calculating dividing head

[e723]

Hello,
I am trying to machine a 71 teeth gear. I have a dividing head with a 40:1 ratio. I don't have many plates for this dividing head. How do you figure out the right number of holes per plate for this application?

 

[Mud]

You'll need a 71 hole plate, and each division will be 40 holes in the 71 hole plate.

 

[Kyle Smith]

Your question made me think of this,
http://www.practicalmachinist.com/vb/showthread.php?t=80118
but it was for a 73 tooth gear, although their may be some answers in it for you.

 

[J.R. Williams]

71 tooth gear

Time to go to the "Machinery's Handbok" and you will find you need more than a division plate. You need a head set up for compound dividing... In addition to a plate with 18 or 27 hioles you need a 72 tooth gear on the worm and 40 tooth gear on the spindle and a 24 tooth idler. This is a set up for a B&S head..

JRW

 

[oldbrock]

71 hole dividing circle

I needed to make a 31 tooth gear and no 31 or 62 circle available on my dividing plates so I went the Gingery route and drilled a 62 circle in a spare space on one of my dividing plates. Cut a strip of paper the width of your plate, longer than the circumference of the plate. Tape one end on the outside of the plate and wrap it around the plate. Pull tight and cut through both thicknesses with a razor knife. you now have a strip the exact circumference of the plate. Lightly tape the ends on a piece of drawing paper and take a line from one end down at about 30 degrees and use dividers to step off 71 spaces so that the 71st is somewhere below the other end of the strip. You need two set squares with one joining the end of the strip and the 71st line. Maintain that angle and strike off your 71 spaces. They will go from 0 to 71. My method was to tape the strip to the plate and mount it in the lathe and use a dremmel mounted in the toolpost to drill the holes and have a solidly mounted pointer and bring each line to it and drill for each mark. Worked for me

 

[HuFlungDung]

Machinery's Handbook has charts for compound indexing. This is a method of using two different hole circles on one plate, to arrive at a very close approximation of the required number of divisions.

It would be preferable to make a plate with 71 holes, and you might be able to fit it on a 5" hole plate. This keeps things simple while you cut the gear. If you screw up making the plate over a time or two, it won't be so hard to bear.

The method is to use the existing plate with 39 and 41 hole circles on it. Use the sector to help count 4 turns and 25 (spaces) in the 39 hole circle with the crank pin. Then, withdraw the pin on the back of the plate (which should be kept in the 41 hole circle) and count an additional 2 turns and 28 (spaces) on the 41 hole circle. Let the crank ride fixed into the plate while you turn the latter amount. Turn everything the same direction so the movement is additive.

This should all work out complete in 13 revolutions of the spindle, so it will look like a skip pattern which will slowly fill in.

Good luck with that. If you can pull it off without an error, you're a very careful machinist

Differential indexing is much easier to operate if you have a universal dividing head and the necessary change gears. Once set up, the mechanism takes care of its own advance of the hole plate. There are a different set of charts in the handbook for that.

 

[Forrest Addy]

The Gingery approach to developing an index circle is lame no matter how careful you are. You get 71 holes but so what if they are all not in position. The best way to generate a new hole circle in a D/H plate is to bore the holes individually from a table of rectangular coordinates, center drill, rough drill undersize, then bore with an endmill ground for boring (backtapered). This way you can locate holes to the resolution of your DRO +/- one count.

I confess to being a blithering incompetent in running a dividing head. I'm forever forgetting to advance the sector after the index, losing count of the turns, or something. It's a wonder I haven't screwed up more splines and gears than I have. It takes focus and attention to detail to index 71 spaces without error.

It's cheating but for reliable indexing I suggest the DivisionMaster and a step motor. The DivisionMaster drives a step motor which is geared or timing belted to the input shaft of the dividing head rotary table whatever. Enter the overall ratio, the number of steps your motor is built for, etc and thereafter poke the button when you want to index. You can index either direction, even backstep a number of spaces: it even overshoots and takes up the backlash when reversing back.

It aint cheap but it's worth the price to avoid screwing up. Prime numbers? Any prime number? No sweat and no unversal indexing ratios to work out.



http://www.jeffree.co.uk/divisionmaster.html

 

[oldbrock]

dividing plate

Fine Forrest but I am old fashioned dude and have no such thing as a dro or a cnc anything. My method ala Gingery worked for the gear I had to cut and you don't hear any variation in sound when the gear train is running. When you are doing things the old way accuracy is in the hands of the craftsman. I rely on my skill and not state of the art technology. I taught cnc but choose to use what works for me with what I have and can afford.Peter

 

[J_R_Thiele]

Forrest and Oldbrock

How about this. Take 71 dowel pins, and turn/lap a disc so all 71 fit the periphery with no play. Secure with a rubber band making sure they are in line with the axis When you are satisfied with the set up, secure them to the disc and each other with threadlocker.

