MEASUREMENTS OF ELECTRICAL AND MAGNETIC QUANTITIES CERTIFICATION OF STANDARD SAMPLES OF ELECTRICAL CONDUCTIVITY D. I. Kosovskii
UDC 537.311.08:658.562
The physical and mechanical properties of metals (their steady-state and dynamic strengths, plasticity, hardness, chemical composition, etc) can be judged by reference to variations in their electrical conductivity. For this purpose, eddy-current instruments types VE-21N and VE-20N have been developed for measuring the conductivity of nonmagnetic materials within the ranges (1-8)-106 and (8-56).106 ~-I.m-i, respectively. We use two types of standard sample (SS) for calibrating and checking these instruments: the single-valued SS intended for calibrating and checking instruments when they are first issued from the factory, and also for use when carrying out periodic checks during operation; a set of SS one instrument enables us to reproduce ten specific values of conductivity; the multivalue equivalent SS intended for adjustment and checking under operating conditions; a set for one instrument comprises one multivalue SS capable of reproducing any value of conductivity within any of the ranges of measurement of the instrument. The present article studies the problems of certifying SS of the first type. The multivalued SS are calibrated and checked against a standard set of single-valued SSs with the aid of an instrument type VE. According to All-Union State Standard (GOST) 22261-74, the ratio of the errors between the standard and working instrument must not be less than 3. Since the permitted measurement errors of instruments types VE-21N and VE-20N are 3%, the errors of the multivalued and single valued SS must not exceed 1% and 0.33% respectively. The electrical conductivity o of the single-valued SS can be determined from the formula 1 o
= - -
R
L
(l)
--,
s
where R is the electrical resistance, L is the length, and S = ab in the o f a n SS i n t h e s h a p e o f a s t r i p o f w i d t h a a n d t h i c k n e s s b.
cross-sectional
area
We d e t e r m i n e d t h e m e a n - s q u a r e d e v i a t i o n f o r e a c h p a r a m e t e r o f t h e SS i n a c c o r d a n c e w i t h GOST 8 . 2 0 7 - 7 6 , c o r r e c t e d to take account of the systematic errors, a n e s t i m a t e w a s made o f the mean-square deviation o f t h e m e a s u r e m e n t s s ( A ) a n d a c h e c k was made o f t h e n o r m a l d i s t r i bution of the results o f 25 o b s e r v a t i o n s f o r t h r e e SS w i t h d i f f e r e n t v a l u e s o f L, a , b , a n d R. The d e v i a t i o n &g o f t h e i n d i v i d u a l p a r t s o f t h e SS was t a k e n i n t o c o n s i d e r a t i o n for the same n u m b e r o f o b s e r v a t i o n s . In this case, the statistical characteristics were found for SSs w i t h m i n i m u m , a v e r a g e , a n d maximum v a l u e s o f 2.
When the physical dimensions of the SS are being measured, the temperature coefficient of linear expansion k of the material is taken into account according to the formula [i]: Z2o= zt ( 1 + k~at),
where z2o and z t are the values of the SS parameters L, a, and b at temperatures of 20~ t~ respectively; At = 20 -- t.
(2)
and
If we bear in mind the fact that k lies in the range (1.2-2.7)-I0-6~ -I, we need only monitor the temperature with an error of not more than il~ when measuring parameters z. The temperature of the material of the sample can vary while we are actually measuring the electrical resistance of an SS. Therefore, the value of o obtained by measuring z and R at temperature t should be corrected to take account of the temperature coefficient of electrical conductivity k o according to formula [i]
Translated from Izmeritel'naya Tekhnika, No. 3, pp. 40-42, March, 1980.
