DC Electric Motors 101

[Allen Smithee]

This question was asked in Gadabout's thread on the superb work he's done on an electric starter for his Seal so I've offered to do a piece on it, which will take a little while. I tend to explain things from first principles because that makes sense to me, but it may not make sense to other people so:

- If I am pitching this at the wrong level please shout. Especially if I'm stating the obvious and talking down to people in an annoyingly patronising manner!
- If something isn't clear please just ask me to clarify further
- If you disagree with something I say please shout. You may well be right and I could learn something!
- I am only going to talk about DC motors. AC motors (synchronous or induction) are a different skillet of cod. We could come to that afterwards (if anyone is still reading) but it's a bigger subject with more maths, so I wouldn't recommended it. But when I say DC motors this includes both normal brushed motors and brushless DC (BLDC) motors because even though they look similar BLDC motors are NOT 3-phase AC motors we will probably talk about that at the end.
- If I have put this thread in the wrong place please feel free to move it

I have to (briefly) start with some very basic stuff about electromagnetism. I have no doubt that you all know this already, but I want to do this brief bit of revision because a heck of a lot of the general misconceptions about electric motors arise because people forget that this is the underlying principle.


Electricity and magnetism are linked. I don't want to go into why or how because I'm no longer current enough to start explaining how magnetism is the inevitable consequence of relativity in electrostatic fields - we don't need to know this! What we DO need to know is what that means in practice. We all know that:

1. If you apply a voltage across a conductor it will cause a current to flow through the conductor
2. If you pass a current through an conductor it produces a magnetic field - the conductor becomes a kind of magnet
3. If you put two magnets near each other they experience a force between them that either attracts or repels
4. If you move a conductor THROUGH a magnetic field (or move a magnetic field past a conductor) it induces a current in the conductor. The faster the movement the bigger the Electro-Motive Force (EMF or "voltage" if you prefer) which induces the current.

The important and basic thing here is that these the are not "either/or" things - they all happen at the same time. So if you take a wire and pass a current through it then it becomes a magnet. If you place the wire in the field of a fixed magnet it experiences a force. If you allow that wire to be MOVED my the force then the external magnetic field also induces a current in the wire. And the important bit is that the current induced by the external field is always in the opposite direction to the current flowing in the wire that produces its magnetic field so in the context of motors we refer to this as the "Back-EMF" because it's a backwards-facing voltage opposing the voltage across the wire. This is a very important concept, so if you don't grasp it to start with please read it agaon until the penny drops. If the penny refuses to drop please ask questions!

The other important concept is what we call "ideal" machines. In science and engineering we have to reconcile the fact that theory is simple, neat and tidy where the real world is often messy and complicated making it very difficult to understand. One of the more common ways of doing this is to start off with a simple, pure theoretical "ideal" that is easy to understand, and when we have that fully sussed out we add in each of the "real" bits separately until the thing we understand looks like the "real" one.

So in the next post I will start talking about an "ideal" electric motor to help understand the basic stuff, and then move on to add the "real" bits.

So if you're sitting comfortably I'll begin...

AS

[Allen Smithee]

So now we consider an "ideal" electric motor. This consists of a perfect coil of resistanceless wire wrapped around a core of soft loss-less iron mounted on a shaft with frictionless bearings. The coil has a perfect commutator which connects it to the DC Voltage source with no losses, only connecting the coil when it is at the correct angle.  This assembly sits inside a par of perfect permanent magnets which have lossless magnetic coupling to the coil. You can ignore most of that - it's just a list f the "real" bits we have to add in later. Lets call the moving part a "rotor" and the static bit a "stator". In a brushed motor the "rotor" has the coil while the "stator" is one or more permanent magnets. When we come to brushless motors we'll see why they put the coil in the stator and the permanent magnets in the rotor, but that doesn't really change anything.

So if we connect the power a current flows in the which creates a magnetic field that attracts/repels the field of the permanent magnets producing a torque that rotates the rotor.

As the rotor rotates the fixed magnetic field induces a Back EMF in the coil which is opposite to the voltage from the power supply, reducing the net voltage on the coil and so reducing the current in the wire.

The bearings are all frictionless, so as long as there is ANY current flowing there will be a torque that accelerates the rotor. It will keep accelerating until it reaches the speed where the Back EMF exactly equals the voltage from the power supply. At this speed there is zero current and zero power but that's OK because our perfect frictionless bearings don't need any to keep the rotor turning. This speed is essentially what's called the "motor characteristic" or "Motor Constant (Kv)" [there is an technical difference but it's not relevant here] which is expressed in RPM per Volt. so if a motor has a Kv of 1,000rpm per volt and you connect it to a 10volt power supply at 10,000rpm the Back EMF would also be 10volts, so it would be expected to turn at 10,000rpm and draw no current.

Now all of that is with no load. If we now use this motor to do actual work on physical load it slows the motor down. This causes the Back EMF to drop, which means the coil now has a voltage across it again and a current flows. This develops power, but only the power that is required by the load we put on it. This is one of the main fundamental differences between electric motors and infernal combustion engines, so it may be worth reading that again until it's clear (and if it isn't please ask for clarification).

With our "ideal" motor the speed returns to the Kv speed (because there is zero resistance in the coil), so the theoretical "ideal motor" runs at a constant speed which is determined by its Motor Constant and the applied voltage, and it draws whatever current it needs to turn the load at that speed.

That sounds like a good place to stop. In the next chapter I'll finally start talking about real motors, and hopefully it will become clear why we had to start with all this theoretical malarky.

AS

[Roger B]

Looks good to me, however I have some knowledge in this area. Any other views?

[Kim]

Very interesting! I've got a background in Electrical Engineering, but I can't say as I know much about electric motors.  And all makes sense to me so far and is quite fascinating.

Thanks for taking the time to write this down, Allen!
Kim

[Allen Smithee]

So, "real" motors, what are the differences and why do we care?

Essentially we can sum these up under three headings and these actually do useful things for us.

1. The coils (windings) of real motors have resistance.
2. The bearings of real motors have friction
3. The magnetic circuit of real motors isn't 100% efficient.

Of these the most important [for us] is (1). If you think back to the "ideal" motor, I said that if we put a load on it then it would slow down and that would reduce the Back EMF so that there was now a voltage across the coil and so it would start drawing current. I also said the coil had zero resistance, so how much current is drawn?

Let's take an example - an ideal 1000rpm/v motor on a 10v battery so turning at 10,000rpm. We put a load on it and slow it down to 9,500rpm so the BackEMF falls to 9.5v and so there is half a volt across the coil. Mr Ohm said:

v=iR, so i=v/R

v=0.5voltrs
R=0 Ohms

Therefore i = (0.5 / 0) = infinity.

