GB2321709A - Thickness measurement - Google Patents

Abstract

Apparatus for measuring the thickness or cross-sectional area of a ferromagnetic sample comprises a source of magnetic flux Ne sufficiently powerful to magnetise the sample to saturation, means for positioning the sample in the vicinity of the source, a flux measurement device N B adapted to measure the magnetic polarisation of the sample, and a computational means for calculating the thickness of a sample from the measured saturation magnetic polarisation of the sample.

Description

THICKNESS MEASUREMENT The present invention relates to an apparatus and method for thickness or cross sectional area measurement of ferromagnetic materials.

It is applicable to ferromagnetic strip, rod or bar stock, amongst others.

Accurate thickness measurement is vital to the production of inter alia high quality electrical steels. In order to determine the power loss of electrical steel in the final finishing line, it is necessary to set accurately the magnetic flux density in the sheet. Accurate values for the cross-sectional area are therefore needed, for inputting into the instrumentation. Since the width and nominal density of the sheet are known, it is necessary to input a thickness value into the instrumentation. This value is normally obtained using radiation thickness gauges, based on gamma or x-ray absorption.

Accurate standards are required for calibration of such gauges.

Whilst these techniques for thickness assessment are well established, there are hazards associated with the use of ionising radiation. Other methods for thickness measurement have therefore been considered such as ultrasonic, eddy current, laser and inductive methods.

The present invention, on the other hand, derives the thickness data from the magnetic properties of the metal. The material is magnetised to saturation and cross-sectional area and thickness values are obtained from sensing the coil output voltages. From the cross-sectional area value, thickness can be calculated given knowledge of the width of the strip.

Sufficient accuracy is available since the saturation polarisation is known for steels of known silicon content. For a given composition of steel, particularly referring to % Si, the saturation magnetic polarisation value is essentially constant. In addition, when strip is magnetised to saturation, an output voltage is generated in a B sensing coil, and this value together with the known value of saturation magnetic polarisation can be inputted into the appropriate equation to generate a value for the strip thickness.

The present invention therefore provides an apparatus for measuring the thickness or cross-sectional area of a ferromagnetic sample1 comprising a source of magnetic flux sufficiently powerful to magnetise the sample to saturation, means for positioning the sample in the vicinity of the source, a flux measurement device adapted to measure the magnetic polarisation of the sample, and a computational means for calculating the thickness of a sample from the measured saturation magnetic polarisation of the sample.

The present invention also provides a method of measuring the thickness or cross-sectional area of a sample of ferromagnetic material, comprising the steps of; providing a source of magnetic flux of power sufficient to magnetise the sample to saturation; positioning the source so as to magnetise the sample to saturation; providing a flux measurement device in the vicinity of the sample's surface and measuring the magnetic polarisation of the sample; calculating the thickness or cross-sectional area of the sample from the measured saturation polarisation of the sample.

The flux source is preferably an electro-magnet. Such an electromagnet preferably operates with alternating current, with a suitable frequency being about 50Hz.

The flux measurement device is preferably a test coil.

The computational means is preferably a computer, suitably programmed.

In a particularly preferred form of the invention, the flux source and the flux measurement device are coupled via a mutual inductor. This enables the quiescent reading (i.e. the reading in the absence of a sample) to be cancelled out. It is further preferred that the mutual inductor is variable with respect to its coupling so as to simplify the process of adjustment.

Where a mutual inductor is provided, it is preferred that it is greater than one metre from the flux source and flux measurement device. This prevents unwanted excess coupling between various devices.

The thickness values as determined by any given technique are usually calibrated in terms of another system traceable to national standards, such as gauge by weight or density method (traceable via mass and dimensions) or micrometer (dimensions). The system of the present invention can be related to the techniques of gauge by weight etc and radiation thickness measurement by straightforward correlation.

The essential requirements of a thickness measuring system are good repeatability and good resolution of measurements. The preferred embodiments of the present invention are capable of satisfying these requirements.

To provide a better understanding of the present invention, the arrangement and results of a prototype set-up embodying the invention will be described by way of example,together with a discussion of the results and the conclusions that can be obtained therefrom. The accompanying figures are as follows: Figure 1 is a schematic illustration of a prototype arrangement for measurement of electrical steel properties according to the present invention; Figure 2 is an illustration of an electrical circuit for use with Figure 1; Figure 3 shows the measured magnetic field within the solenoid of Figure 1; Figure 4 shows illustratively the mutual inductor of Figure 2; Figure 5 shows results in the form of magnetic field strength versus exciting current with and without a sample present; Figure 6 shows the effect of compensation on magnetic polarization measurement; Figure 7 shows the effect of orientation on magnetic polarisation measurement; Figure 8 shows the variation in thickness along a typical steel strip measured with a micrometer to 0.02mm accuracy; Figure 9 shows the effect of silicon content of the steel strip on saturation magnetic polarization; Figure 10 shows results in the form of emf against thickness for strips of a nominal silicon content of 0.2%, part (a) showing emf against exciting magnetic field, part (b) showing emf against thickness of the samples at the peak magnetic field strength of 1 40 kA/m, part (c) showing emf against cross sectional area of the samples at the peak magnetic field strength of 140 kA/m; Figure 11 shows a second embodiment of the present invention in the form of a computer-controlled version of the arrangement of Figure 1; Figure 1 2 shows illustratively an arrangement for measuring the exciting current in the circuit indicated in Figure 11 using a Hall effect current transducer; Figure 1 3 illustrates the switching circuit for use in Figure 11, part (a) showing the thyristor phase angle trigger module circuit diagram, part (b) showing the waveform at different parts of the circuit; Figure 1 4 illustrates the measurement of frequency by cascading two timers; Figure 1 5 illustrates the analogue to digital convertor and related controller; Figure 1 6 shows flow charts for the software for use on the computer of Figure 11, part (a) showing the main program, part (b) showing the interrupt service subroutine for detecting a rising edge in the exciting current, part (c) showing the interrupt service subroutine for analogue to digital conversion.

