The Effect of Electromagnetic Shields on the Parameters of Feedthrough Sensors
Abstract Generated abstract
This paper examines how electromagnetic shields used in through-type electromagnetic flaw-detection transducers affect sensor parameters and sensitivity. Treating the transducer and shield as a coupled electrical circuit, it derives equivalent impedance expressions showing that shielding increases the active resistance and decreases the equivalent inductance, thereby lowering the quality factor and reducing sensitivity to changes in introduced inductance. The authors also analyze a modified shield circuit with an added capacitor and show, with supporting experimental curves, that capacitance can increase the equivalent inductance, quality factor, and sensitivity of the sensor.
Full Text
EFFECT OF ELECTROMAGNETIC SHIELDS ON THE PARAMETERS OF THROUGH-TYPE TRANSDUCERS
I. G. Leshchenko, V. A. Kozhukhov
(Presented by the scientific and technical seminar of the Department of Information and Measuring Technology)
At the present time, in electromagnetic flaw detection, electromagnetic shields are being used ever more widely; these are made in the form of solid copper disks of various thicknesses or short-circuited coils, located in the immediate vicinity of the magnetizing coil of the transducer [1, 2]. The principal purpose of such shields in the above-mentioned works consists in widening the inspection zone near the ends of ferromagnetic products, where, owing to the increasing action of the demagnetizing factor caused by the approach of the end of the product to the transducer, the useful signal decreases.
The shielding action of a shield made of a nonmagnetic metal in an alternating field is determined by the currents induced in the thickness of the shield walls or in its turns and by the magnetic field excited by these currents.
The presence of a shielding region introduces no changes into the field equation, but leads only to a new formulation of the boundary conditions [3]. In the presence of a shield, the field strength at the surface of a longitudinally magnetized product is smaller by the amount of the field produced by the current in the shield:
\[ \overline{H}=\overline{H}_{0}-\sigma_{\text{э}} k \overline{E}_{0}, \tag{1} \]
where \(\overline{H}\) is the magnetic-field strength at the surface of the product in the presence of a shield;
\(\overline{E}_{0}\) is the electric-field strength of the shield.
\(\overline{H}_{0}\) is the magnetic-field strength without a shield;
\(k\) is a coefficient having the dimension of length and depending on the dimensions of the shield;
\(\sigma_{\text{э}}\) is the electrical conductivity of the shield.
Since the transducer operates in conjunction with other electrical and electronic circuits, it is expedient to analyze the effect of electromagnetic shields from the standpoint of the theory of electrical circuits.
For the electromagnetic system transducer—shield, shown in Fig. 1, the following equations are valid:
\[ \dot{U}=\dot{I}_{1}R_{1}+\dot{I}_{1}j\omega L_{1}-\dot{I}_{2}j\omega M, \tag{2} \]
\[ 0=-\dot{I}_{1}j\omega M+\dot{I}_{2}j\omega L_{2}+\dot{I}_{2}R_{2}. \tag{3} \]
From the last equation we find
\[ \dot I_2=\dot I_1\,\frac{M j\omega}{L_2 j\omega+R_2} \]
and, substituting into equation (2), we obtain
\[ \dot U=\dot I_1\left(R_1+j\omega L_1+ \frac{M^2\omega^2R_2-L_2M^2\omega^3j}{R_2^2+(L\omega)^2}\right). \tag{4} \]
Thus, the transducer, together with the electromagnetic shield, has the equivalent total impedance:
\[ Z_{\mathrm{eq}}=R_1+\frac{M^2\omega^2R_2}{|Z_2^2|} +j\left(L_1\omega-\frac{M^2L_2\omega^3}{|Z_2^2|}\right). \tag{5} \]
Fig. 1. Electrical circuit diagram of a transducer with electromagnetic shields
The equivalent active resistance of the transducer increases under shielding by
\[ \frac{M^2\omega^2R_2}{|Z_2^2|}, \]
\[ R_{\mathrm{eq}}=R_1+\frac{M^2\omega^2R_2}{|Z_2^2|}. \tag{6} \]
The equivalent inductance of the transducer under shielding decreases by the amount
\[ \frac{M^2L_2\omega^2}{|Z_2^2|}, \qquad L_{\mathrm{eq}}=L_1-\frac{M^2L_2\omega^2}{|Z_2^2|}. \tag{7} \]
For an absolute-value transducer with impedance \(Z=R+j\omega L\), the principal variable parameter is the inductance \(L\), whose value corresponds to different values of magnetic permeability, hardness of the ferromagnetic product, and other monitored parameters functionally related to it.