In fact ANY drop in Back EMF draws an infinite current in an ideal motor, which is why the RPM is constant. There are paradoxes in this, but it doesn't matter because you can't buy ideal motors. A real motor will have some winding resistance. Typical values for small motors would be 0.01 to 1.0 Ohms, with SPeed 400 size (like that used in the Seal Starter) being around 0.2 Ohms.

So if we repeat the sums using a real resistance we get:

i = v/R = (0.5 / 0.2) = 2.5Amps

Now that's much more like it. So the coil of the motor is now drawing 2.5Amps at 9.5volts, so it is developing 23.75watts of useful power, nearly all of which is going into the load (I'll come to this in a minute).

But we are also putting 2.5Amps through a resistance of 0.2 Ohms, which means we will dissipate some heat:

Power = i²R = (2.5x2.5) x 0.2 = 1.25watts

We call this the "copper losses" = any electrical machine has to do some work against resistance and this appears in the efficiency numbers. It's also one of the two primary "specification limit" characteristics of an electric motor but I just want to get one more bit out of the way before getting to the punch line.

In our list of differences with real motors the second two were friction and magnetic losses. For our purposes w lump these together because they are (within practical limits) constant values in that they change very little with power, speed or load. You won't see any numbers for these in a motor specification, but what you WILL see is a value for "no load current" (usually called "i₀"). This number is the current required to overcome friction and magnetic losses, all wrapped up into one handy parameter. Typical values for small motors can be anything from 0.1A to 5A or more, with a typical Speed400 no-load current being around 0.7Amps This number can to some extent  be taken as a quality indicator - the lower the number the better the bearings & magnets and the finer the internal clearances (small gaps bean lower magnetic losses), but it's not the only guide. We tend to call this the "iron losses", but I personally don't like this term because we're also lumping the friction into it.

So if we now go back to the sums. Lets assume our 10,000rpm/v motor has a winding resistance of 0.2 Ohms and a no-load current of 0.5Amps, and we're driving it from a 10volt battery with a load that draws 2.5Amps.

First of all we look at the current and winding resistance. 2.5Amps into 0.2 Ohms gives us copper losses of 0.5v so the windings are seeing 9.5volts.

Then we deduct the no-load current from the total, so the "productive" current is 2.0Amps. So the "net" power coming out of the shaft is:

Power (out) = Volts * Amps = 9.5 * 2 = 19watts

Of course we also know that the *input* power is simply the input voltage times the total current:

Power (in) = Volts * Amps = 10 * 25 = 25watts

So the efficiency is Power (out ) / Power (in) = 19 / 25 = 76%

One of the great features of electric motors is that you don't need a dyno to know the net (output) power - you can work it out directly.

I mentioned a "punchline", which was probably rather over-selling it, but this is an important concept. I showed we can work out the power dissipated against the copper losses:

Power = (total current²) x Winding Resistance = i₀² x R_m

This power comes out as heat - it heats up the windings. If the windings can't dissipate the heat they get hotter and hotter until they melt. This is what happens when the magic white smoke escapes from an electric motor. This is the only major constraint on the power a motor can deliver. Within certain limits (in a minute - be patient!) you can whack the voltage up as high as you like, but the CURRENT determines how much heat the windings need to shed.

Why is this important? Well we are all used to defining motors/engines in terms of power ratings. We talk about a 1bhp engine or a 500 watt motor. Well for electric motors this is actually only true at one particular voltage. The true "rating" of the motor is simply the maximum current it can take without melting the windings. As this current limit is constant it means that the torque is constant. increasing the voltage leaves the torque value the same, but increases the revs. There is in fact a second "motor characteristic" called "Kt" or the Torque Constant, which is in units of torque per amp (and if you want to use metric units throughout you find that Kt=1/Kv, but don't worry about that). 

This is getting abstract - let me give a real example:

In the electric RC model world one of the most popular small motors was a Czech motor called the Axi 2820/10 which has been in production for something approaching 20 years now. This is a 1200rpm/v motor which can take around 40Amps for over a minute at a time, which means on a 10cell nicad or 3-cell lipo it delivers well over usable 400Watts - well over half a BHP and more than equivalent to a good 2-stroke 0.25 glow motor.

On 3 cells it turns a 10-6 prop and powers a fast 40" aerobatic model at 400watts. But the same motor used on 2cells turns slower and thus turns a bigger prop. In fact it turns something like a 13-6 prop and will tow up a 100-120" electric soarer in a sprightly manner at around 250Watts. But at the other end of the scale I have seen this same motor used in an electric ducted fan unit on a 12-cell (50volt) lipo producing well over 2.2kW (3bhp) and 2kg of thrust - more than some small turbines! Again, a small practical difference here is that many motors can actually take more current at high voltages because the high revs draw more air through the cooling holes than they get at lower revs. The copper losses are the same at all speeds and the iron losses are more or less constant, so I hope you can see that the higher the voltage the higher the efficiency from the same motor.

In all of these cases the motor is operating within its 40A limit, but the voltage determines how fast it turns and with more voltage you get more revs for the same torque. So the motor does not have a power limit, only a Torque limit which comes from the Current limit. There is only a POWER limit at any specific voltage. And that is the fundamental point I wanted to get across.

As far as I can remember there is only one more "in a minute" thing I said I'd come back to. There is (of course) a second limiting factor to the power, but it's one that we very rarely run into so we usually ignore it. I said we can keep increasing the voltage, but there will be a maximum voltage a motor can take. This is partly a matter of whether the voltage is high enough to start blowing holes in the insulation (very, very unlikely) but mainly that thing about higher voltages mean higher revs. If you keep winding the voltage up you can conceivably get to a speed where the motor can't take the centrifugal forces and bursts. I've seen this happen with early inrunner brushless motors that can shed magnets from the rotor, and I've (once) seen it with a cheap outrunner brushless motor with very agricultural machining in its rotor can that resulted in a split along a classical stress-raiser. But for most general uses this can be ignored.

Ok, that's been me in "hosepipe" mode. On the off-chance that anyone's still reading, are there any actual questions?!

 

AS

[crueby]

Great stuff Allen!  I remember back when working on printer R&D learning how the electric motors would change efficiency and power as they got hot during extended use.
 

[Charles Lamont]

Allen, as one of those guilty of making the enquiry, thank you very much for your most thorough exposition, which must have taken quite some time to put together. I have read all three posts in one sitting, and now need to digest that, and to go back over post 3 a couple more times before I will know if I need to ask questions.

You mention in part 2 the motor only delivering the power 'required' by the load. This perhaps needs a little sidebar clarification. The load may well be speed dependent, as, for example, with a centrifugal pump, in which the power absorbed is theoretically proportional to the cube of the speed. So the motor and load will settle to a speed at which the motor power output curve crosses the load input power curve. I don't see that this differs from an IC engine, except in the typical shape of the power curve.   

[Allen Smithee]

Firstly remember that all of this is strictly DC motors. There are similarities in some respects with some kinds of AC motors, but it's a much more complex subject so don't try to apply what I've said to an AC motor*. I also think it probably only applies to sensorless brushless brushless motors - I think sensored ones behave differently (that's something tatt only occurred to me this evening!).