Figures 1 and 2 show the prototype set-up for measuring the crosssectional area or thickness of an electrical steel strip with the saturation magnetic polarisation method. The magnetic field in the strip is produced by a coil wound on a small Tufnol (TM) former. This exciting coil is energised with a sinusoidal voltage of 50Hz from the mains power supply through an isolating transformer. The peak value of the exciting current is measured by means of a non-inductive resistor Rs and a peak detector. The magnetic flux in the strip is measured by a B-coil (NB) wound inside the exciting coil as shown.

In order to obtain an e.m.f. that is just proportional to the crosssectional area and the magnetic polarisation of the strip, the primary winding of a variable mutual inductor is connected in series to the exciting coil while its secondary winding and the B-coil are connected in series opposition. The e.m.f. induced in the B-coil is:

d# dB(t) dH(t) eB(t) =NB =NBAS. +(AB-AS) 0. (1) dt dt dt where B(t), the longitudinal component of the spatial instantaneous flux density in the specimen, is defined as B(t)=J(t)+ 0.H(t) (2) H(t), the longitudinal component of the instantaneous applied magnetic field intensity, is assumed to be of the same value, inside and outside the specimen. This field is proportional to the exciting current, i.e.

H(t) =Kr.i1 (t) (3) Substituting equations (3) and (2) into (1), then

eB(t)=NB.AS. +AB.KI. 0. (4) dt dt where: Ne = the number of turns of the B-coil, As = the cross sectional area of the strip, As = the cross section of the B-coil, J(t) = the instantaneous magnetic polarisation in the strip H(t) = the instantaneous magnetic field strength inside and outside the strip, i1(t) = the instantaneous exciting current, KI = a constant specified by the solenoid. eB(t) in equation (4) consists of two parts: the first part is related to the magnetic polarisation and the cross-sectional area of the strip, and the second part, which is not influenced by the presence of the strip, is only proportional to the exciting current and the cross-sectional area of the B-coil.

The e.m.f. induced in the secondary winding of the mutual inductor is: di1(t) em(t)=Mm. (5) dt where: Mm = the mutual inductance of the mutual inductor, i1(t) = the exciting current in the primary coil.

Combining equations (4) and (5), the differential e.m.f. induced in the mutual inductor and the B-coil is then:

After full-wave rectification, the average value of ed(t) is:

Without strip EU=O Eo can be cancelled out by adjusting the mutual inductance Mm. If a strip is positioned inside the solenoid, it can be shown that the average induced voltage is then given by: = = EM = 4.f.NB.AS.Jpeak (9) Ed is hence only proportional to the cross-sectional area and the peak magnetic polarisation of the strip. In other words, if a strip of known saturation polarisation is saturated, its cross-sectional area can be obtained by measuring the value of Ed in equation (9).

The average value of Ed can be measured with the ac function of a mean sensing multimeter. Since the reading on the ac function is r.m.s. calibrated for sinusoidal signal, the ratio of the reading to the average value of the signal measured is a constant of #= = . So that 2.

substituting equation (10) into equation (9), then

Because of its equal tangential component at either side of the air-strip boundary, the magnetic field strength inside the strip can be measured with an H-coil close to its surface. The e.m.f. induced in the H-coil is also measured with an average type multimeter, so that the peak value of the magnetic field strength in the strip is J2 n read (12) 2.#.AH.NH.f where: AH = the area of the H-coil, NH = the number of turns of the H-coil.

As shown in Figure 1, the solenoid consists of an outer exciting coil and an inner B-coil, both of which are wound on a non-magnetic, insulating rectangular former.

It has been shown that in order to saturate electrical steel strip, the magnetic field in the solenoid should be more than 60 kA/m. In the experimental set-up, a 3060 turn coil was wound with 1.0mm diameter copper wire on a former length 200mm.

The average values of the width and the height were W = 54mm I G = 31 mm separately. The ratio of the magnetic field strength to the exciting current as measured with an H-coil is shown in Figure 3.

To compensate for the e.m.f. induced by the air flux in the B-coil, the mutual inductance Mm of the inductor was chosen from 0 to 0.2 mH with a resolution of 0.1%, its configuration being depicted in Figure 4. In the Figure, a screw bar 4 is used to drive the secondary winding 3 to move along the former of the primary winding 2, which is fixed on to stand 1.

The primary winding of 110 turns, wound side by side with two parallel connected copper wires of 1 .5mm in diameter, can carry a maximum current of 1 OA (r.m.s.). The secondary winding of 337 turns is wound with a copper wire of diameter 0.2mm in one layer.

The compensation is done in the following steps. Firstly, without specimen, the exciting current is chosen to be the maximum value of 10 A r.m.s. Secondly, the mutual inductor is adjusted carefully until the differential e.m.f. induced at the ends of the B-coil and the secondary winding of the mutual inductor is of a minimum value. Then the exciting current is changed in steps to confirm the correct compensation.

