PM Motor theory - formulae etc.

Electric Motors and Controllers
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Re: PM Motor theory - formulae etc.

Post by jumpjack » Dec 02, 2016 6:35 am

ecotech wrote: Why post fourier transformation of trap or trig waves? I think you miss the point here.
To show how armonics increase when "going far" from sinusoidal wave.

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Re: PM Motor theory - formulae etc.

Post by ecotech » Dec 03, 2016 5:26 am

Yes harmonics are not good, what's your view on torque ripple I see so many people trying to minimize it but you decrease motor performance by doing that.

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Re: PM Motor theory - formulae etc.

Post by jumpjack » Dec 03, 2016 10:46 am

ecotech wrote:Yes harmonics are not good, what's your view on torque ripple I see so many people trying to minimize it but you decrease motor performance by doing that.
I don't know what torque ripple is.

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Re: PM Motor theory - formulae etc.

Post by ecotech » Dec 03, 2016 2:53 pm

It's when a motor doesn't have a linear torque curve, it goes up and down in motors and if a small motor has a lot torque ripple you will feel vibation from the motor.

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Re: PM Motor theory - formulae etc.

Post by liveforphysics » Dec 03, 2016 4:14 pm

Torque ripple approaches 0% in a well designed efficient motor/controller setup.

However, it's not something designed to be low torque ripple for the sake of being low torque ripple. It's simply because as you approach the highest efficiency system you create, you're using all the iron and all the magnet evenly and balanced throughout all rotation positions so torque ripple approaches zero.
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Re: PM Motor theory - formulae etc.

Post by ecotech » Dec 04, 2016 5:43 am

Not all motors use iron and magnets. :mrgreen:

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Re: PM Motor theory - formulae etc.

Post by rogervize » Dec 04, 2016 5:59 am

jumpjack wrote:One pitucre explains more than 1000 words :wink:
http://www.lorenzoroi.net/prelievi/sviluppiFourier.pdf
Are you relying on the winding inductance (including reflected mutual inductance) to resolve into a low harmonic current waveform?
At low RPMs that would not be the case and you must surely have high harmonics.. but maybe you are chopping the drive at a fixed high frequency?
Not sure what drive model you are using.

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Re: PM Motor theory - formulae etc.

Post by learningrc » Dec 05, 2016 11:24 am

If you pair an ideal motor with trapezoidal back-emf with an ideal trap drive and do the math, you can see that the harmonics in the back-emf and the harmonics in the current actually work together to produce torque, not losses. In fact, if you compare an ideal trap motor+drive to an ideal sin motor+drive, you will get about an 87% decrease in K_m for a sin motor+drive.

The real issue is that it is really hard to make a motor with an ideal trap back-emf and it is really hard to make currents go from on to off instantaneously. This is where the losses and the torque ripple come in. It is much easier to make motors with a back-emf that is sinusoidal. It is NOT the harmonic content at every square wave edge that causes issues, it is our inability to make perfect square waves.

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Re: PM Motor theory - formulae etc.

Post by liveforphysics » Dec 06, 2016 3:32 am

Making square voltage waves is all our controllers generate.

Getting motors to have sine BEMF is not easy and the dominant portion of motor stator design time. Trap-like BEMF is just a resultant component waveform from a handful of constructive-deconstructive wave forms overlapping.

You're right and I'm not disagreeing trap drive has excellent torque if you're willing to compromise efficiency and listen to a loud vibrating motor.
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Re: PM Motor theory - formulae etc.

Post by rogervize » Dec 10, 2016 4:41 am

Best to drive the winding with a sine rather than rectangular...
Harmonics are bad.. more losses and stress.
Rectangular drive will cause essentially rectangular current especially at low revs

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Re: PM Motor theory - formulae etc.

Post by Buk___ » Jan 23, 2018 12:44 pm

Dumb question of the day; and this old thread seemed like the most appropriate place for it.

Part 1: Output power is torque * rpm. At pull away, rpm is 0, so power is 0, until ...?

Part 2: Torque is dependent upon amps, but not volts. If your controller could deliver its maximum amps at 1V, it would cost substantially less in waste heat/battery drain than starting at maximum amps at maximum volts; whilst still providing the same amount of torque?

If that were true, if your bike wouldn't pull away on a hill start with just minimum throttle input, it wouldn't pull away with WOT -- maximum amps at minimal volts should produce the same torque as the same number of amps at higher voltage -- but that doesn't seem to reflect reality.

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Re: PM Motor theory - formulae etc.

Post by amberwolf » Jan 23, 2018 2:22 pm

There's a few parts to the answer:

What WOT is depends on your throttle control type (how the controller is programmed).

