CC BY
18
Metallurgy and Mineral Processing
UDC 621.3.08
METHOD OF INDUCTION CONTROL OF IRON WEIGHT FRACTION IN MAGNETITE ORE
Ivan N. BAZHENOV, Oleg O. BASOV
Russian Federation Security Guard Service Federal Academy, Orel, Russia
This paper analyzes the peculiarities of existing methods and means of induction control of magnetic susceptibility of the medium are analyzed. It is concluded that these means have a common drawback due to the low measurement accuracy caused by the wave-like dependence of the instrument sensitivity on the gap between the probe and the medium surface. The ways of increasing the instrument sensitivity and measurement accuracy of controlled parameters by means of inductive measuring transducers are revealed. A method for induction resonance control of iron weight fraction in magnetite ore has been developed, and its effectiveness has been estimated using simulation modeling. Practical recommendations for the development of quality control instruments for magnetite ores have been developed. A variant of the quality control unit layout for working with magnetite ores is proposed.
Keywords: method of resonance control of ore magnetic susceptibility, mutual inductance, measuring probe
How to cite this article: Bazhenov I.N., Basov O.O. Method of Induction Control of Iron Weight Fraction in Magnetite Ore. Zapiski Gornogo instituta. 2018. Vol. 230, p. 123-130. DOI: 10.25515/PMI.2018.2.123
Introduction. The main indicator for quality of raw materials for ferrous metallurgy enterprises is the content of the iron weight fraction in iron ore concentrate, the stability of which substantially affects the technical and economic performance of blast furnaces and the cost of cast iron. According to the mineral processing technology used at the end of each technological stage, it is necessary to maintain a certain iron weight fraction [1, 6]. The existing technical tools, such as X-ray and ultraviolet analyzers, are quite complex and expensive and do not allow solving the tasks of complex monitoring of the current iron percentage in the ore mass or after each technological stage at a processing plant [13, 14].
For non-destructive control and assessment of magnetite ore quality it is advisable to use the principle of measuring mutual magnetic induction between two inductance coils located at a fixed distance in a measuring probe. In this case, the sensitivity to the controlled parameter of the ore quality depends not only on the distance between the probe and the surface of the ore-bearing rock, but also on the relative positioning of these coils [2-4, 9].
The general method of induction control of the iron percentage in the ore composition is practically reduced to measuring the amplitude and phase of the signal transmitted to the receiving (measuring) coil from the source inductor, which forms an electromagnetic field in the kilohertz frequency range. In the probe design, these inductors are placed either parallel or perpendicular to the surface of the studied ore, and the percentage of iron in the ore is judged by the amplitude and phase of the signal at the output of the measuring coil [16, 17, 22]. With this indirect method of measuring the ore quality, the calibration of the control devices is carried out directly on specific samples of the ore mass, which differ in their mineralogical composition.
To control the ore processing, they also use magnetic induction signals in the working area of the magnetic separator [16, 17] or perform assessment of iron weight fraction in the concentrate using the signal of the normal component of the magnetic induction vector [14]. As part of the magnetic field sensors, magneto-sensitive resistors are sometimes used instead of the measuring inductors, but their use does not give significant advantages for the sensitivity of instruments controlling
the iron weight fraction in the concentrate. The accuracy of measuring the ore magnetic properties is affected by the methodological error caused by the wave-like dependence of the instrument sensitivity on the distance between the probe and the medium surface.
One of the options for increasing the measurement accuracy and the instrument sensitivity for monitoring the magnetic susceptibility of the ore is to increase the increment of the EMF AE on the receiving coil. To implement such an option, it is proposed to use the resonance mode of the probe. To obtain a resonance the capacitors are connected in parallel to the compensation and measuring coils. In this case, oscillatory circuits are formed, the resonance frequency of which must be set equal to the generator frequency: fr = LnCn , where Ln is the inductance of the compensation
or measuring coil; Cn is the condenser capacitance [10]. The resistance of the oscillating circuits at the resonance frequency is tens of times higher than the inductive resistance of the compensation and receiving coils, which makes it possible to significantly increase the amplitude of the signals on these contours when measuring the magnetic susceptibility of the medium.
