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A multi-coil sensor for tangential magnetic field investigations
Journal of Magnetism and Magnetic Materials 242–245 (2002) 1153–1156
A multi-coil sensor for tangential magnetic field investigations S. Tumanski* Warsaw University of Technology, Institute of Electrical Theory and MeasurementsFIETiME, Koszykowa 75, 006-61 Warsaw, Poland
Abstract The magnetic field above the steel sheet was analysed numerically and experimentally. It was estimated that this magnetic field drops very regularly and slowly (about 10% for 10 mm of the distance). Thus, it is possible to approximate the measured data obtained from several sensors into H ¼ f ðxÞ dependence. Next, this dependence can be used to extrapolate the measured results into the sheet surface. The design of multi-coil sensor is discussed and the model of such a sensor is tested. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Sensors; Electrical steel; Magnetic field; Magnetic measurements
1. Introduction The magnetic field strength in electrical steel sheet can be determined using the indirect method (applying the Ampere’s lawFby measurement of magnetising current) or direct method (by measurement of the tangential field component above the sheet) [1]. The first method can be used only if the length of the magnetic path is well defined, for example in the case of the ring core or Epstein frame. But to tell the truth even in such cases the length of the magnetic path is never known exactly and it is rather established as some kind of agreement (for example, a length of 0.94 m in the case of 25 cm Epstein frame). In the direct method it is assumed that the tangential component of the magnetic field strength is the same in the sheet sample and directly above the surface of the sample. Thus, using the sensors of tangential magnetic field it is possible to determine the magnetic field strength in the sample even if the length of the magnetic path is unknown. To detect the tangential magnetic field various sensors are usedFflat inductive coil (the socalled H-coil), half-ring inductive coil (Rogowski coil), Hall sensors [2] or thin film permalloy magnetoresistive sensors [3].
The H-coil sensors are the most frequently used because they are relatively easy to prepare. Other advantages of the H-coil sensors are as follows: unlimited range of the measured field and excellent linearity, easy to obtain the averaging effect due to large area of the sensor, immunity to the orthogonal field component. The main drawback of this sensor is the necessity of the integration of the output signal, because it depends on the derivative dH=dt: Other important disadvantage of the H-coil sensor is its small sensitivity. To obtain reliable results of measurements the sensor should be placed extremely close to the sheet surface. It should also be as thin as possible. On the other hand, the sensitivity of the H-coil depends on its cross-sectionFto obtain the large output signal the coil should be sufficiently thick. To overcome this discrepancy Nakata proposed to use the two-coil system distanced from the sheet [4]. In such system the magnetic field on the sheet surface can be estimated by the extrapolation of the measurement results into the tested plane. Following the idea of Nakata the multi-coil system has been analysed and tested.
2. The magnetic field above the sheet
*Tel.: +48-22-660-75-25; fax: +48-22-629-29-62. E-mail address: [email protected] (S. Tumanski).
The tangential component of the magnetic field above the sheet has been analysed numerically and experimentally. Fig. 1 presents the results of calculations of
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 1 3 0 2 - 6
1154
S. Tumanski / Journal of Magnetism and Magnetic Materials 242–245 (2002) 1153–1156
Fig. 1. The calculated distribution of magnetic field strength in C-yoke (a) and 2C-yoke (b) circuits (grey-scale the same as in Fig. 3). Fig. 3. The distribution of magnetic field above and under the GO steel on C-yoke (a) and 2C-yoke (b) tested area 3 3 cm.