Right, that's out of the way - to the question:

You mention in part 2 the motor only delivering the power 'required' by the load. This perhaps needs a little sidebar clarification. The load may well be speed dependent, as, for example, with a centrifugal pump, in which the power absorbed is theoretically proportional to the cube of the speed. So the motor and load will settle to a speed at which the motor power output curve crosses the load input power curve. I don't see that this differs from an IC engine, except in the typical shape of the power curve.

How can I describe this? OK, let's go back to the "ideal" 1,000rpm/v motor. If you run this from a 10v battery on a 10-6 prop it will turn it at 10,000rpm and draw something like 50Amps. If you take this prop off and replace it with an 8-6 prop it will also turn it at 10,000rpm, but it will only draw about 25A. Now a "real" 1,000rpm/v motor won't be quite the same in that it will turn the 8-6 prop a little faster than it turns the 10-6 prop - but not A LOT faster. Its main response to the reduced load is to draw less current. Even if you shaft-run a DC motor it will never exceed the characteristic speed for that voltage(in fact this is one empirical method of getting a rough estimate of a motor's Kv value) and it will only ever develop enough torque to drive the load that is applied to it.

This is where it differs from an IC engine. The IC engine at a given throttle/mixture setting will develop a given amount of torque and then increas its speed until the load actually gets big enough to adsorb it**. If you shaft-run an IC engine (unthrottled) it will run up to a huge speed until either the friction holds it back, or the gas flow can't keep up. Of course in reality it usually doesn't get there because the big end bursts and sends a rod through the block long before it hits the friction limit!

The IC engine has a power curve because the torque drops with speed as the friction increases, the gasflow fails to fully charge the cylinders and the combustion speed becomes too slow to heat the charge in time to push the pistons down. The electric motor only has a small increase in friction with RPM. All the other forces act at what are effectively infinite speeds.

Not sure if that answered the question, so please ask again if it doesn't.

AS

* if that's what you want to understand buy yourself a copy of Hughes Electrical Technology and start working your way through it - it was one of my undergrad textbooks and while I still have it I wouldn't claim to be a master of its content these days!

** this is a very simplistic description of the IC engine which ignores tuning effects of intake/exhaust devices and gas flow limitations,  but it's reasonable for this purpose

[dieselpilot]

And if you double the voltage with a given prop current increases by 4!. This is where you get into trouble. Overloaded, the motor pulls as much current as it takes to try to achieve the RPM. With nothing limiting current, a poorly chosen load or voltage results in enough current to destroy motors, controls, wiring, and current sources.

Matching the velocity constant and voltage to the load is vital.

[gadabout]

AS,
Thanks am enjoying and learning!
Maybe the title could be changed to “DC Electric Motors 101” ?
Regards
Mark

[Allen Smithee]

You mention in part 2 the motor only delivering the power 'required' by the load. This perhaps needs a little sidebar clarification. The load may well be speed dependent, as, for example, with a centrifugal pump, in which the power absorbed is theoretically proportional to the cube of the speed. So the motor and load will settle to a speed at which the motor power output curve crosses the load input power curve. I don't see that this differs from an IC engine, except in the typical shape of the power curve.

Not sure if that answered the question, so please ask again if it doesn't.

I was right - I hadn't answered the question!

With something like the centrifugal pump you mention the DC electric motor would turn at its characteristic speed (with the practical variations as discussed above), or at least it would attempt to. If turning the pump at that speed required more current than its windings could handle it would get hot and burn out in the process. This is where it differs from (say) an IC engine which would simply accelerate until (as you say) the engine's torque curve and the pump's torque demand curve intersect and then it would run at that speed.

It works the other way as well - if turning the pump at the motor's characteristic speed only loaded it to a quarter of its current capacity it would simply run at that speed and draw the small amount of current it needed. If a centrifugal pump was turned by an IC engine it would keep accelerating until the load matched the power output. If the pump running at its desired speed presented a load that was a quarter of the engine's power output the engine would keep accelerating until the pump was running fast enough to absorb the power even if this speed was beyond the safe RPM limit of the motor and/or the pump. SO the IC engine needs some kind of speed regulator or throttle where the electric motor is (in this respect) inherently self-regulating.

Is that a clearer answer?

I would just add one other thing. The characteristic speed of an electric motor is determined by many things including the number if turns in the coil and the "strength" of the permanent magnets. The higher this strength the lower the Kv. The permanent magnets will lose their strength if they are overheated - each material has a particular temperature (called its "Curie Point") at which the magnetic properties will fail, and the magnetic properties will start to degrade as this temperature is approached. So if an electric motor is allowed to overheat and that temperature is allowed to spread to the permanent magnets the magnets will degrade, which increases the Kv. Increasing the Kv reduces the Back EMF in the coil, which increases the current, which in turn increases the heat generated by the copper losses. So if an electric motor overheats there is a "runaway" effect that leads to rapid destruction, burn-out and meltdown boring holes down to the core of the earth and ending all life on the planet*.

AS

* I may have made that bit up

[Allen Smithee]

AS,
Thanks am enjoying and learning!
Maybe the title could be changed to “DC Electric Motors 101” ?
Regards
Mark

I tried, but it only changed the title of the first post so perhaps a Mod could do it?

AS

[Jo]

The thread title has changed Pete    But for the on going posts to take on the new title it is the last post that needs changing so people reply with the corrected title.

Jo

[MJM460]

Hi Allen, thank you for a well written, logical and informative primer on dc motors.  My learning in this area has been informal and piecemeal, and no work involvement.  You have put it together beautifully and filled in many gaps in my knowledge.

I am looking forward to the next chapter.

(And perhaps you will add a little on three phase motors at the end.)

MJM460

[Allen Smithee]

I'm not going to do anything on AC motors (single or 3-phase) because it gets very mathematical very quickly, and because I haven't rally done anything with them since university (back in the early Palaeozoic Era). So I'm not sure what you want next? I could do something about brushed vs brushless motors if you like

AS

[MJM460]

Hi Allen, I hope others will also chip in.  For my part, difference between brushed and brushless would be great.  Personally I have very little knowledge of brushless motors so would appreciate your explanation there.

I was interested in your comment the Kt = 1/Kv.  That seemingly simple relationship must have an explanation that eludes me.

Also, I was interested in the calculation of efficiency from the basic parameters as you described.  This seems to open the possibility of using a motor as a generator to measure an engine power output, an application where an estimate of motor efficiency is clearly required.  Or do parameters change when the motor is being driven as a generator?  I probably skipped a step or two there.

No worries about the three phase.  I was thinking it might be helpful for those considering three phase motors for variable speed on their machines.  The characteristics of the three phase motors might help understanding even without too much theory.

