DIY-CNC Machine reality 101 was Re: Rack and Pinion

Dave,

Shut up and quit complaining over 1 thou <G>

Seriously,

Where are you going to place and use this machine? Will it be in an
air conditioned area and maintained at a constant temp? Before you
say yes; will the machine be used for long periods at a time? And if
so, have you a means for dealing with the heat from fricion in the
various component's movement??

Is the machine frame steel or aluminum? Or wood?

Add up all these factors, and a ten degree change in
temperature "eats up" your .001 "error".

Which is really ALREADY GONE becuase the rack and pinion you're using
are likely not ground (so their spec is outside the .001 "error" TOO!
<G>) and even if they were ground and within the error spec, the mesh
of the two is not generally held precisely enough to remove IT as
yet another larger-than-the-error-you're-concerned-about "error"...

Having written all that; let's talk PI.

ANYthing round and moving precisely deals with the "error" you're
discussing; whether a bomb site, or a machine positioning system. For
a given setup you end up with a given error. BUT this error is
averaged by the mechanical aspects, AND compensated by the software
precision.

In other words, no matter WHICH type of drive system you have, there
WILL be errors. The REAL questions are: How many? , How big?, and
What type?

Precision Rolled leadscrews only have a stated tolerance of .003-
.009" per foot, non-cumulative. Rack is not going to be any better,
and will likely be worse. Got any drive reduction belts, chains,
pulleys or gears in the setup? Yep, more errors! Do you really think
the 3mm or 5mm pitch of timing belts is within a thou? What is the
effect of a timing pulley pressed--by a fixing setscrew--to one side
of a hole that is .002? TOO bIG?!?

See, the REAL question is how do we EVER get the AMAZING level of
precision that we do (which is FAR less than most folks think!), when
we're fighting ALL these IMprecisions!<G>

Her's how. They ALL add and subtract their error in repeatable ways.
I did NOT say consistent ways; you can easily have one part of your
drive "worse" than another part. But the worse part will "repeat"
its "worseness" and the good part will repeat its "goodness"

Which means we can compensate for it. These two truths are the key:
ALL the errors add up--ultimately--to some repeatable "final" error.
And we have compensation tools of varying degrees with ALL the
software we use to drive our machines.

But different software has different level of compensation tools
available.

So we may only be able to set integer step size values (I.E., 999,
1000, or 1001 steps per unit. Or we may have oodles of decimal
precision available. (999.98456325) Most new software DOES use and
allow oodles of decimal precision for step size. So we can pretty
easily cancel out the OVERALL TREND of any error sum.

(We will not be able to remove cyclical or periodic errors with this
compensation method.)

For that we need either an overall compensation equation to apply to
the machine travel, and/or we need to "map" the variations and
compensate for them that way. BTW, you can do this mechanically. A
LONG time ago in this group Les Watts told and showed pics of how
this can be done. If you have PGO, a CCED group archive search should
turn up that interesting and potentially useful info.

If you have EMC or Mach3, you can enter "screw" compensation tables--
as is done for most commercial CNC's. (the word screw in quotes
because this type of comp works just as well with other forms of
drive; such as belts,chains, gears, racks, cables, etc.)MAch3 ALSO
has a formula based compensation for things like abbe error. (drive
force not in line with axis movement)

So as you consider that PI is irrational; you can now consider that
considering it is ALSO irrational<BG>

Just measure your machine output, and use the tools available to
remove it--and all the other error components, or at least reduce
it/them to NEEDED levels.

Perhaps MUCH more importantly, simply realise that the level
of "stated" ACCURACY and PRECISION for perhaps 95% of the DIY-CNC
machines discussed here and on other internet groups (Like my DIY-CNC
Yahoo group) is SO FAR OFF THE REALITY that it's more of a bragging
rights thing than actual fact.

As I've posted quite often, even jobber machine shops using multi
tens of thousand of dollars of multi thousands of pounds machinery
STILL only work to a "typical" accuracy of +/- .005 between features
and +/- .001 within small features.

Never forget the amount of MATERIAL and MACHINE STRUCTURE movement
and "growth" that occurs with even fairly docile changes in
temperature (and dont forget that the "ambient" temp YOU feel in the
shop is NOTHING like what the ballscrew and ballnut are feeling... or
rack/pinion, pulley /belt, etc.)

Have a look at the values of thermal expansion for the materials
typically used to build machines. (Machinery's handbook is one
resource;there ar eothers online) THEN consider all the above...

What was that PI thing again?

Oh yeah, Shut up and quit complaining over 1 thou <G>

Hope this helps,

Ballendo





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

>
> Hi all,
>
> I am probably missing something very simple in this.
>
> A spur gear has a unit value as the rack with a pitch diameter
> value of 1 inch. ie: a 12 pitch rack matches a 12 tooth gear when
> the pitch diameter of the gear is 1 inch.
>
> This then means the linear movement equals Pi for one revolution of
> the gear.
>
> Pi does not fit very well into any gear ratios or stepper or

encoder

> ranges.
>
> How then, does one get a 4 foot axis without some accumulated

error ?

>
> I can understand accept the table and machine will probably be

worse,

> but theoretically, the best I get is a little over 1 thou over 72
> inches. ( what did you say?? shut up and quit complaining over 1
> thou ?)
>
> I just don't want to use two jackshafts with 4 timing gears to get
> this theoretical accuracy.
>
> Am I missing something simple ?
>
> I've been looking at 12 and 16 pitch as the rack and gear width

seem

> to be good. Higher pitch seems to be much thiner, maybe too

thin ?

> I do know the larger plasma table makers use much finer pitch, but
> special order racks to get the wide face contact.
>
>
> Dave