Marc Bodmer wrote:
> Dear EMC2 users

> I had to set a pretty high Following Error for high speeds. I've
> set 5mm for FERROR. (max speed is 18000 mm/min).

18000mm/min = 300 mm/sec
5mm error = 0.0167 seconds of movement

Since the PID loops runs every 0.001 seconds, you will never get
below 300mm/sec * 0.001 sec = 0.3mm.  Realistically, you should
expect 2-3 times that amount, perhaps 1mm.

Do you see the following error near 5mm during the steady high
speed portion of a move? Or are the errors largest during accel
and decel, and much smaller during the steady portion?

If the former, try some I gain, and/or FF1.
If the latter, try FF2.

Unfortunately, all I can do is suggest trying some things,
tuning is one of those subjects that is very hard to explain.

  > The actual problem now is that it needs very high cutting speeds
> for plasma cutting (5000 mm/min). But at this speed the corners
> are not sharp anymore (about r=3mm..5mm).

Sharpness of corners at high speed depends on acceleration.

If you are moving along X at 6000mm/min (100mm/sec), and you
want to make a 90 degree turn and go zooming off along Y at
the same speed, X needs to decelerate to a stop and Y needs
to accelerate to 100mm/sec.  The distance the machine takes
to do that determines the radius of the curve at the corner.

 From high school physics:

d = (1/2)*A*t^2
t = V/A

substitute V/A for t, and do some algebra:

d = (1/2)*A*(V/A)*(V/A)
d = V^2/(2*A)

If you are cutting at 100mm/sec, and you have the machine
configured for a maximum acceleration of 1000mm/sec^2, then
V is 100 and A is 1000.  Plug in and solve for d:

d = (100*100/(2*1000)
d = 10000/2000
d = 5

So the turning radius will be about 5mm.

To find out what acceleration is needed for a tighter turn,
you can solve for A:

A = V^2/(2*d)

So, if V is 100mm/sec, and you want the radius of the curve
to be 1mm (d = 1mm), then you get:

A = (100*100)/(2*1)
A = 5000mm/sec^2

Note that the decel and accel times are quite short:

t = V/A
t = 100/5000
t = 0.020 seconds, to go from zero speed to 6 meters/minute.

If your motors can't accelerate that fast, or can't be tuned
to that level of performance, then you won't get 1mm turns.

> => Q5. What is the influence of smaller or higher values of the
> MAX_ACCELERATION value. How does one determine the needed
> acceleration value on an axis?

As described above, acceleration lets you make sharper corners
at higher speeds.

More high school physics:

F = ma

Force = mass times acceleration

If you have a 50kG gantry and you want to accelerate it at
5m/s^2 (5000mm/sec^2), then you can calculate the needed force:

F = 50kG * 5m/s^2
F = 250 newtons

Can your motors and drives deliver that?  If so, its just a
matter of tuning them, and setting EMC's acceleration limit
to 5000mm/sec^2.

If not, figure out what they CAN deliver, calculate how much
acceleration that will give you, subtract 15-30% for friction
and other losses, and use that value for MAX_ACCELERATION, at
least to start.

You can use motor and drive data along with machine information
like weights of parts to calculate approximate performance using
the formulas I've provided.  But that only gets you close, since
there are many factors that can only be estimated.  To find the
real performance of your machine you need to do tuning and testing.

Regards,

John Kasunich


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