MJM460

[Allen Smithee]

Hi Allen, I hope others will also chip in.  For my part, difference between brushed and brushless would be great.  Personally I have very little knowledge of brushless motors so would appreciate your explanation there.

OK, it's on the list

I was interested in your comment the Kt = 1/Kv.  That seemingly simple relationship must have an explanation that eludes me.

I was about to sit down and do the derivation from scratch (I'm currently dialled into the monthly project review on mute - they haven't said anything interesting so far today so I'm not expecting that to change), but I asked Mr google (clever chap - knows everything) and found someone had already written it out here. Note that the relationship "K_v x k_t = 1" only holds true if you use the metric units (rad/sec per volt and Nm per amp).

Also, I was interested in the calculation of efficiency from the basic parameters as you described.  This seems to open the possibility of using a motor as a generator to measure an engine power output, an application where an estimate of motor efficiency is clearly required.  Or do parameters change when the motor is being driven as a generator?  I probably skipped a step or two there.

This very much is possible. In fact as I demonstrated above you can use a motor as its own generator for power measurement purposes and know directly what the efficiency is.

The fundamental concept is that:

Power in = Pi = Voltage x Current = V x I
Power out = Po = (Voltage - voltage losses) x (Current - current losses)

Voltage losses = Current x winding resistance = I x Rm

Current losses = No-Load Current = i₀

Therefore

Po = (V - (I x Rm)) x (I - I₀)

Efficiency = Po / Pi = 100% x [(V - (I x Rm)) x (I - I₀)] / (V x I)

Now if you use a generator as a brake dyno by giving it a variable load, there is absolutely no reason why you couldn't use the same basic approach. In this case the current and voltage losses would need to be added rather than subtracted, but the principle is the same.

AS

[Dan Rowe]

Allen,
Very interesting topic and it made me think about my collection of DC motors. It occurs to me that that regarding the information I have about these motors there are three cases.

1) I have a good set of manufacturer's specifications.

2) I have nameplate data.

3) I have no data only a meter to measure the winding resistance.

I did a google search for DC motor specifications and found an explanation of how to use DC motor specifications.
http://gearseds.com/files/lesson3_mathematical%20models%20of%20motors.pdf

Most of my DC motors are case 3, so with only the winding resistance what is the best way to start the design process?

Cheers Dan

[Allen Smithee]

There are ways you can establish the characteristics to an approximate level.

I₀ can be measured by simply shaft-running the motor from a battery with an ammeter in the circuit

Rm can be measured, although for the higher-current motors you would need an accurate meter that measures at the lowest possible voltage (ideally a bridge to measure under zero voltage and current conditions or a 4-terminal ohm meter).
Kv can me measured to within a few percent by either running the motor and measuring the RPM (optically with a half-coloured disk would be typical) or by turning the motor at known RPM (eg in a lathe) and measuring the voltage generated.

The trickiest one is the current rating. In theory it should be simple enough because you're just looking to ensure the armature doesn't get too hot. If you have an optical pyrometer then you can often check the winding temperature directly (if it is visible through the case). The rule of thumb is around 120-130degC. But if you haven't then you need to use another rule of thumb that suggests 80degC on the outer case is getting too high (at 80degC you can touch the case, but not keep touching it!). So run the motor at progressively higher loads to draw higher currents and let its temperature stabilise until it is too hot to touch. Find a current where you can still touch the case after 60 seconds for the short term rating, and for 10 mins for the long term rating.

AS

[Roger B]

I am using a Torpedo 850 as a starter and a load for my 25 cc horizontal engine. The engine revs to around 3000rpm (50mm stroke) and is coupled to the motor by a 4-1 step up toothed belt. It starts ok with a 12v battery and my load bank goes down to 1 ohm which gives me around 11A at 11V so 120W the efficiency of the motor at full load is given as 60% so I guess the engine is delivering around 200-220W. The spec sheet (attached) is quite detailed.

[Laurentic]

AS - as someone with a healthy distrust of anything that has wires coming out of it borne of long experience and ignorance I have been really pleased to have read your tutorial so far.  I did learn all this basic DC motor stuff and Back EMF nearly 60 years ago, and then promptly forgot it again once I had passed the exam; the theory was needed then far less than the practical hands on stuff, or hands off in my case!

 I must say I have found your writing exceedingly clear and am very grateful you have taken the time to write all this up.  It has been a really interesting and informative discourse and had it been explained to me thus first time round I might have been able to retain more of it.  As it is I am grateful for the knowledge gained here so far.

Now looking forward to the next instalment. (Hope I'm not presuming here, you did mention talking about brushless motors later on........)

Chris. 

PS - AS, you mention Hughs Electrical Technology, that indeed was the text book I worked from back in the early 1960's, the 1960 edition, and I have still got it too (just checked) and was only consulting it the other week, well fancy that!

[gadabout]

AS,
All great stuff, thanks!
Tell me when I pick up an dc electric motor I always turn the shaft, some feel very notchy others almost nothing , what do these characteristics mean? The more notchy the more powerful?!
Also some are marked with their turns, say 27t to one marked 22t, the less turns more powerful or the opposite?
Regards
Mark

[Allen Smithee]

OK - brushless motors, the mystery of turn count and the significance of notchiness or "cogging".

These will be included in the next exciting episode of "Everything you never wanted to know about electric motors but feared I would tell you anyway", the new internet-based insomnia treatment ...

I'll try to do something this afternoon

AS

[Bluechip]

'Hughes  E. T. '  :

https://docs.google.com/file/d/0B2s8MyO6hGENRl9BeTVTeUdRX2VHeGVTSEVOVFpyUQ/edit?pli=1&resourcekey=0-6etVubsNHsQ_hdEGngm0yg

 

 

Dave

[Allen Smithee]

Brushless DC (BLDC) Motors - the simplistic overview

Brushed motors
Let's look at a very simple model of a DC motor. Imagine we have some wire wrapped around a rod, and we connect the wire to a battery so that it turns into an electromagnet - North at one end and South at the other. If we switch off the current and hang this rod in front of the North end of a permanent magnet then when we switch the current on again the North end of the bar gets attracted to the magnet so it swings around until it is pointing at it. If we then reverse the wires  of the coil the South end of the bar becomes the North, so it swings around again. If we keep swapping the wires over the bar rotates, and in its simplest form we have a DC motor.

In an actual motor we have a set of switches (actually wiper contacts) mechanically connected to the shaft that do the connecting/disconnecting automatically, and we also have more than one coil of wire around the core so that several coils can be connected in turn to give smoother, more continuous torque (we can get into poles, slots, teeth etc later if anyone really wants to - but it's not essential). We call the switches the "commutator" because calling it the "coil switcher" might give away that there isn't actually anything complicated involved and that just wouldn't do.  We also have more than one magnet - we typically have several, each one being the opposite polarity to the one before. Another little wrinkle is that there will be an odd number of coils and an even number of magnets. This means that there is not "stable" position and thus always a torque on the shaft when there is current in the coils. This makes the motor self-starting.

