Internal Hemisphere

How would you cut a hemisphere on a manual mill or lathe?

Plunge a ball-end milling cutter is one way.

Larry

Holdridge Radii Cutter for lathe

See this recent post:
http://www.practicalmachinist.com/ubb/ultimatebb.php/topic/30/4123.html

I Would like the the hemisphere to be larger than available ball end mill sizes.
From what I see a radius cutter will not enter the work far enough to cut a complete hemisphere.

Does it have to be a complete hemisphere?

If so a large radius hemispherical hole (complete) could be done with a bar as large as you can make it (for rigidity) and an end to hold the cutting tool that also pivots. Depending on the material you are cutting I would think that rigidity would be your greatest problem.

-DU-...etc...

On a mill.
In short:
1. Flycutter in mill spindle.
2. Tilt head according to desired hemisphere radius.
3. Turn work in rotary table, axis centered on "high" diameter of fly cutter.
4. Move knee up as you cut.
I will provide pics and math formulas tomorrow.
They are in a book at work.
Stay tuned.
SM

Have access to the old Bridgeport cherrying head?

A tracing attachment for a lathe,or mill.I have an old,manual Lehigh tracing attachment for a lathe.It will do 1 1/2" motions,or a 3" dia.hemi..A little tricky getting it to do a truly accurate hemisphere.Slicerman,can you cut a full depth hemisphere that way?If head not tilted to 90 deg.,flycutter arc will be the side of an ellipse? If 90 deg.,arbor of flycutter will hit top of the hole.

deltaenterprizes,

for a lathe, it occurs to me that a bar pivoting horizontally on the compound, away from the workpiece, turning up to centers then turning horizontally back to the workpiece but the tool holder portion skewed 45° toward the front, (or back, cutter inverted) could accomplish more than a hemisphere.

Before the vertical portion can touch the workpiece, the skewd cutter has cleared out of the machined hollow.

While the vertical portion would be limited to less than 180° of rotation, the cutter need only be swung 90 or so degrees to cut "all the way around." The lathe bringing the far side to you.

Since the pivot in this case, would be under the workpiece, there would have to be room between the workpiece and the pivot point for the lower bar.

I'd make it out of as heavy material as possible for the application and of course, a provision for tool advancement would be needed where the skewed portion of the insert holder meets the handle, approximately over the pivot. The handle extends over the swinging post to that point

Please say this makes sense, 'cause my scanner died and the sketch I made with a pencil, would have to be duplicated in a CAD program.

Bob

If you have a lathe with a large enough swing to clear a rotary table you set the rotary table up with an offset tool holder so that the tip of the tool is centered on the axis of rotation of the rotary table and at the same time you have the axis of rotation of the rotary table intersecting the axis of rotation of the lathe spindle. Advance the slide into the work piece mounted on the lathe spindle and generate the hemisphere. If you want to make a hyperhemisphere (greater than 180 degrees) you will need to make a tool holder with an elbow crook in it to clear the edge of the hole. Easier to do on a horizontal boring mill or a big facing lathe.

...listen to SlicerMan...I've seen it done...it works.

Yes, SlicerMan is correct, I have cut concave and convex radii up to around 4" using this method.

I was shown this by an old timer about 25 years ago when we were making laps that were used for eyeglass lenses. We used a flycutter with 2 inserts with a 1/8R that were spaced on a specific radius on the cutter. He had made up a table that showed all the variables such as cutter radius, head angle, X off center, and depth of cut. These are all that come to mind at the moment.
I lost my copy of that table along with a lot of other shortcuts and reference tables to hurricane andrew back in 1992. SlicerMan, please post these formulas when you find them. I may never use them again, but I sure want a copy just in case.

I love Close Works idea of the rotary table, if you have access to a large enough lathe to slide the rotary table under the work.

For clarification, I sketched the idea I offered above;

Cool! My first attempt at posting a drawing and I think it worked.

I'd use Peter Neills tapered roller bearing at the pivot.

I made an error in the isometric, the vertical portion of the tool should be taller for proper scale.

Faster cutting methods for roughing pocket might be useful.

Start the job with the tool retracted to minimum, advance with carriage until the pivot lies under the center of the radius, lock carriage, then complete by advancing the tool in the holder, advancements made with tool swung out of the hemisphere, cut from outside to center.

If you used 16 TPI as an example, for the tool advance screw, a half turn would advance the tool 0.03125"

Drilling the tool holder for say, 5/8" drill rod and grinding a flat on top for the set screws, would avoid having to broach a square hole for a tool bit. Harden drill rod, grind cutting edges and go. What the heck, go crazy and use Peters dovetails.

An alternate would be to mill a pocket for an insert.

I'd scale the tool sections as "thick" as possible, while still allowing clearances.

Substituting worm and sector for the handle, would give full mechanical control.

In any case, it's obvious that a full hemisphere, even a "hyperhemisphere" is possible, given the right geometry.

Now, how you get the ball in is your problem.

Bob

From:
SPIE Vol 472
Precision Optical Glassworking. A Manual for Craftsman and Designers
W. Zschommler
Translated w/ additional Material by G. K. Sachdev and J. Maxwell



Maximum diameter:
Dmax=4cosØ

Not an internal Hemi. Hope it helps.
SM

See Slicerman`s post for calculations.
This will also work for internal sferes.
When pushing the limits on a good machine dimensional accuracy and size within 0.01 mm are obtainable.
(had one of mine measured on a CMM)
Make sure the spindle axis and the dividinghead or rotab axis are in the same vertical plane.
Use a boringhead.

I notice this topic comes up from time to time and there are always those that doubt it works. Having set this up many times in the shop people invariably think I am making a cone. Their astonishment is priceless when they realize I am producing a spherical cut. I learned this technique at Laney College in Oakland back in the early 80's and didn't get a chance to use it for many years. The shop instructor didnot explain the math and as a result I came up with my own series of equations to arrive at the correct destination.

I will spare all the convoluted mess that I came up with and instead recommend a CAD program if you happen to have one. However the formula that Slicerman provided is so easy to use I would rather grab my calculator than fire up the pc. Thank you Slicerman...

I would only like to point out for those who are as mathematically un inclined as I am that it isn't: Theta is equal to the sin to the negative power of 1. Of course I struggled with this for a good while before showing it to a friend and he explained that is just the archaic way of writing arcsin. So, it's theta is equal to the arcsin of r over R. But I'm sure most of you already know that. Please don't laugh too loud.

It might also be useful to know that if you are using an insert or cutter with a radius tip that you need to alter the formula slightly to get the right angle.

The rule for concave spherical milling: Theta equals the arcsin of ( r-t )/(R-t )

Where R is the desired radius of the work, and r is the radius of the cutter, and t is the radius of the insert.

The rule for convex spherical milling : Theta equals the arcsin of ( r-t )/( R+t )

This can be easily confirmed by CAD.

Cheers

When I worked in a mold shop one of the jobs was making a pool ball mold and our grinder man ground all the cavity's using the angle and radius formula.

Here's how I got a full hemisphere:

Bendix PBS Photos by rbehner | Photobucket