Specimens for use in the above experimental set-up were prepared as follows.

As listed in Table 1, forty-two groups of oriented and non-oriented electrical steel specimens corresponding to a range of thickness were obtained and classified according to their silicon contents.

In each group, half the specimens were cut parallel to and the other half normal to the rolling direction of the strips by a method that produced clean, burr-free-edges and minimum stress on the specimens. The sample widths of 30 t 0.2mm were measured with a vernier micrometer of 0.02mm in resolution and their lengths of approximate 180 (or 305)+0.5mum were measured with a ruler with a resolution of 0.5mm. Their compositions were analysed on the second transverse specimen of each group and densities were calculated according to the British Standard (BS6404: part 2). The thicknesses of these specimens were measured with a micrometer, as well as calculated using the following equations.

Cross sectional area = Weight Length x Density (13) Thickness = Cross sectional area Width An H-coil was used to measure the x-component of the magnetic field strength in the solenoid with and without a sample present.

Table 1 Specification of electrical steel specimens

Nominal Identity Si (%) Al (%) Fe (%) Total of P(Si) < 4% 0.17P(Si)- Density Weight Length Width Thickness Thickness Error silicon number others 0.28 < P(Al) (Kg/m ) (g) (mm) (mm) calculated measured t1-t2 content (%) < 0.17P(Si) t1 (mm) with + 0.28 micrometer t2 (mm) ATO.1-2 0.1211 0.0341 99.45 0.39 TRUE TRUE 7853 26.52 178.7 29.9 0.632 0.649 -0.017 BTO.1-2 0.1037 0.0498 99.44 0.41 TRUE TRUE 7853 27.17 180.0 30.1 0.639 0.655 -0.016 CTO.1-2 0.1071 0.0382 99.43 0.42 TRUE TRUE 7854 26.68 179.0 30.1 0.630 0.647 -0.017 DTO.1-2 0.1080 0.0355 99.44 0.42 TRUE TRUE 7854 26.61 178.7 30.1 0.630 0.652 -0.022 ETO.1-2 0.1112 0.0386 99.44 0.41 TRUE TRUE 7854 26.86 179.6 30.1 0.633 0.648 -0.015 GTO.1-2 0.1096 0.0333 99.45 0.41 TRUE TRUE 7854 27.08 181.0 30.1 0.633 0.650 -0.017 HTO.1-2 0.1120 0.0353 99.44 0.41 TRUE TRUE 7854 26.93 180.6 30.1 0.631 0.646 -0.016 Si = 0.1 HTO.1-2 0.1039 0.376 99.44 0.42 TRUE TRUE 7854 26.62 177.4 30.1 0.635 0.650 -0.015 JTO.1-2 0.1154 0.0402 99.41 0.43 TRUE TRUE 7853 26.84 179.5 30.1 0.633 0.650 -0.017 KTO.1-2 0.0931 0.0281 99.44 0.44 TRUE TRUE 7856 26.70 179.0 30.0 0.633 0.649 -0.016 MTO.1-2 0.1113 0.0403 99.42 0.43 TRUE TRUE 7853 27.25 180.7 30.1 0.638 0.655 -0.017 NTO.1-2 0.1065 0.0429 99.45 0.40 TRUE TRUE 7853 27.26 179.5 30.1 0.642 0.659 -0.017 RTO.1-2 0.0944 0.0301 99.43 0.45 TRUE TRUE 7856 27.39 180.2 30.1 0.643 0.660 -0.017 STO.1-2 0.1109 0.0361 99.42 0.43 TRUE TRUE 7854 27.03 179.7 30.1 0.636 0.653 -0.017

Nominal Identity Si (%) Al (%) Fe (%) Total of P(Si) < 4% 0.17P(Si)- Density Weight Length Width Thickness Thickness Error silicon number others 0.28 < P(Al) (Kg/m ) (g) (mm) (mm) calculated measured t1-t2 content (%) < 0.17P(Si) t1 (mm) with + 0.28 micrometer t2 (mm) BTO.2-2 0.2150 0.0346 98.85 0.90 TRUE TRUE 7847 27.48 178.9 30.1 0.650 0.671 -0.021 CTO.2-2 0.1853 0.0343 99.03 0.75 TRUE TRUE 7849 27.83 180.3 30.2 0.651 0.670 -0.019 DTO.2-2 0.2392 0.0289 99.01 0.72 TRUE TRUE 7846 20.52 179.5 29.8 0.489 0.508 -0.019 ETO.2-2 0.2408 0.0303 99.02 0.71 TRUE TRUE 7846 20.46 178.8 30.0 0.490 0.510 -0.020 FTO.2-2 0.2349 0.0419 99.06 0.66 TRUE TRUE 7845 31.22 179.2 30.1 0.738 0.757 -0.019 JRO.2-2 0.2255 0.0382 99.10 0.64 TRUE TRUE 7846 31.57 180.2 30.1 0.742 0.759 -0.017 Si = 0.2 KTO.2-2 0.2096 0.0425 98.77 0.98 TRUE TRUE 7847 27.33 179.6 30.1 0.644 0.668 -0.024 MTO.2-2 0.2066 0.0421 98.77 0.98 TRUE TRUE 7847 27.65 180.3 30.1 0.649 0.871 -0.022 OTO.2-2 0.2282 0.0409 99.08 0.65 TRUE TRUE 7846 31.18 179.1 30.1 0.737 0.757 -0.020 RTO.2-2 0.2086 0.0286 98.99 0.77 TRUE TRUE 7848 20.86 179.8 30.1 0.491 0.509 -0.018 STO.2-2 0.2314 0.0396 99.08 0.65 TRUE TRUE 7846 20.92 178.9 30.1 0.495 0.512 -0.017 CTO.5-2 0.5045 0.1281 98.91 0.46 TRUE TRUE 7818 20.29 180.0 30.1 0.479 0.481 -0.001 ITO.5-2 0.5030 0.1495 98.89 0.46 TRUE TRUE 7816 20.50 179.6 30.2 0.484 0.490 -0.006 Si = 0.5 JTO.5-2 0.5075 0.1281 98.91 0.45 TRUE TRUE 7818 20.43 177.9 30.1 0.488 0.490 -0.002 CTI.3-2 1.3000 0.1382 98.23 0.33 TRUE TRUE 7765 20.79 179.8 30.1 0.495 0.500 -0.005 FTI.3-2 1.3090 0.1350 98.19 0.37 TRUE TRUE 7765 20.29 179.8 30.1 0.483 0.490 -0.007 Si = 1.3 KTI.3-2 1.3060 0.1538 98.20 0.34 TRUE TRUE 7763 26.65 179.4 30.1 0.636 0.643 -0.007