Most common ebike controllers are "speed"---they simply control the overall voltage supplied to the motor via increasing PWM duty cycle, and the motor just spins up to whatever speed that turns out to be with the load it has on it at that moment--i'ts open loop, no feedback. Most of these controllers have a battery current limit, so it will automatically roll back duty cycle (hence total voltage) to keep battery current below that limit, but that's all.

Some controllers have a "power" throttle, where it is adjusting the total power fed to the motor, rather than just trying to increase it's speed. It's more complex and uses feedback from the current and voltage monitoring to determine that power. (The Cycle Analyst can add this type of control to a "dumb speed controller".)

There's other types of throttle control, too, but basically just saying it depends on your controller what WOT actually is--is it just trying to maximize the voltage to the controller, maximizing the motor speed, or is it trying to get the most power out of it, etc.



Next, the work done by the motor is determined by the power thru it, not just the current itself. If you had max current of 100 phase A at 1v, it's still only 100w of power. And the motor can only use so many A before saturation, so if that happens at 50A then it's only actually doing 50w of work, and making 50w of heat. If you needed 1000w of power to get started up the hill, you'd have to give it at least that much power (v x a) more than the efficiency losses to get it to move.

You could probably build a motor that will take 1000A at 1v to do that work; it's just going to have very thick winding wire, and possibly a different stator/lamination design, to not saturate (and so stay efficient at the high current). I suspect it's too big for a typical bicycle hubmotor wheel, though.

I'm no motor expert to know about that part of things, but there's some on here that may chime in.



Next, and not really applicable to your question, but just putting it here for consideration: phase current will only flow at a particular rate if there's enough voltage behind it to push it to that rate. At zero speed, it doesnt' take much voltage because there's no BEMF, but the faster it goes the higher the voltage to counter that from the BEMF.

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Re: PM Motor theory - formulae etc.

Post by Buk___ » Jan 23, 2018 3:16 pm

amberwolf wrote:
Jan 23, 2018 2:22 pm
There's a few parts to the answer:

What WOT is depends on your throttle control type (how the controller is programmed).

Most common ebike controllers are "speed"-...

Some controllers have a "power" throttle,...

There's other types of throttle control, ...
But AFAIK, the only thing the throttle can vary -- with or without the controller's help -- is the duty cycle of the PWM. 100% throttle has to mean 100% duty.

The controller can influence how the PWM ramps up to achieve the 100%, and can also detect amps and volts and estimate flux, and turn things down as the motor approaches the max BEMF, but I'm specifically talking about pull away from stationary.
amberwolf wrote:
Jan 23, 2018 2:22 pm
Next, the work done by the motor is determined by the power thru it, not just the current itself. If you had max current of 100 phase A at 1v, it's still only 100w of power. And the motor can only use so many A before saturation, so if that happens at 50A then it's only actually doing 50w of work, and making 50w of heat. If you needed 1000w of power to get started up the hill, you'd have to give it at least that much power (v x a) more than the efficiency losses to get it to move.
Of course I.m aware of W=AxV. But look back to the 3rd node of this thread where you'll find:
Power (Watts) = Torque (Nm) x Angular Velocity (radians per sec)

Add in the oft-quoted Amps == torque, volts = speed.
amberwolf wrote:
Jan 23, 2018 2:22 pm
Next, and not really applicable to your question, but just putting it here for consideration: phase current will only flow at a particular rate if there's enough voltage behind it to push it to that rate. At zero speed, it doesnt' take much voltage because there's no BEMF, but the faster it goes the higher the voltage to counter that from the BEMF.
The resistance of phase winding are usually measured in millohms. And at startup, there is no BEMF to overcome.

If phase winding resistance is 0.01ohms, then putting 1V across them would draw 100A if the batteries were capable, and/or the controller didn't limit it.

Once the motor begins to turn things get more complicated with impedance, reactance, reluctance et al. which is why I've constrained the question to startup.

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Re: PM Motor theory - formulae etc.

Post by Punx0r » Feb 15, 2018 5:45 pm

Buk___ wrote:
Jan 23, 2018 12:44 pm
Part 1: Output power is torque * rpm. At pull away, rpm is 0, so power is 0, until ...?
True. The power output of a stalled motor (which is what it is at start-up) is zero and efficiency is 0%. What the motor is producing though is torque, it is applying a static force even though it is doing no work. If that force is greater than the forces holding the motor still, slight rotation will occur. Now you have (very low) velocity and so (also very low) power. Things ramp up from there as long as torque remains greater than the load.

