Re: [CAD_CAM_EDM_DRO] tensioned ballscrew

Hey!

I'm kinda waiting for the ups morning delivery right now
so I can do a couple calculations here.

Ok I will consider back to back AC or tapered roller bearing
tensioning a long screw using the screw's own elastic properties. This
implies that EI for its support is much higher.

First thing to note is the block-and tackle driven support blocks
pretty much eliminate buckling problems. A great idea, wot. ;^)

OK now temperature.

I will use 12x10^-6 c-1 as the thermal expansion coefficient
of steel.

For 120" we get 1.44 thousandths (0.00144") for every degree of delta t of
the screw relative to a fixed support.

Lets say it gets warm to the touch in use. Actually they often
get quite warm. But let's say 10c. So that gives 14 thousandths of expansion
of the screw.

Now let's consider the screw tensioning level. 5% max dynamic preload is
common in bearings and is usually refered
to as light preload. For a bearing of about the right size for
that screw it might be about 300 lb for angular and higher
for tapered roller... don't have the TR data but let's say
500 lb. Too high and it will have a lot of drag. (I use 300).

Now how much do we have to stretch that screw to get
500 lb tension? Well that is FL/EA. The effective area of the screw with the
lands is about 0.8 in^2 so we get 0.0025".

Uh oh. There's a problem. A 500 lb preloaded screw
will unload completely with only a 1.7 degree c temperature
rise in the screw. Let me grab Slocum's Precision Machine
Design off the shelf. That's my bible.

Yes there is some on the subject.... he does not reccomend
it. Says it's thermally unstable. Maybe I did the calcs without
arithmetic errors.

But tensioning the ballscrew is a good thing for the reasons you mentioned.
So do it with a preload spring. Something
that can maintain the force over a larger displacement.
I use stacked bellville washers.

Per Slocum I would use simple-simple end fixity with two
bearings preloaded to each other on both ends. One set
is allowed to slide in it's housing a little.

Buckling load is inverse squared to length and with the
travelling support I don't think you need fixed end support.
Slocum mentions the great wear and accuracy advantages of simple support. He
likes kinematic construction.

Oh the other thing to check- torsional loads. I had no problems
with 70"x1" screws but at some point it will be significant.
I am referring to errors generated from twisting the screw.

Let's see.. I need shear modulus G for steel 12x10^6 psi.
Polar moment of area J for a 1" screw is about pi/32
or 0.1 in^4.

Let's have torque at 500 in oz. That is in the middle of the range for
machines of our size. converted to in lb that would
be 31.25.

So worst case twist isTL/JG or 0.003125 radians.
That's 0.18 degrees. Not too bad. Seems a little small
though. Check this. Torsional resonance could magnify it.
A slender ratio of 120 is the outer limits of ballscrew use!

Oh since I decided to post this to the list rather that private
e-mail I want to mention rotating nuts.

Why not just rotate the nut?

I can say why I don't.

Rotating the nut has much much lower inertia than rotating the
screw. There are no rotating end bearings. Critical speed
issues diminish.

Here is my problem: Like many I often get parts surplus new.
Many ballnuts can have ball scuffing and lube starvation issues if rotated
at high speed I'm told. Manufacturers make rotating nut certified units
(internal recirculation helps but is no guarantee) but that is not what I
use due to cost. I don't have
the option to test a unit to failure to see how it does so I
take the conservative route and use the units as specified
by the manufacturer.

Also- the rotating nut transmission is an expensive bit of
precision engineered components- more costly than end bearings.

OK time to run out and build up some little rs-485 differential line
drivers. I am using TI SN75174. Looks good- has enable,
thermal protection and 3-state outputs.

Later

Les



Leslie Watts
L M Watts Furniture
Tiger, Georgia USA
http://www.rabun.net/~leswatts/wattsfurniturewp.html

----- Original Message -----
From: "Doug Harrison" <prototype@...>
To: <CAD_CAM_EDM_DRO@yahoogroups.com>
Sent: Monday, February 18, 2002 9:19 PM
Subject: [CAD_CAM_EDM_DRO] tensioned ballscrew


> I have two ideas that need to be challenged. The screws on the X axis of
my
> router are ten feet long. They are 1" diameter, .25 pitch from Rockford.
>
> 1. We have come up with a way to provide intermediate support so as to
get
> around critical frequency problems. An extra pair of blocks on each
linear
> rail will carry support bushings. These blocks are connected to each
other
> through a beam about five feet long. This beam is tied to the gantry
> through a 2:1 cable arrangement so that the support blocks move at half
the
> speed of the gantry. Thus, the worst case support is when the gantry is
at
> one end and one support block is in the middle of the screw.
>
> 2. Now for the end bearing blocks. I want to use a tapered roller
bearing
> at each end of the screw and tension the screw between them. This poses
two
> possible advantages. First, by tensioning the screw I can further raise
the
> critical velocity (though I've been out of college too long to remember
how
> to calculate just how much). Second, by varying the tension in the screw
I
> should be able to adjust out any first order pitch error (though not
second
> order or cyclic errors).
>
> Of course it would be best to have two bearings at each end of the screw,
so
> I propose putting a regular ball bearing about two inches outboard of each
> tapered bearing in the bearing block. This would take up radial loading
and
> thus improve end fixity of the screw.
>
> I welcome y'alls opinions.
>
> Doug
>
>
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