松动件定位外文翻译松动件位置的技术研究

1、译文：一项评估关于运用wigner-ville分布方法定位松动件位置的技术研究作者：yong beum , seon jae , hae dong , youn won , jin ho 摘要：这篇论文呈述的是一种关于评估运用wigner-ville分布定位所产生影响的方法，这种方法运用了金属板传播的弯曲波离散特性，反应堆中这种弯曲波的传播速率与到达时间的不同与离散特性有着很密切的关系，故而这些不同可以通过使用wigner-ville分布的撞击信号的变化来获得。从撞击位置到信号测量点的距离可以通过运用反应堆中两个弯曲波的传播速度，到达时间的不同来估测。实验结果显示：所提交的定位撞击部位的方法与

2、实际的撞击部位比较，误差在百分之十以内。关键词：松动部件、撞击位置 、 wigner-ville 分布，弯曲波1、简介：由于各种机械方面的原因（例如，流动诱发的震动），rcs中的很多部件都可能从他的原始位置松动由于松动与反应堆中的冷却济一起传送，传播，那么他们就避免不了与rcs中的组建重复的接触，这就可能危及整个结构组建的整体性，因此确定松动件的位置及把他们从rcs中移除就显得尤为必要。鉴于这一必要性，众多的关于估测松动件位置的方式方法已经开展开来了，kryter和shahrokhi在1981年就引入了这样一种定位松动件的方法，即利用弯曲波承载的撞击信号到达接受器的时间不同和运用两个不同的加速

3、度传感器测量得到的撞击信号的衰减值。还有，olama在1985年引入了另外一种方法，即利用同一个加速度传感器侧得的弯曲波中横波与纵波到达时间的不同以及两个波的传播速率来定位。然而，这些方法中的利用到达时间不同的这些定位方法的评估都是基于严格的撞击时间信号的记录和采集，而这些信号有时是无法正确得到的。这篇论文中提及的方法运用了金属板中弯曲波的离散特性-金属板中弯曲波的传播速率会随着频率的改变而变化。弯曲波可以通过撞击信号的wigner-ville分布来发现。到达时间的不同可以利用弯曲波的离散特性更精确的得到。利用两个弯曲波到达时间以及传播速率的不同这一方法，可以更精确的测定松动件与接受信号的距离

4、。实验结果显示，与实际的撞击位置相比，通过此方法定位的位置误差在百分之十范围以内。2、wigner-ville分布： 作为在时频分析领域中众多的使用同步信号分析的一种，wigner-ville分布最近引起越来越大的关注，wigner-ville分布最早由wigner在1932年提出，而这一分的整体概念由ville在1948年重建起来。wigner-ville分布这样来定义,即 （1）这里t, , , s(t)分别表示时间、角频率、时间延迟，以及时间函数，这里的星号表示复合。从公式1中可以看出，wigner-ville分布表示为时间延迟s(t+ / 2 ) . s * ( t - / 2 ) 的

5、傅立叶变换，s(t + / 2 ) . s * ( t - / 2 ) 是一种附属时间的自相关功能。并且反应了能量在时频域的分布。为了从有限记录长度去评估wigner-ville分布，公式1的近似离散值必须计算出来，从而公式1的近似离散值由y.-h. kim and y.-k. park在1994年由以下公式得出，即： （2）这里，k,m和n是整数，n是时间历史数据的个数并且k=2n， =/kt,其中t是抽样时间。如wahl and bolton在1993年提出的利用数据信号有限记录长度的周期性，公式2就可以表示为： （3）从公式3中可以看出，w（mt,n)与gm(k)的离散傅立叶变换有关。3

6、、水平金属板中弯曲波的离散特性： 金属板中弯曲波传播的方程式中可以看出，离散特性能够由fahy1985年提出的波动方程中演变得来，其波动方程如下： （4） （1） （2） 图片一，典型的由加速度传感器侧得的wigner-ville能量分布。这里的cb是弯曲波的传播速率，e.i和m是勇实验中模版的模数，分别为局部两在公式4中，弯曲波的传播速度是与角频率的大小成比例的，并且与传播速度的相位是相同的。cremer and heckl在19872年阐述了水平金属板中群弯曲波的传播速率是相位传播速率的两倍，函数表示为： （5）4、撞击位置的定位方法：一般来说，加速度传感显示器获得的加速度信号重复获得不同

