Magnetic Couple Torque Calculations
Table of Contents
Inputs ...... 1 Calculate Force Vector, Components, & Torque ...... 1 Plot Torque Available Curves ...... 2 Plot Pull Force Curves ...... 3 Plot Torque Available & Required Curves ...... 3 Plot Magnet Layout ...... 4 Outputs ...... 6
This file computes the available torque from the magnetic couple as a function of magnet offset angle. Included are the pull force and required torques for 100W, 90W and 80W power production.
The primary equation used to compute the force between the two cylindrical magnets is as follows:
Inputs
clc; clear; close all;
uo=4e-7*pi; % Permeability of the magnets M=1.6e6; % Magnetization of the magnets R=(.5/2)*(2.54/100); % Magnet Radius t=.25*(2.54/100); % Magnet Thickness th=[0:(pi/3600):(pi/4)]; % Theta (Disk offset) DR=(1.5-R*100/2.54)*(2.54/100); % Outer Magnet Ring Radius DRi=(1.5-R*300/2.54)*(2.54/100); % Inner Magnet Ring Radius s=sqrt((DR.*th).^2+(20e-3)^2); % Linear Distance btwn outer Magnets si=sqrt((DRi.*th).^2+(20e-3)^2); % Linear Distance btwn inner Magnets n=floor(pi*DR/R)-1; % Number of outer Magnets ni=floor(pi*DRi/R)-1; % Number of inner Magnets w=5000:100:10000; % Speed in RPM Calculate Force Vector, Components, & Torque
for i=1:length(s) phi_o(i)=atan(20e-3./(DR.*th(i))); phi_i(i)=atan(20e-3./(DRi.*th(i)));
Fo(i)=((pi.*uo)./4).*(M.^2).*(R.^4).*((1./(s(i).^2))... +(1./(s(i)+2.*t).^2)-(2./(s(i)+t).^ 2)); Fi(i)=((pi.*uo)./4).*(M.^2).*(R.^4).*((1./(si(i).^2))... +(1./(si(i)+2.*t).^2)-(2./(si(i)+t).^ 2));
1 Magnetic Couple Torque Calculations
Fy_o(i)=Fo(i)*sin(phi_o(i)); % Pull Force from Outer Ring Fy_i(i)=Fi(i)*sin(phi_i(i)); % Pull Force from Inner Ring
To(i)=DR.*Fo(i)*cos(phi_o(i)); % Torque from Outer Ring Ti(i)=DRi*Fi(i)*cos(phi_i(i)); % Torque from Inner Ring end T=n*To+ni*Ti; [Tmax,loc_T]=max(T); thmax_T=th(loc_T)*180/pi;
Fy=n*Fy_o+ni*Fy_i; Plot Torque Available Curves
figure(1) plot(th*180/pi,n*To,'-r'); hold on plot(th*180/pi,ni*Ti,'-b'); title('Torque for Available'); legend('Outer Ring Torque','Inner Ring Torque'); xlabel('Theta [Degrees]'); ylabel('Torque [N*m]'); grid minor hold off
2 Magnetic Couple Torque Calculations
Plot Pull Force Curves
figure(2) plot(th*180/pi,n*Fy_o,'-r'); hold on plot(th*180/pi,ni*Fy_i,'-b'); title('Pull Force'); legend('Outer Ring Force','Inner Ring Force'); xlabel('Theta [Degrees]'); ylabel('Force [N]'); grid minor hold off
Plot Torque Available & Required Curves
figure(3) set(figure(3), 'Position', [0 0 1024 768]) subplot(2,2,1); plot(th*180/pi,T) grid minor xlabel('Theta [Degrees]'); ylabel('Torque [N*m]'); title('Torque for Available');
Torquereq2=(100./w).*(60./(2.*pi));
3 Magnetic Couple Torque Calculations
subplot(2,2,2); plot(w,Torquereq2) grid minor xlabel('RPM'); ylabel('Torque [N*m]'); title('Torque Required for 100W');
Torquereq3=(90./w).*(60./(2.*pi)); subplot(2,2,3); plot(w,Torquereq3) grid minor xlabel('RPM'); ylabel('Torque [N*m]'); title('Torque Required for 90W');
Torquereq4=(80./w).*(60./(2.*pi)); subplot(2,2,4); plot(w,Torquereq4) grid minor xlabel('RPM'); ylabel('Torque [N*m]'); title('Torque Required for 80W');
Plot Magnet Layout
figure(4);
4 Magnetic Couple Torque Calculations for i=1:n x(i)=DR*cos(i*2*pi/n); y(i)=DR*sin(i*2*pi/n); ang=0:0.01:2*pi; xp=R.*cos(ang); yp=R.*sin(ang); plot(x(i)+xp,y(i)+yp) hold on end for i=1:ni xi(i)=DRi*cos(i*2*pi/ni); yi(i)=DRi*sin(i*2*pi/ni); plot(xi(i)+xp,yi(i)+yp) hold on end xc=0;yc=0;rc=1.5*2.54/100; xp=rc.*cos(ang); yp=rc.*sin(ang); plot(xc+xp,yc+yp) axis equal axis off title('Magnet Layout'); hold off
5 Magnetic Couple Torque Calculations
Outputs
fprintf('Magnet Size:\n\tDiameter: %1.3f[in]\n\tThickness: %1.3f[in]\n\n',... 200*R/2.54,100*t/2.54); fprintf('Number of Magnets:\n\tOuter: %1.0f\n\tInner: %1.0f\n\n',n,ni); fprintf('Magnet Placement:\n\tOuter: %1.2f[in]\n\tInner: %1.2f[in]\n\n',... 100*DR/2.54,100*DRi/2.54); fprintf('Max Torque: %1.3f [N*m] at %1.3f [deg]\n\n',Tmax,thmax_T); fprintf('Max Pull Force: %1.3f [N]\t%1.3f [lbf]\n\n',... max(Fy),max(Fy)*0.2248);
Magnet Size: Diameter: 0.500[in] Thickness: 0.250[in]
Number of Magnets: Outer: 14 Inner: 8
Magnet Placement: Outer: 1.25[in] Inner: 0.75[in]
Max Torque: 0.414 [N*m] at 21.950 [deg]
Max Pull Force: 50.132 [N] 11.270 [lbf]
Published with MATLAB® 7.13
6