Investigation of the Magnetic Field in the End Zone of a Ferromagnetic Product
Abstract Generated abstract
This paper examines the magnetic field behavior near the end of a cylindrical ferromagnetic product during electromagnetic inspection with a feed-through transducer. Using Maxwell’s integral relation for a ferromagnetic medium, the authors analyze how the approach of the product end to the magnetizing coil changes the balance between the coil current contribution and the magnetization contribution, as flux closure increasingly involves an air gap. Experimental measurements at 50 Hz for a 10 cm magnetizing coil show that the end region produces a redistribution of the field along the product, increases field inhomogeneity, and breaks the symmetry of the magnetic-field distribution about the coil center.
Full Text
INVESTIGATION OF THE MAGNETIC FIELD IN THE END REGION OF A FERROMAGNETIC PRODUCT
I. G. LESHCHENKO, V. A. KOZHUKHOV
(Presented by the Scientific and Technical Seminar of the Department of Information and Measurement Technology)
In electromagnetic inspection of elongated ferromagnetic products in feed-through transducers, the end of the product is practically not inspected.
The length of the uninspected section is a complex function of the electromagnetic parameters of the material of the product, the frequency of the alternating field, the geometrical dimensions of the product, and the dimensions of the magnetizing coil of the transducer.
With low-frequency remagnetization (50 Hz), the length of the uninspected end reaches 15–20 cm.
The purpose of the present work is to investigate the magnetic field of a cylindrical ferromagnetic product as its end approaches the transducer.
The approach of the edge of the product to the magnetizing coil of the transducer leads to a redistribution of the magnetic field in the ferromagnetic product, to a change in the ratio between the terms of Maxwell’s integral equation for the given ferromagnetic medium [1]
\[ \oint_l \overline{B}\,d\overline{l} = \mu_0 \int_s \overline{\delta}\,d\overline{S} + \mu_0 \oint_l \overline{J}\,d\overline{l}, \tag{1} \]
where \(\delta\) is the current density in the magnetizing coil of the transducer;
\(J\) is the magnetization of the ferromagnet.
The first term of equation (1), \(\mu_0 \int_s \delta\,dS\), equal to the total current produced by the magnetizing coil, remains constant during the experiment owing to the prescribed-current mode. The second term of equation (1), \(\mu_0 \oint_l \overline{J}\,d\overline{l}\), decreases as the end of the product approaches the transducer, which is caused by an increase in the air gap through which the magnetic lines of force of the field close. Therefore part of the magnetizing force of the magnetization, caused by the elementary currents of the ferromagnet, is spent on conducting the induction flux through the increasing air gap.
Figure 1 presents experimental distribution curves of the gradient of the tangential-to-the-generatrix component of the magnetic field as the end approaches the magnetizing coil of the transducer, for various distances \(\lambda\) of the end of the cylinder from the edge of the magnetizing coil of length \(L = 10\) cm, at a remagnetization frequency of 50 Hz.
Fig. 1. Dependence of the distribution function of the gradient of the tangential component of the magnetic field on the relative position of the end of the product in the pass-through sensor.
Analysis of the experimental data makes it possible to conclude that bringing the end of a ferromagnetic product closer to the magnetizing coil leads to an increase in the inhomogeneity of the product’s magnetic field, to its redistribution along the product, and to a disruption of the symmetry of the magnetic-field distribution relative to the center of the magnetizing coil.
References
- K. M. Polivanov. Ferromagnets. Moscow, GEI, 1957, p. 12.