making "spherical" surfaces with a boring head (?)

[mjautek]

so I'm trying to repair the Kopp variator in my lathe. basically it's a continuously variable transmission using two drive cones with balls in between them. changing the axis of rotation of the balls changes the ratio between the two drive cones. the variator has worked OK for the whole time I've had the lathe (... 5 years! oh how time do fly), until recently when I did an oil change (to the correct oil!) and now it's incredibly loud. go figure.

variator removed from my Holbrook Minor

I took the variator apart and the balls and drive cones have some smearing on them. a guy on a different forum hardturned the drive cones on his variator, and found that the variator was quite quiet when reassembled.
so I could resurface the cones by hardturning maybe or with a tool post grinder probably; the balls on the other hand I'm not so sure. scotch brite barely does anything and sandpaper affects the finish on the balls, which I would assume to be critical to the operation of the variator. so I had the idea to make a spherical lap and lap them back to round (maybe a bad idea since I've never lapped anything before??)

SO - I've heard of the technique to make spherical surfaces with a boring head and a rotary axis, so I gave it a shot. set the boring head to the ball diameter (70mm), set the dividing head to 45° to allow for tool access (as I thought the proper technique was) and let er rip. but to my surprise the "radius" made is completely wrong:

setup. the FP1 is pretty fun - I had the dividing head tilted the other way and ran out of travel - and then I realized given that the base is offset the correct way would be to move the dividing head to the other side.

looks alright...

hmmmmmm

at first I was sure there must be something wrong with my setup - centering, boring head setting, something. if the boring head isn't dead on center there generated curve would be more like a revolved "w"... but a quick check with the centering microscope shows that if I'm off it's not enough to explain the change in radius. and I checked the boring head setting quickly with a ruler; again it's within the ballpark.

so what's going on? I think the answer is that this technique doesn't actually generate spherical surfaces, but rather elliptical ones. if you can imagine the circle projected onto a plane 45° offset from the spindle axis, the shape it traces isn't a circle anymore when viewed from the work plane:

quick solidworks thinkonometry...

template check: it's the correct radius in this plane...

...but in the plane that actually matters

and since the shape is not actually circular there's no radius correction factor or the like to get the right diameter. and the greater the angle is between the cutter plane and the axis of work rotation, the greater the ellipticity (is that a word) will be. and this should hold true for convex shapes made with this technique also.

am I correct in saying the above? I thought lenses were ground with a similar technique to this, and aren't lenses spherical (not talking about intential aspheres here)?

"curve generator" via brittanica.com

and therefore if I want to use a boring head to generate a spherical surface then the tool plane and workpiece axis of rotation need to be parallel (i.e. spindle and dividing head at right angles to each other)?


I,m having a real "low brain" day today so some thoughts would be appreciated...

 

[quitereal]

How are you setting the tool height? Touch off top edge and go down 24.75? I want to believe that should create a sphere but my brain creaks like an old wood boat while thinking about it lol. Nice mill, those things look versatile af.

 

[jorogi]

so I'm trying to repair the Kopp variator in my lathe. basically it's a continuously variable transmission using two drive cones with balls in between them. changing the axis of rotation of the balls changes the ratio between the two drive cones. the variator has worked OK for the whole time I've had the lathe (... 5 years! oh how time do fly), until recently when I did an oil change (to the correct oil!) and now it's incredibly loud. go figure.

View attachment 60454
variator removed from my Holbrook Minor

I took the variator apart and the balls and drive cones have some smearing on them. a guy on a different forum hardturned the drive cones on his variator, and found that the variator was quite quiet when reassembled.
so I could resurface the cones by hardturning maybe or with a tool post grinder probably; the balls on the other hand I'm not so sure. scotch brite barely does anything and sandpaper affects the finish on the balls, which I would assume to be critical to the operation of the variator. so I had the idea to make a spherical lap and lap them back to round (maybe a bad idea since I've never lapped anything before??)

SO - I've heard of the technique to make spherical surfaces with a boring head and a rotary axis, so I gave it a shot. set the boring head to the ball diameter (70mm), set the dividing head to 45° to allow for tool access (as I thought the proper technique was) and let er rip. but to my surprise the "radius" made is completely wrong:

View attachment 60455
setup. the FP1 is pretty fun - I had the dividing head tilted the other way and ran out of travel - and then I realized given that the base is offset the correct way would be to move the dividing head to the other side.

View attachment 60456
looks alright...

