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Automated system with an optimum speed non-destructive testing of steam generator and condenser pipesV. V. Chegodaev
Obninsk Institute of Nuclear Power Engineering, Obninsk, Russia.
For normal work of nuclear power plants (NPP) is necessary planned non-destructive testing of equipment. The special attention is given to pipes. On NPP the plenty of pipes is contained by steam generators and condensers. The technological stop (idle time) NPP is indispensable for realization of non-destructive testing of pipes. The technological stop NPP demands minimum time for testing. The testing consists of following stages: equipment preparation for measuring, measuring and results record, results analysis. Preparing of the equipment occupies, as a rule, little time. The analysis of testing results disconnected directly with controlled object. After measuring and results record object testing can be thought finished. The minimization of temporary expenditures of testing is possible at maximum testing speed. The testing of pipes is made, as a rule, by eddy current method with the bulkhead sensor.
The process of the testing realizes as follows. In advance sensor is established opposite pipe (guidance of sensor). Then sensor is entered inside of pipe and is moved along wall of pipe onward and after backwards. The registration (record) of sensor signal is produced in process of movement. The defects of metal are determined at the signal analysis of sensor.
The time of guidance of sensor depends on mechanism of movement from pipe to pipe and optimality of a runway. The testing of movement implements the computer where these requirements are allowed, therefore time is spent for guidance a little. The main time of testing is spent on moving the sensor in pipe, consequently, minimization of time of testing is reduced to determination of optimum of speed the sensor in pipe. From afore said will select following major factors determining speed of movement :
The main factor determining speed of movement is the ability of sensor to give the signal from minimum defect. Considering sizes of minimum defect and driving frequency (signal) of sensor possible to calculate the maximum speed of movement the sensor.
The metal of wall of pipe can have different defects. The cross-section of defects derivated during manufacturing is well approximated by rectangular or triangular cross-section. The cross-section of defects developed at exploitation has not the sharp borders and is approximated by a continuous function. To reveal the defect is means on sensor signal to fix the function describing the cross-section of defect.
Any function with limited spectrum according to readout theorem (the theorems V.A. Kotelnikova) can be simple definite on its selective importances through interval DX = 1/(2B). Parameter B is width of spectrum of function provided that a spectral concentration S(w) of this function at wE >= 2 p B is a zero.The spectral concentration S(w)is calculated on the basis of a function describing cross-section of defect.
In Fig.1 is shown cross-section of defect, describing by function
where b - half - width of defect; X - coordinate of sensor moving; h - depth of defect.
Spectral concentration of function (1) is the following:
In Fig.2 is shown cross-section of defect describing by function:
Spectral concentration of function (3) is the following:
In Fig.3 is shown cross-section of defect, describing by function
||where b - half - width of defect, under which depth in e times as less its maximum value.
||Spectral concentration of function (5) is the following:
The spectrum of these functions is limited. For practical purposes it is enough to consider as a higher frequency of a spectrum such frequency at which one function S(w
) receives the first zero value or if zero values the function has no on a level 0,1 from maximum quantity.
The equation (2) receives the first zero value at w E = p /b and the equation (4) has the first zero value at w E = 2p/b. The equation (6) monotonous decreases, therefore decision w Ewhen S=0.1*Smax is w E = 1,5174/b.
The interval of readouts for defect in a Fig. 1 evaluate D X £ b, in a Fig. 2 - DX £ b/2, in a Fig. 3 - DX £ 2b. At the testing there can be all kinds of defects, therefore interval of readouts is necessary to accept such as this interval simultaneously contents(fits) all kinds of defects and so DX £ b/2.
The interval of readout is determined by width of defect. The minimum width of defect is set. Time space between readouts that is pulse repetition period of readouts is connected to speed of movement the sensor by following expression:
where DX - interval of readouts on coordinate X; Dt - time period of readouts (D
t = T); T - sample period; V - speed of movement the sensor.
The optimum speed of movement the sensor depends on minimum sizes of defect and sampling (driving) frequency ¦ = 1/T and is determined according (7):
One of possible testing system construction variants shown in Fig. 4.
|Fig 4 : Block diagram of automated testing system.|
The sensor 1 moves by movement machinery: vertical 2, horizontal 3, onward and backwards 4. Movement machinery are operated by blocks of control 5, 6, 7 by command from computer 9 of type IBM. The block 8 forms the signal of sensor and passes this signal for record on computer.
At given minimum width of the defect (2b) and sampling (driving) frequency of the sensor it is possible to calculate the maximum speed of movement. For example, if b=0.01mm and f=100 kHz then the speed of movement of the sensor must not be more then 50 cm/sec.
The reduced calculations imply that the width of sensor much less than width of cross-section of defect. In practice the sizes of electromagnetic sensors are commensurable with the sizes of cross-section of defect or more. In this case the sensor is divided into elementary segments. Herewith the full sensor signal from a defect is determined by responses sum of elementary segments during movement along a defect.
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