Isotropic vector hysteresis represented by superposition of stop hysteron models

Abstract

The present paper first shows that the scalar stop hysteron model has the property of equal vertical chords for back-andforth input variations of the same amplitude. This property leads to an identification method of the scalar model. Secondly, identification methods are developed for the 3-D and 2-D isotropic vector models that are constructed by the superposition of scalar stop hysteron models. Numerical simulations show that these methods identify the scalar and vector models satisfactorily.

Stop Model With Input-Dependent Shape Function and Its Identification Methods

“…It is assumed that the input has no extrema other than . A previous work [15], [16] has shown that the vertical difference between does not depend on (6) In other words, the back-and-forth input variations of the same amplitude produce equal vertical chords regardless of the dc bias. A previous study [17] has shown that magnetic characteristics of a silicon steel sheet do not satisfy the property of equal vertical chords regardless of dc bias.…”

“…However, the function , given by (1) and (2), has a hysteretic property even when . In order for to become a single-valued function when , the operator is defined as the following: The stop model (1) has the property of equal vertical chords regardless of dc bias [15], [16] as follows. Let and be the outputs on ascending and descending curves, respectively, for a back-and-forth input variation given by (5) having amplitude (5) where is an arbitrary dc bias (see Fig.…”

“…Fig. 3 shows the -curves given by the stop model identified from the measured symmetric -loops, where the shape function is determined by the identification method in [15], [16] with 20 stop hysterons. Fig.…”

“…A previous study [15], [16] has proposed an identification method for the scalar stop model from measured -loops. It showed that the stop model can simulate an inverse of the Preisach model.…”

“…It showed that the stop model can simulate an inverse of the Preisach model. However, another study [17] has shown that the stop model cannot sufficiently represent the hysteretic characteristics of a silicon steel sheet because the magnetic characteristics of the silicon steel sheet do not satisfy the property of equal vertical chords regardless of dc bias [15], [16]. Representation by the stop model requires that the property be satisfied.…”