View attachment 60457
hmmmmmm

at first I was sure there must be something wrong with my setup - centering, boring head setting, something. if the boring head isn't dead on center there generated curve would be more like a revolved "w"... but a quick check with the centering microscope shows that if I'm off it's not enough to explain the change in radius. and I checked the boring head setting quickly with a ruler; again it's within the ballpark.

so what's going on? I think the answer is that this technique doesn't actually generate spherical surfaces, but rather elliptical ones. if you can imagine the circle projected onto a plane 45° offset from the spindle axis, the shape it traces isn't a circle anymore when viewed from the work plane:

View attachment 60458
quick solidworks thinkonometry...

View attachment 60459
template check: it's the correct radius in this plane...

View attachment 60460
...but in the plane that actually matters

and since the shape is not actually circular there's no radius correction factor or the like to get the right diameter. and the greater the angle is between the cutter plane and the axis of work rotation, the greater the ellipticity (is that a word) will be. and this should hold true for convex shapes made with this technique also.

am I correct in saying the above? I thought lenses were ground with a similar technique to this, and aren't lenses spherical (not talking about intential aspheres here)?

View attachment 60461
"curve generator" via brittanica.com

and therefore if I want to use a boring head to generate a spherical surface then the tool plane and workpiece axis of rotation need to be parallel (i.e. spindle and dividing head at right angles to each other)?


I,m having a real "low brain" day today so some thoughts would be appreciated...

Thanks a lot, now I have a headache.

 

[Susquatch]

I have a cold so I can't think clearly either. But happy to throw one at you anyway.

The boring head cuts a circle where the radius of the circle is the radius of the boring head set point. When you rotate the cut object you are cutting various arcs that all have the boring head radius.

To get what you want, I think the rotating work must be moved close enough to touch (intersect) the center of rotation of the boring head.

I also THINK... That the axis of rotation of the work also has to be at 90° to the axis of rotation of the boring head.

 

[quitereal]

Set the cutter to 70mm and itll be 24.75 deep. Gun for a depth of 35 and the cutter would be 100mm???

1.414 (sq root of 2) x stock diameter for cutter, touch off top and go down 49.5? Still not a sphere?

 

[David]

I'm thinking about how a boring head can be mounted on a lathe toolpost, perpendicular to the work and turned through a 180 degree arc to cut a radius on the end of stock as it rotates in the chuck.
I agree with @Susquatch, the axis of rotation of the work has to be 90 degrees to the axis of rotation of the boring head.

 

[Mike R]

I think you are off axis with your setup. See my crude sketch on your pic below. Black is the current setup axis, you need to have it on the red line, intersecting the vertical axis at the plane the boring head is cutting.

 

[quitereal]

Set the cutter to 70mm and itll be 24.75 deep. Gun for a depth of 35 and the cutter would be 100mm???

View attachment 60465

1.414 (sq root of 2) x stock diameter for cutter, touch off top and go down 49.5? Still not a sphere?

Ok that dont sound quite right either, the cutter should be 70mm but should be down and in 49.5, ie past centerpoint of cutter wrt to left edge.... surely that would be a sphere

 

[PeterT]

so what's going on? I think the answer is that this technique doesn't actually generate spherical surfaces, but rather elliptical ones. if you can imagine the circle projected onto a plane 45° offset from the spindle axis, the shape it traces isn't a circle anymore when viewed from the work plane:

if I understand, I think I agree. If the objective is to make a spherical socket, then to kind of prove it in reverse, generate the that circular cut profile. Here it is in section view.

rotate the stock 45-deg like you have it positioned. The hz line represents a plane representing sweep of boring head.
I don't think it matters where its positioned vertically or depth just to examine the geometry

Now looking down perpendicular to boring head swing tool plane, the spherical cutout appears elliptical
Which means your boring head is defective. You bought the circular cutter not the elliptical cutter. Fortunately I offer a disposal service for these low value items. Just remit to me & I cover shipping.

 

[Susquatch]

In the clear light of a good night's sleep, anything other than the two axis at 90 degrees to each other will cut an ellipse. The rotating cylinder needs to be 90 degrees to the spindle axis - ie parallel to the table.

 

[Susquatch]

To see it in your minds eye, simply do a plunge cut all the way through a non rotating cylinder anything other than 90 degrees cuts an ellipse. When you rotate the work it just becomes a spherical ellipse.

A sphere can only occur if the two axis of rotation are at right angles to each other.

You cannot aggregate ellipses into a sphere other than at a right angle to the eliptical axis.

I'm sorry that I can't add drawings to illustrate. But I'm not sure I could put what my brain sees on paper even if I knew how.