To use mount the disc- and set a DTI to it will slide off of one onto the next as the disc is turned. Pick a "zero" on the DTI. to go from one location to the other- turn the disc and stop when your "zero" is indicated again.

An alternative to the DTI would be a piece to fit into the spaces between the dowl pins.

Quicker than making 71 toolmaker buttons.

You could use balls from a bearing- but there is much less surface to glue.

 

[juergenwt]

On a B&S Universal Dividing Head you use an 18 hole index circle.Disengage the dividing head spindle from the main worm.Make sure the dividing head spindle turns freely. This will help you to set up your gear train.Now you have to gear the the dividing head spindle to the dividing head worm. Add a 40 tooth gear on the spindle and make sure you have the key back in place.( A special bar fits inside the spindle with a place to hold the gear)
On the worm of the dividing head ( not the main worm but the one that is connected to the index plate and has a shaft on the left side for the gear ) put a 72 tooth gear and use a 24 tooth gear as an idler to connect the worm to the spindle. Make sure you push in the pin that locates the index plate on the dividing head so the plate can move.Look for it behind the index plate. Re- engage the main worm that cranks the main spindle. Now when you turn the indexing pin the gear ratio between the spindle and the worm will advance or reverse the index plate the required amount to give you 71 teeth. A 10/18 hole set up will give you 72 teeth (10/18 = 40/72) so the geared index plate must move to make up for that one tooth.
To cut move your indexer on the dividing head 10 holes on the 18 hole circle for each cut (set your dividers to include 10 holes). Sounds complicate - but is actually very easy to do. When you cut your teeth make sure you always approach the hole from the same side. If you overshoot - go back and take out the backlash. Put a little drag on the dividing head spindle by tightening the lock screw slightly. Consult your Machinist Handbook for O.D. and dept of tooth also you must have the right cutter for diametrical ( or Modul - metric) pitch, pressure angle and number of teeth. The method is called "Indirect dividing". Only way to do it unless you have a CNC with live tooling.
After 71 moves you should be back to " o ". Make a dry run first. You are pushing my memory back a long time. Good luck. Juergenwt.
Have you tried "Boston Gear"?

 

[dp]

You'll need a 71 hole plate, and each division will be 40 holes in the 71 hole plate.

Buy a 71 tooth gear and use it for an index.

 

[Forrest Addy]

Oldbrock. What works, works. I've divided circles a zillion different ways but I thought the DivisionMaster was the simplest and most painless. I love technology that saves me time and effort. Simple and compound indexing works well and I've dome it odd and on form many years but you have to keep on your toes. The disk and dowel pin method brought up by JR sure seems workable. Push a pin out one by one to stop at an indicator zero is hard to beat for simple.

Most of the Gingery solutions to knotty machine shop problems I've seen are workable even ingenious but a few are very shakey in terms of precision and repeatability. I'd hate to think a noob would buy into some of these shakier notions as orthodoxy. One of my knottiest tasks as a teacher of apprentices back in the day is "unlearning" the utter but plausible nonsense learned fron respected mentors.

That said who am I to deny people the rewards/consequences of their own informed decisions?

As for "good enough" is it really good enough? What works for hand cranked may not perform well at motor speeds or turbine speeds - which is another way of saying there's a cost benefit assessment to be made at every step in this goofy trade.

 

[HuFlungDung]

On a B&S Universal Dividing Head you use an 18 hole index circle.Disengage the dividing head spindle from the worm.Make sure the dividing head spindle turns freely. Now you have to gear the the dividing head spindle to the dividing head worm. Add a 40 tooth gear on the spindle and make sure you have the key back in place.( A special bar fits inside the spindle with a place to hold the gear)
On the worm of the dividing head put a 72 tooth gear and use a 24 tooth gear as an idler to connect the worm to the spindle. Make sure you push in the pin that locates the index plate on the dividing head so the plate can move.Now when you turn the indexing pin the gear ratio between the spindle and the worm will advance or reverse the index plate the required amount to give you 71 teeth.
To cut move your indexer on the dividing head 10 holes on the 18 hole circle for each cut (set your dividers to include 10 holes). Sounds complicate - but is actually very easy to do. When you cut your teeth make sure you always approach the hole from the same side. If you overshoot - go back and take out the backlash. Put a little drag on the dividing head spindle by tightening the lock screw slightly. Consult your Machinist Handbook for O.D. and dept of tooth also you must have the right cutter for diametrical ( or Modul - metric) pitch, pressure angle and number of teeth. The method is called "Indirect dividing". Only way to do it unless you have a CNC with live tooling.
After 71 moves you should be back to " o ". Make a dry run first. You are pushing my memory back a long time. Good luck. Juergenwt.
Have you tried "Boston Gear"?