Nominal Identity Si (%) Al (%) Fe (%) Total of P(Si) < 4% 0.17P(Si)- Density Weight Length Width Thickness Thickness Erro silicon number others 0.28 < P(Al) (Kg/m) (g) (mm) (mm) calculated measured t1-t2 content (%) < 0.17P(Si) t1 (mm) with +0.28 micrometer t2 (mm) CTI.8-2 1.7720 0.3678 97.54 0.32 TRUE TRUE 7709 20.92 179.0 30.1 0.504 0.510 -0.006 DTI.8-2 1.8140 0.3889 97.47 0.33 TRUE TRUE 7704 20.32 179.4 30.1 0.489 0.492 -0.003 Si=1.8 ETI.8-2 1.8120 0.3831 97.46 0.34 TRUE TRUE 7705 26.68 180.0 30.2 0.637 0.640 -0.003 AT2.9-2 2.9020 0.0000 96.94 0.16 TRUE FALSE FALSE 8.93 176.0 30.1 FALSE 0.229 FALSE BT2.9-2 2.9590 0.0000 96.98 0.16 TRUE FALSE FALSE 8.93 177.6 29.9 FALSE 0.227 FALSE CT2.9-2 2.9520 0.0000 96.94 0.11 TRUE FALSE FALSE 11.86 177.5 30.1 FALSE 0.299 FALSE DT2.9-2 2.9860 0.000 96.90 0.11 TRUE FALSE FALSE 11.61 176.8 30.1 FALSE 0.298 FALSE Si=2.9 ET2.9-2 2.9870 0.0000 96.82 0.19 TRUE FALSE FALSE 10.35 177.6 30.1 FALSE 0.262 FALSE FT2.9-2 2.9980 0.0000 96.81 0.19 TRUE FALSE FALSE 10.33 177.6 30.1 FALSE 0.258 FALSE GT2.9-2 2.9300 0.0000 96.90 0.17 TRUE FALSE FALSE 13.69 176.6 30.1 FALSE 0.342 FALSE HT2.9-2 2.9170 0.0000 96.92 0.16 TRUE FALSE FALSE 13.48 178.5 29.9 FALSE 0.335 FALSE As a result of the redistribution of the magnetic field caused by the presence of the specimen, the measured magnetic field is decreased by 4.5%. But this decrease will not affect the measurement of saturation magnetic polarisation when the specimen has been fully saturated (see Figure 5). The relationship between the exciting current and the magnetic field strength was found (in the particular set-up employed) to be: H,(peak) = 9.61 (peak) (14) H5(peak) = 9.224(peaA) (15) where H(peak) and ln(peak) are the peak values of magnetic field strength and exciting current when no specimen is in the solenoid, H,(peak) and ls(peak) are the peak values of magnetic field strength and exciting current when a specimen is in the solenoid.

A 0.1% silicon specimen (ATO.1-2) was then positioned at the centre of the solenoid. For compensated and uncompensated situations, the exciting current was changed from 0 to 10A (r.m.s.) and the differential e.m.f. induced in the mutual inductor and the B-coil was recorded using an average type multimeter (Thurlby 1503). The peak values of the magnetic field strength were calculated from equations (14), (15) and that of the exciting current were measured with the peak detector. The curves of e.m.f. against the magnetic field are drawn in Figure 6.

Curve 1, measured without compensation, increases linearly with the magnetic field when Hp > 7OkA/m. This means that the specimen is saturated and the increase of e.m.f. is due to the increase of the magnetic field strength in the air. This result was further confirmed by curve 3 measured when the air flux was compensated. Curve 2 shows that the e.m.f. induced in the mutual inductor increases with the same slope as that of curve 1 in the higher magnetic field range. Hence, the above described magnetic polarisation is capable of producing an e.m.f. substantially independent of external factors.

As shown in Figure 7, two 0.1% Si specimens from one group but with different orientations were measured with the experimental set-up when the r.m.s. value of the exciting current was changed from 0 to 10A. In the measurement, the peak value of the exciting current was obtained by sampling the voltage across the non-inductive resistor R5, as shown in Figure 1, using a peak detector. The magnetic field was calculated from equation (15). The cross-sectional areas and the thicknesses of these specimens were obtained from equation (13).