7、频率下的弯曲波的特性。加速度信号能够转化成wigner-ville能量分布，这一分布反应了不同频率下的各个弯曲波的的能量分布（如图片一所示）在一定的频率下，wigner-ville弯曲波的能量分布有一些峰值，第一个峰值源于原始弯曲波的能量值最大，它不受反射波和余下峰值的影响，这就是反射波的最大能量。因此，连接信号wigner-ville分布第一个峰值的曲线（称作能量到达时间曲线）反应的是在同一个测量点、不同频率下弯曲波的能量到达时间。图片2所示的就是典型到达时间曲线的样本，它来自于a、b两个不同点所接收信号的wigner-ville能量分布。在已知一定频率下，我们就可以估测a、b两点距离弯曲波

8、的传播速率就可以由传播时间表示为 （6）这里的表示的是以为频率弯曲波的传播速率，表示的是从撞击点到a点的距离，表示以为频率，a，b亮点之间，弯曲波的传播时间间隔。因此，如果分别一f1 f2为频率下a、b两点弯曲波的传播速率、a点两个弯曲波的到达时间、均为已知了，那么距离就可以表示为： （7） 一样地，和的距离也可以得出来。如果重叠围绕中心点a、b、c画出的圆的半径，那么所有圆的交叉点就可以表示成所有松动件的撞击位置了。5、 实验结果:有很多的实验都可以用来证实所提交方法的实用性。实验的背景条件如图片三所示。一金属圆盘挂在两个支撑点的下方，金属圆盘必须是规则的长方形，宽、长、高分别为1.5米、1

9、.2米、5毫米,并且该金属材料的密度和yongs模数必须分别为7860kg/m3和200g帕。加速度传感器分别安装在a、b、c三点，并在o点产生一个撞击。信号的传播时间到达a、b、c三点时间如图4所示。a点的加速度信号到达时间的wigner-ville能量分布如图5所示。第一条轮廓线（靠近t=0轴）表示的是a点在不同频率弯曲波的到达时间，剩余的轮廓线表示的是反射波到达a点的到达时间。图片6曲线分别表示的是到达a、b、c三点的时间。一个测量点所得到的不同的弯曲波的到达时间可以从图片6得到。并且弯曲波的传播速度可以从这撞击实验和两个测量点的一系列实验中获得的公式6中得到，最后，撞击位置分别到a、b

10、、c三点的距离可以由公式7计算得到从表一中我们以得到ra rb rc三个值的大小，于实际的距离相比，所得距离的误差在百分之十以内。6、结论：这一运用wigner-ville 分布评估松动件位置的方法是基于这样一种假设的，即这些结果部分都有同样的材料性质和同样的厚度。当把这一方法运用实际带有管道、弯曲部分、以及管口的结构中时，就有必要把实际材料厚度以及材料性质变化的影响考虑进去。利用安置在具有相同厚度，传播速率以及相同到达时间的金属圆盘中传播的弯曲波的离散特性，可以得到wigner-ville 分布。同一个测量点，在不同的频率下的离散特性，可以得到wigner-ville 分布。在同一个测量点不

11、同的频率下，利用两个不同弯曲波的到达时间差别和传播速度就可以测得测量点到撞击位置的距离了。与实际的距离相比，同种材质的金属板得到的实验结果的相对误差在百分之十以内。7、参考文献： (1)、cremer l., heckl m. (1972), structure-borne sound, springer-verlag, berlin. (2)、fahy f. (1985), sound and structural 1,7bration, academic press, london. (3)、kim y.-h. and park y.-k. (1994), wigner-ville int

12、erpretation of musical sound and transient vibration signals, westprac 1994, 752. (4)、kryter r. c. and shahrokhi f. (1981), summary o studies on methods jor detecting, locating, and characterizing metallic loose parts in nuclear reactor coolant system, u. s. nuclear regulatory commission report nure

13、g/cr-2344. (5)、olma b. j. (1985), source location and mass estimation in loose parts monitoring of pwrs, prog. nucl. energy 15,583. (6)、ville j. (1948) theorie et applications de la notion de signal analitique. cables et transm., 2a(1), 61-74 (7)、wahl t. j. and bolton j. s. (1993), the application o

