Head angle 45°, boring tool set to cut radius of arc. Same as cutting a part spherical depression. Boring tool sweeps out the rim of a section through the centre of a sphere which must be a circle.

Clive

P.S. Asking on Practical Machinist as well is cheating.  Early enough over there that their brains are still awake not shutting down for bed-time.  Ought to have mremebered the lens makers equation tho' as I programmed a BBC B to figure that out for the optics shop "not telling you how many" years ago.  (Adcok Shpleys lens tooling version od the 1ES is one wierd looking beast.)

Edited By Clive Foster on 10/12/2015 23:24:36

John

I just turned this up with a quick google search

sin C = D/2Rc



where C = angle of cutter with axis of work surface

D = cutter dia

Rc = desired radius of surface



Exquisitely covered in A Treatise On Milling and Milling Machines, Third Edition (1951), Page 583

Phil

Clive, I've never made a cut like this, but surely the actual depth of the cut (i.e. from the edges of the rack to the trough in the centre) will be less than would be made if the boring tool was run horizontally. Because it can't be run horizontally for such a small radius cut, the angled-head is used, but the radius set on the boring head needs to be smaller than the desired radius of the cut. Without going through the geometry with a pencil and paper, I'd guess that for a 45deg angle of the head, the boring radius would be something like 1/root2 (i.e. 0.707) of the desired radius. So that would mean setting the boring tool to 26.51mm.

No guarantees!

Roger

Edited By Roger Head on 10/12/2015 23:44:39

John

Here's another

http://www.angelfire.com/ks/mcguirk/generatingradius.html

My dad used this technique to make new wood blocks for the rear wheels of our Fowler road loco.

He used a big slitting saw tilted over to end up with a curve in the block to fit a 7 foot diameter wheel.

Phil

The same technique is used to initially grind telescope mirrors and lenses. Convex or concave. I think it also slightly relates to how snooker balls are made.

John

–

Phil P

"Exquisitely covered in A Treatise On Milling and Milling Machines, Third Edition (1951), Page 583"

Any chance that you could scan/copy/xxx that bit, and post it?

Thanks, Roger

As the Season of GoodWill is upon us

… Try here

Individual pages are downloadable as PDF, without 'Partner login'

MichaelG.

John,

i'm going on theory, not practice, so I will stand correction , but I think you can get a true arc at 37.5 rad if you set your boring tool to 37.5 (70 dia.) and do a compound incline of the cutter head. The inclinations should be equal but to save any complications its probably easiest to do both at 45 degrees, sins and cosine being equal. As Clive Foster suggested early on, your cutter describes a spherical path which forms a gutter (what your after) as it progresses along the X axis.

Bob D

Les, that set up is how I used to produce the dies for oil and fuel filter housings. The dies I made had a round form but the principal was the same just rotated on the rotary table. Providing the wall section was OK no one measured the end result ! CNC now does it better and with great accuracy. Chris.