The sensitivity of any device is determined by the ratio of output value U increment to the measured parameter x, i.e. Sx = AU/Ax. In our case, with a constant amplitude of the signal on the generator winding, the output parameter is the voltage on the measuring coil. When the metal sheet is brought to a fixed distance (for example, h = 10 cm), the increment is Ax = const, so the sensitivity of the inductive converters can be unambiguously compared to the voltage on the measuring coil with and without resonance mode.
Theoretical studies of the induction sensors sensitivity with different mutual arrangement of the source and receiving induction coils. During the research, inductors with square cross-sectional area of windings were used. They were chosen due to the ease of manufacturing under conditions of industrial production. According to the recommendations of [11], the coil with the square cross-section area of the windings has the highest inductance L, if the ratio of the average diameter d of the winding to the length a of the inductor is d « 3a. When coaxial placement in the probe of the source and receiving coils of the same diameter with the same number of turns of windings w at a distance y from each other (Fig. 1, a), their mutual inductance is determined by the formula [11]
M = kL = —8,497w2kd , (1)
4n
where k - coefficient of magnetic coupling of coils, it depends on the relation y / a = (3^) / d; L - coil inductance, H; - magnetic constant, H/m; w - number of turns of a winding; d - average diameter of a coil, m.
a -^->| b
Fig. 1. Arrangement of induction coils of square cross-section: a - coaxial to each other;
b - parallel to each other
Ivan N. Bazhenov, Oleg O. Basov
Method of Induction Control of Iron Weight Fraction in Magnetite Ore
The mutual inductance of coils moved far away from each other ( y > 2a ) is determined by the method of equivalent circular contours. In this case, each inductor is replaced by a single circuit having a diameter
dt = d (1 + a 2/6d2) = d (1 +1/54) = 1.01852d.
(2)
The mutual inductance M{ of two of these contours located coaxially at a distance of x = y + a from each other is calculated by the formula
Mj = w2M,.
(3)
The mutual inductance M{ of equivalent contours moved far away from each other is calculated by the formula
M, =
^ y3 i1 _ 3y2 + _ 245..6
16
512
Y +
6615 16384
(4)
where R = dj2 - contour radius, m; y = 2R/x - equivalent contour parameter.
A similar mutual inductance of coils with a rectangular cross-sectional area of windings with parallel axes (Fig. 1, b) is calculated by the formula
n 2 d
M2 =— RoW — 32 a
4 r
Z Z
A
v b
2
y y
(5)
where d and a - respectively, the average diameter and length of the coils; b1 a2 + y2 ; y - distance
between coil axes, m; Z =p2 — afp^C^^«4(2P6P2 + ^^Cy^ — ^(PA + ^4)^1) + . - cal-
2
8
32
culated parameter; p„ = 1 + ""^p2 + _ 1)(n_ 2)(n _ 3) p4 +... + n(n _1)(n _ ^^1 p" ; ttl = d/2b, ;
3!
5!
(n +1)!
P (Y) =
1 dn
(y2 _ 1)" - spherical Legendre functions of the n-th order [15], n - whole number;
2n (n)! dyn
Yj = a/bl; parameter Z2 is similar to Zx when replacing yj with y2 = 0 and a,j with
a2 = d/(2b2) = d/(2y).
In the course of studies using the Mathcad program, we have calculated the mutual inductance of two coils having the same number of turns wj = 1000, w2 = 2000 and w3 = 3000, and various geometric dimensions: a1 = 0.005 m, a2 = 0.01 m, a3 = 0.02 m, with a change in the distance between them y = 0.05; 0.1; 0.15; 0.2; 0.25; 0.3, m.