I respectfully disagree. You have alluded to a differential indexing setup, but I can't see how, if the worm is disengaged, that you've got any kind of a working mechanism.

 

[juergenwt]

Thanks HUFlungDung for pointing it out. The disconnect of the main worm is for set-up only to let you turn the gear train to insure a free movement. My mistake for not pointing this out. Thank you. I have corrected my post.Juergenwt.

 

[Highpower]

Hello,
I am trying to machine a 71 teeth gear.......

Buy a 71 tooth gear and use it for an index.

What's wrong with this picture?

 

[ichudov]

If your mill has a DRO, making a custom dividing plate with 71 holes is very easy. Some DROs support "bolt hole pattern" calculations out of the box. Some do not, and you can use trigonometry to calculate coordinates of each hole.

Here's my perl script for doing so.

#!/usr/bin/perl

# If you have a mill with a DRO, and/or a rotary table then you may find
# this script handy when dividing circles. To print the angles (in
# degrees, minutes and seconds) you just specify the number of
# divisions.
#
# If you want to calculate bolt hole pattern given a certain radius
# (assuming that coordinate (0,0) is the center of the circle), you give
# this script an optional argument --radius.
#
# Copyright(C) 2009, Igor Chudov.
# Distributed under the terms of the GNU PUBLIC LICENSE V2
#

use strict;
use warnings;

use Getopt::Long;

my $radius = undef;
my $pi = 3.141592653589793;

GetOptions(
"r|radius=f", \$radius,
);

my $divisions = shift @ARGV || die "USAGE: $0 <number>";

$divisions =~ /^\d+$/ || die "USAGE: $0 <number>";;

foreach( my $i = 0; $i < $divisions; $i++ ) {
my $angle = 360/$divisions*$i;

my $degrees = int( $angle );
my $minutes = int( ($angle - $degrees) * 60 );
my $seconds = int( int( ($angle - $degrees - $minutes/60)*60*60 ) );

my $xy = "";
if( $radius ) {
$xy = sprintf( ", x = %.4f, y = %.4f",
$radius * cos( 2*$pi*$angle/360 ),
$radius * sin( 2*$pi*$angle/360 )
);

}
print sprintf( "%d: %03d %02d' %02d\" (%f) %s\n", $i+1, $degrees, $minutes, $seconds, $angle, $xy );
}

 

[ichudov]

Here are the coordinates for a 71 hole circle with radius of 2 inches, which strikes me as a reasonable radius. Center of the circle has coordinates (0,0).