0543-1972/80/2303- 0241507.50
9 1980 Plenum Publishing Corporation
241
020 = ot(l •
(3)
kaAt),
where k o = k0/(l + kpAt); k O is the temperature coefficient of electrical resistivity. Since ~ = 0.004 K-I, the temperature of the sample has to be monitored by a type TR-I thermometer No. 5 and No. 6 with measurement ranges of 16-20 and 20-24~ respectively, and with an error of not more than •176 The systematic error of the SS, which depends upon the accuracy with which its physical dimension can be guaranteed, the nonuniformity of the conductivity of the material from which the SS is made, and the instrument error of the instrument used to measure the parameters of the SS can all be reduced to a minimum by the correct choice of measurement method and instrument (bearing in mind the purposes for which the device being studied is intended). A comparison of the systematic error 0 with the mean square deviation of the measurements s(A) for parameters z, R, and Ao shows that 0/s(A) = 0.3-0.5. Therefore, in accordance with GOST 8.207-76, we take the random error, which for 25 observations comprises s = 2.06s(A) with a probability of 0.95, as our measurement error. The ratio of the random error ~ to the arithmetic mean of the observations A for each of the parameters of the SS at various values of ~ is assumed to be constant, remaining independent of the material out of which the SS is made. Multiple measurements of L, a, b, R, and Ao show that their values can be determined with the necessary degree of accuracy from three observations, under the condition that
So (A)
Amax3--Arums
"rl
A~
~A2~
(Ai--A~5)~ i=]
n (n-
I)
(4)
where Amax3 and Amins are the highest and lowest values of the three observations; TI and T2 are the Student coefficients, with a probability of 0~ and for 25 and 3 observations respectively; A3 and A2s are the arithmetical means for 3 and 25 observations respectively. It has been shown experimentally that the error so(A) in the certification of a singlevalued SS is distributed between the measured parameters in the following manner: it comprises 0.05% for L, 0.05% for a, 0.20% for b, 0o10% for R, and 0.20% for Ao. Let us consider how we can ensure that the metrological characteristics we have listed can be satisfied when an SS is being certified. The length of an SS is the distance between the potential contacts of the terminal set in which the SS is fixed when the electrical resistance is being measured. Since the cross~ectional area of an SS is relatively large, we should strive to obtain as high a value as possible when measuring the resistance, which we can do by increasing L. However, the length of the certified part of the SS cannot be increased indefinitely; it is defined as that part of the SS in which the deviations in thickness, width and conductivity of the material remain within the limits bounded by the specific values of so(A). The value of L is usually 200-300 man. It is measured by calipers with a reading error of 0.02 mm. The systematic error is negligable in relation to the random error. We take the arithmetical mean of the three measurements as our SS, subject to the provisio that the condition so(L) ~ 0.005 is satisfied in accordance with (4). When the value of o of the certified part of the SS is being calculated, we should take into account the differences in cross-sectional area and electrical conductivity along the length of the SS. To reduce the influence of variations in these parameters, we divide the length L of the SS into sections in such a way that the cross-sectional area and conductivity are constant within a particular section, within the limits of measurement error. The crosssectional area of the certified part of the SS is found as the arithmetical mean of the areas of the sections into which the SS is divided. Experiments have shown it to be possible to calculate o from the averaged cross-sectional area S for the various parts of a strip whose thickness varies in steps. By comparing the electrical conductivity of a part of a strip of constant thickness with the conductivity for parts of the strip that incorporate various numbers of stages of different thickness, we can show that the values of o calculated from measurements taken on various parts of the strip
242
tend to be in closer accord w i t h each other when the accuracy with which the geometrical parameters and resistances of the parts is increased. The width and thickness of an SS should be chosen in such a way that the cross-sectional area is a minimum, since this leads to an increase in the electrical resistance, and a higher resistance can be measured w i t h a smaller relative error. However, the width of the SS cannot be reduced below 20 mm. A deviation of 0.01 m m in width over a length of 200-300 mm is not difficult to ensure with existing technology. The difference in width over the length of the sections into w h i c h the certified part of the SS is divided does not exceed the reading error of a lever micrometer w i t h a scale division of 0.002 nan. Consequently, the systematic error in measuring the width of each section does not exceed 0.01%. The w i d t h of the SS was measured at 15-20 points uniformly distributed along its length. The arithmetical m e a n of the measurements made of the various sections was taken as the width of the SS: n m:
n
where a k is the width of the SS, defined as the a r i t h m e t i c a l m e a n of the three measurements in the k-th section, subject to the condition that relationship so(a) ~ 0.0005 is maintained. Tests carried out on plates of identical electrical conductivity but of different thickness, using instruments type VE, have shown that the measurements do not depend upon the thickness, provided its value satisfies the expression
b
=
(5)
3
where @ is the depth of penetration of the electromagnetic field; quency of the eddy currents of instruments types VE-21N or VE20N; free space.
