Re: Servo drives- exploding head

--- In CAD_CAM_EDM_DRO@yahoogroups.com, "Leslie Watts" <leswatts@a...>
wrote:

> Dave , I thought about this a bit. I want to talk a little
> about the effects of inertia matching, but without exploding heads.
> I think I have a way to do this....let's see how it goes.
>
> Moment of inertia can be confusing. The second moment of area
> ( often called moment of inertia) of a circle of radius r
> is 1/2* PI* r^4. The mass moment of inertia of a thin disk
> of radius r and mass M is 1/2*M*r^2. For units you see things
> like oz*in*sec^2. You also see kg* m^2. or N * m * s^2. The last two
> are actually the same.
>
> OK, the cranial pressure is building!

The examples were a great representation of the extreems we can go to
when trying to solve for only one criteria.

Reading it a few times, I think I got the idea that everything is a
trade-off. Smaller motors require higher gear ratios. larger motors
might be able to be connected directly.

The example was for a ballscrew and not a rack and pinion. 2 TPI
screws or 4.24 IPR (inch per rotation) rack and pinion changes things
by a factor of 8.

That means the motor is 8 times weaker on the final gear, and the
corner radius is 8 times better.

It also means that an 8:1 gear reduction will bring these two back
close to your numbers.

In other words, we are not making power, nor loseing it, we are mearly
directing how we are using it. (I think this is one of the things
it took me awhile to understand. I thought you got more shaft HP by
gearing. but, you get more torque at lower speed so HP remians unchanged)

OK, what I am missing from your post is the original formual. You
reference radius, but I cannot figure out what radius ?

"The second moment of area of a circle of radius 'r' is 1/2* PI* r^4"

1/2 is 1/2 of the radius ?

Also, "The mass moment of inertia of a thin disk of radius r and mass
M is 1/2*M*r^2."

The ballscrew is a verly long and heavy object, but with a very small
diameter.

a 60 tooth aluminium pulley and 1.25" dia gear would have much
different values.


Lastly, a 2 TPI screw direct drive would need a 2,000 count encoder to
get 0.001" resolution.

The 8:1 gearing for a rack and pinion would mean 500 count encoder
would offer 0.0005", acceptable.

Dave