Hi,
if you plan on hooking your new steppers direct to the leadscrews then this is the calculation:

Leadscrew, 16mm diameter, 16mm pitch.
The radius of action (where the ball contacts the groove) will be a little less than the radius of the leadcsrew, say 7mm.
The stall torque of the stepper is 7.5Nm or 0.75kg(force) at 1m which is equivalent to 0.75 X1000/7=107 kg(force)
at the radius of action. The circumference of the circle described by a radius of 7mm is 2x 3.141x7=44mm. If the leadscrew
rotates one turn the axis will advance 16mm. The mechanical advantage of the leadscrew is 44/16=2.75.

Thus the stall thrust of a 7.5Nm stepper on a direct coupled 16mm diameter screw of 16mm pitch excluding frictional losses
will be 107x2.75=294kg(force) or 2.94kN. Not too shabby.

Of course if you had a belt or gear reduction the stall thrust would go up by the reduction ratio and given that these steppers
are likely to be way WAY WAY quicker it would still not count against your ultimate top speed.

Remember that stall thrust is a somewhat slanted or unusual measure of a machines thrust.

Its more realistic to assume that approximately half of the available torque (equivalent to thrust) is used to accelerate the
axes and mass of the workpiece/gantry or whatever and the other half be available to supply the cutting forces required.
A detailed calculation would require much more data on the kinematics of the machine and a much more thorough knowledge
of the cutting forces, the sort of thing professional mechanical engineers thrive on. Its dubious that as hobbyists we need that
sort of detail. If however you were designing and building a $100,000 plus machine for production work you want/absolutely
need to know before you start....and after all mechanical engineers want a job too!

Craig

Hi.
if you follow the calculation so far try imagining this:

Desired theoretical max top speed=6000mm/min. Therefore the leadscrew must rotate at 6000/16=375 rpm.
If you had a 3:1 belt reduction the stepper rpm would be 375x3=1125rpm. The low inductance steppers are
such that you will retain approx. 50% of holding torque at 1125 rpm so the available torque from the stepper
at 1125 rpm we estimate to be 0.5x7.5=3.75Nm. With a 3:1 reduction the torque at the leadscrew is3x3.75=11.25Nm.
The resultant thrust as a result of mechanical advantage of the leadscrew, indentical to my previous post, is
2.94 x11.25/7.5=4.41kN or a little over 400kg(force).

Allowing 50% for acceleration that still allows 200kg(force) for cutting forces at 6000mm/min.

As you can see using a belt or gear reduction would allow you to exploit the full potential of your new steppers
and still go as quick as you dare.

Craig

Hi,
as a matter of comparison the servo that I ordered today has a rated torque of 1.27Nm and a rated speed of 3000rpm.

If this were fitted to your machine through the same 3:1 reduction I am proposing then the calculation is something
like this:

max speed is 3000/3 x16=16000 mm/min
torque at the leadscrew is 3x 1.27=3.81Nm so the thrust of the axis is 3.81/7.5 x2.94=1.49kN

So a servo equipped machine is about 2-3 times faster but about half the static thrust. With a servo however a short term
overload does not cause a stall as it would with a stepper, the servo just 'digs in'. The overload torque of my new
servo is 3.8Nm so its short term thrust at 16000mm/min is 4.48kN, ie about the same as your stepper but at nearly
three times the speed. Additionally my servo gives has an ultimate resolution of about 0.2 arc min or on a 3:1 reduction
16mm pitch leadscrew a linear resolution of 0.05um!!!

That sort of performance doesn't come cheaply but this calculation shows just how superior servos are in practice and why
they dominate in pro equipment.

Craig

Hi,
as a matter of comparison the servo that I ordered today has a rated torque of 1.27Nm and a rated speed of 3000rpm.

If this were fitted to your machine through the same 3:1 reduction I am proposing then the calculation is something
like this:

max speed is 3000/3 x16=16000 mm/min
torque at the leadscrew is 3x 1.27=3.81Nm so the thrust of the axis is 3.81/7.5 x2.94=1.49kN

So a servo equipped machine is about 2-3 times faster but about half the static thrust. With a servo however a short term
overload does not cause a stall as it would with a stepper, the servo just 'digs in'. The overload torque of my new
servo is 3.8Nm so its short term thrust at 16000mm/min is 4.48kN, ie about the same as your stepper but at nearly
three times the speed. Additionally my servo gives has an ultimate resolution of about 0.2 arc min or on a 3:1 reduction
16mm pitch leadscrew a linear resolution of 0.05um!!!