The relative change in the total impedance of the transducer, corresponding to its sensitivity to the introduced inductance \(\Delta L\), is equal to
\[ \varepsilon=\frac{\Delta Z}{Z}=\frac{j\omega\Delta L}{R+j\omega L} =\frac{\sigma}{1-\dfrac{j}{Q}}, \tag{8} \]
where
\[ \sigma=\frac{\Delta L}{L} \]
is the relative change in the inductance of the transducer;
\[ Q=\frac{L}{R} \]
is the quality factor of the transducer.
According to (8), a decrease in the quality factor of the transducer caused by the electromagnetic shield leads to a decrease in the variation of the total impedance, i.e., to a decrease in sensitivity. Experimental studies of the sensitivity of the transducer to the introduced inductance \(\Delta L\) confirm this. Figure 2 presents graphical dependences of the transducer sensitivity on the shielding coefficient of the shield, whose value is equal to
\[ \Theta=\frac{\dot\Phi_{\mathrm{c/s}}}{\dot\Phi_{\mathrm{b/s}}}, \tag{9} \]
where \(\dot\Phi_{\mathrm{c/s}}\) is the magnetic flux with the shield;
\(\dot\Phi_{\mathrm{b/s}}\) is the magnetic flux without the shield.
The sensitivity of the sensor can be increased if a capacitor is included in the shield circuit.
For the circuit shown in Fig. 3, the following equations are valid:
\[ \dot U=\dot i_1 R_1+\dot i_1 j\omega L_1-\dot i_2 j\omega M; \tag{10} \]
\[ 0=-\dot i_1 j\omega M+\dot i_2 j\omega L_2 -\dot i_2 j\frac{1}{\omega C}+\dot i_2 R_2. \tag{11} \]
Fig. 2. Change in the relative sensitivity of the sensor as a function of the shielding coefficient
Fig. 3. Electrical circuit of a sensor with capacitors connected into the circuit of the shielding coils
After transformations similar to the case without a capacitor, we obtain
\[ R_{\text{eq}}=R_1+\frac{M^2\omega^2 R_2}{|Z_2^2|}; \tag{12} \]
\[ L_{\text{eq}}=L_1-\frac{M^2\omega^2 L_2-\dfrac{1}{\omega C}}{|Z_2^2|}. \tag{13} \]
Analysis of formulas (12) and (13) makes it possible to conclude that including a capacitor in the shield circuit helps to increase the equivalent inductance of the sensor and leads to an increase in its sensitivity, which is confirmed by the experimental curves in Fig. 4.
Fig. 4. Change in the relative sensitivity of the sensor as a function of the shielding coefficient with capacitors present in the shield circuit
Conclusions
The use of electromagnetic shields leads to an increase in the equivalent active resistance of the sensor and to a decrease in its inductance—the principal parameters on which the sensitivity and quality factor of the sensor depend.
Including capacitors in the shield circuit leads to an increase in the equivalent inductance of the sensor, its quality factor, and its sensitivity.
References
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I. G. Leshchenko, N. M. Malyshenko. Investigation of the influence of end effects on the spectral composition of the e.m.f. of feed-through transducers. Reports of the 2nd All-Union Seminar “Nondestructive Testing of Ferromagnetic Materials and Products by the Higher-Harmonics Method.” Tomsk, 1971, p. 33.
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A. V. Puzanchikov, V. P. Markov. On electromagnetic shielding of transducers of induction devices. Proceedings of the Ryazan Radio Engineering Institute. Information and Measurement Technology. Issue 39. Ryazan, 1972, p. 24.
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K. M. Polivanov. Ferromagnetics. Moscow–Leningrad, GEI, 1957, p. 208.
- Order 2609.