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Newsgroups: rec.crafts.metalworking
Subject: Re: "fudging" a metric thread
Summary:
Expires:
References: <853972049.12856@dejanews.com> <5c93i0$1ae@newshost.netrix.com> <854384246.3460@dejanews.com>
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Organization: Department of Electrical Engineering, Sydney University
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Cc:
In article <854384246.3460@dejanews.com>, <kevin@aquilagroup.com> wrote:
>
>I don't mention his name, lest he be deluged with requests
It was me. Here's the program: change Ngears to the number of gears you have,
the leadscrew_pitch to your lathe's (note that it is expected to be METRIC, ie
in millimetres) and the array gear[Ngears] should have your gear sets teeth
numbers (in no particular order). The program will grind through all possible
combinations of your gear set and print out the combinations that have the
desired pitch within your given tolerance. This was only a quickie, like most
of my metalworking programs, because I want the answers fast, not caring about
nice interfaces etc. Apologies to any C purists out there...
/*
DISCLAIMER
Copyright (C) 1997 by Adrian Philip Whichello. All rights reserved.
I, Adrian Philip Whichello, MAKE NO WARRANTY ON THIS SOFTWARE, EITHER EXPRESS
OR IMPLIED, WITH RESPECT TO QUALITY, ACCURACY, MERCHANTABILITY, OR FITNESS FOR
A PARTICULAR PURPOSE.
IN NO EVENT WILL I BE HELD RESPONSIBLE FOR DIRECT, INDIRECT, SPECIAL,
INCIDENTAL, OR CONSEQUENTIAL DAMAGES RESULTING FROM ANY DEFECT OF THE SOFTWARE.
I RELEASE THIS PROGRAM AS FREEWARE. YOU MAY COPY, GIVE AWAY AND USE THIS
PROGRAM, PROVIDED THIS NOTICE REMAINS ATTACHED AT ALL TIMES.
/* I think that about covers it :-) */
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#define Ngears 10
#define Ngears_1 Ngears-1
#define leadscrew_pitch 2.0
main(argc, argv)
int argc;
char *argv[];
{
int gear[Ngears] = {28, 30, 42, 49, 56, 63, 70, 84, 98, 105};
int headstock, leadscrew, stud1u, stud1l, stud2u, stud2l;
float pitch, desired_pitch, tolerance, pupper, plower;
printf("Desired pitch (in mm), tolerance (%%)? ");
scanf("%e %e", &desired_pitch, &tolerance);
plower = pupper = desired_pitch;
pupper += 0.01 * tolerance;
plower -= 0.01 * tolerance;
for (headstock = 0; headstock < Ngears; headstock++) {
for (leadscrew = 0; leadscrew < Ngears; leadscrew++)
if (leadscrew != headstock)
{
pitch = leadscrew_pitch * gear[headstock] / gear[leadscrew];
if ((pitch >= plower) && (pitch <= pupper))
printf("%dX%d %e (mm) %e (tpi)\n", gear[headstock], gear[leadscrew],
pitch, 25.4 / pitch);
for (stud1l = 1; stud1l < Ngears; stud1l++)
if ((stud1l != headstock) && (stud1l != leadscrew))
{
for (stud1u = 0; stud1u < Ngears; stud1u++)
if ((stud1u != headstock) && (stud1u != stud1l)
&& (stud1u != leadscrew))
{
pitch = leadscrew_pitch * gear[headstock] / gear[stud1l]
* gear[stud1u] / gear[leadscrew];
if ((pitch >= plower) && (pitch <= pupper))
printf("%dX%d|%dX%d %e (mm) %e (tpi)\n",
gear[headstock], gear[stud1l],
gear[stud1u], gear[leadscrew], pitch, 25.4 / pitch);
for (stud2l = 0; stud2l < Ngears; stud2l++)
if ((stud2l != headstock) && (stud2l != stud1l)
&& (stud2l != stud1u) && (stud2l != leadscrew))
{
for (stud2u = 0; stud2u < Ngears; stud2u++)
if ((stud2u != headstock) && (stud2u != stud2l)
&& (stud2u != stud1u) && (stud2u != stud1l)
&& (stud2u != leadscrew)
&& (gear[stud1u] + gear[stud2u] > gear[stud1l] + gear[stud2l]))
{
pitch = leadscrew_pitch * gear[headstock] / gear[stud1l]
* gear[stud1u] / gear[stud2u] * gear[stud2l] / gear[leadscrew];
if ((pitch >= plower) && (pitch <= pupper))
printf("%dX%d|%dX%d|%dX%d %e (mm) %e (tpi)\n", gear[headstock],
gear[stud1l],
gear[stud1u], gear[stud2u], gear[stud2l], gear[leadscrew],
pitch, 25.4 / pitch);
}
}
}
}
}
}
}
The instructions: Say you wanted to cut an 10tpi thread. This is
1/10" or 2.54mm pitch. Lets have a tolerance of 0.05mm for the sake of
argument (and to make the demo work!). Then, running the program, we get:
Desired pitch (in mm), tolerance (%)? 2.54 0.05
28X49|84X63|70X42 2.539683e+00 (mm) 1.000125e+01 (tpi)
(plus a *lot* more possible combinations)
which means we have 28T on the headstock, engaging (X) a 49T driving (on the
same shaft as) an 84T (|) on the first idler stud. The 84T engages a 63T, which
drives a 70T on the second stud and finally, this gear engages a 42T on the
leadscrew. Simple, isn't it! One of my (very) long term projects (and the
reason I wrote the program) is to put a set of change wheels on the Unimat 3 I
have at home to cut threads, made from an oddball collection of 24dpi gears I
picked up (not the set used in this copy of the program - I really mean
oddball: 31T etc!).
Kevin mentioned the following caveats:
"Remember that, even using a computer, it is good practice to check the
carriage travel/rev using an indicator, as insurance against mistakes. My
machinist friend has a change-gear that came from the factory marked with the
wrong number of teeth. Now ground off (well almost..he likes to show people)
and re-marked. He caught this with the indicator before scrapping a part. If
he had used a computer, he might have been less cautious about checking his
calculation. The marking was cast into the blank...guess one got in to the
wrong box. This took him a couple days to track down, as he had a lot more
faith in the machine (and so the gears) than in his math."
--
Dr Adrian Whichello Phone: +61 2 9351 4824
Imaging Science and Engineering Laboratory Fax: +61 2 9351 3847
Sydney University Electrical Engineering Email: adrianw@ee.usyd.edu.au
Australia WWW: http://www.ee.usyd.edu.au/~adrianw
"I wish to God these calculations had been executed by steam!" - C. Babbage