14、f the wigner distribution to the identification of structure-borne noise components, j. sound and vibration 163(1 ), 101. (8)、wigner e. (1932), on the quantum correction for thermodynamic equilibrium, physical review 40, 749原文：a study on technique to estimateimpact location of loose part usingwigner

15、-ville distribution yong beum kim a, seon jae kim a, hae dongchung a, youn won park a, jin ho park h mechanical and material department, korea institute of nuclear safety, r o. box114, yusong, taejon, korea, 305-600b advanced reactor development, korea atomic energy research institute, 150duck-jin d

16、ong, yusong,taejon, korea, 305-353 presented in this paper is a method to estimate impact location of a loose part using the wigner-ville distribution. the method uses dispersion characteristics of bending waves propagated in a plate. the power propagation velocity and arrival time of difference ben

17、ding waves related to the dispersion characteristics can be obtained through the transformation of impact signals using the wigner-ville distribution. the distance from the impact location to the signal measuring point can be estimated using the information on the power propagation velocity and the，

18、arrival time difference of two bending waves. the experimental results show that the proposed method estimates the impact location with relative percentage errorwithin 10% compared with the actual impact location. 2003 elsevier science ltd.all rights reserved.keywords： loose part,impact location,wig

19、ner-ville distribution, wigner-ville ，bending wave，1. introduction： many parts of mechanical components in the reactor coolant system (rcs) can be loosened from their original location by various mechanisms such as fatigue damage due to flow-induced vibration. since the loose part circulates with re

20、actor coolant in the rcs, it may make repetitive contact with the components of the rcs. this may damage the structural integrity of the components so it is necessary to identify the location of loose parts and to remove them from the rcs. due to this necessity, much research has beencarried out for

21、 the development of a method to estimate the location of the loose part.kryter and shahrokhi (1981) introduced a method to estimate the impact location using both the arrival time difference and the damping value of impact signals measured with two accelerometers. olma (1985)also introduced a method

22、 by using both the arrival time difference between longitudinal and transverse waves measured with one accelerometer and the propagation velocity of the two waves. however, the estimation of the arrival time difference in these methods based on only the shape of time history of impactsignals result

23、in sometimes incorrect estimation of the arrival time difference. the method proposed in this paper uses dispersion characteristics of bending waves in a plate, where propagation velocity varies with frequencies. the dispersion characteristics of bending waves can be fund through the transformation

24、of impact signals using the wigner-ville distribution. the arrival time difference can be obtained more accurately using the dispersion characteristics of bending waves. the distance from the impact location to the signal measuring point can be estimated more accurately usingthe information on the p

25、ower propagation velocity and the arrival time difference of two bending waves. the experimental results show that the proposed method estimates the impact location with relative percentage error within 10% compared with the actual impact location.2. wigner-ville distribution as one of the methods e

26、nabling simultaneous signal analysis in time and frequency domain, the wigner-ville distribution has been drawing a lot of attention lately. the wigner-ville distribution was first proposed by wigner (1932), and the concept of the distribution was re-established by vitle (ville, 1948).the wigner-vil

27、le distribution, w(t, co ) is defined as （1） where t, , , s(t) represents the time, the angular frequency, the time delay and the time history respectively, and the asterisk (*) denotes the complex conjugate. from eq.（1）the wigner-ville distribution is regarded as fourier transform for the time dela

28、y r of s(t + / 2 ) . s * ( t - / 2 ) which is a time-dependent autocorrelation function, and represents the distribution of power on the time-frequency plane.in order to calculate the wigner-ville distribution from a signaldata of limited record length, an approximate discrete value of eq. (1) must

29、be calculated. the approximate discrete value of eq. (1) is suggested by y.-h. kim and y.-k. park (1994) as （2） where and k, m and n are integers and n is the number of time history data. also, k=2n, =/kt and t is the sampling time. using the periodicity of signal data with limited record length as

30、suggested by wahl and bolton (1993), eq. (2) can be expressed as) （3） it can be seen from eq. (3) that w（mt,n) is related to the discrete fourier transform (dft) of gm(k).3. dispersion characteristics of bending waves in a flat plate the equation of bending wave propagation on a flat plate, showing