In the range of the magnetic field smaller than 60kA/m, the magnetic polarisation of the specimen along the rolling direction is higher than that in the transverse direction. Both of their magnetisation curves increase non linearly with the magnetic field. In the range of exciting magnetic field strength greater than 60kA/m, both specimens are saturated and the difference between their saturation magnetic polarisation is smaller than 0.1%.

When the applied magnetic field strength is higher than 1 OOkA/m, the increase of the saturation magnetic polarisation is lower than 0.08% for a 20% increase of the magnetic field strength. This means that, to some degree, the accuracy of the saturation magnetic polarisation measurement will not be influenced by the fluctuation of the exciting current and further increasing the magnetic field strength seems not necessary for measurement with a required accuracy of 0.1%.

As shown in Tables 2 and 3, the saturation magnetic polarisation of eleven specimens with the main composition of 0.1 % silicon (ATO. 1-1 -12) and twenty-three of 2.9% silicon (AT2.9-1 ~ 24) were measured. The lengths and widths of the specimens were first measured with a ruler of 0.5mm in resolution and a vernier micrometer of 0.02mm in accuracy, respectively. The measurements were averaged over three points.

The differential e.m.f. was measured with an average type multimeter at the constant exciting current of 10A (r.m.s.). The saturation magnetic polarisation of each specimen was calculated from equation (11).

Because of the variation in thickness, the average deviation of saturation magnetic polarisation for these specimens from the same original sheet is approximately 0.002T or around 0. 1% of their saturation magnetic polarisation. The e.m.f. induced in the B-coil is only proportional to the local cross-sectional area where the B-coil is located. But the cross-sectional areas listed in Table 2 and 3 are the average ones. Due to the variation in thickness verified in Figure 8, the average cross-sectional areas may be different from the local ones. So, in order to determine the saturation magnetic polarisation more accurately, a more accurate knowledge of the local cross-sectional areas is essential.

As shown in Table 4, specimens with different silicon contents were classified according to the thicknesses of the samples, which was obtained by the method described above. Each of these specimens was located, separately, in the solenoid with the same lengths of overhang on both sides of the solenoid, and its saturation magnetic polarisation value was measured at the exciting current of 1 OA (r.m.s.) as well as plotted against their silicon contents. This is shown in Figure 9.

This Figure shows that the saturation magnetic polarisation value of these specimens decreases linearly by around 0.05T with a 1% increase of silicon content. This agrees well with the result investigated by Gumlich (Gumlich, E., 1918). As long as their silicon content is the same, these specimens are of identical saturation magnetic polarisation value even though their thicknesses are different.

Table 2 Saturation Magnetic Polarisation values for 0.1% silicon strips

Composition Identity Weight (g) Length (mm) Width (mm) Thickness Cross- Induced Saturation number calculated sectional area average magnetic t1 (mm) (mm) volage (mV) polarisation at I = 10A (T) ATO.1-1 45.81 306.5 30.04 0.6335 19.03 178.9 2.117 ATO.1-3 46.04 306.5 30.09 0.6357 19.13 179.5 2.113 ATO.1-4 45.80 306.5 30.07 0.6328 19.03 178.7 2.114 ATO.1-5 46.13 306.5 29.83 0.6426 19.17 179.6 2.110 Si = 0.1211 ATO.1-6 46.13 306.5 29.93 0.6404 19.17 179.5 2.109 Al = 0.0341 ATO.1-7 46.07 306.5 30.01 0.6377 19.14 179.5 2.112 Fe = 99.45 ATO.1-8 45.60 306.5 30.05 0.6305 18.95 177.8 2.113 Density = ATO.1-9 45.80 306.5 30.10 0.6322 19.03 178.6 2.113 7853kg/m ATO.1-10 45.73 306.5 30.05 0.6323 19.00 178.2 2.112 ATO.1-11 46.05 306.5 29.99 0.6380 19.13 179.2 2.109 ATO.1-12 46.11 306.5 29.97 0.6392 19.16 179.5 2.110 Aver. value 30.01 0.6359 19.08 179.0 2.112 Aver. 0.20 0.53 0.37 0.28 0.09 deviation (%) Table 3 Saturation Magnetic Polarisation values for 2.9% silicon strips