As a result, we have obtained the calculated dependences of the mutual inductance of the coils on the distance under coaxial and parallel placement relative to each other, according to which a six-fold increase in the distance between the source and measuring coils leads to an exponential decrease of the mutual inductance between them by approximately two decimal order (Fig.2)
It is established that the parallel placement of inductance coils in the design of the probe leads to a decrease in
M, H
110
M0 ■■
M0-5 ■
110
M0
0
0.1
0.2
0.3 y, m
Fig.2. Calculated dependences of the mutual inductance of coils placed at some distance when they are coaxial
and parallel to each other (a = 0.005 m) 1, 2 - W1 = 1000; 3, 4 - w = 2000; 5, 6 - w, = 3000
8
the mutual inductance of approximately twice as compared to coaxial coils, and at different distances between them. In addition, an increase in the number of turns in the source and measuring coils in the range from w1 = 1000 to w3 = 3000 allows approximately 10 times to increase the absolute values of the mutual inductance for different locations of the coils.
Based on the calculations, it was also found that an increase in the winding size from a1 = 0.005 m to a3 = 0.02 m results in an increase of mutual inductance of the coils in about 40 times, while maintaining the exponential dependence of its decrease with increasing distance y between the coils.
The analysis of the obtained mutual inductance dependences on the distance between the coils showed that the electromagnetic field produced by the source coil under conditions of coaxial arrangement exerts a larger side effect on the receiving coil when measuring the magnetic susceptibility. The geometric dimensions and number of coil turns affect the absolute values of the mutual inductance, while the form of the dependence remains exponential. Taking into account the data obtained to select the design of the probe and to assess its sensitivity to the controlled magnetic environment, a full-scale experiment with a metal plate
The results of a full-scale experiment to assess the sensitivity of a measuring probe to a controlled magnetic medium. The scheme of the experiment is shown in Fig. 3. With the same number of turns w = 1000 in source and receiving coils, a capacitor with a capacitance C = 0.5 was connected in parallel to the receiving coil through a keyswitch to obtain a parallel oscillatory circuit with a resonance frequency fr = 1140 Hz.
During the research, the source and receiving coils were located at different distances from each other. A sinusoidal voltage Ug = 10 V with a frequency fr = 1140 Hz was applied to the source coil. A digital voltmeter measured the voltage on the receiving inductor in three cases: without a ferromagnetic
core, with the introduction of a ferro-magnetic core with a diameter of 1 cm into the receiving coil and when a resonant capacitor C was connected to a receiving coil with a ferromagnetic core. The magnetic medium was a metal plate of size 0.05 x 1.0 m, the apparent magnetic susceptibility of which could be taken to be xmax = 2 SI, which was located at a distance of 0.1 m from the source and receiving coils. The distance between the coils varied from 5 to 30 cm.
As a result of the influence of the electromagnetic field, a voltage (in volts) of mutual induction Upr = MIg arises at the clamps of the re-
Source coil
Receiving coil Fig.3. Experiment layout
U, mV 1104
1103
100
10
0.1
а = 0.01 m w = 1000
0.1
0.2
0.3 m
Fig.4. Dependence of voltage at receiving induction coil in resonance Urez (1) and non-resonance Unrez (2) mode on the distance to the source coil
ceiving inductor, where Ig is the current flowing
along the source coil, A; M is the mutual inductance, H [18].
Fig.4 shows the voltage dependence on the receiving inductor from the distance to the source coil in the resonant Urez and without the resonant Unrez operating mode.
To assess the sensitivity of the probe with different arrangement of the coils, the dependences of
the voltage increment on the receiving coil with their coaxial AU1g, (AU2g) and parallel AU1v (AU2v) placement from the distance y to the source coil in the presence and absence of a metal plate and in the absence were obtained (Fig. 5).