The commutator is almost always made of metal conductor plates on the shaft with sprung-loaded "brushes" rubbing against them. It works well enough, but there are always resistance and friction losses in the commutator even when the brushes are made from graphite or sintered bronze. There can be advantages in specific applications to varying the timing of the commutator - motors can be made more efficient if they have commutator timing optimised for a particular direction (there is a version of the Graupner Speed 480 called the "Speed 480L" which is intended for use with a single-stage geared propeller drive and so is reverse-timed). Some of the more expensive buggy motors (eg the Kyosho "le mans" series) had adjustable timing with graduated timing marks on the casing.

Brushless motors
"Brushless" DC (BLDC) motors are identical in almost all respects EXCEPT that they have no commutator. Instead of the brushgear they have a piece of electronics to do all the switching. To make it simpler they also swap over the electric coils and the magnets so that the coil stays stationary (becoming the "stator" and the magnets rotate (becoming the "rotor"). This immediately eliminates the electrical and friction losses of the commutator, and also allows complete freedom to mess with the timing at will. These motors almost invariably have their coils arranged in three "phases" (these are NOT phases and are in no way related to the 3-phase AC motor concept we are perhaps familiar with). To confuse matters further they can also be arranged in star or delta configurations - with the same three windings the Delta configuration has root three (1.732) times the Kv of the Star config. There might be anything from three to sixty or more actual coils (always an odd number, each coil having anything from 2 to 100 or more turns of wire), but grouping them into three "phases" for electrical switching purposes makes for simple, more effective electronic control. This goes back to that "slots, poles, teeth" thing I mentioned earlier, which you really don't need to know about!

The original BLDC motors had optical or magnetic timing sensors to tell the electronics unit when to do the switch-over. These "sensored BLDC" motors are still made for applications that need high levels of initial torque and high starting torque, so electric RC cars use sensored motors and the BLDC motors seen in the smaller lathes & milling machines are almost all sensored. The electronic control unit of a sensored brushless motor operates at a defined speed that produces the rotating magnetic field. When you adjust the speed it just changes the timing of the field rotation, which is why they give very large low-speed and starting torques.

But a while back someone came up with a cunning plan. If you remember back in the distant history when this whole thread was just starting and there were still people actually reading it, I talked about getting "Back EMF" when the motor was rotated. Of course this isn't constant - it's actually a pulse of volts each time a coil passes a magnet (which is actually how a Magneto works - don't you love it when a plan comes together?). This led to the thought that this pulse could be used to indicate the relative position of the coils and the magnets. And thus was born that wonder of the modern world - the "sensorless BLDC Motor". It is such a wonderfully elegant machine, having just a fixed set of windings and a shaft with some magnets attached, yet it is capable of extraordinary levels of power and efficiency.

A BLDC control unit (called an Electronic Speed Controller, or ESC) takes a DC source and feeds out on three wires to the motor. It switches these wires around in sequence so that there is a rotating magnetic field around the magnets on the motor shaft. The same wires detect the back-emf pulses and so adjust the timing of the next change depending on speed and load. Most ESCs have adjustments which vary the timing from "soft" to "hard" depending on the remagnetisation time required by the particular motor (you don't need to know about this unless you want to). along with other parameters, but in all honesty for most uses they are "fit and forget" units which can safely be left to default or self-adjusted settings. As the field rotation timing is "automatic" the speed control of sensorless brushless motors is done by chopping the current just like it is for Brushed motors. That inherently means that at very low speeds they spend less time with the current "on" and so have poorer low-speed & start-up grunt.

And that is really all there is to Brushless motors. There is one feature about their construction which I could touch on. As I said above while a brushed motor has a rotating armature carrying the coils inside a can lined with permanent magnets, a brushless motor has a fixed stator carrying the coils with a rotating shaft carrying the permanent magnets. But these come in two configurations called "inrunner" and "outrunner".

The Inrunner is exactly what you might expect - a shaft with magnets fixed to it, rotating inside a can lined with coils of windings. The magnets are usually bound with epoxied kevlar thread to stop them making a break for freedom. These are now quite rare because they are expensive to make and tend to have a high Kv - the Czech "Megamotor" range are mostly inrunners.

The outrunner is a different animal. It has a set of fixed windings in the middle and a rotating can around the outside, with magnets fixed to the inside of the can:



This is both easier (and thus cheaper) to make and has an inherently larger magnetic moment, so they are far and away the most common type of brushless motor around today. They are extremely good - for example I have a Czech  Axi4120/18 which is the size of a satsuma, weighs under 12oz but on a 6s (25v) battery turns a 14x8.5" prop at over 9,300rpm. That's 1.3kW or 1.7bhp, roughly the usable power of a 4stroke .91 glow motor.

I think that's all I have on brushless motors, but as ever do ask if you have any questions. Next episode will be on turn counts and cogging.

Stay safe,

AS

[Laurentic]

Allen - many thanks for that explanation, that was great, and in addition to explaining brushless dc motors you have also answered answered a question that has been bugging me for ages but haven't asked - the difference between inrunner and outrunner motors. Now I know!

I occasionally read a model flying mag and go on their website - sister to the ME website - and get baffled by the shorthand used, for IC engines terms like 60-70engine - is that 0.6 to 0.7cc?, why not say so and make it clear - and for the rapidly upcoming electrical engines which now seem to be the engines of model aeroplane choice, again baffling, the sizes of engines, the need for an ESC (you have explained, an Electronic Speed Controller, so know that bit now too) and the batteries; ah yes, the batteries, another baffling bit. 

Say someone quotes a 40C/80C 2s 2200mAh lipo is required for a certain motor.  I deduce lipo is type of battery and 2200mAh is battery 'capacity' for want of a better word, but 2S?  What the devil is 2S? And 40C/80C - what does that mean?  All well and good when you are into it and know what it all means but when you don't - and I certainly don't! - I really don't know what anyone is really taking about. 

I know I am digressing from your DC motor subject in a way, and apologise for that, but batteries are an integral of the dc motor set-up.  If only there was an idiots guide to model radio control which also encompassed the battery/ESC/motor/servo bit I might be a happier bunny!

But thanks again for your input to date - really good, and I am sure I am not the only one still reading on!!

Chris

 

[Allen Smithee]

OK the scope is getting bigger, but I'm happy to continue this as long as (a) people are interested and (b) people don't get upset about talking about this stuff in this forum!

Just as a quickie on the engine sizes. The tradition used to be that small diesels were sized vaguely in CCs, so a PAW249 is 2.5cc and an AM10 was 1cc. But glow motors tended to follow the American system and were sized in cubic inches. So a Webra 61 was 0.61cu in or 10cc, an OPS 40 is 0.4cu in or 6.6cc and a Cox TD010 is 0.01cu in or 0.16cc. More recently people got lazy and just talk about a 40 or a 60, but they mean the cubic inch sizes and all the modern 4-stokes follow the same scheme. The big glow motors are mostly sized in cubic inches, so an Irvine 150 is a 1.5cubic inch (25cc) engine, but the Supertigre 2000, 2500 and 3000 are 20, 25 and 30cc respectively even though all the other Supertigres are sized in cubic inches - because the really great thing about standards is that there are so many to choose from... 

