the optimal control force is taken as the maximum designed control force, while the maximum control force of MR damper can be decreased by 85% compared with the maximum optimal control force. The decrease in the designed control force can not only significantly increase the capability of MR dampers, but also reduce the dimension of MR dampers for pratical application in engineering.

研究表明，当设计值取最优控制力的平均绝对值或均方根值时，MR阻尼器的最大控制力比最优控制力的最大值降低了85%，而控制效果降低不多，可以满足对结构的控制要求；降低最大控制力设计值后，不但可以充分发挥MR阻尼器的出力性能，而且可以缩小MR阻尼器的设计尺寸，便于工程应用。

Taking the damping and rigidity of automobile seat and suspension system as design variables, the root mean square value of acceleration seat and relative dynamic loading of tire as objective function, two optimization design models of passive suspension parameters were established according to riding comfortableness and pavement breakage.

以汽车座椅和悬架系统的阻尼与刚度作为设计变量，综合考虑车辆的乘坐舒适性和对路面的损坏性，以座椅加速度均方根值和轮胎相对动载荷均方根值作为目标函数，建立被动悬架参数的两目标优化设计模型。

Finally, the average value, root-mean-square value, maximum, minimum, spike factor of wind force, wind force moment are analyzed to studied the mutually interference influences to the base force of high buildings and group of buildings.

最后分析不同状态下风力、风力矩的平均值、均方根值、最大值、最小值和峰值因子，探讨了风荷载下高层建筑的相互干扰和群楼对建筑物风力影响。

In this article, the effect on the surface topography of the same material was analyzed by different processing methods, the value of surface parameter arithmetic mean R, root-mean-square roughness R and gradient root-mean-square value Z were used to appreciate the surface topography, and the data were processed with the software Matlab.

分析不同加工方法对同一种材料表面形貌的影响，采用表面形貌统计参数中的轮廓高度算术平均值R、轮廓高度均方根值R、坡度均方根值Z，对表面形貌进行评价，结果表明，准分子激光加工表面的R、R，和Z，值均比研磨加工表面小。

In this article, the effect on the surface topography of the same material was analyzed by different processing methods, the value of surface parameter arithmetic mean Ra, rootmean-square roughness Rq and gradient root-mean-square value Zq were used to appreciate the surface topography, and the data were processed with the software Matlab.

分析不同加工方法对同一种材料表面形貌的影响，采用表面形貌统计参数中的轮廓高度算术平均值Ra轮廓高度均方根值Rq、坡度均方根值乙对表面形貌进行评价。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。