Fig. 2. The dependence of the field around the stripe versus distance form the sheet calculated for 1C and 2C yoke system.
magnetic field strength for the case of 3 cm stripe on the C or 2C yoke with poles 25 30 mm distanced by 8 cm. It was assumed that the air gap is equal to 0.01 mm. The calculations were performed using 3D OPERA software of Vector Fields. Magnetising conditions have been selected to obtain the flux density of about 1.3 T in GO steel. Fig. 2 presents the dependence H ¼ f ðxÞ determined numerically for the field in the central part of the stripe. Similar investigations have been performed experimentally applying the magnetovision method [5]. The maps illustrating the distribution of the magnetic field around the stripe are presented in Fig. 3. The main difference between calculated and experimental data is caused by the heterogeneity of the grainoriented steel (not taken into account in the numerical model). To compare both results the H ¼ f ðxÞ dependency was this time calculated as the average value for 3 3 cm area (Fig. 4). For investigations of electrical steel the 2C yoke is usually strongly recommended. But the application of
Fig. 4. The dependence of the magnetic field above the steel sheet versus distance from the sheet determined experimentally.
the multi-coil system seems to be more difficult in this case. The decrease of the field versus the distance is less significant and to obtain sufficient difference of the coil signals the sensors should be more distanced. This separation of the sensors is limited by the construction of the yoke. Moreover, very close to the sheet surface the dependence H ¼ f ðxÞ is disturbed by the stray field from domain and grains boundaries. Thus, the first coil should be inserted with certain distance (about 1–3 mm) from the sheet. In certain applications the asymmetrical C-yoke cannot be substituted by a 2C yoke. For example, author developed the measuring system for 2D measurements using movable C-yoke [6]. Surprisingly for multicoil measurements this system is advantageous. The magnetic field above the sheet drops very regularlyFabout 10% for the 10 mm of the distance. Thus the sensor can be placed above the sheet even with a
S. Tumanski / Journal of Magnetism and Magnetic Materials 242–245 (2002) 1153–1156
distance of several millimetres and it is not necessary to place the coil directly close to the sheet surface.
3. The design of the multi-coil sensor The output signal of the sensor E can be calculated using the expression: E ¼ 8p2 107 fzðt þ dÞðw þ dÞ H;
ð1Þ
where t and w are the thickness and the width of inner dimensions of the coil. d is the diameter of the wire, z is the number of turns and f is the frequency. The H-coil with dimensions 25 25 mm and inner thickness 0.5 mm wounded using 0.1 mm wire (about 150 turns) exhibited a sensitivity of only 0.8 mV/(A/m). This corresponds with the output signal of about 20 mV for the typical grain-oriented steel at a flux density of 1 T. The sensitivity can be enlarged using thinner wire. The sensor with the same dimensions but wounded with a wire of diameter 0.05 mm (about 400 turns) exhibited a sensitivity of about 3 mV/(A/m) (see Table 1). As the magnetic field drops very regularly the coils have not to be very thinFit can be designed even as the multi-layer coil. For the multi-layer coil with thickness T the expression (1) can be rearranged into: E ¼ 4p2 107 f
ðT tÞw ðt þ dÞðw þ dÞH: d2
0.5 0.5 0.5
The multi-layer H-coil of thickness T ¼ 1 mm wounded with a 0.05 mm wire exhibited a sensitivity of 22 mV/(A/m). Fig. 5 presents the dependence of the field above the stripe versus the distance tested using the H-coil sensor. This dependence is close to linearFthe non-linear part 0:01x2 was smaller than 0.2%. But random deviations from the linear approximation line was sometimes larger than 1%. Thus, the application of only two coil sensors may result in quite significant incidental error. Three or better four coil sensors ensures enhanced reliability of the whole measuring system due to better accuracy of approximation. After substitution of the two-coil system by three-coil one, the author estimated that nonrepeatability of measured results enhanced from part of percent to the hundredth part of percent. Fig. 6 presents two examples of the multi-coil sensor design. Author applied the multi-coil sensor for two-dimensional measurements [6]. In such case, both components of the magnetic field can be measured using the multicoil system with orthogonal sensed H-coil sensors (Fig. 6b).
(a)
(b)
ð2Þ
Table 1 The parameters of the H-coil sensors t (mm)
1155
w (mm)
d (mm)
z
S (mV/(A/m))
20 25 25
0.1 0.05 0.05
150 400 2000
0.84 2.8 22
Fig. 6. The multi-coil sensor design (a) three-coil sensor, (b) sensor for two-dimensional measurements.