The "big" petrol engines are nearly all sized in CCs, so a Zenoah 62 is 62cc, and a DA150 is 150cc.

Of course Turbine engines are mostly sized in thrust rating, measured in newtons. But that's a different skillet of mullet altogether.

Batteries - these days most electric models use "Lithium Polymer" (actually Lithium-cobalt, but that's just being picky) cells. They are nominally 3.7volts per cell at mid-discharge, or 4.2v/cell when fully charged and these days they are both very good and very cheap. The standard nomenclature would be something like a "3s2000/30C". This means a 2,200mAh capacity with three cells (nominally 11.1volts or 12.6volts off a fresh charge).

The "30C" is the current rating - it means the cell is nominally rated to be discharged at 30-times it's one-hour rate which (for the 2,200mAh cell) would be:

30 x 2,200mA = 66Amps

The "C-rating" is really a sort of "quality indicator" relating to the technology and construction of the cells which why they use the generic C-rate rather than the specific current rating for the cell. They often quote two numbers for the rating, the second being a "burst" rating. It's also true that most C-ratings beyond 40C are hopelessly optimistic marketing B/S! It doesn't really matter, because no one actually flies a model pulling a 60C current - you'd drain the pack in under a minute!

In a previous post I mentioned a setup I use with an Axi 4120/18 chucking out 1.7bhp at full throttle. The motor actually pulls 58.5Amps from a fresh 6s3300 battery so at full chat it should being out of juice after 3 minutes. I actually get 12 minute flights out of it because it doesn't even need full power for a vertical climb (let alone take-off)! But I digress...

AS

[Charles Lamont]

Allen, I reallly appreciate the time you are putting into this. It would have taken me all day write as much as you have already today.

At the risk of trying your patience, I would like to take you back to my original question, because, although you have probably answered it, I have not understood the answer.

My engine cranking tests were carried out with a Graupner Speed 320 motor, specified as 7.2V, 21,000 free rpm, 0.3A free current, and one site says max current 12A. I can't find a resistance figure, and don't seem to be able to get a sensible answer from my multimeter.

By trying different gear ratios I found that the greatest cranking speed I could achieve, and therefore the maximum motor power*, was at about 17,000 motor rpm, drawing about 3A. With a smaller reduction ratio the motor speed dropped away dramatically, despite drawing a much larger current. At higher ratios, the motor was more lightly loaded and ran, as you have said, somewhat faster, but not enough to compensate for the increased ratio.

Now, I am happy with these results and the motor appears to suit what I want to do.

The problem I have is with understanding the motor power curve. From what little I understand, and so far as I can see your explanations confirm this, the torque should drop as a straight line from 0 to max speed (cos the back-EMF is proportional to speed), and that this should result in max power at half of max speed, at least in theory. So why am I getting max power at around 80% of free running speed?

* that might not be immediately obvious - I can explain   

[Ginger Nut]

What an amazing insight thanks

Sent from my SM-T580 using Tapatalk

[Admiral_dk]

A VERY informative thread and explained in a (for me at least) very understandable language 

Please continue 

I admit that as an electronic technician, I might have a headstart on the tech stuff you explain.

Per

[MJM460]

Thanks Allen.  So the Io value adequately allows for friction, wind age and other losses that contribute to the overall efficiency?

Thanks also for the section on brushless motors.  Looking forward to the next chapter.

I don’t think you are in any danger of having no one reading.  Clearly there is interest in these things.

MJM460

[Allen Smithee]

Backing up a bit - I promised to cover cogging and turn count.

A while back I mentioned poles, teeth and slots as details that we'd try to skip over, but it looks like we can't. I've been deliberately using the vague term "coils" to avoid confusion, but we'll have to go back to basics again. This is another area where text on the interweb isn't a good medium. As Jo will tell you (we used to work together) my natural medium is scribbling on a whiteboard with coloured pens - I think engineers think best in pictures! But creating pictures for this takes more time than I have, so we're stuck with text.

Remember that a DC electric motor is based on the force that a current-carrying conductor (aka "a piece of wire") experiences when it's placed in a magnetic field. If you place a bit of iron or steel in a magnetic field it is attracted to the magnet, but if you put a copper wire carrying a current into a magnetic field it experiences a force which is at right angles to both the magnetic field and the current. This is usually visualised using what's called "Flemming's left hand rule" which is why you see people in Physics and Electrical engineering exams waving a hand with the fingers making a Horus, Tau, Spock or "down wiv da kids" shape (depending on your age and cultural background). While we're at this it is worth pausing for a moment to focus on the point that the force is produced by the CURRENT. Voltage pushes the current along, but it's the CURRENT that makes the force. Remembering that may assist in understanding a lot of this stuff. This also means that if you take the wire around the back and then along the path again the same current gets used again to make more force. So four "turns" of the same piece of wire carrying the same current gives four times the amount of force. We'll come back to this.

So to make a motor you need to align your magnetic field so that it is across the shaft axis (think spoke of a wheel) and then you need the current to be flowing parallel to the shaft so that the direction which is at right angles to both is a tangent to the rim of the spoked wheel. In the very simplest DC motor a wire is wrapped around a centre core "front to back" (parallel to the shaft) so that when the shaft rotates the current in the wires on one side is all flowing front to back and on the other side it is flowing from back to front. This means that the force on each side of the rotating part is in opposite directions, and so we get the classical force couple that produces rotation. And we then use our commutator (physical switches in a brushed motor or electronic wizardry in brushless motor) to swap the direction of the current as soon as the rotor goes past  the magnet so that the force on the shaft is always in the same direction as we covered above.

That's the basic stuff. When you apply this to a "real" motor and make something that's reasonably efficient you want to get as much current into the small space as possible and you want to get the best magnetic field you can. The first you achieve by using lots of turns of wire, and the second is achieved by winding them around a core of magnetically "soft" iron. I'm not going to explain that any further - if the details of the ferro-magnetic stuff interests you then you'll find the answer in books like Hughes (but it's not exactly bed-time reading).

So we want to use a whole load of wires to add up all the forces we get from the current, and we want to bunch them all together so that they pass the magnet at the same time - this allows us to time it to get the maximum effect when we switch the current on and off with the commutator (similar to timing a camshaft). and we want a soft iron core to optimise all the magic magnetism. Give this a few seconds of thought and the obvious solution is to make the core of the rotor from a lump of iron and mill a slot in each side so that all the wires can be stuffed in the same radial place. This works fine - the core actually has to be made from a stack of insulated laminations due to a thing called "eddy currents" that you can look up for yourself (they won't be in the exam) so the slots aren't really milled (the laminations are usually either punched or photo-etched), but we have just made the motor more efficient.

