лабораторная работа / мэмс / 10lw
.docxMinistry of science and education, youth and sport of Ukraine
Zaporozhie National Technical University
Department EEA
Report
Laboratory work#10
Done L.A.Askerova
Checked T.M.Kornus
Zaporozhie
2012
TOPIC : Modeling of electromagnetic processes in magnetic circuits of a direct magnetic flux in MATLAB environment. Part 2.
PURPOSE OF THE WORK: Problem statement, development of the program of calculation of a nonlinear magnetic circuit by the Newton method using discrete models of nonlinear resistance and their spline-interpolation.
Variant#1
The design of a magnetic system is represented in figure 10.1.
Figure 10.1 – The modeled magnetic circuit
Let parameters of a circuit are given:
Length of average magnetic lines according to fig. 10.1:
|
Var #
|
L1, mm |
L2, mm |
L3, mm |
L4, mm |
L5, mm |
L6, mm |
L7, mm |
L8, mm |
L9, mm |
L10, mm |
L11, mm |
I1, A |
I2, A |
N1 |
N2 |
|
1 |
20 |
80 |
25 |
80 |
20 |
25 |
80 |
0.02 |
0.02 |
25 |
25 |
10 |
10 |
60 |
60 |
Thickness of the core:
dlt=L11=0.025 m;
Curve of magnetization of core B (H) is shown in figure 9.2.
а).
а) – general view;
Figure10.2 – Magnetization curve B(H) of the core steel
According to the second Kirchhoff law it is possible to transfer MMF source Fm into a branch containing conductance G1 and then to transform it to a source of magnetic flux FmG1. The equivalent circuit according to these transformations is offered in fig. 10.3.
Figure 10.3 – The equivalent transformed circuit with magnetic flux source FmG1
The system of the potential equations looks as:
Where
,
,
,
,
The node magnetic fluxes:
The Block-diagram
The program of calculation in MATLAB environment
The main program:
% Newt6
% CALCULATION OF THE NONLINEAR MAGNETIC CIRCUIT BY THE NEWTON %METHOD
n=30; % number of iterations of the Newton method
h=0.001;% a step for realization of numerical derivation
I1=10;I2=I1;
N1=60;N2=N1;
I=I1; N=N1; % Current and loops of windings
mu0=4*pi*1e-7;
L1=20;L2=80;L3=25;L4=80;L5=20;L6=25;L7=80;L8=0.02;L9=0.02;L10=25;L11=25;
l1=0.5*(L1+L6+L3)+L7+0.5*(L10+L1)+2*L2+0.5*L3; % length of magnetic branches
l2=l1;
l3=L7+0.5*(L6+L10+L1+L5)+L2+L3+L4;
D1=L5;D2=L5;D3=L3; % breadth of magnetic branches
dlt=L11; % thickness of the core
luft1=L9;% thickness of the air-gap
luft2=L8;
Fm1=N1*I1;
Fm2=Fm1;
S1=D1*dlt; S2=D2*dlt; S3=D3*dlt; S31=L5*dlt;S32=S31; % cross-section area of magnetic branches of the core
Rm2=luft1/(mu0*S31); % magnetic resistance of the air-gap
Rm1=luft2/(mu0*S32);
Gm2=1/Rm2; % Magnetization curve of steel
Gm1=1/Rm1;
B = [-2.1,-2,-1.98,-1.96,-1.94,-1.92,-1.9,-1.86,-1.84,-1.8,-1.7,-1.6,-1.4, -1.2,-1, -0.8, -0.4, -0.2, -0.1, 0, 0.1, 0.2, 0.4, 0.8, 1, 1.2, 1.4, 1.6, 1.7, 1.8, 1.84, 1.86, 1.9, 1.92, 1.94, 1.96, 1.98, 2, 2.1];
H = [-1000000,-11820,-5331,-3191,-2249,-1625,-1218,-660,-520,-295,-97,-51.4,-31.9,-26.2, -23.2,-20.8,-15.2,-10.8,-7.58, 0,7.58, 10.8, 15.2, 20.8, 23.2, 26.2, 31.9, 51.4, 97, 295, 520, 660, 1218, 1625, 2249, 3197, 5331, 11820, 1000000];
Flux (1,1)= 0.02; % the initial approximation of magnetic fluxes
Flux (2,1)= 0.015;
Flux (3,1)= 0.01;
% Iterative calculation of magnetic fluxes in the linear network containing
% discrete flux models by node potentials method
for k=2:n
% calculation of discrete flux models conductivity for K-1 iteration
U1=l1*spline (B, H, Flux (1, k-1)/S1);
G1=S1/l1*der7 (H, B, U1/l1, h);
U2=l2*spline (B, H, Flux (2, k-1)/S2);
G2=S2/l2*der7 (H, B, U2/l2, h);
U3=l3*spline (B, H, Flux (3, k-1)/S3);
G3=S3/l3*der7 (H, B, U3/l3, h);
% the fluxes of discrete sources for K-1 iteration
Flux1=Flux (1, k-1)-U1*G1;
Flux2=Flux (2, k-1)-U2*G2;
Flux3=Flux (3, k-1)-U3*G3;
% node conductivities for K-1 iteration
G33=G3+G1+G2;
G11=G1+Gm1;
G22=G2+Gm2;
G13=G1;
G12=0;
G23=G2;
G = [G11, -G12, -G13;
-G12, G22, -G23;
-G13 -G23 G33];
% the node fluxes for K-1 iteration
Fluxnode = [Flux1;-Flux2;Flux3+Flux2-Flux1-Fm1*G1+Fm2*G3];
phi=G\Fluxnode; % calculation of the node potentials for K iteration
% magnetic fluxes for K iteration
Flux (2, k) =(-phi(2)*Gm2+Flux(2, k-1)*2)/3;
Flux (3, k) =(Flux3-phi(3)*G3+Fm2*G3+Flux(3,k-1)*2)/3;
Flux (1, k) =(phi(1)*Gm1+Fm1*G1+Flux(1,k-1)*2)/3;
eps1=Flux(3,k)+Flux(2,k)-Flux(1,k);
if abs(eps1)>abs(eps1f)
eps1f=eps1;
end
end
% Construction of the graphics of convergence of iterative processes of the magnetic fluxes calculation through the core
p=1:n;
F1=Flux(1,n)/S1
F2=Flux(2,n)/S2
F3=Flux(3,n)/S3
epsi=eps1f
plot (p, (Flux (1, p)/S1), p, Flux (2, p)/S2, p, Flux (3, p)/S3);grid on
legend('B1','B2','B3',-1); title ('Magnetic induction')
xlabel('iterations');
The subprogram -function der7 of calculation of derivative in the given point is performed in methodical directions to laboratory work # 8.
Listing of the program
B1 =
0.0222
B2 =
-0.0019
B3 =
0.0193
eps1 =
-0.0048
In figure 10.4 graphical functional dependences of calculated values of induction in the magnetic circuit (fig. 10.1) accord to each step of iteration are represented.
Figure 10.4 – Calculated curves of magnetic induction in limbs of the core according to iteration step
Conclusion: The magnetic induction in limbs of the core according to iteration step was found. The graph is presented. Accuracy is ok.