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Graduating a vernier scale - maths inside!
This is going to make you guys laugh! Though I fear for the wrong reasons.
As I am refurbing an Atlas 7B shaper, I decided to do something about the original p*ss poor 7/8ths diameter graduated collars for the cross feed and for the downfeed, ....them guys sure had good eyesight back in the '40's!
So I turned up some bar and settled on a 1.800" diameter grad ring, a suitably stepped diameter with a knurl on to set it off and then transferred it to the mill with the dividing head on to scribe the 100 graduations on the diameter, with fullest lines at 0.010" intervals and intermediate lines at the 0.005" intervals, every 0.001" being about 0.1" long.
Set the DH up with a 36 hole plate (well it was already on the DH!) and calculated that:-
36*40/100=12 ~ therefore 12 hole indexing steps would give a 100 graduations over the periphery of the dial. No problem so far!
I realised that because of the larger dial size the datum line scribed on the fixed crossfeed bracket would also need to be increased in size to match the new graduations. No problem, so I turned up a thin disc 0.2" thick with a 1/2 hole through it for the crossfeed shaft and attached it to the previous bracket with a couple of 8-32 c'sks.
Rather than put a mark on the fixed datum with something as uncouth as a saw blade! I decided to mount the disc on a mandrel and scribe it off in the DH again (as the mill was still set-up with the DH and the scriber on centre line). Then the bonus of having a vernier scale to read in 0.0002" increments took hold and I thought I'll put the vernier markings on either side of the datum line, and I can then read it positive going, or negative going. What a bright little b*gger I am!
Since that point the maths has left me confused as to which way to go with the indexing. So far as I can see, given the dividing head plates are as follows:-
#1 plate = 22,24,29,36,37,49,57,63
#2 plate = 16,27,30,33,41,47,53,61
#3 plate = 23,25,28,31,39,43,51,59
I calculated that what was needed was a 20% increase in the spacing of the original 100 divisions. So converting the original 100 divs to degrees gives 360/100=3.6* per div; 3.6* + 20% = 3.96* so that divs required will be 360/3.96 = 90.909, which will round out to 91 divs, 63 hole plate #1 ~ 28 holes, and use a 72T x 32T differential gearing, or 90 divs without using the diff. gearing.
Then I looked at the possibility of using direct indexing by looking for a 100 division setup, with an even number of hole indexing steps that had a factor of 5 in them. This I thought I'd found in the following:-
Plate #3 ~ 25 holes. Gives 25*40 = 1000, therefore 100 divs = 1000/100 = 10 step indexing. Alright so far! Now if I factor 10 by +20% I get 12. So 12 holes will give me a 1/100th div + the 20% for the 0.0002" vernier scaler.
But on rechecking I now find that 25*40 = 1000, and 1000/12 = 83.3333. This looks to be the inverse of 90.909. Where have I gone wrong? (yes! I know - thinking that having a 0.0002" vernier scaler on a shaper was a bright idea!!)
Please help, you maths whizz-kids.
RR
As I am refurbing an Atlas 7B shaper, I decided to do something about the original p*ss poor 7/8ths diameter graduated collars for the cross feed and for the downfeed, ....them guys sure had good eyesight back in the '40's!
So I turned up some bar and settled on a 1.800" diameter grad ring, a suitably stepped diameter with a knurl on to set it off and then transferred it to the mill with the dividing head on to scribe the 100 graduations on the diameter, with fullest lines at 0.010" intervals and intermediate lines at the 0.005" intervals, every 0.001" being about 0.1" long.
Set the DH up with a 36 hole plate (well it was already on the DH!) and calculated that:-
36*40/100=12 ~ therefore 12 hole indexing steps would give a 100 graduations over the periphery of the dial. No problem so far!
I realised that because of the larger dial size the datum line scribed on the fixed crossfeed bracket would also need to be increased in size to match the new graduations. No problem, so I turned up a thin disc 0.2" thick with a 1/2 hole through it for the crossfeed shaft and attached it to the previous bracket with a couple of 8-32 c'sks.
Rather than put a mark on the fixed datum with something as uncouth as a saw blade! I decided to mount the disc on a mandrel and scribe it off in the DH again (as the mill was still set-up with the DH and the scriber on centre line). Then the bonus of having a vernier scale to read in 0.0002" increments took hold and I thought I'll put the vernier markings on either side of the datum line, and I can then read it positive going, or negative going. What a bright little b*gger I am!
Since that point the maths has left me confused as to which way to go with the indexing. So far as I can see, given the dividing head plates are as follows:-
#1 plate = 22,24,29,36,37,49,57,63
#2 plate = 16,27,30,33,41,47,53,61
#3 plate = 23,25,28,31,39,43,51,59
I calculated that what was needed was a 20% increase in the spacing of the original 100 divisions. So converting the original 100 divs to degrees gives 360/100=3.6* per div; 3.6* + 20% = 3.96* so that divs required will be 360/3.96 = 90.909, which will round out to 91 divs, 63 hole plate #1 ~ 28 holes, and use a 72T x 32T differential gearing, or 90 divs without using the diff. gearing.
Then I looked at the possibility of using direct indexing by looking for a 100 division setup, with an even number of hole indexing steps that had a factor of 5 in them. This I thought I'd found in the following:-
Plate #3 ~ 25 holes. Gives 25*40 = 1000, therefore 100 divs = 1000/100 = 10 step indexing. Alright so far! Now if I factor 10 by +20% I get 12. So 12 holes will give me a 1/100th div + the 20% for the 0.0002" vernier scaler.
But on rechecking I now find that 25*40 = 1000, and 1000/12 = 83.3333. This looks to be the inverse of 90.909. Where have I gone wrong? (yes! I know - thinking that having a 0.0002" vernier scaler on a shaper was a bright idea!!)
Please help, you maths whizz-kids.
RR
Besides, thats a lot of holes. Solution, drill holes in the jack every 1.5" and three holes in the sleeve spaced 1" apart vertically. Presto, vernier jack with 1/2" adjustment.
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