Linear Stepper 1.

Hi-Torque Half Stepping!

A better way to get 400 steps/rev... 

Roman Black - Aug 2002
This concept is Hippyware
 

Here is a little-known method for half-stepping,
that has great advantages over conventional half-stepping
techniques:

* more torque than any normal half-step system
* equal torque on every half-step
* equal total current on every half-step
* excellent anti-resonance properties


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First the 2 "normal" ways to do half-stepping.

Understanding that full steps require 4 steps to a complete
"cycle" giving 200 steps/rev, and that all forms of half-stepping
must have 8 steps to the same complete cycle (400 steps/rev).

Here are the stepping systems shown as currents through the
2 motor phases A and B. The current can be from 0% to 100%.
These current % tables are valid for both unipolar and bipolar
motors alike. 

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First is an example of full stepping, using the current %
table:

Full step (2-phase on):
Step    A       B
1      +100    +100
2      -100    +100
3      -100    -100
4      +100    -100

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Now the simplest form of half-step is "crude" half step as
done in many hobby stepper apps using the most primitive
circuits. Crude half-step is the only option when you don't
have fractional currents and the circuit can only perform
on/off coil switching:

Half-step CRUDE
Step    A       B
1 *    +100    +100
2         0    +100
3 *    -100    +100
4      -100       0
5 *    -100    -100
6         0    -100
7 *    +100    -100
8      +100       0

This crude half-step system has many problems. The steps
marked with the * are the same as the fullsteps in the table
above, and have TWO coils on. The other half steps only have
ONE coil on, and the resulting problems are low torque in
some steps and excessive current consumption in other steps.

Unfortunately in the real world the pull-out (rotating) torque
is only as good as the weakest link which is the lowest torque
step.



Half-step CRUDE score:
worst torque = 1
average current = (1+2)/2 = 1.5
max current = 2 (if it stops on those steps!)
torque compensated = NO

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The second form of half-step system is the Torque-compensated
half step and requires a driver that can have 2 different
current levels for the whole motor (and the ability to turn
phases on/off of course).

This can be done with ONE current adjustment for the whole
motor.

With TC half-step the goal is to keep the torque for all
steps equal. As the 100%,0% steps are already running a coil
at full current the only way to equalise torque is to REDUCE
the current for the steps where 2 phases are on.

ie; you can't improve the weak steps, so you make the strong
steps weak too.

The math model for TC half-step shows that phase currents
of 70.7% in each coil, through both coils, will give the same
torque as the weaker one phase on steps.

With real world motors the fiqures are quite different, and
are around 60% with the motors I've tested. This is due to
the poles of the motor being designed for max holding torque
in the both phase on positions.

Half-step TORQUE COMPENSATED
Step    A       B
1 *     +60     +60
2         0    +100
3 *     -60     +60
4      -100       0
5 *     -60     -60
6         0    -100
7 *     +60     -60
8      +100       0

Half-step TORQUE COMPENSATED score:
worst torque = 1
average current = (1+1.2)/2 = 1.1
max current = 1.2 (if it stops on those steps)
torque compensated = YES

Although TC half-step has advantages of lower total current
consumption and equal torque steps, the one great limitation
of TC half-step is that the torque is still limited to the
max of 1, ie the same torque as a "weak" (one phase on) step.

So ALL steps are weak. But having the same torque on each
step has advantages, as does the reduced and more regular
current consumption.

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The 3rd (and little known) way of half-stepping:


Hi-Torque Half Stepping!




This is a system that I discovered recently, although I doubt
I was the first to do so. This is a standard principle in
quarter-stepping, but I have seen no mention of it as a complete
half-stepping system. Maybe this web page will help to popularise
a "new" half-stepping system that has a lot of benefits. :o)

To do high torque half-step you need a driver that is capable of
2 different current levels, one for each phase. Then you run one
at 100% current, and the other at 40% current. They coils are
never off, they are either 100% or 40%.

The HT half-step system relies on the fact that there is another
logical way to do half-step, ie when the half-steps chosen are
exactly BETWEEN the standard half step positions.

Half-step HIGH TORQUE
Step    A       B
1      +100     +40
2       +40    +100
3       -40    +100
4      -100     +40
5      -100     -40
6       -40    -100
7       +40    -100
8      +100     -40

So there are still 8 steps to a cycle, and 400 steps/rev, like
all other forms of half-step.

But it now runs at the MAXIMUM current and torque of any possible
half-step system.

No coil is ever off, and the current (and magnetic field) are
equal for every step, so it doesn't need to be tuned to give
equal torque on each step, although it may need tuning for step
angular position.

Also, since stepper motor pole construction is optimised for
max torque at positions where both phases are on, there is a
significant torque advantage to always having some phase current
and bringing the rotor closer to the (stronger) pole position.
In my case the motor tested at 28% more torque which is very nice
to have when building a machine. :o)

Half-step HIGH TORQUE score:
worst torque = 1.28    (every step)
average current = 1.4  (every step)
max current = 1.4      (every step)
torque compensated = YES

Another nice benefit I found is that resonance is greatly reduced,
and the motor performs more like a microstepped motor. This is
because these new angular step positions are less "in phase" with
the full step pole positions where the maximum resonance occurs.

Of course having 28% more torque and no torque ripple helps a lot
and the motor performs well both at high and low speeds.
-end

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