DC Electric Motors 101

[Laurentic]

Allen, having got you to explain if engine sizing and lipo battery terminology it is very remiss of me not to have thanked you.

However, before I could, having read your explanation, a big gall stone attacked me, blocking up the bile duct causing considerable pain and a prolonged session of violently throwing up for England, ending in some very nice paramedics taking me off to the local hossie where they are still sorting me out.

But just to say I am very grateful for all your explanations, most of which I now need to read again and understand.

Thank you Sir, a very good job well done.

Chris

[Allen Smithee]

Ouch!

I can empathise, having had four bouts of kidney stones over the last 40 years (two in the last eight months). Serious pain and vomiting were very much the top of the daily task lists.

AS

[Allen Smithee]

I've been trying to think of anything I might have left out of the above. As I said, I'd prefer not to get into AC motors partly because once you get past the basic descriptions of induction vs synchronous (and the various flavours like capacitor-start, resistance-start, split-phase etc) it degenerates into maths and phasors quite quickly but mainly because there are many people on here who are far more knowledgeable than me about them! The thing that did occur to me was the subject of dynamic braking, so I thought I'd add a simple explanation.

In one of the early posts we looked at how a basic motor works. An electric current in a coil of wire siting in a magnetic field would cause a force couple between the rotor and the stator and so make the rotor rotate.

We then observed that the coil rotating inside the magnetic field (brushed motor) or the magnetic field rotating around the coil (brushless motor) would induce a voltage in the coil that we called the "back-EMF" because its direction was always opposite to the voltage driving the current in the coil.

We put these two together and realised that the back-emf reduced the net voltage on the coil to the point where that voltage would drive just enough current through the coil resistance to produce the torque needed to drive the load.

From this we deduced that if the load was zero (in a perfect motor with no resistance, friction or magnetic losses) the required current was zero, so the back-emf must have risen to precisely match the voltage applied to the coil - and this was the root of the motor characteristic "Kv" which describes a DC motor in terms of the rpm per volt it will turn at with no load. And if the motor was turned FASTER than this speed the back-emf would be greater than the applied voltage, so the motor would experience a torque in the reverse direction - something that slows it down.

So what happens if we take our motor, spin it up with a battery and then remove the battery? Well obviously the applied voltage is removed, but the motor is still turning so the back-emf is still there. Remember that the back-emf is produced by the motion of the motor, and it matches the voltage defined by the Kv characteristic - apply 10 volts to a 1,000rpm/v motor and it will try to turn at 10,000rpm and will suck in whatever current it needs to achieve that.

Now if instead of connecting a 10v battery we connect the two wires *together* we are effectively fitting a zero-volt battery. So the motor will try to turn at zero rpm, and it will suck current around the windings in the opposite direction as required to achieve it - it will stop dead or melt its windings in the attempt! If you want to see just how hard a motor will try just fit a prop to a motor, mount it securely, connect a battery so it's running nicely and then WHILE STANDING BEHIND IT disconnect the battery and short the wires together. The motor will probably come to a dead stop in what seems like half a turn, and almost certainly throw the prop.

This brake function is available in almost all modern speed controllers - it's main use is to rapidly stop a folding prop so that it will fold rather than windmill. The stop can be made less violent by connecting the wires through a resistance so that the current induced in the windings develops a voltage across the resistor and reduces the voltage across the coil. In a speed controller the softer settings are usually achieved by switching in some FETs rather than resistors, but the effect is the same.

But note that the effect is proportional to speed, so it won't work as a parking brake, and you can turn the motor over slowly without noticing the brake is on - it's a *dynamic* brake only.

AS

[Roger B]

The only comment I would make is that you have been talking about permanent magnet motors that react like shunt wound ones with a relatively constant field. Series wound motors are capable of running away as when the back EMF rises the field current drops reducing the back EMF.

[dieselpilot]

Motor(generator) braking can be regenerative, sending current back to the source even when motor BEMF is below source V. This is dependent on the controller design and is not 100% efficient as with everything.

[Allen Smithee]

The only comment I would make is that you have been talking about permanent magnet motors that react like shunt wound ones with a relatively constant field. Series wound motors are capable of running away as when the back EMF rises the field current drops reducing the back EMF.

Yes, I'm restricting my scope to permanent magnet DC motors. It's over 40 years since I had to do the sums for field windings and over- and under-compounded motors (mandatory second-year subject - passed the exam and forgotten within the month), but if anyone wants to cover them please do jump in!

AS

[MJM460]

Hi Allen, as I have mentioned before, you have filled in many of the gaps in my knowledge of DC motors, in particular the brushed type.  I am hoping the brushless ones will follow in due course.

I decided to test out my new knowledge by applying it to a Speed 600 BB that I have on hand.  I chose it because I also have the original box with some manufacturers data.  It is actually quite old, possibly purchased in the 80’s.

There was no torque data or Kv value so I tried to find these on the web, but obviously was looking in the wrong places.  But I did find a range of stall currents.  Also no winding resistance data.  The manufacturers home page kept giving an error.

So I took 55 amp as the stall current (actually the lowest of three that I found), and assumed the no load rpm was a suitable estimate for Kv based on the rated voltage of 7.2 V.

I noticed in your equation that the winding losses equal the applied voltage at stall when output power is obviously zero, so divided the voltage by stall current to estimate winding resistance at 0.131 ohms.

I calculated Kt as you described, so calculated the torque at stall current and no load current, and worked out the equation for a straight line between the two as the speed-torque curve.

You might be interested in the results.  The first attachment tabulates the data and calculated factors, and also has the table of calculated results.

The second shows the results in graphical form.  The mechanical power curve uses the mechanical formula,

P = 2 x pi() x N x T/60, while the other power out is from the electrical parameters using the formula you provided.

The maximum efficiency looks to be around 67% compared with the manufacturers 76% (at 12 A), and the two power curves agree within approx 10%, which seems pretty satisfactory.  Using the mechanical power out and assuming 11 amps gives 76.9% which looks very close to the manufacturers figure.

I did try a few “what if” experiments to see if adjustments would reduce the difference in the power curves but I did not discover anything useful.  Probably missing the obvious.

Now if only I can arrive at a good way to predict the torque speed curve of my (boat) propellor, I should be able to match it to that best efficiency point.

Thanks for all your effort in providing the motor explanations,  I hope this is of interest.

MJM460

[dieselpilot]

Estimating the load of the prop is easy, the Astroflight book covers that. I just remembered that the book is available for download for free. http://astrobobb.com/

The hard part about achieving maximum efficiency is the dynamic load. This goes virtually any application. The real world in motion loads and operating speeds are tough to nail just right. However, some testing with a few different props will get you pretty close. You need to measure or log data in real time to be very accurate. If it's a slow ship it's probably good enough to use the static loading figures.

[MJM460]

Thanks Dieselpilot, that is a very interesting site.  I had not seen it before, though I have read the story of Gossamer Condor.  I have downloaded some holiday reading.

MJM460