But not THAT much more efficient - we can do better. We can put a magnet on each SIDE, and indeed make the magnets the shape of a half-cylinder so that there is a large field over most of the circumference of the rotor (half "north-inwards" and half "north outwards") and the wires experience forces for almost the whole of the rotation. That's another big improvement. But then we look at the rotor and realise that there's actually a lot of iron and not much wire with just two slots. So the next step is to have multiple slots in the iron, and to thread the wire "windings" around the slots in creative patterns so that a multi-switch commutator can actually switch them on and off in a sequence to give almost constant force on the wires. This is one of the biggies - take the armature our of a typical DC motor and you'll see it might have anything from four to a dozen or more contact pads with lots of wires soldered to each. And if you look at the armature itself you see the iron core has lots of slots in it to get the maximum amount of wire into the space, and here FINALLY we get to the terminology that was the question for this piece!

We call the permanent magnets the POLES. When a current carrying conductor is next to a pole it experiences a force, and when any conductor moves in the field produced by a pole it induces a voltage in the conductor (and a current if there is a circuit). If you think that one through and remember that iron is a conductor you're on the path to understanding the eddy current thing and why the core must be laminated. If the motor has two magnets we call it a 2-pole motor - one will be a "north" and the other will be a "south". The number of poles in a motor must therefore always be an even number.

As already detailed, the iron core has cavities we stuff the wires in which we call SLOTS. In higher-performance motors it's quite common for the slots to have undercuts so they have a T cross-section to help get the maximum amount of wire into the smallest space. While it's not a fundamental requirement it is normal to have an odd number of slots (to make the motor self-starting as mentioned previously) and it is usual but not universal to have a number divisible by three because it makes the commutator configuration simpler. From the motor design perspective the critical features are the slots and the poles. But people see a feature and like to name it, so the part of the pole between two adjacent slots is called a TOOTH. The tooth is not really an important aspect of the design except that it leads to the phenomenon called "cogging" (which was the question that triggered this!).

"Cogging" is the thing you see on some electric motors that almost feels like turning the motor over a compression stoke, or more usually several compression strokes, so it feels like a radial engine. It occurs in motors whose windings are laid out around the teeth of a soft iron core (ie most of them). We covered how the force on the wires due to current is at right angles to the motor axis and tangential to the rim. But the core itself is a chunk of iron that experiences simple attraction to the pole magnets. This is the effect we call "cogging" - the teeth of the core grabbing the poles as they rotate. If you have a small number of poles and/or a small number of teeth the effect is very marked, whereas with a large number of both the effect is less noticeable. It's only important if you want to do slow-speed running and need it to be smooth, because excessive cogging can make make slow-speed running very lumpy which could be a problem for (say) a gramophone turntable drive or an astronomical telescope tracker. It is often said that strong cogging is an indicator of a low-quality motor and there is some truth in it, but it is not universally true.

Now all of the above implied that the poles ae static and the wires are moving - ie that we were looking at a brushed motor. It is all equally applicable to a brushless one where the poles rotate and the wires are static, but the brushless one has another trick up its sleeve. If you look at the picture of a brushless outrunner I posted above you will see that the rotor has more than two poles - it actually has 14 (those silver-looking bars are rectangular nickel-plated neodymium). These alternate north/south around the circumference. The stator has 15 slots, so five iterations of the three switches in the commutation sequence. Bit the real advantage is that as each pole is narrow it allows the wire to be wound AROUND each tooth, because the current flowing on the other side of the tooth (and thus in the opposite direction) will be in the field of the NEXT pole which is of opposite polarity. This allows a motor which is much more progressive - it has a much lower Kv or (if you prefer) much "torquier" making the motor a more practicable power unit which is less likely to need a gearbox. There is a general rule of thumb that the higher the pole count the lower the Kv. It's not universal but it holds pretty well.

It is possible to do the multi-pole thing with a brushed motor but the commutator becomes extremely complex and intricate so it generally isn't done except in very large motors.

I didn't get to turn-count - I'll do that next time.

AS

[Allen Smithee]

Thanks Allen.  So the Io value adequately allows for friction, wind age and other losses that contribute to the overall efficiency?

We generally take the I₀ value as mopping-up the mechanical and magnetic losses into a single easy-to-measure number. It's not literally true, but it's almost always extremely close - enough that DIN and ISO standards will use it as if it was.

PDR

[Admiral_dk]

I spottet a single error so far :

you want to get as much current into the small space as possible and you want to get the best magnetic field you can. The first you achieve by using lots of turns of wire

It's more a bit missing, than wrong .... The magnetic force would be Current multiplied with the number off turns on the coil and the magnetic properties of the Core. Just putting more turns on, usually means more Resistance in the wire + more Inductance => less current .... a compromise .... and I'm sure you can explain it much better than me (you have done this so far).

[Allen Smithee]

I'm trying to keep it simple. I purposely haven't mentioned magnetic lines of force or flux densities or indeed anything to do with magnetic circuits at all because I don't think people need to understand that. But I have alluded to "turns" above where I mentioned that you can feed the same current through again by wrapping the wire around the core. I was going to expand on this in the next bit which is about turn count...

AS

[dieselpilot]

Sensorless startup really isn't a problem today unless you have very high inertia to overcome. Some controllers are better than others. But you still wouldn't use it in a case where you want the fastest response guaranteed. I've cranked engines with sensorless BLDC.

For trivia, it's possible to build a half turn (one conductor per slot) BLDC motor. This isn't common, and is mainly practical in larger motors. A carefully wound motor can pack more copper into the slots to reduce losses. Some hobbyists rewind motors to take advantage of this by rewinding with larger wire than the factory machine wind and laying it neatly in the slots. Large motors can incorporate many other tricks to improve efficiency which are not practical in small sizes.

Disregard number of turns unless you're interested in (re)winding motors. For the application, it's the electrical characteristics which determine performance. That is to say Kv and Rm are most important. Kv and Rm are related to the number of turns for any one motor design. Turns don't really anything when comparing different motor types.

If you are going to get into the concept of outrunner and slot/pole counts we can't ignore winding factor. Most of this is irrelavant unless you're designing motors, or have a highly optimized application where knowing this might help with selection. Fundamanetally, outrunner layout increases airgap area for a given diameter, which is what increases torque.

Cogging only really influences starting current and very low speed running(like a servo drive). Motors can be designed to eliminate cogging completely (skewed armature or magnets) or don't exhibit any by design(slotless, ironless).

No load current Io is a generalization. If it really matters, measuring it at the intended operating RPM can get a more accurate figure.

Generally, I've found the highest quality motors operate closer to calculated figures. Cheaper motors have losses that can't easily be accounted for. But using these formula, you can easily get within 10% or real world performance.