A/m
60
40
20
0
-20
-40
-60
-80 0.0
Fig. 5. The dependence of the field above the stripe versus distanceFdetermined using H-coil sensor.
0.5
1.0
1.5
2.0
2.5
Fig. 7. The output signal of the four coils used in the multi-coil sensor.
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S. Tumanski / Journal of Magnetism and Magnetic Materials 242–245 (2002) 1153–1156
To obtain satisfying results of approximation the output signals of each coils should be distinctly separated. Thus, it is not recommended to place the coils very close each other. Fig. 7 presents the four output signals of the four-coil sensor with the coils distanced by 2 mm. The signals were pretty different and the approximation was easy to realise by appropriate software. The whole sensor was completed into one package in the form of a rectangular prism.
asymmetrical yoke system, the magnetic field above the steel sheet drops regularly and at a long distance. Using several H-coils it is possible to estimate the magnetic field directly at the sheet surface by simple extrapolation of the output signals of the coils. The sensor consisting of three H-coils distanced by 2 mm has been constructed and tested with satisfying results.
References 4. Conclusions The presented numerical and experimental analysis of the field above the steel sheet shows that it is not necessary to place the sensor extremely close to the investigated surface. Moreover, it is not necessary to design the sensor as very thinFthicker sensor enables to obtain better sensitivity. Especially in the case of
. [1] H. Pfutzner, . P. Schonhuber, IEEE Trans. Magn 27 (1991) 778. [2] H. Pfutzner, . Z. Elektr. Inf. Energ. 10 (1980) 534. [3] S. Tumanski, J. Magn. Magn. Mater. 75 (1988) 266. [4] T. Nakata, et al., IEEE Trans. Magn. 23 (1987) 2596. [5] S. Tumanski, M. Stabrowski, Meas. Sci. Technol. 9 (1998) 488. [6] S. Tumanski, T. Bakon, J. Magn. Magn. Mater. 223 (2001) 315.
A multi-coil sensor for tangential magnetic field investigations S. Tumanski* Warsaw University of Technology, Institute of Electrical Theory and MeasurementsFIETiME, Koszykowa 75, 006-61 Warsaw, Poland
Abstract The magnetic field above the steel sheet was analysed numerically and experimentally. It was estimated that this magnetic field drops very regularly and slowly (about 10% for 10 mm of the distance). Thus, it is possible to approximate the measured data obtained from several sensors into H ¼ f ðxÞ dependence. Next, this dependence can be used to extrapolate the measured results into the sheet surface. The design of multi-coil sensor is discussed and the model of such a sensor is tested. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Sensors; Electrical steel; Magnetic field; Magnetic measurements
1. Introduction The magnetic field strength in electrical steel sheet can be determined using the indirect method (applying the Ampere’s lawFby measurement of magnetising current) or direct method (by measurement of the tangential field component above the sheet) [1]. The first method can be used only if the length of the magnetic path is well defined, for example in the case of the ring core or Epstein frame. But to tell the truth even in such cases the length of the magnetic path is never known exactly and it is rather established as some kind of agreement (for example, a length of 0.94 m in the case of 25 cm Epstein frame). In the direct method it is assumed that the tangential component of the magnetic field strength is the same in the sheet sample and directly above the surface of the sample. Thus, using the sensors of tangential magnetic field it is possible to determine the magnetic field strength in the sample even if the length of the magnetic path is unknown. To detect the tangential magnetic field various sensors are usedFflat inductive coil (the socalled H-coil), half-ring inductive coil (Rogowski coil), Hall sensors [2] or thin film permalloy magnetoresistive sensors [3].
