Hi,
in the NSK ballscrew technical literature there is a calculation that can be done to arrive at the recommended top
rotational speed for a given diameter ballscrew.
The principle determinants are the diameter of the screw and the maximum un-supported length. For instance I did the
calculation for my ballscrews (20 diameter,400mm max unsupported length) and it advised me that the maximum recommended
speed before the onset of ballscrew whipping was 2500 rpm. As these screws have a pitch of 5mm that would be equivalent to
12500 mm/min, a factor of ten faster than I actually use them. Since the rotational limit was that much higher than my intended
use I quietly forgot about it.
Two days ago I took delivery of my new Delta 400W B2 series servo and drive. I was of the opinion that I was going to have
to buy a 3:1 or a 5:1 planetary reduction box to bring the rated 1.27Nm torque of the servo up to around 4-5Nm to match
the thrust capabilities of my existing steppers/10:1 planetary combination. The torque/stiffness of the Delta servo is very
high indeed, far
FAR exceeding my expectations. I am inclined now to try the servo in my mill direct coupled as see what
happens. If I do then I would anticipate that the servo could, if I allow it, drive the ballscrew in excess of the 2500 rpm
recommended maximum that I calculated six years ago when I was designing it. For the first time I am going to be able
to push the boundaries and see what happens.
You are aiming for about 6000mm/min or the screw rotational speed of 375rpm. Unless your screws are very long or the
non driven end is left un-supported, ie no bearing block, then I don't think you will have any problem. Whether you could
drive then to 1000 rpm or 3000 rpm with a direct coupled servo is another question.
Is there a calculation to getting the acceleration setting close to start with?
A professional mechanical engineer would probably come up with a reasonable prediction. It would require detailed measurements
of your machine, particularly the rotational inertial moments of the screw/stepper rotor combination and the mass of the
gantry/table/workpiece that is being accelerated. All in all it is probably beyond us and experimentation at with the machine
with the steppers installed will yield the required limits faster and more reliably than any calculation we could perform.
If you have followed my previous calculations then a sketchy calculation is this:
stepper torque at 375 rpm (estimated)=6Nm
thrust at 375rpm considering the mechanical advantage of the screw=235kg(force) or 2.35kN
assuming half the available thrust is consumed combating cutting forces then the thrust available for acceleration
is about 1.2kN
According to Newtons Law a=F/m thus with a gantry weight of 100kg
a=1.2K/100=12 m/s
2 or about 1.2g. This is a very
VERY respectable result for a hobby machine.
Note that I have not allowed for any rotational inertia in this calculation so I would expect it to be optimistic but none the
less even without a belt reduction I suspect your machine will accelerate very smartly. With a belt reduction
it would be stellar!
The procedure goes, set the max velocity in Machs motor tuning to be a very low value, say the equivalent of only
100 stepper rpm and then increase the acceleration in steps until you find a maximum where either the steppers stall
or the machine starts flexing alarmingly
or the machine starts bouncing all around the workshop. Then back
of 25% from that maximum. Now start increasing the max velocity until the same conditions indicate a practical maximum
and then back off 25%.
Methodical experimentation is the key......persue the limits of just one variable at a time until you have arrived with a clear
and repeatable result. Then and only then move onto the next variable by setting all previously discovered at a level that
will not unduly interfere with experiments concerning the current variable.
Craig
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