# Brushless DC motors



## gerd1022 (Jun 9, 2008)

It was my understanding that a Brushless DC motor (BLDC) is simply a permanent magnet motor inside out... in other words, instead of having the magnets stationary and on the outside and the coils moving, it has the magnets moving and the coils stationary. This way, you dont have to worry about the wires to the coils getting all wound up (which is why they used brushes in the first place)

In order to make the BLDC work, you have to turn on and off the coils at the right time, which is why you need a more complex controller. 

We learned in one of my design classes that BLDC and perm mag motors have approximately the same power curves once you implement the controller. In other words, torque = K*V/R - K^2*N/R and t = K*i
where K is a motor constant (known at torque sensitivity), V is voltage, R is motor resistance, N is angular speed, and i is the current. This is neglecting losses.

with a PWM controller, you are effectively changing the voltage, which shifts the curve.

On a different thread, someone mentioned that BLDC motors have a constant torque speed curve. Is this just because of the limitations that the controller puts on it (ie current limit).


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## 3dplane (Feb 27, 2008)

(quote)
It was my understanding that a Brushless DC motor (BLDC) is simply a permanent magnet motor inside out... 

--That would be an outrunner,but BLDC can also be the conventional kind reffered to as inrunner where the stationary windings are on the outside,
and the magnet assembly is made on to the shaft.

(quote)
On a different thread, someone mentioned that BLDC motors have a constant torque speed curve. Is this just because of the limitations that the controller puts on it (ie current limit). 

-- I would rather use the word "function" or "ability" instead of limitation because you can always use a controller with a rating higher then what the motor could withstand. I'm not picking on your words please understand. 
Now! I can't go into all the mathematical formulas because I'm simply not smart enough but I've messed around with BLDC motors (small ones) enough to know a little bit about them.
I guess their torque is a relation of the strenght of the magnetic interaction between the PM (Permanent Magnet) and the maximum flux created by the coils...and ofcourse the ability of the controller to make that happen wich has a lot of variables like timing,switching speed etc.
Barna


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## gerd1022 (Jun 9, 2008)

right... i guess my point is that any dc motor with permanent magnet instead of field windings is going to have a linear torque speed curve. this curve will have a peak torque at stall, and a no lead speed at zero torque.

due to heat generation, the continuous duty line for the motor will be lower than the actual motor characteristic, which is why you need current limiting. 

for permanent magnet motors (including BLDC), the motor curve looks like the attachment.

The continuous duty line can be moved up with fans and other cooling methods. A PWM controller varies the voltage which shifts the actual motor curve left and right. Current limiting is used to keep the motor underneath the duty line. (Of course, you can run the motor higher than the continuous duty line for less time...)

I dont have as much information for wound motors, but the principle is the same, it is just the shape of the motor curves that differs. It would be really nice to have the equations for our series wound motors (or even the motor constants) because this would allow us to spec out the exact amount of cooling needed to run at different speeds for different lengths of time...


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## ice (Sep 8, 2008)

Hi,

Is it true that In such motors, current and torque, voltage and rpm are linearly related?


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## gerd1022 (Jun 9, 2008)

Torque and current are definitely linearly related in permanent magnet motors. However, the voltage and RPM relationship is a little more complex. 

If you start off cruising in a car at a constant speed and constant voltage, increasing the voltage will give you more torque at the same RPM (initially you would be going the same speed in your car, thus the motor spins at the same RPM). However, this extra torque will cause you to speed up a bit, but as you do, the torque will decrease (as RPM increases, torque decreases) until you reach an equilibrium point that is a bit faster than what you started with. 

So the short answer is that voltage and RPM seem linearly correlated in a car, but it is really a result of the changed motor characteristic line that I described in my last post.

Ill add another post to clear this up.


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## gerd1022 (Jun 9, 2008)

ok so ive made a diagram to illustrate my point. in the diagram, the red line is the approximate load line for a car. It takes a near constant amount of torque to move the car at lower speeds (an effect of rolling resistance) and at around 30-40 mph, air resistance becomes the significant factor and the amount of motor torque (which translates into wheel force through the gearing) needed to travel at constant speed inceases.

Note that this line is number one, a very approximate mspaint spline, and 2, neglecting acceleration. In other words, the red line is the amount of torque needed to cruise at constant speed.

Ok, now the blue lines are motor curve lines at different voltages. We can say that the one on the left is X volts and the ones to the right increase the voltage. (Note, for this kind motor, the offset linearly corresponds to voltage, in other words, the distance from the origen to the no load speed, or x-intercept for 24 volts is double the distance for 12V)

The intersection of the two lines is where your operating point is at. So clearly, to go fast, you need higher voltage. Note that you also need more torque, which is directly related to current. This is why it takes more current to run at higher speeds. And, since torque times speed (ok its torque times rotational speed, but its the same thing once you take the gearing and tire size into account) is equal to power, with increases with increased speed.


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## ice (Sep 8, 2008)

Wow, its to complex for me...but i do understand the logic.thank you!


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