
Steppers,
Servos, and Backlash Simulator 
If
you've done some reading and perhaps looked over my CNC
Dictionary, you have at least an intellectual idea of the concepts
of steppers, servos, backlash, closed loop, and open loop operation. You
will have heard that backlash is very bad, and that a closed loop or servo
system is much better than an open loop or stepper based system for CNC.
What's lacking is an intuitive feel for why? Or, how bad is it really?
What will happen if I choose a stepper based open loop system with lots
of backlash?
In
order to answer those questions, I developed a simulator in Excel that
may be used to explore the concepts. The spreadsheet model is pretty simple.
It assumes you want to command the machine to cut a circle. I chose the
circle because they're inherently a bit of a torture test for this problem
because the axes change direction as you move around the circle.
If
you'd like to play with the model, download by clicking here.
I have samples and conclusions below if you don't want to take the time
to play with it yourself.
There
is a set of parameters you may enter:

Circle Diameter, in inches. Pretty selfexplanatory, but I like
to do 1" or smaller circles because the errors are "blown up"
in the graphs, which display larger than 1".

X and Y Backlash, in inches. Enter the amount of backlash in your
system. Check the CNC Dictionary to
see what backlash is and how to measure it.

% Errors: The circle is simulated as 360 commanded moves, or 1
degree around the circumference for each commanded move. % Errors determines
what percentage of the time these moves will be ignored due to lost steps
or problems in the machine other than backlash. Take a look under "Lost
Steps" in the CNC Dictionary to
see what some potential sources of these errors are, and be aware that
a servo system is capable of "catching up" with the errors again.
Note that a lost step occurs in both axes at once, which makes the result
unusually symmetrical. It is not realisticeach axis should have had
an independent error simulation, but it serves for the educational purposes
this simulator is intended for. Another source of inaccuracy in the model
is that the lost steps are truly random. In a real machine, once you lose
a step, the probability of losing an adjacent step is much higher (perhaps
resistance at that point on that axis is unusually high for some reason),
so the errors will tend to "clump". Again, this hardly matters
for educational purposes.

Servo Catchup Speed: The Servo Catchup Speed is a crude way of
measuring how much of the following error (See "Following Error"
in the CNC Dictionary!) can be eliminated
in each step. Put another way, if I enter "4" here, 1/4 of the
following error will be eliminated each step. This again is exclusive
of backlash, and refers entirely to the errors introduced by the "%
Errors" parameter. Like the over simplifications on losing steps,
this model is also too simple for the real world. For example, it assumes
constant speed of error catchup, while a real servo has gain and would
accelerate as the error got larger.
The
model itself is segmented by columns whose headers alternate blue and
yellow as follows:

Commanded Position: The commanded position is the idealized X and
Y coordinates the machine should go to if it performed perfectly and stayed
on the circle exactly.

Axis Errors: Axis
errors computes when a random error occurs and step is missed. If the
error occurs, the entire step is simply ignored, and the next commanded
move is made relative to the prior position. The axis errors are generated
completely randomly, and you may wish to experiment with overriding my
formulas and forcing constant errors at particular locations or perhaps
on just one axis.

Stepper w/ No Backlash:
This block of columns shows the result of running a step motor that gets
the Axis Errors as defined, but has no backlash. Step X, Step Y show where
the machine wound up, while Step Dev X, Step Dev Y show how far that is
off from the commanded position.

Perfect Motor w/ Backlash:
This block shows the result of a perfect motor (i.e. one that never gets
an error) with backlash. Backlash X, Y show where the backlash error is
injected. Note that the model assumes maximum backlash for an axis whenever
an axis changes direction as well as at the outset, which is admittedly
worst case. Cmd + Bklsh X, Y shows where the axis winds up, and there
is a Dev X,Y to show the error.

Stepper w/ Backlash: This
block adds together the effects of lost steps and backlash. The result
can sometimes be hideous if it happens just right, triggering backlash
in more than the normal number of places.

