Re: Servo drives- exploding head

> Jon Elson wrote :
> No, no no! Gearing down doesn't increase horsepower.
> Mechanical power is torque times speed.
> If you gear down, you increase torque exactly in
> proportion to reducing the speed,
> so the power remains the same.
>
> Jon

OK, you trade torque for speed in exact proportions so the product
(torque times speed) remains constant. This is one of those things
that has not fit nicely into the preconceived notions I have been fighing.

> Les Watts Wrote :
>
> Well first bit is to decide the velocity, acceleration,
> and size of the machine.
>
> Important motor factors include:
>
> Motor torque
> motor velocity
> motor rotor inertia
>
> Mariss mentioned inertia matching.
> I usually keep it within 5 or so.
> The important thing is to consider that
> moment of inertia analysis is crucial
> to achieving a proper design.
> I promise no heads will explode, Dave.

OK, if I reference Mariss's 2 cents post (Message 77354 )

" Power is torque times RPM or linearly, force times velocity.
Specifically, Watts = RPM * in-oz / 1351 or linearly, Watts = IPM *
Lbs / 531 "

and

"If you apply 10 Lbs on a 5" diameter crank, you should get 400 in-oz
of torque."

Using those as my reference,

I can convert that from a 5 tpi at 400 oz-in to a 1 tpi at 2,000 oz-in
and further to a rack and pinion (1 inch pitch or 3.14159 inches per
rotation) to 6,283 oz-in on the spur gear. ( 1 inch / 3.14159=0.31.
so, 2,000 /0.31 = 6,283 oz-in when using a 1 inch spur gear.)

That tells me the force I need to be able to handle with bearings and
mounts for the final gear part of the drive. (ie: the final drive
gear much be beefy enough to handle the torque at that point)

Working back from there, and assuming rapids of, say, 250 ipm on a
router or plasma, we can figure that if one spur gear rotation is
3.14159 inches, then a 1,000 RPM motor will be a tad too much. (not
many people want 3,141 ipm rapids, or 52 inches PER SECOND is a tad
fast for a 48 inch wide machine)

A 10:1 reduction would spin the motor at 1,000 RPM, and the final gear
at 100 RPM or 314 ipm. Good enough.

The 10:1 reduction would be required to be in two stages as you cannot
get that from timing belts in one set of gears. (actually 10:1 is
hard to get in two stages.)

But, although one has a theoretical 6,283 oz-in on the spur gear, with
the 10:1, then the motor needs to be 628 oz-in.

If, we used the 5:1 target ratio, then that would effectively double
the 628 to 1,250 oz-in at the motor and still have the 6,283 at the gear.

Now, the original thesis was for a person applying cutting forces on
the Bridgeport, not transport speeds for a plasma or cutting speed for
a router. I would assume that a metal router might use the same
forces, so for a metal cutting router, the 1,250 oz-in might be a
realistic top end. For plasma, it could certainly be less.

Working in reverse, 3.14 inches per gear rotation and 250 IPM means a
drive shaft speed of 79 RPM and a motor shaft speed of 400 RPM or so.
That is in the range of stepper speeds.

Now, the motor rotation is 400 RPM and the force is 1,250 OZ. So we
do the 400 times 1,250 and divide that by 1,351 to get 370 watts.
Further 1hp is 746 watts so 370/746= slightly less than 1/2 hp.

OK, I took liberties in that the original number is for cutting
forces. But a router table will also have cutting forces. Probably
not as much as the Bridgeport, but much higher than the plasma.

I didn't take in any factors for acceleration.

(I should be looking for something to catch the grey matter soon)

A servo is not great at 10% of it's full rated speed (treadmill at
5,500 RPM) so running it an absolute max of 400 RPM leaves something
to be desired.
Even a specific duty servo motor at 1,700 RPM is missing that 80%
sweet spot by major amounts.

A simple treadmill motor is rated for 1-1 /2 hp at 5,500 rpm or some
such, but a Gecko 320 likes less than 80 volts. A 48Volt transformer
as the basis of a power supply offers 66 volts.

That's 57% of the nameplate voltage, so one gets 57% of speed and HP.
So, the treadmill motor at 66 volts offers 3,157 RPM and 0.86HP

(grey matter starting to look for exits….)

…something happens here with torque and hp and all that….


(Quick. Look at wife, and smile…)

change direction…

A 370 watt stepper is also out of the sweet spot for steppers.

OK, a 28 tooth pulley is the smallest listed for use on a 1 /2 inch
shaft and a two stage gear reduction with a 32 drive and 72 driven on
each section will yield a final drive ratio of 5.06:1 so that part
can be achieved. OF course, there is NO simple set of pulleys that
move to 0.001" or 1.0000 inches. Everything is off by some amount,
and care needs to be taken so the cumulative error over the table is
not too great.

Then.. THEN,,, youse guyse toss in inertial matching and moment of
inertia to add some excitement to help the veins stick out just that
little bit more.

And you think my feeble skull can keep in the throbbing grey matter ?

I did put this into a spreadsheet to try to make it all easier to follow.

Dave