Research on Distributed Parameter Model of Permanent Magnet in Robust Design of Electromagnetic Relay

Analytical Method for the Magnetic Field Line Distribution of a Fan-shaped Permanent Magnet and the Calculation of Leakage Permeance

“…Combining (1), (2), and (7), the magnetic field line of the front side of the PM can be expressed as (8) Where x m is the point on line P 00 P 11 , which can be calculated as follows (9) Where n is the number of segmented, i = 1, 2, 3, ..., n.…”

“…Line P 0 P 1 can be expressed as (10) Formulae (8) and (10) can be used to obtain the point of intersection (x 01 , y 01 ) on line P 0 P 1 , and y 01 > 0. Substituting (9) into (10), allows y m to be obtained.…”

“…According to (20) or (21), leakage permeance can be calculated by the permeance formula (22) Where l p is the average length of the magnetic flux tube, which can be obtained from (8) and (13). A is the adjustment parameter, which is a variable that regulates the error change over PM height, angle, inner, and outer radius.…”

“…Some researchers have done a lot of work on fast calculations for electromagnetic systems with PMs using mathematical models [2][3][4][5]. In some cases, the calculations focus on the characterization of bar PM magnetic field lines distribution in the electromagnetic system, which simplifies the processes of the operations based on the calculation of leakage permeance, thus making it easier to understand [6][7][8]. The research on electromagnetic systems with fan-shaped PM is mainly focused on motor field based on FEA to acquisition of motor systemic characterization [9][10][11][12].…”