composition Identity Weight Length Width Thickness Cross- Induced Saturation number | (g) | (mm) | (mm) | calculated | sectional | average | Magnetic tl (mm) area voltage Polarisation (mm) | (mV) | at I=10A (T) GT2.9-1 23.26 305.0 29.74 0.3346 9.95 88.4 2.00 GT2.9-3 23.83 305.0 30.14 0.3381 10.19 90.4 2.00 Si= 2.9300 GT2.9-4 23.76 305.0 30.16 0.3372 10.16 90.1 2.00 Al = 0.0000 GT2.9-5 23.77 305.0 30.14 0.3371 10.17 90.0 l.99 Fe = 96.90 GT2.9-6 23.70 305.0 30.18 0.3363 10.14 90.0 2.00 Density = GT2.9-7 23.51 305.0 30.12 0.3332 10.05 89.2 2.00 7666 kglm GT2.9-8 23.91 305.0 30.16 0.3395 10.23 90.5 1.99 GT2.9-9 23.74 305.0 30.12 0.3366 10.15 89.9 1.99 GT2.9-10 23.84 305.0 30.22 0.3385 10.20 90.3 1.99 GT2.9-11 23.84 305.0 30.14 0.3375 10.20 90.4 2.00 GT2.9-12 23.41 305.0 30.18 0.3322 10.01 88.8 2.00 GT2.9-13 23.02 305.0 29.76 0.3263 - 9.85 . 87.3 2.00 GT2.9-14 23.76 305.0 30.18 0.3414 10.16 90.1 2.00 GT2.9-15 23.91 305.0 30.19 0.3388 10.23 90.6 1.99 GT2.9-16 23.81 305.0 30.18 0.3373 tO.18 90.1 1.99 GT2.9-17 23.85 305.0 30.18 0.3380 | 10.20 | 90.4 2.00 GT2.9-18 23.71 305.0 30.16 0.3360 10.14 89.8 1.99 GT2.9-19 23.59 305.0 30.10 0.3345 10.09 89.5 2.00 GT2.9-20 23.86 305.0 30.12 0.3391 10.21 90.3 1.99 GT2.9-21 23.80 305.0 30.16 0.3380 10.18 89.8 1.99 GT2.9-22 23.76 305.0 30.20 0.3370 10.16 89.9 1.99 GT2.9-23 23.78 305.0 30.16 0.3367 10.17 89.9 1.99 GT2.9-24 23.47 305.0 30.14 0.3328 10.04 88.9 1.99 Aver. value 23.69 305.0 30.12 0.3364 10.13 89.8 1.99 Aver. 0.66 0.00 0.23 0.65 0.69 0.63 0.12 deviation (%) Table 4 Effect of silicon content on saturation magnetic polarisation

Nominal Identity Si(%) Density Weight Length Width Thickness Cross e.m.f. at Freq. Saturation thickness number (kg/m ) (g) (mm) (mm) t1 (mm) sectional I=10A (Hz) magnetic (mm) area (mm) (mV) polarisation (T) STO.1-3 0.1109 7854 46.00 306.5 30.01 0.6368 19.11 178.6 49.94 2.107 ITO.1-3 0.1039 7854 45.90 306.5 30.02 0.6352 19.07 178.6 49.94 2.111 t=0.635 KT1.3-3 1.3060 7763 45.59 306.8 30.07 0.6365 19.14 174.6 49.93 2.057 EET-3 1.8120 7705 45.28 306.5 30.16 0.6357 19.17 172.0 49.94 2.022 RTO.1-3 0.0944 7856 46.52 306.5 29.94 0.6454 19.32 180.7 49.92 2.109 KTO.2-3 0.2096 7847 46.78 306.5 30.08 0.6467 19.45 181.2 49.92 2.101 BTO.2-3 0.2150 7847 46.88 306.5 30.17 0.6460 19.49 181.3 49.96 2.096 T=0.647 CTO.2-3 0.1853 7849 47.02 306.5 30.01 0.6513 19.54 181.9 49.95 2.098 MTO.2-3 0.2066 7847 46.83 306.5 30.02 0.6486 19.47 180.8 49.94 2.093 T=0.495 STO.2-3 0.2314 7846 35.87 307.0 30.00 0.4964 14.89 138.5 49.92 2.098 CT1.3-3 1.3000 7765 35.51 306.7 30.10 0.4954 14.91 135.8 49.92 2.054 T=0.484 ITO.5-3 0.5030 7816 35.02 307.0 30.14 0.4843 14.60 134.8 49.92 2.083 FT1.3-3 1.3090 7765 34.70 306.6 30.10 0.4842 14.57 132.5 49.93 2.050 For the strips with the same nominal silicon content, variation in saturation magnetic polarisation value, due to the silicon content change of no more than 0.1%, is as little as 0.005T or 0.25% of the nominal saturation magnetic polarisation value.

At room temperature, specimen ATO. 1-3 was measured in r.m.s., the period between two successive measurements being about thirty minutes.

The frequency of the exciting current was monitored with a frequency counter of 1 0-4Hz in resolution. All the measurements together with their average values and average deviations are listed in Table 5.

When the fluctuation of frequency is taken into account, the average deviation of the saturation magnetic polarisation is lower than that of the induced voltage. Further analysis showed that the deviation of saturation magnetic polarisation is mainly due to the accuracy (0.2% x read + 0.32 mV) of the multimeter, and the change of temperature produced by the power loss in the exciting coil. So, to enhance the accuracy of the measurement, stabilising the frequency of exciting current and using an average meter with higher accuracy to measure the induced voltage seems necessary.

Firstly, six specimens from different batches of 0.2% silicon strips were divided into three groups according to their thicknesses calculated from equation (13). Then, the e.m.f. induced by these specimens were measured using the experimental set-up. Figure 10 shows the results of the measurements in which the r.m.s. value of the exciting current was changed from 0 to 10 Ampere and the frequency of the exciting current was monitored with a high resolution frequency counter.

Table 5 Reproductibility of the saturation magnetic polarisation measurements

Measurements (at approx 30 minute intervals) Aver. Aver.

Value Dev(%) 1 2 3 4 5 6 7 8 9 10 Induced 179.5 179.4 179.5 179.3 179.4 179.5 179.6 179.5 179.8 179.6 179.5 0.052 Voltage (mV) Frequency 4.93 49.92 49.97 49.93 49.97 49.99 50.03 49.96 50.03 50.00 49.97 0.063 (Hz) Saturation 2.116 2.115 2.114 2.113 2.113 2.113 2.113 2.114 2.115 2.114 2.114 0.039 Magnetic Polarisation(T) It is seen from Figure 10 (a) that, as long as the peak value of the exciting field is more than 70kA/m, these specimens are magnetically saturated and the increase of the induced voltage is smaller than 0.15% for a 30% increase of magnetic field. Comparing Figure 10 (b) and (c), there is a higher degree of linearity in the induced voltage curves against the crosssectional area than those against the thicknesses of the specimens using the saturation magnetic polarisation method, the widths of the specimens must be measured with a good degree of accuracy.

