Formula for Energy Loss in Soft Magnetic Materials and Scaling

Abstract

Basing on scale invariance of considered system an improvement of the Bertotti formula for energy loss in soft magnetic materials has been achieved. Assumptions of the Bertotti theory were discussed and criticized. As an alternative to this theory a new approach basing on the scale invariance of complex systems has been presented. The generalized description of energy loss has been recently postulated by us in the form of the homogeneous function in a general sense which leads to a series expansion for the energy loss. On the basis of measurement data it has been proved that only two first terms of the series are relevant. New measurements of the energy loss in soft magnetic materials have been performed which confirms the scaling theory. The obtained formula enables very simple description of the energy loss in soft magnetic materials, taking into considerations wide ranges of frequency and magnetic induction. The revealed data collapse of energy loss enables comparison of energy losses data taken by different methods. This phenomenon also supplies new criterion for correctness of empirical data.

Data Collapse of Energy Loss in Soft Magnetic Materials as a Way for Testing Measurement Set

“…(1) has been confirmed empirically by Yuan et al [3]. In the same period the further confirmation of the scaling in SMM, as well as its mathematical and physical background, have been presented by the authors of this paper [4]. Due to the second degree of (1), it was possible to obtain the data collapse by the appropriate scaling.…”

“…The second set contains some of our results [2,4] for the energy losses in the following alloys: amorphous ribbon P 1 = Fe 78 Si 13 B 9 , Co-based amorphous alloy P 2 = Co 71.5 Fe 2.5 Mn 2 Mo 1 Si 9 B 14 , nanocrystalline alloy P 3 = Fe 73.5 Cu 1 Nb 3 Si 15.5 B 7 .…”

“…Applying to P tot the scaling hypothesis [2,4], we have derived the scaled formula (1) in the form of infinite series. In most cases this series converges very fast.…”

“…For the purposes of this paper we distinguish the two of them: the geometry of the sample (size, shape) and the way for assessment of uncertainty contributions. Taking from [1] the idea of the inter-comparison of measurement data of the energy losses in soft magnetic materials (SMM), we perform such an inter-comparison with data taken in two laboratories [2][3][4], however under the conditions of axial and alternating flux. We show that the interference of the sample's geometry can be scaled off and this factor does not interfere on the data inter-comparison.…”

The modified procedures in coercivity scaling

“…The proposed scaling analysis of coercivity made use of the Widom procedure, which was previously applied in the power loss modeling of soft magnetic materials [10][11]. The Widom procedure is based on the hypothesis that a functional dependency describing the scaling phenomenon is a generalized homogenous function, defined as follows:…”