Bevels. The only difficult thing about bevels is the maths
in the end I found what I needed to cut the bevels for the 1/6th S&T. (I suggest you put the equations in a spreadsheet and let that do the calculations for you.
) These are 45 degree straight cut bevels, also known as mitre bevels which simplifies the maths for us. I need 16 tooth bevels, of 32 DP.
Face angle = pitch angle = cutting angle = 45 deg.
Inner pitch diameter = no teeth / DP of the cutter = 12.7
Outer pitch diameter = 1.4* inner pitch diameter = 17.8
Inner cone length = Inner PD * (2 * Sin Pitch angle) = 8.9
Face length = 0.35 * inner cone length = 3.144
Blank diameter = Outer PD + (2 cos pitch angle / DP of cutter)
Cutter number for pinion = (no teeth in pinion * 1.25) / COS pitch angle = 28 teeth
Did you notice the number of teeth we have calculated is different than the number of teeth we will have in the gear! 28 teeth means a number 4 cutter profile, which I have.
Cutter offset = 3.142 / (4 * DP of cutter) = 0.623
Next job we need to think about the dividing head we are going to use, the one I used for this has a 40:1 ratio worm. What I need is to be able to divide by 16 teeth * 4 = 64, so looking through the dividing plates I found one with 16 holes that will give me a division of 640. So divide by 64 = 10 holes, divide by 16 = 40 holes. The sector arms were set for 10 holes.
We are ready, so first job cut two lengths of bar that will fit in the dividing head and cut the profile
Ok off to the mill, I have set the dividing head up at 45 degrees, lined up the centre of the correct cutter with the blank and we are ready to take our first cut:
First job setting the tooth depth, this is easy take the cutter up to the blank until it just touches, zero the DRO and wind in the depth of the tooth. It is now a simple job of winding the y axis in and out, moving the dividing head around 40 holes and making the next cut? What you end up with is this:
Now comes the important bit, we are now going to move the dividing head back 10 holes which is a quarter of a tooth width and we are going to change the height of the cutting head by our calculated cutter offset
.
The offset must be applied in the same direction that the bevel has just rotated. And we take a second cut all around.
We then reverse the offset so that we are taking a third series of cuts but on the other face of the tooth to that which we just did. For this I rotated the dividing head by 20 teeth and offset the head the 0.63mm in the other direction. To avoid getting confused with my counting I have taken to marking up the holes that the pin should end up on on the dividing head with marker:
An aching arm later and I have cut the first pair of bevels:
So now back to the lathe to cut the rear 45 degrees and to part off:
So two bevels, you may note I have a third cut, this shows the problem with straight cut bevels you are limited to how much you can cut towards the centre before you start cutting into the adjacent tooth:
So a pair of Bevels as promised:
My arm is telling me no more today
.
Jo