The conclusions which can be reached from the above are as follows.

In the measurement of electrical steel strips by use of the above saturation magnetic polarisation method, the effect of silicon content on saturation magnetic polarisation can be easily compensated by the linear relationship between them. For strips of the same nominal silicon content, it is not necessary to compensate the influence of silicon content since only small variations occur among these strips. The uniform distribution of saturation magnetic polarisation in the strips from the same original sheet means that the differential induced e.m.f. is only proportional to the crosssectional area of the strips and is not influenced by their orientations.

Because of the variation in thickness along the length of the strips, the optimum B-coil design needs to be selected with the desired measurement in mind. A shorter B-coil may be used to measure the local cross-sectional area of a strip, but a longer one can be used to measure the average crosssectional area of the strip. In both cases, the waviness and slow vibration of the strip if used on the production line do not influence the e.m.f. induced in the B-coil. The saturation magnetic polarisation method is more suitable for the measurement of cross-sectional area than for the measurement of thickness since the latter is limited by the accuracy of the determination of width. One way to eliminate the error is to use wider strips (i.e. sheets) rather than the narrow ones. All the experiments show that the magnetic field produced by the solenoid has been high enough to fully saturate the specimens.

Owing to the minimum usage of active components, a good reproducibility has been realised in the experimental set-up. The compensation of air flux by the mutual inductor has been verified to be successful, the uncompensated voltage of lower than O.OlmV being only approximately 0.01% of the e.m.f. induced by a specimen. Coupling between the mutual inductor and the solenoid can be eliminated by separating them by at least im. Although stabilisation of the exciting current is not necessary, a variation of about 0.4% in frequency should ideally be compensated for in the measurement of saturation magnetic polarisation. The ratio of the induced voltage to the cross-sectional area of the specimen measured is approximately 9 mV/mm2.

The above prototype system can be improved by use of computer control. This would enable the whole process of measurement of magnetic properties of an electrical steel strip to be completed in seconds. The exciting current can be several times higher than when operated manually, and the measurement of electrical steel strips with high demagnetising factor, i.e. wider and shorter samples, can be carried out. Furthermore, the accuracy and reliability of the measurement can be enhanced by substituting some functions realised in the above embodiment through electronics with software.

Figure 11 shows the computerised set-up for measuring the magnetic properties of electrical steel strips under saturation magnetic polarisation conditions. As before, the magnetic field in the strip is produced by a coil energised with a sinusoidal voltage of 50Hz from the mains through an isolating transformer. Exciting current in the coil is measured with a Hall effect current transducer and sampled by an A/D converter. The magnetic polarisation in the strip is measured by sampling and then integrating the differential induced voltage between the B-coil (Ne), wound inside the exciting coil, and a compensating mutual inductor located outside. The zerocrossing of the exciting current, detected using a comparator, is used to start, stop and control the whole measurement process. The frequency of the exciting current is measured by counting a 1 MHz clock in one cycle of the exciting current. The exciting current is switched on/off by two thyristors controlled by a dc voltage from port PAO of the I/O board, via an SCR phase angle controller. Across the thyristors is an RC snubbed network and voltage-sensitive resistor connected in parallel to protect them. The amplitude of the exciting current is adjusted with a Variac.

Figure 1 2 shows in principle the method by which the exciting current is measured. The current 1exit in the wire will produce a proportional magnetic field at the gap of the core. The magnetic field in the gap is detected using a Hall-effect element. The Hall voltage across this element is linearly proportional to the magnetic field and hence the current 1exit flowing in the wire. The sensitivity of the transducer can be adjusted by changing the number of times that the current carrying wire passes through the centre of the core, i.e. "multi-turning". The main advantage of the transducer is its electrical isolation between the current carrying wire and the Hall-effect element, as well as its wide band of frequency that is required to measure the distorted exciting current in the experimental set-up. Such a transducer can measure a current range of 0-200A to 1% (at 230 C) in the frequency range from DC to 25kHz at a signal conditioning level of 200A4is.

The exciting current is controlled by thyristors, which in turn are controlled by a dc voltage from the host computer through a phase angle trigger, shown in Figure 13. The reference voltage from the mains power supply was first converted into a square wave and then used as the power supply for the two optically coupled isolators. The sawtooth signal from a synchronised ramp generator is compared with the applied trigger voltage.

When the sawtooth signal is bigger than the trigger voltage, a negative pulse is generated at the output of the comparator A2. Then, the isolator whose diode is positively energised will send out a trigger pulse. By adjusting the trigger voltage, the conducting phase angle of the thyristors can be varied from 0 to 1800. In the experimental set-up shown in Figure 1, the trigger voltage is chosen at either the maximum or the minimum, so that the resulted conducting phase angle is either 1800 or 00, and therefore the exciting current is maintained sinusoidal.

The frequency of exciting current is measured indirectly by counting a clock of fixed frequency in one cycle of the exciting current. as shown in Figure 14, both counter 1 and counter 2 are programmed into mode 3. The output of counter 1, which is generated by dividing a 4MHz clock by 4, is used as a clock of counter 2. The time constant of counter 2 is set as $FFFF, and its gate is switched by a square wave from a 1/2 frequency divider (see Figure 11). In the first half cycle of the square wave, the gate is high level engaged and counter 2 starts counting. In the second half cycle, when the low-level of the 72 square wave is detected via port PBO, counter 2 stops counting and the reading of counted number is carried out.