31、dispersion characteristics, can be derived from the wave equation on a flat plate suggested by fahy (1985) as （4） technique to estimate impact （1） （2） figure 1 typical wigner-ville power distribution of signals measured with accelerometer where cb is the propagation velocity of the bending wave and

32、e. i and m is the youngs modulus of the plate, the cross-sectional second moment per area and the mass per unit area of a fiat plate, respectively. in eq. (4), the propagating velocity of bending waves is proportional to the square root of the angularfrequency and is the same as the phase propagatio

33、n velocity.cremer and heckl (1972) suggests that the group velocity of bending waves on a flat plate is twice the phase velocity as ： （5)4. method for estimating impact location in general, the acceleration signal obtained at an accelerometer displays manifold characteristics of bending waves with v

34、arious frequencies. using eq. (1), the acceleration signal can be transformed into a wigner-ville power distribution, which represents the time dependent power distribution of each bending wave with various frequencies in time and frequency domain as shown in fig. 1. the wigner-ville power distribut

35、ion of a bending wave with a certain frequency has several peaks. the first peak corresponds to the maximum power of the original bending wave, not influenced by reflected waves and the remaining peaks signify the maximum power of reflected waves. therefore, the curve connecting the first peaks of t

36、he wigner-ville power distribution of signals (called power arrival time curve) represents the power arrival time of the bending waves with various frequencies at a measuring point. a typical example of the arrival time curve is shown in fig. 2, which is derived from the wigner-ville power distribut

37、ion of signals received at two points a and b. from fig. 2, we can estimate the traveling time that the power of a bending wave with a certain frequency proceeds by the distance from the point a to the point b. the power propagation velocity of a bending wave can be obtained from the traveling time

38、as (6)where is the power propagation velocity of a bending wave with frequency , the distance from the impact location to the point a, and， the power traveling time of a bending wave with frequency by the distance of . therefore, if two power propagation velocities of bending waves with frequencies

39、， and thepower arrival time difference between the two bending waves at the point a, are known, the distance ra can be obtained as： （7）similarly, the distance of rb and rc can be estimated. if overlapping the circles drawn around the center points of a, b, and c with corresponding radii ra, rb, and

40、rc, the intersection point of the circles can be estimated as the impact location of a loose part.5. experimental results： experiments were carried out to prove the applicability of the proposed method. the experimental setup is shown in fig. 3. a plate is hung at its upper two supports. the plate i

41、s rectangular shaped, with width, length, and thickness of 1.5 m, 1.2 m, and 5 mm, respectively, and the material is steel with a density and youngs modulus (e) of 7,860 kg/m 3 and 200 gpa, respectively. accelerometers are mounted at the points a, b, and c on the plate, and an impact is made at poin

42、t o.the time history of the signals measured at the impact hammer and three accelerometers are shown in fig. 4. contour lines of the wigner-ville power distribution in time-frequency plane for acceleration signal at point a are shown in fig. 5. the first contour line (closest to the axis of t=0 ) re

43、presents the power arrival time of bending waves with various frequencies at point a. the remaining contour lines signify the power arrival time of reflected bending waves at the point a. fig. 6 presents the power arrival time curves at points a, b, and c, which correspond to the power arrival time

44、of bending waves at points a, b, and c. the power arrival time difference between the two bending waves at one measurement point can be obtained from fig. 6. also, the power propagation velocity of a bending wave can be estimated using eq.(6) from the experiment that the impact point and two measuri

45、ng points lie in series.finally, the distance from the impact location to the measurement points a, b, and c, respectively, can be estimated using eq. (7). in table 1, the estimated ra, rb, and rc values are shown and relative percentage error of the estimated results is within 10% compared with the

46、 actual distance.6. conclusions an improved method to estimate impact location of loose part using wigner-ville distribution is established under the assumption that a structure has homogeneous material property and uniform thickness. when applying this method to a real structure connected with pipes, elbows, nozzles, etc., it is necessary to take into account the effect from change of material property and thickness for the real structure. using dispersion characteristics of bending waves propagated in a homogeneous plate with uniform thick