Dynamic exponential model of ferromagnetic hysteresis

Abstract

We introduce a dynamic exponential model of ferromagnetic hysteresis that unifies the cooperative exponential model with the Néel fluctuating field, Jiles-Atherton approach to the anhysteretic and a Preisach convolution integral over a field distribution function. Dynamic effects such as viscous field advance and eddy current field delay are modeled directly by the model parameters. The dynamic effect of creeping in the direction of the previous maximum susceptibility due to viscosity as predicted by Street is observed and is modeled using the proposed method. Negative tilting of asymmetric minor hysteresis loops (lower susceptibility) with cycling is also observed and is also modeled using the proposed model as increased Néel's “opposition” in our cooperative field, Hcoop. Shearing of hysteresis loops is modeled as an averaging of the exponential model <Xexp> over viscous advance and eddy current delay fields, causing truncation and broadening. Detailed measurement procedures are described for a hollow cylinder and thin and thick rings of Fe94Ni3Cr2Mo1 steel with variable frequency sine, triangle and step field waveforms.