1
1
2
0
a b
Fig.5. Dependences of voltage increment at receiving coil with coaxial and parallel placement from source coil with and without metal plate: а - in resonance mode (1 - AUiv; 2 - AU1g); b - in non-resonance mode (3 - AU2v; 4 - AU2g)
As a result of the carried out experimental researches it is has been established:
1) in the known scheme of the measuring probe containing the source and receiver coils without cores when the probe coils are arranged, for example, coaxially, the voltage on the receiving coil changes in the range AUnrez = 0.41^197 mV as the distance y between coils increases from 5 to 30 cm;
2) when the capacitance is connected, the voltage on the receiving coil operating in the resonant mode rises by approximately 30 times, and with a similar change in the distance y between the coils changes in the range AUrez = 14.7^4302 mV;
3) comparison of voltage increments on the receiving coil with different mutual placement of the source and receiving coils showed that the use of a parallel arrangement of the coils allows approximately 1.5 times to increase the sensitivity of the probe to the iron content (Fig. 4, b);
4) relative sensitivity to the iron content does not depend on the operating mode of the receiving coil and varies inversely with the square of the distance h from the coils to the metal sheet surface, however, the use of the resonance mode of operation allows to increase the absolute sensitivity values approximately in AU1v/AU2v = 10 times (Fig.5);
5) amplitude of the voltage on the receiving coil is proportional to the mutual induction with the source coil and decreases inversely proportional to the square of the distance between these coils, which corresponds to the calculated graphs (see Fig. 2). As a result, the voltage on the receiving coil decreases to hundreds of tens of microvolts at a distance between the coils of y = 0.3 m, which leads to instability of the results of controlling the iron content in the ore mass because of the influence of interference from the electrical equipment when the monitoring device is operating under production conditions.
A comparative analysis of the obtained results allows us to work out the practical recommendations for the development of quality control instruments for magnetite ores:
1) the source and measuring coils should be placed parallel to each other and perpendicular to the controlled surface of the ore, which allows about a 1.5-fold increase in the sensitivity of the monitoring device to the metal content in the ore mass;
2) the amplitude of the signal on the receiving coil can be increased by introducing a ferromagnetic core. In this case, the source coil should be without a core, since the intensity of the generated magnetic field H = Igw depends only on the number of turns w and the alternating current Ig [12],
and at a constant amplitude of the voltage at the generator output, the magnetizing current decreases due to an increase in the inductive resistance of the winding (from insertion of a core);
3) to increase the amplitude of the receiving coil signal, a resonance mode of operation should be used, it allows, first, to increase the level of the measured voltage and, secondly, to weaken the relative influence of industrial disturbances on the result of control.
In addition, to increase noise immunity at a large distance between the source and receiver coils, it is advisable to measure the voltage on the receiving coil by the weight function method [7, 8], which allows approximately 60 dB (or 1000 times) to reduce the effect of network interference with a frequency of 50+1 Hz on the result of control.
Practical implementation of the method of induction control of the iron weight fraction in magnetite ore. A variant of the circuit implementation of the method of induction control of the iron weight fraction in the ore is presented in Fig.6 [5]. To receive the resonance, parallel to the compensating coils (with inductance Li and L2, respectively) and measuring (with inductance L3), three capacitors are connected (with capacitances C1, C2 and C3, respectively). The resistance of the formed oscillatory circuits at the resonance frequency is tens of times higher than the inductive resistance of the compensating and receiving coils, which makes it possible to significantly increase the amplitude of the signals on these contours with a change in the magnetic susceptibility of the medium.
The control device (Fig.6) works as follows. When alternating current flows from the generator of the sinusoidal voltage along the turns of the source coil, an alternating electromagnetic field is created in the surrounding space. Structurally, the receiving coil is mounted in the probe at a fixed distance lgp from the source coil. The first compensation coil is located at a distance of 0.2lgp, and the second compensation coil is at a distance of 0.8lgp from the source coil. In the air in the absence of a magnetic medium, this electromagnetic field induces on two counter-connected compensation coils equal in magnitude and EMF opposite in phase, E1 and E2.
When the probe is placed above the investigated medium, it is magnetized by the alternating electromagnetic field of the source coil. The secondary magnetic field that appears in this case induces a different in amplitude EMF in the receiving and compensating coils. As a result, a difference EMF AE1 of the output signals of the receiving and first compensating coils appears at the input of the first amplifier, and the differential EMF AE2 of the output signals of the receiving and second compensation coils at the input of the second amplifier. After the amplification of the differential EMFs AE1 and AE2 by amplifiers and their rectification by synchro-
Fig.6. A sample of layout for implementation of method of induction control of iron weight fraction in magnetite ore
nous detectors, constant or slowly varying signals are amplified by direct current amplifiers and fed to the first two inputs of a calculating unit based on a microcontroller containing an input switch and an analog-to-digital converter for obtaining and processing control results in digital form. The third input of the calculating unit receives pulses from an ultrasonic sensor that determines the distance h from the probe to the medium to correct the conversion results that are output to the recorder. The magnitude of the digitally fixed result determines the magnetic susceptibility of the medium.