f is the excitation fre~o is the permeability of
Taking (5) into account and bearing in mind the need to obtain a minimum cross-sectional area of sample, the best thickness would appear to be b = 3@. It is best for SS to be made out of rolled tape or strip of appropriate material and thickness, only the one dimension being adjusted: the width. It has been shown that in order to find the average thickness of an SS with an acceptable level of error, we have to take measurements at n = 40-60 points, uniformly distributed along the whole of a surface of length L. Under these circumstances, the distance between points must not exceed i0 ram. If this method is applied, we can expect in practice to introduce an error in the mean value of thickness of the same order as the instrument error. The thickness should be measured with the aid of a clock gage having a scale division of not more than 0.0005 m m (see GOST 14712-69). The thickness
of the certified
part of the SS will be n
E\ 1--
k~l
,
n
where bk is the thickness of the SS determined by means of three measurements at the k-th point, subject to the proviso that the relationship so(b) s 0.002 is satisfied. When an SS is being certified, its electrical conductivity must take into account the divergence Ao among its constituent parts. It is best to use instruments type VE to estimate the nonuniformity. These enable us to test parts of an SS that do not exceed the crosssectional area of the transducer. In order to certify an SS with a given degree of accuracy, we have to estimate the nonuniformity in electrical conductivity with a relative error not exceeding 0.2% of the value being measured. However, instruments available at present are only capable of measuring o with an error of 3%; this error can be reduced by increasing the sensitivity, and this can be achieved by increasing the gain of the amplifier in the signal channel of the instrument. The accuracy of the readings can be increased by reducing the scale division of the instrument. The instrument is prepared for use in measuring nonuniformity by adjusting it over those parts of the SS being checked which have the greatest difference in o. In view of the fact that this difference is small, the scale of the
243
instrument represents a very small part of a holograph within which the variation of the informational parameter of the instrument is a linear function of o [2]. Consequently, we do not need to calibrate the scale divisions of the instrument. The number of scale divisions can be determined from the expression m~
A($max - - AO'min ar
I
where AOma x and AOmi n are the deviations over the sections of the SS with greatest and least electrical conductivity; o ~ 0.i~/i00 is the error in determining nonuniformity. We should mention that an increase in the gain leads to a sharp increase in the sensitivity of the instrument due to variations in the airgap between the transducer and t h e surface of the SS. To exclude the effect that airgap fluctuations have on the measurement of o in various parts of the SS, we use a microscope type BMI-I. First of all, before we start to determine Aa, we measure the irregularities in the surface of the SS with the aid of a thickness gage type VT-3ON, designed for use with dielectric coatings. For this purpose, the SS is fixed to the column of the microscope, while the transducer of instrument type VT30N is fixed to the bracket of the microscope. A gap of 0.03-0.05 mm is established between the surface of the SS and the convertor by means of a clock gage positioned above the bracket. The SS is then moved and the irregularities in the surface of the SS are determined from the readings of the VT-30N instrument. Then, we use an instrument type VE-20N or VE-21N in place of the transducer of the VT-30N instrument. By installing the transducer over the sections of SS being tested and establishing the necessary gap, we obtain the readings of the instrument. The whole of the certified part of the SS is scanned with a step of i0 mm. We can then determine the arithmetical mean deviation of these measurements:
A~
k=l ~
