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Modeling a Step Motor Generator

Oct
28
by Jeff Kordik

In our last post, we explored the possibility of connecting a step motor to a small gas engine for use in recharging a 12 volt battery. The effort resulted in a computer model which we hoped to use to optimize the design without having to expend excessive time and effort on trial and error. Our first concern was whether the step motor had the optimal number of winding turns on the stator. Changing the winding of a step motor is a difficult experiment because of the complexity of reprogramming a winding machine and loading it with a different size wire. Using a computer simulation makes it easy. With the standard winding of the off-the-shelf HT23-601 step motor and a 50 ohm load we were able to achieve a maximum output current of 1.01 amps. Is that the best we can do? Let's find out. But first, consider some fundamentals. The output voltage of our generator depends on Ke, the back EMF constant and w, the shaft speed.

V_Ke_w

If we change the number of winding turns (n), Ke will change in direct proportion:

Ke_n

Changing the winding turns also affects inductance and resistance. As you may recall from your electrical engineering studies, the inductance of a coil varies according to the square of the turns:

L_nsquared

Resistance also varies by turns squared. How can that be? If I double the number of winding turns I'll use twice as much wire, so the resistance should only double. However, we must fit those extra turns into the same space inside the stator. In order to fit twice as many turns, we have to use thinner wire, with half the cross sectional area (see illustration below), which doubles the resistance again.

R_nsquared

Now that we understand the relationship of Ke, R and L to winding turns, we can update the model, allowing us to scale the winding of the HT23-601 to anything we want. We tried a range of windings of 0.3n to 2.5n and obtained the following results:

output current vs winding turns

Reducing the turns to 0.5n allows us to generate much more current than the original winding. Since we're really after output power, we also plotted power versus winding turns and the results are even more promising: an 84% increase in output power by reducing the winding turns to ½.

Power vs Winding Turns

Let's consider one more factor: the load resistance. Is there anything magical about our choice of 50 ohms? Let's find out; now that we have a computer model, we can easily try many values.

Power vs load resistance

With 0.5n winding turns, we can get a few percent more power by reducing the load resistance from 50 ohms to 40. The act of modeling this system has allowed us to get 88.4% more power output from the system at no increase in cost. We also gained valuable insight into how the system works. For example, the system is quite sensitive to winding turns. The relative flatness of the load resistance curve tells us that load resistance is less of a factor than winding turns, but still important. And we did it all much more quickly than building 16 different motors and testing them with 15 different load resistors.

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