Re: where's the torque ?

--- In CAD_CAM_EDM_DRO@yahoogroups.com, "turbulatordude"
<dave_mucha@y...> wrote:

> I've been running thru the torque numbers for motors and seem to be
> missing something.
>
> A 1-1/2hp treadmill motor with 5,100 RPM has 296 oz-in torque.
>
> On a rack and pinion. and using a 1.25" pitch, we can round the
> distance per gear rotation to 4 inches. 1.25*pi=3.926, so 4 is

close

> enough.
>
> When we calculate for a leadscrew, we come back to inches of table
> movement. do we also do that for routers ?

You are mixing leadscrew and rack and pinion. Leadscrew formula
(close estimate) is Force = 2pi(R)*Torque*efficiency/lead where lead
is the distance travel by the nut in one revolution (.2 for a 5TPI
leadscrew). For a 90% efficient ballscrew driven with a 600oz-in
motor and a 1/2" dia leadscrew (R=.25), the number would be 6.28(.25)
*600*.9/.2 or 4710 oz-in of torque.

In a rack and pinion the torque is reduced as you stated because the
root circumference of the gear becomes the distance it travels so you
have to reduce the torque per inch by 600/4 or 150 oz-in. Then using
a 4:1 belt reduction we are right back to the 600 oz-in number (less
frictional losses) YOu get 1 inch of movement with one rev of the
motor. With a standard step motor your resolution (smallest distance
you can move with a single step) is 1/200 inch (.005).

Smaller diameter gears will change the equation so a .5 root diameter
gear with a root circumference of 1.5708 yields 600/1.571 or 381.92
oz-in and with a 4:1 belt reduction the number becomes 1527.68 oz-
in. The distance you travel in one rev is .3927 and therefore the
resolution is .393/200 or .00196 (distance traveled with one applied
pulse)

So reducing the gear diameter increases the resolution, increases the
torque and lowers the speed. If you use 800 RPM as the top stepper
speed you could still get 1256 IPM!

If you plug in the smaller dia gear with a 350oz-in motor and 3:1
belt reduction you will see that you get pretty nice rapids and good
torque at reasonable stepper RPM.

Driving with a servo that needs to run at about 600 to 1500 (3000 RPM
full speed) RPM in the cutting speeds calls for more drastic gear
reductions.

>
> I mean that we put on a 600oz-in motor, then multiply that by 5TPI

to

> get 3,000 OZ-IN that would mean 3,000 per inch, no ?
>
> That would make the motor 296/4=74 oz-in if it were direct drive.
> using 6:1 pulleys would then multiply that up to 444 oz-in. or 444

per

> inch ?
>
> The leadscrew moves 1 inch per 5 motor rev or 0.2" per rev while the
> rack moves 1.5 revs per in. Gearing up to get 5 rev's per inch

would

> mean a 20:1 pulley to the 1:4 rack gear. If course that would
> multiply the 296 by 5 for 1,482oz-in.
>
> Since I've seen routers and plasma cutter run with much smaller

motors

> and much smaller ratios (3:1 on a 350 oz-in stepper) it seems I'm
> missing something.
>
> Anyone see my mistakes or what I've overlooked ?
>
> Dave