where $'k is the deviation of Ao at the k-th point, determined from three measurements, subject to the proviso that relationship So(O) ~ 0 o 0 0 2 is observed. Taking into consideration the physical dimensions that have been found, and determining the deviation Aa of the sections involved, we choose the length of the part of the SS whose electrical conductivity is being certified, for which the error of the measured parameters corresponds to the values of so(A) given above. The electrical resistance was measured on type U303 apparatus using a single-double bridge type R-39, which guarantees a tolerance of 0.02% over the resistance range 10 -3 to i0 -~ ~. We then turned our attention to the transfer resistance at the point where the potential contacts of the terminal assembly makes contact with the SSo Our criterion for assessing the validity of the measurements was to determine the resistance by calculation from the physical dimensions of the SS and to find o by measurement with the aid of an instrument type VE, and then to reproduce the measured resistance on the type U303 apparatus. Before each resistance measurement, the SS was reinstalled and reconnected to the terminals. We found that the error caused by the transfer resistances depends mainly on the elasticity and flatness of the SS. This error comprised 0.02%. As the resistance of the certified part of the SS, we took the arithmetical mean of three measurements with the condition so(R) 0.001 satisfied. The value of a determined according to (i) is an averaged value of the electrical conductivities of the individual sections of the SS, and corresponds best with the part for which the value of Aa, determined by the type VE instrument, differs least from the arithmetical mean deviation. Therefore, in order to test instruments type VE with the least possible error, the transducer of the instrument should be installed on that part of the SS whose deviation in o from the arithmetical mean is a minimum. The error in determining the o of the SS with 25 observations and for a probability of 0.95 can be found from the formula
244
apa = 2 . 0 6
/
s ~ (L) "f"
s 2 (a)
s z (b) s 2 (R) "i- _ -6 +
(Ao___ s ~ ___)) o'
where s(L), s(a), s(b), s(R), and s(Ao) are the mean-square deviations of the measurements of parameters L, a, b, R, and Ao respectively. CONCLUSIONS The electrical conductivity should be determined for that part of cross-sectional area can be found and the nonuniformity of the material ation with the necessary degree of accuracy. The value of o determined corresponds most closely with that part of the SS for which Ao deviates the arithmetical mean deviation for all sections of the SS. Therefore, noted and used for checking the instrument.
the SS in which the taken into consideraccording to (i) least of all from this part should be
LITERATURE CITED
l. 2.
I. I. Kikoina (editor), Tables of Physical Quantities [in Russian], Atomizdat, Moscow (1976). V. S. Sobolev and Yu. M. Shkarlet, The Adjustment and Screening of Transducers [in Russian], Nauka, Moscow (1967).
UTILIZATION OF SQUARE-WAVE SIGNALS FOR TESTING OF ELECTROMECHANICAL INSTRUI~NTS M. Ya. Mints and V. N. Chinkov
UDC 621.317.7.089.6
At present, sinusoidal signals are used in the testing of ac electromechanical instruments. However, obtaining sinusoidal reference signals and tuning and stabilizing their parameters to a high degree of accuracy are difficult technical problems to overcome. It is significantly simpler to shape reference signals in the form of square waves. Such a signal was proposed in [i] for the graduation and calibration of instruments using a built-in source of calibration voltage. In this case the source works across a given load with given stable parameters. When tested using a square-wave from various measurement instruments that have different active and reactive parameters in their measurement circuits, their readings due to higher harmonics in the presence of the signal will differ. However, if the reactive elements weakly influence the instrument readings, then the systematic error will be small. Below we examine an estimate of this error for various instruments as a function of the parameters of the measurement circuits. Use of square-wave signals without corrections that would take account of the influence of the parameters of the measurement circuits is possible only for those instruments whose systematic error can be ignored in comparison with that of the instrument being tested. ~ First we will obtain estimates for the systematic error of the ammeters and voltmeters. The generalized equivalent circuit for testing of these instruments is shown in Fig. I, where G is the square-wave signal generator (voltage or current); Z1(jw) is the frequency-dependent portion of the total impedance of the instrument Z(j~), i.e., Z1(jw) = Z(j~) -- Z(0); Z(0) is the resistance of the instrument under constant current (pure active); R is the sum of the output generator resistance, the active resistance of the instrument Z(0), and the limiting resistance connected in series to the instrument (for testing of voltmeters, the limiting resistance may be absent). R ~
~
Fig. i
Translated from Izmeritel'naya Tekhnika, No. 3, pp. 42-44, March, 1980. 0543-1972/80/2303- 0245507.50
9 1980 Plenum Publishing Corporation
245