Hot motors

You are trying to drive a sinusoidal constant current through the motor. The frequency of that sinusoid (AC current) is determined by the speed (revs/second) of the motor times the number of full steps per revolution. If your motor runs at 6.5 revs/sec and you have a 200 step motor then the frequency would be 6.5 x 200 = 1300 Hz. You can look at the magnitude of the impedance presented by the coil inductance and the coil resistance at that frequency and pretty quickly determine if you have enough voltage to do the job. For most of these motors the inductance is not large enough to increase the impedance much at all at ~ 1 KHz. The motor is essentially a pure resistance at the frequencies we step them at. The driver *does* need a little more voltage than the motor runs for switch losses and a few other things. If you have 20% more voltage on the driver than the motor is spec'd for - you should be fine. Anything over that simply will heat up the driver a little more. Your +12V power supply also will be working harder with a higher current motor.

We have determined in this post that the makerfarm motors are half amp motors. Not the normal one amp. Half your vref and work from there. I have first hand knowledge of at least one guy doing so and they run the printer fine. I guarantee the manufacturer didn't design these motors to run that hot. Anything running that hot is going to break down soon than it would if running at normal temp.

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uncle_bob
You are trying to drive a sinusoidal constant current through the motor. The frequency of that sinusoid (AC current) is determined by the speed (revs/second) of the motor times the number of full steps per revolution. If your motor runs at 6.5 revs/sec and you have a 200 step motor then the frequency would be 6.5 x 200 = 1300 Hz. You can look at the magnitude of the impedance presented by the coil inductance and the coil resistance at that frequency and pretty quickly determine if you have enough voltage to do the job. For most of these motors the inductance is not large enough to increase the impedance much at all at ~ 1 KHz. The motor is essentially a pure resistance at the frequencies we step them at.

I was trying to keep this simple for the OP, but since you want to get technical, then I can do that. Let's take for example a commonly specified Reprap motor the Kysan 42BYGH4803. It has a resistance of 1.8ohms, and an inductance of 4.8mH. The impedance of the winding at 1300Hz is X = 2 * pi * f * L= 2 * 3.14159 * 1000 * 0.0048 = 30 ohms. So, in the case of this motor, the impedance due to the inductance alone is mostly limiting the current. Other motors I found were 2.8mH, so they would have been a bit better, but the impedance of the inductance would still dominate the maximum current at high step rates. I run my motors at 24V though, so at least it can build current in the winding a bit faster than at 12V, which will yield a higher step rate. I would imagine that the Makerfarm motors would be quite high inductance, since they are also a higher resistance, and higher voltage motor. This would generally indicate that they have more turns of wire in the coils.

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Mike Anton
[manton.ca]
[laserlight.wikidot.com]

( Just to keep this readable for any poor person trying to follow along, the Kysan motor mentioned is a 1.5A / 2.8V part. )

So that comes out to >45 volts for a 1.5A motor current. Something is wrong with the math as I typed it... backing up a bit:

The Allegro A4988 data sheet (figure 12) shows one basic mistake - the micro steps are per 1/16 of a full step, but they make a full sine wave every 4 full steps (not every step). That's a 4:1 drop.

Unless you are a bit speed crazy, your printer is not going much over 100 mm per second. That would be 2.5 revs / sec not 6.5. (not quite 3:1).

The frequency would be 125Hz at 100 mm / sec with a 80 step / mm motor (typical X or Y motor).

Inductive reactance would be 2* pi * 125 * 0.0048 = 3.7 ohm

Reactance and resistance are close, so we need the magnitude of the impedance in this case. If they were further apart it would just be round off error.

Magnitude of the impedance would be square root of (3.7*3.7 + 1.9 * 1.9) = 4.15 ohms

For the more typical (mHy = ohms x 1.4) stepper at 2.8 mHy and 1.9 ohm resistance, the magnitude of the impedance would be 2.9 ohms.

If you put 1.5A through 3 to 4 ohms you get 4.5 to 6 volts. If you decide to cool off your hot motor and run 0.75A instead of 1.5A you are at 2.25 to 3 volts.

Yes it scales a bit for 150 or 200 mm / sec. The 7.7 ohms you get with the high inductance motors pretty close at 12V, 1.5A, 200mm / sec. That's pretty fast for the printers I've seen with these motors to be printing accurately.

If you need to run 400 mm / sec at full power, then yes, you need to do something. There's a bit more to it, so exactly what is a "that depends" sort of thing. That speed / power is way outside the scope of your typical printer. I'd bet a number of things will run hot in that case....

What you say makes more sense. I thought the resistance seemed a bit high.

I often run my motors at 300mm/sec for non-printing moves, so the magnitude of the impedance would be 11.5 ohms. I'm not sure though that it is all about being able to get the correct current into the motors. Doesn't it also matter how fast you can get the current to rise (at least that is what I read a long time ago for another project)? Higher voltage definitely helps this.

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Mike Anton
[manton.ca]
[laserlight.wikidot.com]

The "that depends" stuff gets pretty long and complicated:

If it's a reactive load (mostly L not much R) then the voltage and current are 90 degrees out of phase. The voltage maximums is at the current minimum. The driver may look at the "I need zero current" and just not switch on the PWM at all.

Looking at this in the time domain is a headache. What you wind up with are a bunch of numbers that relate to distortion. The current DAC isn't real high resolution, so there are already errors there. They also have a charge / decay process that will get into the picture. Much easier to look in the frequency domain.

If you are doing a move at 400 mm/sec you have a bunch of mass all going at once. You can't start / stop instantly. There's an acceleration limit and a jerk limit. Both will impact what you can do. Once you are running, the question is weather you have enough power to get the job done. You essentially are dropping the current a bit when you go to fast. Inertia will probably keep the rate correct. Phase errors will correct out when you are out of voltage limit.

I'm sure that's only the surface and I'm not even close to sure if the other stuff isn't more important that what's there. The simple answer is that it works. You don't loose X/Y position when you shove the head around a bit and come back to start. I know that's cheating. It's a lot like looking at the AC voltage on your stepper first and then backing into the math. Next time I'll use an oscilloscope....

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The heart of all of this is "how much horsepower do you need?". That's not really very well defined. The faster you go the more you will need. The more dirt on your rails, the more you will need. My dirty fast machine may need a *lot* more than your well maintained rational speed machine. If we both have the same motors, mine will need to be hotter than yours to get the job done.

Edited 1 time(s). Last edit at 11/03/2013 06:55PM by uncle_bob.