## Motor Efficiency Plots

In Chapter 6 the question of efficiency plots of electric motors was addressed. An example was given in Figure 6.7. It is very useful to be able to print this sort of diagram, to see the operating range of electric motors, and where they operate most efficiently. Furthermore, this can be done very effectively and quickly with MATLABĀ®. The script file is given below.

% A program for plotting efficiency contours for % electric motors.

% The x axis corresponds to motor speed (w),

% First, set up arrays for range.

x=linspace(1,18 0);% speed, N.B. rad/sec NOT rpm y=linspace(1,40); % 0 to 40 N.m

% Allocate motor loss constants.

kc=1.5; % For copper losses ki=0.1; % For iron losses kw=0.00001; % For windage losses

ConL=2 0; % For constant motor losses

% Now make mesh

Output_power=(X.*Y); % Torque x speed = power B=(Y.A2)*kc; % Copper losses

% Iron losses

Input_power = Output_power + B + C + D + ConL; Z = Output_power./Input_power;

% We now set the efficiencies for which a contour % will be plotted.

V=[0.5,0.6,0.7,0.75,0.8,0.85,0.88]; box off grid off contour(X,Y,Z,V);

xlabel('Speed/rad.sA-A1'), ylabel('Torque/N.m'); hold on

% Now plot a contour of the power output % The array Output_Power has

% already been calculated. We draw contours at % 3 and 5 kW. V=[3000, 5000];

contour(X,Y,Output_power,V);

This program was used to give the graph shown as Figure 6.7. In Figure A.1 we shown the result obtained for a higher power, higher speed motor, without brushes. All that has happened is that the motor loss constants have been changed, and the ranges of values for torque and angular speed have been increased as follows:

Figure A.1 A plot showing the efficiency of a motor at different Torque/speed operating points. It shows the circular contours characteristic of the brushless DC motor

100 200

300 400 500 600 700 800 900 1000 Speed/rad.s-1

100 200

300 400 500 600 700 800 900 1000 Speed/rad.s-1

x=linspace(1,1000); % N.B. rad/sec, not rpm y=linspace(1,250);

% Allocate motor loss constants.

kc=0.2; % For copper losses ki=0.008; % For iron losses kw=0.00001; % For windage losses

ConL=400; % For constant motor losses

Also, the values of efficiency were changed, and the last lines that plot constant power contours were removed.

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