1: 000 00' 00" (0.000000) , x = 2.0000, y = 0.0000
2: 005 04' 13" (5.070423) , x = 1.9922, y = 0.1768
3: 010 08' 27" (10.140845) , x = 1.9688, y = 0.3521
4: 015 12' 40" (15.211268) , x = 1.9299, y = 0.5248
5: 020 16' 54" (20.281690) , x = 1.8760, y = 0.6933
6: 025 21' 07" (25.352113) , x = 1.8074, y = 0.8564
7: 030 25' 21" (30.422535) , x = 1.7246, y = 1.0127
8: 035 29' 34" (35.492958) , x = 1.6284, y = 1.1612
9: 040 33' 48" (40.563380) , x = 1.5194, y = 1.3006
10: 045 38' 01" (45.633803) , x = 1.3985, y = 1.4298
11: 050 42' 15" (50.704225) , x = 1.2666, y = 1.5478
12: 055 46' 28" (55.774648) , x = 1.1249, y = 1.6537
13: 060 50' 42" (60.845070) , x = 0.9743, y = 1.7466
14: 065 54' 55" (65.915493) , x = 0.8162, y = 1.8259
15: 070 59' 09" (70.985915) , x = 0.6516, y = 1.8909
16: 076 03' 22" (76.056338) , x = 0.4819, y = 1.9411
17: 081 07' 36" (81.126761) , x = 0.3085, y = 1.9761
18: 086 11' 49" (86.197183) , x = 0.1326, y = 1.9956
19: 091 16' 03" (91.267606) , x = -0.0442, y = 1.9995
20: 096 20' 16" (96.338028) , x = -0.2208, y = 1.9878
21: 101 24' 30" (101.408451) , x = -0.3956, y = 1.9605
22: 106 28' 43" (106.478873) , x = -0.5673, y = 1.9178
23: 111 32' 57" (111.549296) , x = -0.7346, y = 1.8602
24: 116 37' 10" (116.619718) , x = -0.8961, y = 1.7880
25: 121 41' 24" (121.690141) , x = -1.0507, y = 1.7018
26: 126 45' 38" (126.760563) , x = -1.1969, y = 1.6023
27: 131 49' 51" (131.830986) , x = -1.3339, y = 1.4902
28: 136 54' 05" (136.901408) , x = -1.4604, y = 1.3665
29: 141 58' 18" (141.971831) , x = -1.5754, y = 1.2321
30: 147 02' 32" (147.042254) , x = -1.6781, y = 1.0880
31: 152 06' 45" (152.112676) , x = -1.7677, y = 0.9355
32: 157 10' 59" (157.183099) , x = -1.8435, y = 0.7756
33: 162 15' 12" (162.253521) , x = -1.9048, y = 0.6096
34: 167 19' 26" (167.323944) , x = -1.9513, y = 0.4389
35: 172 23' 39" (172.394366) , x = -1.9824, y = 0.2647
36: 177 27' 53" (177.464789) , x = -1.9980, y = 0.0885
37: 182 32' 06" (182.535211) , x = -1.9980, y = -0.0885
38: 187 36' 20" (187.605634) , x = -1.9824, y = -0.2647
39: 192 40' 33" (192.676056) , x = -1.9513, y = -0.4389
40: 197 44' 47" (197.746479) , x = -1.9048, y = -0.6096
41: 202 49' 00" (202.816901) , x = -1.8435, y = -0.7756
42: 207 53' 14" (207.887324) , x = -1.7677, y = -0.9355
43: 212 57' 27" (212.957746) , x = -1.6781, y = -1.0880
44: 218 01' 41" (218.028169) , x = -1.5754, y = -1.2321
45: 223 05' 54" (223.098592) , x = -1.4604, y = -1.3665
46: 228 10' 08" (228.169014) , x = -1.3339, y = -1.4902
47: 233 14' 21" (233.239437) , x = -1.1969, y = -1.6023
48: 238 18' 35" (238.309859) , x = -1.0507, y = -1.7018
49: 243 22' 49" (243.380282) , x = -0.8961, y = -1.7880
50: 248 27' 02" (248.450704) , x = -0.7346, y = -1.8602
51: 253 31' 16" (253.521127) , x = -0.5673, y = -1.9178
52: 258 35' 29" (258.591549) , x = -0.3956, y = -1.9605
53: 263 39' 43" (263.661972) , x = -0.2208, y = -1.9878
54: 268 43' 56" (268.732394) , x = -0.0442, y = -1.9995
55: 273 48' 10" (273.802817) , x = 0.1326, y = -1.9956
56: 278 52' 23" (278.873239) , x = 0.3085, y = -1.9761
57: 283 56' 37" (283.943662) , x = 0.4819, y = -1.9411
58: 289 00' 50" (289.014085) , x = 0.6516, y = -1.8909
59: 294 05' 04" (294.084507) , x = 0.8162, y = -1.8259
60: 299 09' 17" (299.154930) , x = 0.9743, y = -1.7466
61: 304 13' 31" (304.225352) , x = 1.1249, y = -1.6537
62: 309 17' 44" (309.295775) , x = 1.2666, y = -1.5478
63: 314 21' 58" (314.366197) , x = 1.3985, y = -1.4298
64: 319 26' 11" (319.436620) , x = 1.5194, y = -1.3006
65: 324 30' 25" (324.507042) , x = 1.6284, y = -1.1612
66: 329 34' 38" (329.577465) , x = 1.7246, y = -1.0127
67: 334 38' 52" (334.647887) , x = 1.8074, y = -0.8564
68: 339 43' 05" (339.718310) , x = 1.8760, y = -0.6933
69: 344 47' 19" (344.788732) , x = 1.9299, y = -0.5248
70: 349 51' 32" (349.859155) , x = 1.9688, y = -0.3521
71: 354 55' 46" (354.929577) , x = 1.9922, y = -0.1768

 

[Conrad Hoffman]

I have a spreadsheet for various things, including dividing heads on my site at http://www.conradhoffman.com on the software page.

IMO, the best way to make new plates is to carefully turn them to size, put the right size mounting holes in them, and make them look really nice. Then go to the nearest real machine shop and say, "Please Mr. CNC man, would you pop the holes in this for me?" No idea what the cost will be, but the holes will be in the right place and you won't have to remove that broken bit on the last one.

Best,
CH

 

[Boris]

As a side note
Reading through this thread reminds me of my apprenticeship days where I had to use a dividing head and index plate in order to make some weird gears and do the calculations for linking a dividing head to a leadscrew for machining helical slots.
All I can say is this
"Thank gawd I don't have to do this anymore"

Boris

 

[stephen thomas]

J.R. Thiele, you method is probably not the first one I'd use, (would borrow time on a buddies ancient 2.5 axis BP, and drill/bore with programmed offsets)

However, why not use a bandclamp instead of a rubber band & glue? Also, each pin could be pre-ground (spindex) to a uniform reduced dia on one end. Then a taper latch could be used instead of a DTI and fiddling.

smt