When it comes to motor selection, a concept the should be understood is that motor size is related to it efficiency. A 90% efficient motor of the same size as a 80% efficient motor will be capable of making twice the power. This is due to heat dissipation. The physical size determines how much heat can be shed. Efficiency determines how much heat is required to be shed. If the motor can shed 20W of heat, the 80% motor can handle 100W, while the 90% motor can handle 200W. So in turn if you need 80W output the 90% eff. motor can be smaller. Heat is the limiting factor.

[dieselpilot]

The problem I have is with understanding the motor power curve. From what little I understand, and so far as I can see your explanations confirm this, the torque should drop as a straight line from 0 to max speed (cos the back-EMF is proportional to speed), and that this should result in max power at half of max speed, at least in theory. So why am I getting max power at around 80% of free running speed?

This can probably be explained with verifying measurements. I see the battery was quite large, but did you measure motor voltage under load? If the voltage was sagging as current increased, this would explain most of it.

[Allen Smithee]

The problem I have is with understanding the motor power curve. From what little I understand, and so far as I can see your explanations confirm this, the torque should drop as a straight line from 0 to max speed (cos the back-EMF is proportional to speed),

No, because this sort of defined power curve and torque curve is a feature of IC engines, not electric motors. The forces are the result of the interaction between the magnetic fields and the current in the windings (not the voltage). The current varies with load and so the torque depnds on the torque demans, so comparing it to the power curve of an IC engine is a chalk & cheese thing.

If your load is only drawing three amps and is not turning fast enough then the only way you're going to turn that load faster is to increase the voltage. Try doubling it.

AS

[Admiral_dk]

OK - so I know just enough to get into trouble ..... again .... 

[Ginger Nut]

Great stuff look forward to reading it fully spent yesterday reading 1st 3 posts

Thanks
Ray

Sent from my SM-T580 using Tapatalk

[gunna]

Thank you so much, Allen. I spent my entire working life in electronics but not much to do with motors. This has been brilliant!
Ian.

[Charles Lamont]

No, because this sort of defined power curve and torque curve is a feature of IC engines, not electric motors. The forces are the result of the interaction between the magnetic fields and the current in the windings (not the voltage). The current varies with load and so the torque depnds on the torque demans, so comparing it to the power curve of an IC engine is a chalk & cheese thing.

If your load is only drawing three amps and is not turning fast enough then the only way you're going to turn that load faster is to increase the voltage. Try doubling it.

For a given motor, with a constant supply voltage, and a variable load, if you increase the load the motor slows down so that the back-emf reduces, so the current increases, so the torque increases to match the load. At different loads you get different speeds. There is a load at which the motor will stall, and a speed at which the motor delivers no torque. A graph can be plotted of torque against speed. Surely?

(I don't have a problem with my application, I am trying to understand the theory).

Charles

[Allen Smithee]

Ah, OK - I didn't realise you meant with a constant voltage. Always keep in mind that a DC motor has a fixed characteristic "Torque per amp" (Kt), but the relationship to speed depends on the voltage. When it comes to  relating torque (or power) to RPM it can only be defined for a particular motor & voltage source system (not for the motor in isolation).

AS

[Don1966]

Ah, OK - I didn't realise you meant with a constant voltage. Always keep in mind that a DC motor has a fixed characteristic "Torque per amp" (Kt), but the relationship to speed depends on the voltage. When it comes to  relating torque (or power) to RPM it can only be defined for a particular motor & voltage source system (not for the motor in isolation).

AS

Excellent presentation Allen, I have dealt with motors and generators for over 55 years and you tutor is well presented for the novice to understand. Thank you for keeping it simple without all the engineering terminology to confuse readers. I have to say even I am picking up a few pointers I had forgotten. A big “ thank you Allen “ for taking the time to help others less educated on this subject.

Regards Don

[Allen Smithee]

You are all far too kind. All this flattery isn't good for my ego, you know...

I think the outstanding item was about "turns count". This is an artificial term mainly used where there is a standard motor "size". The good example here would be  the motors used in RC cars and buggies - these are almost all a "can motor" (ie one based on a deep-drawn steel casing) based on the Mabuchi RS-540 family of industrial motors. This is simply because Tamiya put these motors in the kits* for the very first "proper" RC cars back in the mid 1970s (the XR311 and Cheetah off-roaders), and when other manufacturers joined the market they used the same motors so that they could allow their customers to take advantage of the large ecosystem of aftermarket performance add-ons (motors, bearings, brushes, pinions etc) which had sprung up.

These original cars ran on a 6-cell nicad, but they soon offered 7 cell upgrade packs. Also the same motor format was used in things from basic RC cars to off-road buggies, racing trucks and even motorbikes (I still have one of the original graupner RC bikes - with no gyros or anything!). To some extent the differences in requirements could be accommodated with gearing, but the RS540 was an industrial motor that was available in a range of different Kv versions which offered more flexibility. These alternate versions were described to the Car people as "different winds", and soon the demands of RC car competition led people to tinker by replacing Mabuchi's stock windings with their own, perhaps using different wire sizes or a different number of coils to get the best performance for their needs**.

Now as I said previously the route to maximum performance involves getting as much current through each slot as possible. This is achieved by wrapping "turns" of insulated copper wire around each tooth of the iron core. Essentially the number of turns per tooth determines the Kv (more turns means lower Kv) while the size of the wire determines the amount of current they can handle (this isn't completely true, but it's a good rule of thumb). I hope it's fairly obvious that in a given size slot you can fit a large number of turns of thin wire or a small number of turns of thick wire. Those are your design choices. A "nine turn" RS540 will have a higher Kv than a 13-turn one, and it will have a higher current capacity.

This is also where you can see that "Kt=1/Kv" relationship. The smaller the turns count the fewer the number of times the current passes through the slot so the smaller the torque per amp of current.

There is another wrinkle here. The coper wires are usually round, while the slots in the iron are usually square (or at least rectangular) and you know what they say about fitting round things into square holes. So when looking for the optimum it might be that each turn is actually made of several strands of a thinner wire in parallel, because the thinner wire can better fill the cross-sectional area of the slot. The downside of this is that all the strands are insulated, and as you go smaller in wire size a greater proportion of the overall cross-section might be consumed by the insulation. Optimising the wind layout is a specialist subject that I'm not going to talk about in any detail - this was just a taster of the sort of issues which must be considered in the design.

So in summary "Turns count" is just another way of talking about Kv for a specific size of motor.

I think that covers all the specific questions, but if I've missed anything or if there are more questions just shout!

AS

* To be strictly accurate they originally included the smaller Mabuchi RS380 with the RS540 being offered as a "performance upgrade" - it was convenient because it had the same mounting configuration and shaft size so it could be easily swapped

** One of these was a young lad from Stevenage who at the age of eight was embarrassing the adults by regularly wiping the floor with them to become a multiple champion even though he was using inferior equipment. His name was Lewis Hamilton.

[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