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1. Commercial Standard Magnets
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Ceramic FLux_RMS = 0.0175
EMF_RMS = 3.6075
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Alnico FLux_RMS =0.0168
EMF_RMS = 5.1619
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NdFeB FLux_RMS = 0.0459
EMF_RMS = 9.4262
2. Loud Speaker Magnet
FLux_RMS = 0.0171
EMF_RMS = 3.4987
Appendix B
Matlab code for sketching the output emf and flux of the generators
% EMF calculation from FEMM
%By Maribini Manyage
clc
clear all; close all;
P = 2;
w = 1912; %mechanical speed in rpm
freq = (w*pi/30)*P/(4*pi); %frequency
XA = load('flux_link_A.txt');
XB = load('flux_link_B.txt');
XC = load('flux_link_C.txt');
beta = XA(:,1); % angle between Is_r and d-axis [elec degrees]
alpha = beta - beta(1,1); % Rotor position in [elec degrees] from Zero
time = alpha*(pi/180)/(2*pi*freq);%*1000; %time
flux_link_A = 2*XA(:,2);
flux_link_B = 2*XB(:,2);
flux_link_C = 2*XC(:,2);
% Perform spline in order to differentiate flux linkage vs time
pp_flux_A = spline(time,flux_link_A);
pp_flux_B = spline(time,flux_link_B);
pp_flux_C = spline(time,flux_link_C);
% extracting piecewise polynomial coefficients and derivation
[hgt,wdth] = size(pp_flux_A.coefs);
clear AA;
for k = 1:hgt
AA(k,:) = polyder(pp_flux_A.coefs(k,:));
end
dpp_flux_A = MKPP(time,AA)
[hgt,wdth] = size(pp_flux_B.coefs);
clear AA;
for k = 1:hgt
AA(k,:) = polyder(pp_flux_B.coefs(k,:));
end
dpp_flux_B = MKPP(time,AA);
[hgt,wdth] = size(pp_flux_C.coefs);
clear AA;
for k = 1:hgt
AA(k,:) = polyder(pp_flux_C.coefs(k,:));
end
dpp_flux_C = MKPP(time,AA);
%back emf
emf_A = ppval(time,dpp_flux_A);
emf_B = ppval(time,dpp_flux_B);
emf_C = ppval(time,dpp_flux_C);
figure(1);
plot(time*1000,flux_link_A,'r-');
hold on;
plot(time*1000, flux_link_B,'b-');
plot(time*1000, flux_link_C,'g-');
title('Flux linkage - under noload');
xlabel('Time [ms]'),ylabel('Flux linkage [WbT]')
grid;
figure(2);
plot(time*1000,emf_A,'r-');
hold on;
plot(time*1000, emf_B,'b-');
plot(time*1000, emf_C,'g-');
title('Back Emf - under noload');
xlabel('Time [ms]'),ylabel('Back EMF [V]')
grid;
x = length(flux_link_A);
FLux_RMS = norm(flux_link_A)/sqrt(x)
y = length(emf_A);
EMF_RMS = norm(emf_A)/sqrt(y)