Dumb question about belt-driving vs direct driving a ballscrew

I have a wood cnc machine i'm replacing the ballscrew on for .. reasons :)

It's currently a 32mm ballscrew, with a 32mm lead.
It is currently driven by a belt/pulley setup, with gearing at 44/12.
The reduction is almost certainly being done to trade speed for torque. In this configuration, at the rated speed of the servo motors, they'll get 1000-1250 inches per minute out of the setup with 3.6 times the torque.

Here's the dumb question: As far as i know, the driving torque of the ballscrew is dependent on the lead anyway. So this 32mm lead ballscrew takes ... twice the torque to drive as a 16mm lead ballscrew. The calculations in all the manufacturer catalogs back this up. The lower lead ballscrews have no spec-wise disadvantage (higher loading capacity, etc).

So what is the advantage to belt driving this screw?
Shouldn't direct driving a lower lead ballscrew should end up with exactly the same result as this belt setup?

Other info:
The motors are rated for enough RPM to direct drive a 8mm lead or 10mm lead ballscrew at the same total speed.
You can assume the small torque difference (the gearing is really equivalent to a 32/ (44/12) = 8.72mm lead) difference that you'd get with a 10mm lead is completely immaterial.

I assume somebody decided belt drive made sense, but i can't for the life of me figure out why.
What am i missing?

What you are missing is the critical rpm of the ball screw. As the speed increases the chances of whipping increases. Depends on the length of the ball screw.

EDIT Radial acceleration comes into play also.

Could be a number of things other than speed and torque. A stepper hanging off the screw makes the machine longer. Easier to build, align or tighten everything. Belts are durable so no real disadvantage. Motor vibration doesn’t transmit into the axis? In the end I’ll bet it doesn’t matter.


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Hi DB _ What is the length of the screw? Peter

Quote:

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Originally Posted by Jim Dawson

What you are missing is the critical rpm of the ball screw. As the speed increases the chances of whipping increases. Depends on the length of the ball screw.

EDIT Radial acceleration comes into play also.

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Thanks Jim, for this setup, this is likely the reason - it's a single bearing on both sides, so probably can't handle the RPM it would need.

Hi,
by and large I follow your argument, if you halve the ballscrew pitch but double the rpm then the speed remains the same, and assuming a constant torque motor
the torque will double.

As Jim points out there is a rotational speed limit beyond which ballscrew whip becomes a limiting factor, but there is another maybe even more important restriction.
32mm ballscrews have a significant angular momentum, and thus demands high torque from your stepper/servo to accelerate.

As an example I have 32mm 750mm long and 5mm pitch ballscrews on my new mill. There is no way I can spin them fast enough for ballscrew whip to be an issue.
I'm using 750W Delta servos, and they have a first moment of inertia of 1 x 10^-4 kg.m^-2. The first moment if inertia of the ballscrew is 4.5 x 10^-4 kg.m^-2, ie five
times the servo inertia. Despite the axes weighing 115kg each the linear momentum is only equivalent to 0.5 x 10^-4 kg.m^-2 ie only 1/10th of the momentum of the ballscrew.
Thus the ballscrew momentum is by far and away the largest determinant of accleration/dynmanics of my machine.

Before you go changing anything it would pay to do the calculations regarding angular momentum, the results can SURPRISE....and not always pleasantly.

Craig

Quote:

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Originally Posted by joeavaerage

Hi,
by and large I follow your argument, if you halve the ballscrew pitch but double the rpm then the speed remains the same, and assuming a constant torque motor
the torque will double.

As Jim points out there is a rotational speed limit beyond which ballscrew whip becomes a limiting factor, but there is another maybe even more important restriction.
32mm ballscrews have a significant angular momentum, and thus demands high torque from your stepper/servo to accelerate.

As an example I have 32mm 750mm long and 5mm pitch ballscrews on my new mill. There is no way I can spin them fast enough for ballscrew whip to be an issue.
I'm using 750W Delta servos, and they have a first moment of inertia of 1 x 10^-4 kg.m^-2. The first moment if inertia of the ballscrew is 4.5 x 10^-4 kg.m^-2, ie five
times the servo inertia. Despite the axes weighing 115kg each the linear momentum is only equivalent to 0.5 x 10^-4 kg.m^-2 ie only 1/10th of the momentum of the ballscrew.
Thus the ballscrew momentum is by far and away the largest determinant of accleration/dynmanics of my machine.

Before you go changing anything it would pay to do the calculations regarding angular momentum, the results can SURPRISE....and not always pleasantly.

Craig

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Yeah, given what i calculated already i won't change it without some careful calculations.