As you say, BEMF of a stalled motor is zero and the resistance seen by the controller is indeed only the (very low) winding resistance. If you connect a controller without current-limiting and apply full throttle, phase current will indeed be I = V/R = lots. If the motor doesn't start turning and generate BEMF the current will remain high and if the controller cannot handle this stall current it will crap out. This is traditionally what happened when cheap RC controllers, which had no current limiting, were used to drive a large vehicle.

An appropriate controller will limit this initial surge AFAIK with a throttle ramp that prevents 100% throttle being applied instantly and allows the current sensor time to detect the over-current and roll back the throttle/PWM.

As you say, into a stalled motor the phase voltage may only be a handful of volts. Conversely, the phase current is very high but battery current is very low (power in to the controller = power out [minus small efficiency loss]).

If you keep demanding 100% throttle, as the motor spins up BEMF rises, and at some point, the phase voltage is no longer sufficient to push maximum (limited) current any more, the current limiter disengages and phase voltage = battery voltage & phase current = battery votlage. Phase current and torque starts to reduce. This is the gradual tapering off of acceleration you feel as your vehicle gets closer and closer to its top speed. Eventually the torque exactly balances the load (friction and air drag) and acceleration reaches zero. This is top speed.

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Re: PM Motor theory - formulae etc.

Post by Buk___ » Feb 15, 2018 8:01 pm

Punx0r wrote:
Feb 15, 2018 5:45 pm
Buk___ wrote:
Jan 23, 2018 12:44 pm
Part 1: Output power is torque * rpm. At pull away, rpm is 0, so power is 0, until ...?
...

As you say, BEMF of a stalled motor is zero and the resistance seen by the controller is indeed only the (very low) winding resistance. If you connect a controller without current-limiting and apply full throttle, phase current will indeed be I = V/R = lots. If the motor doesn't start turning and generate BEMF the current will remain high and if the controller cannot handle this stall current it will crap out. This is traditionally what happened when cheap RC controllers, which had no current limiting, were used to drive a large vehicle.

An appropriate controller will limit this initial surge AFAIK with a throttle ramp that prevents 100% throttle being applied instantly and allows the current sensor time to detect the over-current and roll back the throttle/PWM.

As you say, into a stalled motor the phase voltage may only be a handful of volts. Conversely, the phase current is very high but battery current is very low (power in to the controller = power out [minus small efficiency loss]).

If you keep demanding 100% throttle, as the motor spins up BEMF rises, and at some point, the phase voltage is no longer sufficient to push maximum (limited) current any more, the current limiter disengages and phase voltage = battery voltage & phase current = battery votlage. Phase current and torque starts to reduce. This is the gradual tapering off of acceleration you feel as your vehicle gets closer and closer to its top speed. Eventually the torque exactly balances the load (friction and air drag) and acceleration reaches zero. This is top speed.
All of that makes sense. I mean to me; rather than the rest of the world which you already knew :)

But ... (Ya knew it was coming ... :) there is still a gap in my intuition about what happens right at the very start. The bit emboldened below
Punx0r wrote:
Feb 15, 2018 5:45 pm
True. The power output of a stalled motor (which is what it is at start-up) is zero and efficiency is 0%. What the motor is producing though is torque, it is applying a static force even though it is doing no work. If that force is greater than the forces holding the motor still, slight rotation will occur. Now you have (very low) velocity and so (also very low) power. Things ramp up from there as long as torque remains greater than the load.
There are many things that can break the status quo. The rider presses on a pedal. Or has a slight tendency to lean forward. Or the bike is on a slight decline. Or the air pressure from a passing bus nudges the bike ever so slightly....

Or, more likely, the net difference of the forces attracting the magnets, and those repelling the magnets -- due to the exact rotational relationship of the rotor and stator at the moment power is applied -- is such that it pulls a tad more than it pushes.

Any of these can start the snowball rolling and physics takes over.

Where I get really vague -- despite looking hard -- is how does the controller ensure that the motor takes off forward?

Let's stick with a sensorless controller for now, and I can see that a sensored controller can interpret the 3 hall signals and determine the current -- stationary -- phase alignment of the rotor. I'm not sure that they do; but they could.

But in a sensorless controller, there is no BEMF until the (snow)ball is rolling, so how do they ensure that the motor starts up the right way?

I can see that they could just apply power, run until they detect BEMF, and then reverse things if it was going the wrong way, but it seems to me that it would require at least 120° (electrical) and possibly more to determine the direction of rotation; and on any motor with a low pole count, that -- 1/3rd or 1/2 turn the wrong way -- would be noticeable, but it does not appear to be so, even on 4-pole fan motors.

In short, how does a sensorless controller chose which phase to power first to ensure that the motor takes off in the right direction?

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Re: PM Motor theory - formulae etc.

