## General Motion Control

# Understanding how torque is produced II

**Bob Parente**| June 19, 2012

In our last posting we showed that the holding torque a step motor develops follows a sine wave as the shaft is moved from its stable position. This posting we’ll take a look at the torque that is produced by micro stepping (uStep) the step motor.

We now know, through the past several blogs, that we can control the current in the motor’s winding in very small increments by using a bipolar chopper drive.

We also know that the current in one phase follows a sine wave and the current in the other phase follows a cosine wave, then we can micro step the motor.

The sine, cosine current wave forms are shown in figure one along with a step resolution of four micro steps per full step.

Let’s assume that the windings are energized at the sine equal to zero degree point where the current in phase A is zero and the current in phase B is 1.414 amps. I’m going to assume that our one amp, one millihenry, one ohm can produce 100 oz-in of torque.

We’re also going to put a torque wrench on the motor’s shaft and instead of turning it, like we did last time, we’re going to hold it steady so the shaft can’t move.

Then we’re going to take one uStep and record the torque that is generated by taking that step. We’ll repeat the process until we plot the torque, with position 1b as our starting point, over four full steps (+/- 16 uSteps) CW and CCW

Figure two below shows the results of our experiment.

Wait a minute; we have the same torque curve that we had before when we moved the rotor with the torque wrench. What’s up with that? In other words the torque generated is the same whether we move the rotor in a fixed energized (stator) state or hold the rotor stable and electrically rotate the stator. That makes sense when you think about it, but I know many applications where the customer and the sales engineer were surprised at the results.

The general equation for determining the torque that is produced by micro stepping is:

*(The motor’s holding torque)*sine (90 ^{o}/(uStep resolution*(1/ the number of steps taken)))*

If we take only one uStep we get:

*(100 oz-in)* sine (90 ^{o }/ (4*(1/1)))*

Or

*100 sine (22.5) = 38.3 oz-in.*

if we take two uSteps we get:

*100 sine (90 / (4*(1/2))) = 100 sine (45) = 70.7 oz-in*

If we take 4 uSteps we get:

*100 sine (90 / (4*(1/4))) = 100 sine (90) = 100 oz-in*

One full step, or 4 uSteps, which is changing the stator’s magnetic field from position 1b to position 2b produces 100 oz-in, so rotating any smaller steps has to produce a lesser amount of torque.

This lower torque per uStep is a very important thing to know about.

Why, you might ask?

#### Let’s take this knowledge into the “real world.”

Let’s assume our 100 oz-in motor is driving a 5 revolution per inch Acme lead screw.

One revolution of the motor will move our load linearly 0.200” and one full step will move the load 0.001”

Let’s also assume that the system has 40 oz-in of “sticky friction” or stiction.

(The force required to cause one body in contact with another to begin to move)

Thus, each full step of the motor generates 100 oz-in, which is greater than the 40 oz-in stiction level and the load moves linearly for every full step taken.

Now the load doesn’t move the full distance because it’s going to get “stuck” again as it gets close to its destination and that’s another important point that we have to take into consideration. Why, because the torque goes to zero when it’s exactly in the proper location, like when it’s sitting in position 1b.

So here’s where the “trap” takes place. The customer wants to have a finer position resolution, and the sales engineer says just change your drive to a micro stepping drive and we can break down each full step into 4 uSteps and delivery 0.00025” resolution.

Everyone is happy. The sales engineer sells a new drive and the customer thinks their going to get finer resolution…until they try it.

### What’s going to happen?

If everything is perfectly aligned and the motor takes one uStep, it generates only 38.3 oz-in of torque. Not enough torque to over come the 40 oz-in of stiction. The load, in fact doesn’t move at all. It’s still sitting where it was. The second step causes the motor to generate 70.7 oz-in of torque and the load finally moves.

What’s needed is a motor that will generate a lot more torque per uStep than the stiction level to get it moving and to get it reasonable close to its destination before it gets stuck again.

I remember back to when micro stepping first came out and one of the manufactures had a 25,000 step per rev drive. It broke a full step down into 125 uSteps. Amazing!

They even showed a video of it rotating a mirror and reflecting a laser beam some 30 feet to a target on the wall to show how accurate and repeatable it was.

Well if that motor generated 100 oz-in of holding toque then it would generate:

*100 sine (90/125) = 1.26 oz-in per uStep.*

This was enough torque to overcome the bearing friction and position the mirror and the laser beam, but move a load that had even a small amount of stiction and those small steps wouldn’t have taken place.

*Next up: The dynamic performance of a stepper motor.*

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