When the probe is placed above the flat surface of the medium under study, the difference EMFs A£1 = Е0G1% and AЕ2 = Е0G2% depend on the product of the EMF Е0 induced in the air, the geometric factors of the probe G1, G2 and the magnetic susceptibility of the medium % = I/ Н proportional to its magnetization I on the strength H of the electromagnetic field. The values of the geometric factors of the probe G1, G2 depend on the arrangement of the compensation coils relative to the source coil and vary over a wide range of values, depending on the ratio of the distance to the investigated medium and the probe length h / lgp.
The difference EMFs AE1, AE2 are amplified and detected by amplifying-conversion blocks with conversion coefficients K1, K2, so the voltages at the two inputs of the computational block are
To obtain the same maximum values of the measured voltages AU1max and AU2max, it is necessary to fulfill the condition KjG1max = K2G2max, that when using amplification-conversion blocks with equal conversion factors K = K2, is reduced to providing equal maximum values of the geometric factors of the probe G1max = G2max. This equality can be achieved by reducing by 4 times the number of turns in the first compensation coil in comparison with the number of turns in the second one (provided they are placed at distances 0.2lgp and 0.8lgp from the source coil).
The use of an ultrasonic sensor makes it possible to create a resonant method for controlling the iron weight fraction in magnetite ore, which is invariant to the geometric factor. The ultrasonic sensor detects the distance h from the probe to the studied medium and applies pulses of different duration to the third input of the calculating unit, which automatically changes the conversion factor of the signals AU1k and AU2k coming from the direct current amplifiers, compares them and extracts the highest one, its value is used to calculate the magnetic susceptibility of the studied medium for its output to the data recorder.
An increase in the amplitude of the signals on the two compensating and one receiving loops makes it possible to use amplifiers of alternating voltage with small gain factors and to generate voltages per unit volt at the inputs of synchronous detectors. This reduces the effect of instrumental errors of synchronous detectors and the temperature drift of DC amplifiers on the accuracy of the conversion.
Almost by increasing the amplitude of the signals at the outputs of the compensating and receiving oscillation circuits, the relative influence of external interference and interference is further weakened, and the random error of the transformation decreases.
To evaluate the effectiency of the proposed technical solution, the device was simulated on a PC in the Electronics Workbench Pro software, which resulted in the following:
1) when a sinusoidal voltage with amplitude U = 10 V and frequency f = 1 kHz is supplied to the source coil, a change in the inductance of one of the compensation coils by 10% relative to the initial value of L = 0.1 H leads to the appearance of a differential voltage AU « 2.28 mV;
2) when connecting capacitors with the same capacitance C = 200 nF parallel to the compensation coils, a change in the inductance of one of them by ±10% changes the differential voltage to
AUlk = K1E0G1%, AU2k = K2E0G2% .
(6) (7)
AUr - 80 mV at the resonance frequency fr = 1 kHz contours at input impedances of the AC voltage amplifiers of 10 kQ, i.e. the amplitude of the measured signal increases approximately in K = AUJAU = 80.2/2.28 - 35 times.
Conclusion. The paper has described the method of induction control of the iron weight fraction in magnetite ore, its theoretical justification is presented, and effectiveness for instruments of magnetite ores quality control is proved experimentally.
It is established that the use of the resonance mode of operation of the receiving and compensating circuits makes it possible to increase the sensitivity of the monitoring device by a factor of tens to the change in the electromagnetic field and makes it possible to increase the sensitivity of the device by more than 30 times.
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Authors: Ivan N. Bazhenov, Employee, bazhen-orel77@mail.ru (Russian Federation Security Guard Service Federal Academy, Orel, Russia); Oleg O. Basov, Doctor of Engineering Sciences, Employee, oobasov@mail.ru (Russian Federation Security Guard Service Federal Academy, Orel, Russia).
The paper was accepted for publication on 4 April, 2017.
