Design, Analysis, and Experiment of Multiring Permanent Magnet Bearings by Means of Equally Distributed Sequences Based Monte Carlo Method

Table 1

Nomenclature.

Letter	Means	Letter	Means
, α	Polar coordinates of magnetic charge A	D	n-dimension range
, β	Polar coordinates of magnetic charge B	I	The product of the measure () and the expectation of Function f
,	Moving polar coordinates of the inner ring relative to the outer ring	MD	The corresponding measure of D
R1, R2	Inner and outer radii of the inner magnet rings	MC	The measure of a hypercube
R3, R4	Inner and outer radii of the outer magnet rings	N	The number of the uniformly distributed points
	Radius vector of the magnetic charge A and B	m	The number of points falling statistically in D
x0	Axial displacement of rotor		The expectation of Function f
l	Axial length of the inner magnet rings		The equidistant point series
L	Axial length of the outer magnet rings		Irrational number
H	Radial thickness of the outer magnet rings	Ps	The uniform distribution of Point Sequences in an Ultra-cuboid Containing Integral Region
h	Radial thickness of the inner magnet rings	Fy/Fz	The radial force of the PMB
g	Length of the air gap	FX	The axial force of the PMB
Br	The magnetic remanence of magnet	n	The number of pair(s) of magnetic rings
	Vacuum permeability		The introduced error factor