The H-coil sensors are the most frequently used because they are relatively easy to prepare. Other advantages of the H-coil sensors are as follows: unlimited range of the measured field and excellent linearity, easy to obtain the averaging effect due to large area of the sensor, immunity to the orthogonal field component. The main drawback of this sensor is the necessity of the integration of the output signal, because it depends on the derivative dH=dt: Other important disadvantage of the H-coil sensor is its small sensitivity. To obtain reliable results of measurements the sensor should be placed extremely close to the sheet surface. It should also be as thin as possible. On the other hand, the sensitivity of the H-coil depends on its cross-sectionFto obtain the large output signal the coil should be sufficiently thick. To overcome this discrepancy Nakata proposed to use the two-coil system distanced from the sheet [4]. In such system the magnetic field on the sheet surface can be estimated by the extrapolation of the measurement results into the tested plane. Following the idea of Nakata the multi-coil system has been analysed and tested.
2. The magnetic field above the sheet
*Tel.: +48-22-660-75-25; fax: +48-22-629-29-62. E-mail address: [email protected] (S. Tumanski).
The tangential component of the magnetic field above the sheet has been analysed numerically and experimentally. Fig. 1 presents the results of calculations of
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 1 3 0 2 - 6
1154
S. Tumanski / Journal of Magnetism and Magnetic Materials 242–245 (2002) 1153–1156
Fig. 1. The calculated distribution of magnetic field strength in C-yoke (a) and 2C-yoke (b) circuits (grey-scale the same as in Fig. 3). Fig. 3. The distribution of magnetic field above and under the GO steel on C-yoke (a) and 2C-yoke (b) tested area 3 3 cm.
Fig. 2. The dependence of the field around the stripe versus distance form the sheet calculated for 1C and 2C yoke system.
magnetic field strength for the case of 3 cm stripe on the C or 2C yoke with poles 25 30 mm distanced by 8 cm. It was assumed that the air gap is equal to 0.01 mm. The calculations were performed using 3D OPERA software of Vector Fields. Magnetising conditions have been selected to obtain the flux density of about 1.3 T in GO steel. Fig. 2 presents the dependence H ¼ f ðxÞ determined numerically for the field in the central part of the stripe. Similar investigations have been performed experimentally applying the magnetovision method [5]. The maps illustrating the distribution of the magnetic field around the stripe are presented in Fig. 3. The main difference between calculated and experimental data is caused by the heterogeneity of the grainoriented steel (not taken into account in the numerical model). To compare both results the H ¼ f ðxÞ dependency was this time calculated as the average value for 3 3 cm area (Fig. 4). For investigations of electrical steel the 2C yoke is usually strongly recommended. But the application of
Fig. 4. The dependence of the magnetic field above the steel sheet versus distance from the sheet determined experimentally.
the multi-coil system seems to be more difficult in this case. The decrease of the field versus the distance is less significant and to obtain sufficient difference of the coil signals the sensors should be more distanced. This separation of the sensors is limited by the construction of the yoke. Moreover, very close to the sheet surface the dependence H ¼ f ðxÞ is disturbed by the stray field from domain and grains boundaries. Thus, the first coil should be inserted with certain distance (about 1–3 mm) from the sheet. In certain applications the asymmetrical C-yoke cannot be substituted by a 2C yoke. For example, author developed the measuring system for 2D measurements using movable C-yoke [6]. Surprisingly for multicoil measurements this system is advantageous. The magnetic field above the sheet drops very regularlyFabout 10% for the 10 mm of the distance. Thus the sensor can be placed above the sheet even with a
S. Tumanski / Journal of Magnetism and Magnetic Materials 242–245 (2002) 1153–1156
distance of several millimetres and it is not necessary to place the coil directly close to the sheet surface.
