Development of Numerical Analysis Software for the NDE by Using Dipole Model

Abstract

The magnetic field distribution around a crack can be calculated more easily and quickly by using a dipole model than finite element method (FEM). This paper reports the development of numerical analysis software that uses an improved dipole model to analyze the magnetic field around cracks. The preprocessor in this software includes the crack formation software, which can distribute the magnetic charge per unit area, m, on the crack section area. Also the lift-off, measurement area and sensor interval, and magnetization direction can be considered in the preprocessor. Also, the postprocessor presents functions, such as the natural magnetic field distribution and ∂B/∂x, ∂B/∂y, as results. Also, the physical characteristics of the magnetic optical sensor and the Hall sensor are included in the postprocessor, and the magnetic field distribution can be changed to optical intensity and electrical signal distribution. The experiment results, which are obtained by using the magnetic camera on the crack, are compared with analysis results obtained by using the dipole model analysis software.

Measurement of Thinned Water-Cooled Wall in a Circulating Fluidized Bed Boiler Using Ultrasonic and Magnetic Methods

“…Figure 1 shows the simplified 2D dipole model of the thickness changing on the boiler water-cooled wall tube due to corrosion [21,22]. A U-type magnetizer is placed on the surface of the membrane.…”

“…The corrosion depth and length are d and D/2 + W, respectively. The distance between the magnetizer and the specimen, i.e., lift-off, is expressed as h. Then, the lift-off at the corrosion is h + d. In the dipole model, magnetic charges ±m per unit area are assumed to be distributed along the length of the magnetizer poles, membrane length, and corrosion length according to the assumption in the dipole model [21,22]. The magnetic flux density in the y-axis direction at the position of P(x p ,y p ) is the summary of the magnetic field produced from the magnetic charges, as expressed in Equation (1).…”

“…poles, membrane length, and corrosion length according to the assumption in the dipole model [21,22]. The magnetic flux density in the y-axis direction at the position of P(xp,yp is the summary of the magnetic field produced from the magnetic charges, as expressed in Equation (1).…”

Theoretical Model of Self-Magnetic Flux Leakage and Its Application in Estimating the Depth Direction of a Fatigue Crack

“…Several studies have presented a theoretical equation for the leakage flux generated around a crack using a dipole model [22][23][24][25][26][27][28][29][30][31]. A formula was presented for the magnetization of a specimen by an external magnetic field, assuming that the magnetic dipole moment per unit area occurs at the crack surface.…”

“…A formula was presented for the magnetization of a specimen by an external magnetic field, assuming that the magnetic dipole moment per unit area occurs at the crack surface. The formula has been used as a model that simulates the qualitative (and partially quantitative) change in MFL based on the presence of defects [22][23][24][25][26][27] and sensor designs [28,29], and is used for quantitative evaluation [22][23][24][25][26][27][29][30][31]. However, it is difficult to apply it to very narrow cracks, such as fatigue cracks.…”