View Single Post
  #29   Report Post  
James Waldby
 
Posts: n/a
Default Attach Rotary Table Vertically to Mini-Lathe? / divide by 7

Rex B wrote:
....
As John Martin pointed out, 7 doesn't go into 360 degrees
evenly. If you decide you need the precision then the cheap
indexer won't do. You would need an indexer with a index plate
that has a number of holes divisible by seven.
It may be possible to get a replacement index plate for that Enco
that has the right number of holes. Anyone know if that is possible?


An earlier post ref'ed a webpage with Robert Bastow's comments
on ball-bearing-based divisions. He said the 20 millionths
tolerance of standard bearings was way too much, and the proper
thing to do is make precision toolmaker's buttons. Anyhow, the
idea is to capture a ring of n buttons between an inner cylinder
and an outer ring, all parts made to high accuracy.[1] It
immediately occurred to me that cylinder diameter is non-critical
if we use two rows of balls, rather than one. For example, rather
than making an inner cylinder of diameter .652382" and putting 7
..500000" balls around it and a 2.404286" ID ring around that,
put 7 .5000" bearings around a 1" cylinder, then a ring of 7
more .5000" bearings around that, and then a ring clamp outside
to hold it all together. This could be used to make a first-
generation index plate, which then could be used with a rotary
table to make a more-accurate plate, as he suggested elsewhere
in that page.
-jiw

[1] For n balls of radius b and inner cylinder radius r, let
angle g = pi/n radians = 180/n degrees. Then b=(r+b)*sin(g)
and r=b*k with k=(1-sin(g))/sin(g). For one row of balls,
ring radius p = b+r. For two rows and exact fit,
p = b + h + s where h = b sqrt(3) and s = sqrt(r^2+2*r*b).
Eg, for n=7 and b=.25, sin g =.4339, k=1.3048, r=.3262,
h=.4330, s=.5191, p=1.2021.