Post by Punx0r » Feb 16, 2018 3:54 am

My limited experience of sensorless operation on ebike controllers is they are not good. From a start under load they can initially hunt backwards and forwards a fraction of a turn until finding forwards. Generally it's good to get the bike rolling with an initial push before applying throttle.

This quote from Allaboutcircuits may help:
When the motor's rotor is not turning, no back EMF generated. Without back EMF, the drive circuitry lacks the information it needs to properly control the motor.

For this problem, Texas Instruments offers two solutions as stated in their DRV10983 datasheet (page 17):

1.Use the DRV10983's initial position detect (IPD) feature to determine the rotor position "based on the deterministic inductance variation, which is often present in BLDC motors."

2.Or, use the align-and-go technique. With this method, a voltage is applied across one of the phases to force the rotor into a known alignment.
Option 2 seems to be the most popular.

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Re: PM Motor theory - formulae etc.

Post by Buk___ » Feb 16, 2018 4:49 am

Punx0r wrote:
Feb 16, 2018 3:54 am
My limited experience of sensorless operation on ebike controllers is they are not good. From a start under load they can initially hunt backwards and forwards a fraction of a turn until finding forwards. Generally it's good to get the bike rolling with an initial push before applying throttle.

This quote from Allaboutcircuits may help:
When the motor's rotor is not turning, no back EMF generated. Without back EMF, the drive circuitry lacks the information it needs to properly control the motor.

For this problem, Texas Instruments offers two solutions as stated in their DRV10983 datasheet (page 17):

1.Use the DRV10983's initial position detect (IPD) feature to determine the rotor position "based on the deterministic inductance variation, which is often present in BLDC motors."

2.Or, use the align-and-go technique. With this method, a voltage is applied across one of the phases to force the rotor into a known alignment.
Option 2 seems to be the most popular.
Thanks for the references. Its nice to know my intuition isn't totally screwed.

The above implies that sensored controllers must probably do use the static hall signals to make there start up determination.

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Re: PM Motor theory - formulae etc.

Post by Punx0r » Feb 16, 2018 7:57 am

They do :)

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Re: PM Motor theory - formulae etc.

Post by Buk___ » Feb 16, 2018 10:13 am

Punx0r wrote:
Feb 16, 2018 7:57 am
They do :)
So, my "must probably" wasn't definitive enough for you :)

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Re: PM Motor theory - formulae etc.

Post by amberwolf » Feb 16, 2018 4:16 pm

There are also advanced controllers like Lebowski's that can use halls for startup, then run sensorless after that.

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Re: PM Motor theory - formulae etc.

Post by Buk___ » Feb 18, 2018 1:26 am

amberwolf wrote:
Feb 16, 2018 4:16 pm
There are also advanced controllers like Lebowski's that can use halls for startup, then run sensorless after that.
Indeed. I just need crash courses in: PCB construction methodology; repentance* instrumentation techniques; access to a fully equipped electronics lab and a new set of eyes for the detailed soldering work; and I can make my own :)

I also read that some controllers can use/get-by-with less than 3 halls working; but that throws a whole other set of disconnects into my mental model of these things :(

(*My collective noun for reactance, reluctance, impedance and resistance! :) )

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Re: PM Motor theory - formulae etc.

Post by amberwolf » Feb 18, 2018 3:58 am

Buk___ wrote:
Feb 18, 2018 1:26 am
Indeed. I just need crash courses in: PCB construction methodology; repentance* instrumentation techniques; access to a fully equipped electronics lab and a new set of eyes for the detailed soldering work; and I can make my own :)
I sympathize...I'm still collecting parts as I build a pair of them, but I'm using thru-hole PCBs cuz I seriously doubt I could correctly work on SMT stuff these days, even with the closeup-camera/monitor setup I have for that purpose. Heck, I have to use that just to do the thru-hole stuff sometimes! (I'm only 50 (in two and a half months) but I feel a decade or more beyond that most of the time. :/ )


I also don't pretend to understand much of what goes on in the design and theory of these things, but give me a parts placement diagram and parts list / reference, and I can put something together. If there's also a schematic I can probably test it out to make sure it's all correct, too. And I may not even let out too much smoke from the parts before I get it installed. :lol:

The best thing about the Lebowski controllers is that there's test-as-you-build documentation to follow, to make sure different sections are working as intended. :) So it's kinda like the old Heathkit radios and scopes and stuff, in that department.

There's also been some development of partly-to-mostly pre-built controllers in a few threads here, but I don't recall if any are finished and available yet.


There are also other controllers that do the hall-to-start-then-sensorless thing, but I only know the name of the one. ;)

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