ON THE QUESTION OF CHOOSING THE MAGNETIZING CURRENT IN ALTERNATING-CURRENT COERCIMETERS

V. P. DOLGOPOLOV

(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)

The development of an instrument for quality control of ferromagnetic products by electromagnetic methods is always preceded by extensive investigations aimed at establishing relationships between the monitored and electromagnetic parameters. One stage of these investigations is to find the magnitude of such a magnetizing field in which the relationship between the parameters is manifested most clearly and has an unambiguous character.

In an alternating-current coercimeter, the operating principle of which is described in the literature [1], what is measured is not the dynamic coercive force itself, but the difference between the coercive forces of the tested product and of a reference specimen. This difference is measured from the time interval between the instants at which the inductions in the tested and reference products pass through zero. In [2] a formula is given that establishes the dependence between the time interval and the difference of coercive forces:

\[ \Delta t = \frac{ \arcsin \dfrac{H_{c2}}{H_m} - \arcsin \dfrac{H_{c1}}{H_m} }{\omega} \tag{1} \]

or

\[ \Delta(\omega t)=\arcsin \frac{H_{c2}}{H_m} - \arcsin \frac{H_{c1}}{H_m}, \tag{2} \]

where

\(t\) — time; \(\omega\) — angular frequency of the magnetizing current;

\(H_{c1},\ H_{c2}\) — dynamic coercive forces of the reference and tested products at a given value of the magnetizing field \(H_m\).

In order to facilitate the measurement of the interval \(\Delta t\) (or \(\Delta\omega t\)), and thereby to simplify the measuring equipment, it is desirable that this interval be as large as possible. It follows from expression (2) that the interval \(\Delta(\omega t)\) depends on the ratio of the coercive forces \(H_{c2}\) and \(H_{c1}\) and on the amplitude of the magnetizing field \(H_m\). When the amplitude of the magnetizing field is increased above the value at which practical saturation of the specimen occurs and the quantities \(H_{c1}\) and \(H_{c2}\) reach a maximum and thereafter cease to change, the interval \(\Delta(\omega t)\) decreases. In fields smaller than the saturation field, the interval depends both on \(H_m\) and on the ratio \(H_{c1}\) and \(H_{c2}\).

Fig. 1.

Visible labels in the figure: \(H_c\); \(H_m,\ \mathrm{A/cm}\); \(f,\ \mathrm{Hz}\); \(\Delta(\omega t)_c = f(H_m)\); \((18^\circ\!-\!31')\). Curves are labeled 1, 2, 3, 4, 5, and 6.

Fig. 2.

Axes: \(H_c,\ \mathrm{A/cm}\); \(H_m,\ \mathrm{A/cm}\).

Curves: 1, 2, 3, 4.

To determine the magnetizing field required for the operation of a coercimeter, it is necessary to have the dependences of the dynamic coercive force \(H_c\) on the amplitude value of the field, \(H_m\). Figure 1 gives the dependences \(H_c=f(H_m)\) for cast-iron specimens made in the form of rings and quenched at different temperatures: the lowest curve 2 corresponds to the lowest quenching temperature, and the upper curve 6 to the highest temperature. It is evident from the figure that, for sufficiently large magnetizing fields \(\left(50\ \text{and more } \frac{\mathrm{a}}{\mathrm{cm}}\right)\), there is an unambiguous dependence between the quenching temperature and the dynamic coercive force, i.e., as the temperature increases, the coercive force increases. An unambiguous dependence is also observed for sufficiently small fields \(\left(\text{within } 8 \div 20\ \frac{\mathrm{a}}{\mathrm{cm}}\right)\), but in this region it has the opposite character: the coercive force decreases as the temperature increases. Thus, it may be concluded that control of the quenching temperature of cast-iron products is possible in the region either of large or of small magnetizing fields.

In the same Fig. 1 the curve of the change in the interval \(\Delta(\omega t)_{1,2}=f(H_m)\) for specimens 1 and 2 is given, the data for plotting which were calculated by formula (2). In the region of large fields, \(\Delta(\omega t)=11 \div 15\) electrical degrees; in the region of small fields, where an unambiguous dependence between the parameters is observed, \(\Delta(\omega t)=30 \div 20\) electrical degrees, i.e., considerably greater than in the region of large fields. From the standpoint of convenience in measuring the time interval, the region of small fields is preferable.

It is also evident from Fig. 1 that, at a certain value of the amplitude of the magnetizing-field intensity, namely at \(H_m=25\ \frac{\mathrm{a}}{\mathrm{cm}}\), for specimens 1 and 2 the time interval \(\Delta(\omega t)=0\), despite the fact that the quenching temperatures of these specimens differ sharply. Consequently, the field must be chosen so that there is no intersection of the curves \(H_c=f(H_m)\), since \(\Delta(\omega t)=0\) means that, at the given field amplitude, the coercive forces of the compared products are identical and the quenching temperatures must be identical. In Fig. 2, as an example, dependences are given of the coercive force on the amplitude of the magnetizing field \(H_m\) for specimens of steel ShKh-15. On the basis of the analysis carried out above, it may be asserted that control of the quenching temperature of products made of steel ShKh-15 by dynamic coercive force is possible only in large fields, since in small fields the curves \(H_c=f(H_m)\) intersect.

REFERENCES

1. I. G. Leshchenko, V. A. Malin. Installation for sorting parts by coercive force. Advanced Scientific-Technical and Production Experience. Moscow, 1964, No. 2-64-282/8 (GOSINTI).

2. A. M. Gruznov, V. P. Dolgopolov, I. G. Leshchenko, V. D. Sartakov. Measurement of the hardness of steel products using an alternating-current coercimeter. Defektoskopiya, 1967, No. 4.