ON THE POSSIBILITY OF NONDESTRUCTIVE TESTING BY GATING THE OUTPUT SIGNAL OF AN ELECTROMAGNETIC SENSOR

I. G. LESHCHENKO, V. S. PLOTNIKOV, V. Yu. SOSNIN

(Presented by the scientific and technical seminar of the Department of Information and Measurement Engineering)

Multiparameter methods of nondestructive testing are finding wide application in various branches of industry [1]. For the purposes of multiparameter testing, the known method of gating the instantaneous values of the sensor output signal may be used.

In this case, the output signal of the sensor can be represented analytically by the expression

\[ U_{\text{out}}(t)=f(x_1,x_2,x_3,\ldots x_n), \tag{1} \]

where \(x_1\) and \(x_2, x_3 \ldots x_n\) are, respectively, the monitored and interfering parameters, the set of which forms the factor space.

By gating the sensor output signal \(U_{\text{out}}(t)\) at different instants of time \(t_i\), we obtain a system of equations

\[ \left. \begin{aligned} U_{\text{out}}(t_1)&=f_1(x_1,x_2,x_3,\ldots,x_n),\\ U_{\text{out}}(t_2)&=f_2(x_1,x_2,x_3,\ldots,x_n),\\ U_{\text{out}}(t_3)&=f_3(x_1,x_2,x_3,\ldots,x_n),\\ &\cdot\quad \cdot\quad \cdot\quad \cdot\quad \cdot\\ U_{\text{out}}(t_n)&=f_n(x_1,x_2,x_3,\ldots,x_n), \end{aligned} \right\} \tag{2} \]

where \(U_{\text{out}}(t_i)\) are the instantaneous values of the sensor output signal at the time instant \(t_i\), with \(i=1,2,\ldots n\).

Solving the system of equations analogously to [1], we obtain

\[ X_1=\sum_{i=1}^{n} b_i U_{\text{out}}(t_i)+b_0, \tag{3} \]

where \(b_i, b_0\) are, respectively, the weighting coefficients and the constant term of the equation.

Equation (3) can also be obtained in another way, for example, by the method of multiple regression [2]. With the selected quantitative and qualitative composition of the informative components \(U_{\text{out}}(t_i)\), \(i=1,2,\ldots n\), and with a specified form of the equation relating the monitored parameter \(x_1\) to the informative components \(U_{\text{out}}(t_i)\), the application of regression-analysis methods makes it possible to find the optimal values

coefficients of equation (3) for which the mean square of the deviations of the estimated value of the controlled parameter from its true value is minimal.

The main condition for the existence of a composite relation equation (3), according to which the estimate of the controlled parameter is significantly more accurate than by any one of the informative components, is the presence of linear independence of the selected informative components in factor space.

The fulfillment of these conditions was investigated in monitoring the nitrocarburizing depth of products made of 18KhGT steel from instantaneous values of the output signal of an electromagnetic sensor for three batches of specimens that had undergone gas nitrocarburizing with oil quenching and low-temperature tempering. In the manufacture of each batch of products, all parameters of the heat-treatment process were stabilized except the temperatures: quenching \(t_z\), tempering \(t_o\), and oil \(t_m\). In this case, the first batch of products was manufactured only with variation of the quenching temperature within \(800 \pm 50^\circ\text{C}\), the second—with variation of the oil temperature—\(160 \pm 20^\circ\text{C}\), and the third—with variation of the tempering temperature—\(180 \pm 40^\circ\text{C}\).

The products were magnetized in a specified-current mode, which had a trapezoidal form. At the same time, the influence of instability in the quenching, tempering, and oil temperatures on the instantaneous values of the sensor output signal was evaluated. To investigate the dependences of the instantaneous

Fig. 1. Dependences of the relative sensitivities on the gating phase of the output signal of an electromagnetic sensor

values on the depth of the nitrocarburized layer, the hardened layer was mechanically removed from one specimen and the sensitivities of the instantaneous values of the sensor emf to the magnitude of the remaining hardened layer \(S(h)_j,\ j = 1, 2, 3, \ldots, m\), were determined, where \(m\) is the number of gated values of the sensor signal. The sensitivities determined in this way are equivalent, with some approximation, to the sensitivities to the depth of the nitrocarburized layer.

The sensitivities of the instantaneous values of the sensor emf to changes in the quenching temperature \(S(t_z)\), the tempering temperature \(S(t_o)\), and the oil temperature \(S(t_m)\) were then determined, and their relative values were found:

\[ \gamma_{1j}=\frac{S(t_o)_j}{S(h)_j}; \]

\[ \gamma_{2j}=\frac{S(t_z)_j}{S(h)_j}; \]

\[ \gamma_{3j}=\frac{S(t_m)_j}{S(h)_j}. \]

Figure 1 shows the dependences of the relative sensitivities on the phase of gating of the emf.

It is evident from the figure that the dependences of the relative sensitivities on the gating phase are not constant, and also are not linear combinations of one another.

This testifies to the linear independence of the informative components \(U_{\mathrm{out}}(t_i)\) in the factor space formed by the variables: depth of the nitrocarburized layer \(h\), quenching temperature \(t_z\), oil temperature \(t_m\), and tempering temperature \(t_o\).

Thus, the method of gating the sensor signal makes it possible to carry out separate control of the parameters considered.

REFERENCES

1. V. G. Pustynnikov. Root-mean-square methods and devices in the technology of nondestructive multiparameter testing. Collection “Multiparameter Testing in Mechanical Engineering.” Rostov-on-Don, RISKhM, 1969.

2. L. Z. Rumshinskii. Elements of Probability Theory. Moscow, Nauka, 1970.