Servo w/ No Backlash:
Finally, we show the effects of close loop control, wherein the servo
motor "catches up" by systematically correcting out the error
over time to get back on track.
I
didn't bother to show a servo with backlash. Once you see the differences
in just these models, it will be clear what impact each is having. Moreover,
I am simulating a closed loop system that measures rotation of the leadscrew,
not actual table motion with linear scales, so it can't correct for backlash
in that way anyway. The servo system will get the characteristic backlash
"ears" just like the idealized "Perfect Motor w/ Backlash."
Above the column
headers is a line marked "Max Deviation". It provides a sort
of absolute measure of how far from the ideal each model gets at its worst.
There
are a set of charts on the "Graphs" tab that show what's happening
pictorially. They're on the sheet 2 wide, so scroll vertically to get
to the ones you can't see:

Commanded Figure: A very boring, but perfect, circle.

Commanded + Backlash: From here on, I show the commanded as one line,
yellow, and the others in other colors. On this one, you can see the characteristic
backlash "ears" or glitches when describing a circular toolpath:
Backlash "Ears": 1" diameter circle,
0.020" backlash on both X and Y axes...
You can see
the little blue "ears" are quite pronounced and would be an
unhappy result if you were trying to machine a circle. 0.020" is
quite a lot of backlash, but certainly not unheard of.
 Stepper w/
No Backlash: This graph shows the effect of lost steps. As mentioned above,
you can adjust the likelihood of losing steps. I have no idea what a reasonable
real value is, but after playing with the simulation I can clearly understand
why people tune stepper systems to such slow speeds that there is almost
no chance of losing a step! Here is a graph with a 2% step loss:
Stepper system losing 2% of steps...
You can see
that the problem is once you lose a step, you never get it back and the
errors just accumulate, making things worse and worse as the CNC program
runs on. The result is scrapped parts or worse, a crash of some kind on
your machine.
 Stepper with
Backlash:
Wow! Backlash and Steppers are Incompatible!
This graph
is particularly glitchy and bad. What's happening is the lost steps are
triggering backlash due to direction changes as the machine hesitates.
This is probably not that realistic a simulation, but if it was only half
right, it shows how bad things can bit if you take a system with lots
of backlash and run it open loop.
 Servos
with No Backlash: This graph is a comparison of servo vs stepper with
no backlash.
Servo vs Stepper, Assuming No Backlash...
The sample
assumes 2% lost steps (very high, puts the stepper in a bad light) and
that the servo system can correct only 10% of the error in a given step
cycle (seems slow to me, but I really don't know what a "real"
number might be). What is obvious is that the servo can track extremely
well, and basically stays right on the circle (not quite, you can see
little bits of blue), and the stepper does the exaggerated walk of the
path that we saw before.

Conclusions 
While this simulation is
crude, it does give one an intuitive sense of the effects of backlash
and closed loop on accuracy. We can clearly see that backlash introduces
"glitches" each time an axis changes direction (which is often
on a circle). Yes, there is backlash compensation in some software, but
it will force the axis to stop while it winds out the backlash from the
screw, and so there will still be some kind of a glitch. It seems as though
backlash can also really trip up an open loop system if we're not careful
too.
We can also see that a closed
loop system has the potential of catching up and eliminating the error
pretty quickly. The only answer available in an open loop system is that
there must not be lost steps. One can come closer to this ideal than many
would expect by using big step motors and conservative speeds, adding
some gearing down to further increase torque, so all is not lost. Likewise,
Closed Loop does not fix all the sins either. Here is a case where the
lost step rate is very high (25%) and the ability to correct for lost
steps is slow (taking 100 steps). We are little better off here than with
an open loop system (also depicted):
When your servos are too slow to correct following
error, closed loop is no advantage...
When you hear
someone discussing having to slow down their speeds for their servo system
to achieve accuracy, think of this graph. Also think of getting some bigger
motors to reduce the errors!
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