3. The design of the multi-coil sensor The output signal of the sensor E can be calculated using the expression: E ¼ 8p2 107 fzðt þ dÞðw þ dÞ H;
ð1Þ
where t and w are the thickness and the width of inner dimensions of the coil. d is the diameter of the wire, z is the number of turns and f is the frequency. The H-coil with dimensions 25 25 mm and inner thickness 0.5 mm wounded using 0.1 mm wire (about 150 turns) exhibited a sensitivity of only 0.8 mV/(A/m). This corresponds with the output signal of about 20 mV for the typical grain-oriented steel at a flux density of 1 T. The sensitivity can be enlarged using thinner wire. The sensor with the same dimensions but wounded with a wire of diameter 0.05 mm (about 400 turns) exhibited a sensitivity of about 3 mV/(A/m) (see Table 1). As the magnetic field drops very regularly the coils have not to be very thinFit can be designed even as the multi-layer coil. For the multi-layer coil with thickness T the expression (1) can be rearranged into: E ¼ 4p2 107 f
ðT tÞw ðt þ dÞðw þ dÞH: d2
0.5 0.5 0.5
The multi-layer H-coil of thickness T ¼ 1 mm wounded with a 0.05 mm wire exhibited a sensitivity of 22 mV/(A/m). Fig. 5 presents the dependence of the field above the stripe versus the distance tested using the H-coil sensor. This dependence is close to linearFthe non-linear part 0:01x2 was smaller than 0.2%. But random deviations from the linear approximation line was sometimes larger than 1%. Thus, the application of only two coil sensors may result in quite significant incidental error. Three or better four coil sensors ensures enhanced reliability of the whole measuring system due to better accuracy of approximation. After substitution of the two-coil system by three-coil one, the author estimated that nonrepeatability of measured results enhanced from part of percent to the hundredth part of percent. Fig. 6 presents two examples of the multi-coil sensor design. Author applied the multi-coil sensor for two-dimensional measurements [6]. In such case, both components of the magnetic field can be measured using the multicoil system with orthogonal sensed H-coil sensors (Fig. 6b).
(a)
(b)
ð2Þ
Table 1 The parameters of the H-coil sensors t (mm)
1155
w (mm)
d (mm)
z
S (mV/(A/m))
20 25 25
0.1 0.05 0.05
150 400 2000
0.84 2.8 22
Fig. 6. The multi-coil sensor design (a) three-coil sensor, (b) sensor for two-dimensional measurements.
A/m
60
40
20
0
-20
-40
-60
-80 0.0
Fig. 5. The dependence of the field above the stripe versus distanceFdetermined using H-coil sensor.
0.5
1.0
1.5
2.0
2.5
Fig. 7. The output signal of the four coils used in the multi-coil sensor.
1156
S. Tumanski / Journal of Magnetism and Magnetic Materials 242–245 (2002) 1153–1156
To obtain satisfying results of approximation the output signals of each coils should be distinctly separated. Thus, it is not recommended to place the coils very close each other. Fig. 7 presents the four output signals of the four-coil sensor with the coils distanced by 2 mm. The signals were pretty different and the approximation was easy to realise by appropriate software. The whole sensor was completed into one package in the form of a rectangular prism.
asymmetrical yoke system, the magnetic field above the steel sheet drops regularly and at a long distance. Using several H-coils it is possible to estimate the magnetic field directly at the sheet surface by simple extrapolation of the output signals of the coils. The sensor consisting of three H-coils distanced by 2 mm has been constructed and tested with satisfying results.
References 4. Conclusions The presented numerical and experimental analysis of the field above the steel sheet shows that it is not necessary to place the sensor extremely close to the investigated surface. Moreover, it is not necessary to design the sensor as very thinFthicker sensor enables to obtain better sensitivity. Especially in the case of
. [1] H. Pfutzner, . P. Schonhuber, IEEE Trans. Magn 27 (1991) 778. [2] H. Pfutzner, . Z. Elektr. Inf. Energ. 10 (1980) 534. [3] S. Tumanski, J. Magn. Magn. Mater. 75 (1988) 266. [4] T. Nakata, et al., IEEE Trans. Magn. 23 (1987) 2596. [5] S. Tumanski, M. Stabrowski, Meas. Sci. Technol. 9 (1998) 488. [6] S. Tumanski, T. Bakon, J. Magn. Magn. Mater. 223 (2001) 315.