The counted number N and the frequency f of the exciting current are related by Td 1 N.Tc = = 1/f or f = (18) 2 NTc where: Tc is the cycle of clock 2, Td is the cycle of the output of 72 frequency divider f is the frequency of exciting current.

In the first set-up, the frequency of the exciting current is 50Hz, while the frequency of clock 2 is 1 MHz. So, in one cycle, the counter number is about 2x104, and hence the resolution of the frequency measurement is 2x104+1 z 1 or 0.005%.

The Analogue to Digital (A/D) converter is shown in Figure 1 5. A 12 bit A/D converter is wired for Mode 1 operation with parallel output format in bytes. Its conversion is initiated by a low going pulse on Convst that is generated by programming and cascading counter 0 and counter 1 of an 8253 interval timer on the same board in Mode 3 and Mode 2 separately to give a sampling rate of 40kHz. At the end of a conversion Busy goes low, and generates an interrupt request IRQ5 to the host computer. When it is acquainted, the host computer executes an interrupt service subroutine and read out the data converted in two steps, the reading of higher 4 bits is followed by the lower 8 bits. Since the 1 2 bit data is coded in the form of 2s complement with the most significant bit inverted, a transfer program has been used to transfer this into pure binary.

The two input voltages VM(t) and V,(t) of the A/D converter are sampled alternatively by switching a multiplex. Sampling rate for each channel is therefore half of the A/D sampling rate, i.e. 20kHz, and sampling points for each channel is around 400 for the input frequency of 50Hz.

To eliminate the influence of any instability of the components on the A/D board, the system is calibrated by sampling the reference voltage of a standard cell before each measurement is conducted.

Figure 1 6 shows the flow chart for the program. It starts by displaying a menu of three items on screen to allow the operator to choose.

With the selection of " 1", the program exits to DOS system, "3" draws a B H curve and displays parameters of the sample measured, and "2" starts a new measurement.

In the process of measuring a new sample, the first step is to initialise the system and switch on the thyristors by sending a high-level voltage to PAO. Then, when a rising-edge of the exciting current is detected, an interrupt service subroutine is executed and A/D conversion is started. After this, the computer waits for the interrupt request from the A/D converter.

When it is responded, the computer saves the converted data and alternates the channel to the other input voltage. A/D conversion will not be stopped until an interrupt requested by the next rising-edge of the exciting current is responded.

After the measurement for one cycle of the exciting current has been completed, the host computer compares the results obtained this time with the last one. If the difference between the two measurements is smaller than a critical value, the thyristors will be switched off, the sampled data is converted into voltages, and the results are displayed. If a new measurement is needed, the program will be restarted from the main menu again.

Through the above described computer-controlled system, the magnetic field produced by the experimental set-up can reach as high as 300 kA/m in about 0.6 seconds. Sampling frequency of the A/D board is 40kHz with a sampling number of 800, or 400 for each of the two channels, in one cycle of exciting current. The use of digital filter, digital integration and shifting compensation in software makes the design of hardware much easier. By limiting the maximum number of exciting current cycles, the overheating of the exciting coil has been eliminated.

It will be appreciated that the above described embodiments are set forth by way of example only. Hence, many variations thereto can be made whilst still employing the present invention.

Claims (11)

1. CLAIMS 1. Apparatus for measuring the thickness or cross-sectional area of a ferromagnetic sample, the apparatus comprising a source of magnetic flux sufficiently powerful to magnetise the sample to saturation, means for positioning the sample in the vicinity of the source, a flux measurement device adapted to measure the magnetic polarisation of the sample, and a computational means for calculating the thickness of a sample from the measured saturation magnetic polarisation of the sample.
2. 2. Apparatus as claimed in Claim 1 wherein the flux source is an electro magnet.
3. 3. Apparatus as claimed in Claim 2 wherein the electro-magnet operates with alternating current.
4. 4. Apparatus as claimed in any one of the preceding Claims wherein the flux measurement device is preferably a test coil.
5. 5. Apparatus as claimed in any one of the preceding Claims wherein the computational means is a computer, suitably programmed.
6. 6. Apparatus as claimed in any one of the preceding Claims wherein the flux source and the flux measurement device are coupled via a mutual inductor.
7. 7. Apparatus as claimed in Claim 6 wherein the mutual inductor is variable with respect to its coupling.
8. 8. Apparatus as claimed in Claim 6 or Claim 7 wherein the mutual inductor is at a distance greater than one metre from the flux source and flux measurement device.
9. 9. A method of measuring the thickness or cross-sectional area of a sample of ferromagnetic material, comprising the steps of; providing a source of magnetic flux of power sufficient to magnetise the sample to saturation; positioning the source so as to magnetise the sample to saturation; providing a flux measurement device in the vicinity of the sample's surface and measuring the magnetic polarisation of the sample; calculating the thickness or cross-sectional area of the sample from the measured saturation polarisation of the sample.
10. 10. Apparatus for measuring the thickness or cross-sectional area of a ferromagnetic sample substantially as herein described and as described with reference to the accompanying drawings.
11. 11. A method of measuring the thickness or cross-sectional area of a sample of ferromagnetic material substantially as herein described and as described with reference to the accompanying drawings.