Latvian Maritime academy

the machine, combination and technological harmonics. The latter are caused by the technological
parameters - axis misalignment of the rotor and stator, tapering and ellipse form of rotor, eccentricity of
the stator bore, defects of the bearing units.
The mathematical description of the magnetic field in the air gap of electric machine
The investigation of the influence of the above mentioned defects of bearing units on the magnetic
field of induction machine was based on the calculation of stationary magnetic field system of the electric
machine.
rotH
divB
0 ,
B H
where:
H - the intensity of magnetic field;
- density of electrical current;
B - the induction of magnetic field;
- the magnetic permeability of steel
The Poisson equation mathematical description is considered for the calculation of three-dimension
stationary magnetic field [8]:
Ay
y x
z
A
x z
Az
y
x
where:
z
Ax
x y
Az
x
A
y
z
y
y
A
z
z
Ax
y
y
Az
x x
z
Ay
x x
y
A
z
x
Az
y
x
y
z
(1)
, (2)
A x , A y , A z , x , y , z
– the components of the vector magnetic potential and current density
vector along axes x, y, z correspondingly.
On the basis of the system of pre-set currents and magnetic parameters of different space sectors it is
necessary to calculate the space distribution of vector A, meeting the equations of the system (2) and
boundary conditions of the space size.
The task of calculation of the magnetic field is solved minimizing the functional:
F
V
1
B
0
x
By
1
BxdBx
Ax
x
BydBy
0
1
A
y
y
B
0
z
BzdBz
Az
z
dV.
(3)
For the minimization of functional (3) the investigated size is divided into the set of finite elements.
The finite element is selected as a tetrahedron.
Minimum of functional (3) is found solving the equations system:
16