**Smoked Motor Theory**

So what changes to a theoretical motor model are required to incorporate a smoked motor effect?

1) Assume the smoke results from shorted windings in the motor armature that effectively reduces the number of windings on the armature.

2) Assume motor R, kt and ke are proportional to the number of windings. So a shorted motor has c*R,c*kt,c*ke constants where 0< c < 1 is the proportional degradation constant.

In the pure resistive motor model

torq = kt*i – torq_0;

i = (V – w*ke)/R where w = motor speed.

so replacing the motor parameters R,kt,ke with cR,ckt,cke gives the more general smoked motor equations. c typically is less than 1. c = 1 represents a non-smoked motor.

torq = c*kt*i – torq_0;

i = (V – w*c*ke)/(c*R);

Eliminating i in the torq equation gives

torq = kt*V/R – c*w*ke*kt/R – torq_0 ;

Now suppose we have a smoked motor where c != 1 . Lets see what happens to measurable parameters… _s subscript is a smoked parameter

i_free_s =torq_0/(c*kt) = i_free/c

w_free_s = (V – torq_0*R/kt)/(c*ke) = w_free /c

torq_stall_s =V/R*kt -torq_0 = torq_stall

because with w = 0 the decrease in kt is compensated by a decrease in R.

At a given torque, the speed of the smoked motor is

w_s = w/c and

i_stall_s = i_stall/c

**So a smoked motor is better??**

With the two assumptions, the smoked motor shows a higher speed at a given torque, no change in the stall torque, higher currents at all torques . So long as you can supply the current, the motor will provide more power at a given voltage. Huh? This seems counter to what we are seeing. We know the smoked motor climbs are a little slower. Well, if the assumptions are correct, then the reason for the slower climb must lie with the series resistance in the motor circuit. The higher currents cause a corresponding voltage drop across the series resistance and the motor voltage is smaller.

There are three main sources of series resistance…. the internal motor series choke (approx .2 ohms) , the wire resistance (approx .01 ohms) and the battery series resistance (approx .4 to .6 ohms Nimh per this ref) . The spec motor resistance is 1.6 ohms including the series choke so the motor resistance actually must be written as R = R_choke + R_armature = .2 + c*1.4 ohms.

**Example torq loss with series resistance included**

Lets look at what happens to the stall torq when the series resistance is included and the motor has a c = .8 or 20% smoked degredation factor. The resistive motor model equations are valid for a zero series resistance and the V is the voltage across the armature not the motor itself. So we must add another equation that gives V =14 – i*.7 ohms. Here we assume that the battery internal resistance = .5 ohms and the choke resistance is .2 ohms and the noload battery voltage is 14 volts. R = c*1.4 ohms which is the armature resistance.

Then i_stall = (14 – .7*i_stall)/(c*1.4) or i_stall = 10/c – .5/c*i_stall so

i_stall = 10/c/(1+.5/c)

torq_stall = c*kt*i_stall – torq_0

= 10/(1+.5/c)*kt – torq_0

If c =1 then torq_stall = 6.7 *kt -torq_0

If c = .8 then torq_stall = 6.15*kt – torq_0 or > 9% reduction in the torq for the same battery voltage.

This is more consistent with what we are seeing on the pole. At the San Diego regionals we were able to run new motors with the PTC fuses and get up the pole without tripping for most of the day. We had a bad deployment that probably smoked the motors. We could nolonger climb the pole without tripping the PTC’s. So the motors were drawing higher current but when we bypassed the PTC’s the minibot had a climb speed that was only slightly slower.

**Really badly smoked motors**

Well, we have smoked three motors so far. All are operational but some were smoked several times and show highly degraded torque. I decided to measure one today and it came out at 44% of a new one.

Test procedure was simply to hook up a 1 in torque arm directly to the motor w/o its gear box. I applied around 4.3 v and measured the force exerted with a force sensor. Results:

.07 in_lbs @4.3v -> .227 in_lbs (3.63 oz in) @ 14v by linear scale up. Using the test results posted for the 14v actual motors corrected for no gear box the max torq is 8.3 oz in. So the effective torque is 3.63/8.3 or 43.7%. Rats.

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