Linear Synchronous Motors, 2nd Edition

Appendix A

Magnetic Circuits with Permanent Magnets

A.1 Approximation of Demagnetization Curve and Recoil Line

The most widely used approximation of the demagnetization curve is the approximation using a hyperbola, i.e.,

B=BrHc−HHc−a0H⁢(A.1)

where B and H are coordinates, and a₀ is the constant coefficient that can be evaluated as [19]

a0=BrBsat=2γ−1γ⁢(A.2)

or

a0=1n∑i=1n(HcHi+BrBi−HcHiBrBi)⁢(A.3)

where (B_i, H_i) are coordinates of points i = 1, 2, … n, on the demagnetization curve, arbitrarily chosen, and n is the number of points on the demagnetization curve.

The recoil magnetic permeability is assumed to be constant and equal to [19]

μrec=BrHc(1−a0)⁢(A.4)

The above equations give a good accuracy between calculated and measured demagnetization ...