That sort of performance doesn't come cheaply but this calculation shows just how superior servos are in practice and why
they dominate in pro equipment.

Craig

Hi Craig

My new motors and power units have arrived, I should be fitting them soon..

At 16000mm/min my ball screws would be spinning at 1000rpm as direct drive which is probably not advised for longevity. What would you recomend that max rpm of the 16mm dia 16mm pitch screws, also where do you think my new motors will start to max out rpm and acceleration wise?. Is there a calculation to getting the acceleration setting close to start with?

Mark

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/s² 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

Hi,
Excellent information thank you, I'm possibly going to try cutting some aluminium and again possibly use Imachining, that's if I can get enough speed from the axis. Servo's certainly would be the way to go but I'm not ready yet to take that leap.
I guess running these new steppers to around 600 rpm would still be viable, torque would be less than 375 rpm obviously. You did say they were many times faster because of the lower inductance compared with the old ones.
Is there much gain to be had on running either or/and higher kernal speed and 10 micro stepping rather than 8, more micro steps would be a smoother drive but not sure if I would be then better with a smooth stepper board, even drop the parallel port set up and go with the ESS network port smooth stepper.
With my current high torque slow speed steppers i tried to cut a 700mm diameter at 5000mm / minute as a test on them and they slower axis didn't sound so great when it was nearing a stop as it was cutting the circle. Having not done that before it maybe the same with all steppers?

So for instance 10000 mm/min, 625 stepper RPM

(200*10000)/60 = 33333khz


So 25000 khz is not enough for this speed.

I understand the test, would you just manual jog (at full velocity) one axis at a time back and forth between the limits or create a program to interpolate both axis running together for X and Y? What sort of velocity increments 500 ok? and fine tune from there. Maybe 100 increments for acceleration?

"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%."

Hi,
changing the microstepping will marginally affect smoothness but will have no effect on stepper torque and therefore acceleration.
Lower microsteps will bring the required pulse frequency down and allow you to go faster at 25kHz kernel or alternately increase
the kernel speed to as much as your PC can handle.

If you use an ESS then it so fast that kernel speed is irrelevant and is worthwhile aside from being smoother motion and the PC very much
less inclined to stutter and stall.

To really effect an increase acceleration without losing top speed you need a gear or belt reduction of 2:1 to about 4:1.
If that does not appeal try direct coupling to the screws first. If that's adequate all well and good. If you want more torque
at speed and maintain your top speed a belt reduction may well be the only way to achieve it.

I understand the test, would you just manual jog (at full velocity) one axis at a time back and forth between the limits or create a program to interpolate both axis running together for X and Y?

You need to create a program that goes back and forth multiple times but only one axis at a time.
g0 x0 y0 z0
g0 x100
g0x0
g0x100
g0x000
g0x100
g0x0
etc...

Try a low acceleration and work up, I should suggest a large increase to the extent it stalls in acceleration phase then back off.
You don't want or need to take all day over this, be reasonably aggressive in your increments and narrow the increments as you establish
the outer limits and refine you guesses.

Craig

Hi,

I've got this torque curve for my new motors but don't understand it, sorry not very good with graphs and I'm just trying to learn more about the mechanics of my components.

Torque is the motor torque in Nm.
Pulse rate?
400 pulse rev?

The leadshine graphs you popped up had Rpm on the bottom line hence my confusion. How do i convert the pulse rate shown here to Rpm

Mark

Hi,

Torque is the motor torque in Nm.
Pulse rate?
400 pulse rev?

The driver in this measurement is set to half stepping, that is 400 pulses per rev as compared to 200 pulse per rev for
full steps. Thus 400 pps (pulse per second) is 1 revolution per second. So 1000 rpm is equivalent to (1000/60)x400=6666 pps.

Pulse per second(half stepping regime)= RPM/60 X400

Torque at low rpm =5.5Nm = 3.7ft.lb =718 oz.in
Torque at 1000 rpm (6666pps)=1.8Nm=1.2 ft.lb=235 oz.in

Ratio of torque @1000rpm compared to 0 rpm =1.8/5.5 =33%

Craig