 

[Susquatch]

@mjautek - just to add to my thoughts above, I can't seem to stop myself from visualizing your challenge. Even when I think about my ToDo list for today, your sphere pops into view.

So right now, I'm fussing about clearance on the tool bit in the boring head. Since the two axis have to be at right angles, there is no clearance to cut anything other than an extremely shallow bowl in the work..... Crap!

However, if you mount the cutter in the side of a small boring head, you could cut a deeper bowl.

In either case, you can never cut to a full hemisphere because the spindle diameter or tool body diameter will interfere.

A fly cutter will no doubt cut a deeper sphere - albeit still not a full hemisphere. A fly cutter might work a lot better too simply because a HSS cutter can be sharpened on both the top and the bottom. Very helpful as the sphere gets deeper. Ideally, you would grind a curved edge on the fly cutter face with the same radius as the final radius of your target sphere.

Thanks for posing this question. My poor brain needed some focus to help fight the fogginess of my cold.

 

[Lucky7]

Interesting thread.

Have been in the guts of two variators (three balls, not a six like yours) but just replaced bits. Didn’t dare remachine! This was years ago (ha! decades ago) when spare parts were easily available from a place in south Mississauga. As I understand their operation, they require maximum contact with drive cone to balls and use drag of oil as drive force. How do you propose to get the relationship of radial distance of cone to angle of center of drive sphere correct? If remachining/grinding the drive cone, the angle cannot be the same as originally machined.

Just a guess- I think the cone will need a ground surface, not just hard turned.

 

[mjautek]

ok so had a bit of a think and yell with the bossman at work, farted around in cad a bit and then consulted the sacred text (Tom Lipton's "metalworking: doing it better") and with some formulae and diagrams in front of me things are making more sense. Too bad I couldn't find this online earlier - all of the old forum threads I could find have missing pictures and the couple of youtube videos I skipped through don't really show it (and skipping through a 20 minute video to find information is rather annoying, but that's a topic for another day...)

I think Andy and PeterT have it basically correct; I cut a spherical shape but my radius is off by sqrt(2) = 1.41 ... I'll summarize what's written in the book later this week but my brain is fried right now lol

How do you propose to get the relationship of radial distance of cone to angle of center of drive sphere correct? If remachining/grinding the drive cone, the angle cannot be the same as originally machined.

oh that's an interesting point, didn't think of that. my immediate thought is that it doesn't matter too much if I'm only removing a couple thou but I shall think about that a bit more....

thanks for the input everyone !

 

[Martin w]

I don't know the math but, I have made gearshift knobs with this technique. I will have to look at the pictures of my setup, but I don't think my rotary table was set at 45 degrees. If I remember right, it was something like 15 degrees. I know if I do it again, I would make a driveshaft to a cordless drill to turn the rotary table. The other thing I learned , was it is difficult to get a perfect sphere. You need to leave quite a bit for the ball to stay attached until the turning is done, especially a steel ball. Very sharp cutters also help prevent chatter and light cuts.
I will dig up a picture tonight when I get home.
Martin

Edit: My table was at 90degrees with a 15-degree spacer. So 75degrees included angle. This was to clear the boring head tool.

 

[Dan Dubeau]

Mike R has the solution. The critical thing here is that the spindles align for the correct radius offset on the boring head. That will change depending on where you "slice" the sphere. Above or it will be smaller than the sphere diameter. Easy to figure out in CAD, but the math for this makes my head spin and eyes glaze over. I'm a visual guy.

This is just a quick sketch, but hopefully it shows better than I can explain. If you want me to draw up the settings for your particular ball and setup, I'd be more than happy to.


I have to wonder though, if a different approach might yield acceptable results. I'm not sure how accurate this method is as preserving the spherical geometry, but a 3 cup sphere polishing machine might resurface your balls to a level that's greater than you can acheive hard milling them. It might be difficult to control size, if you need all balls exactly the same, but it might be an alternative to look into.

 

[Dan Dubeau]

Ok, just dropped Thing #1 off at the bus, and while waiting to drop Thing #2 off I had a quick poke at your setup....Don't machine based off these #'s, I only scaled your pic assuming that bar of Al was 2.5" dia....Hopefully this will illustrate the correct radius setting on the boring head for your relative position, and how it all relates.

As I can see from the pic, you've either got the cutter set too low (25.07) for the radius setting, or the boring bar set too big (should be 48.84 dia) for the Z positioning. There are a lot of variables at play here, and changing one throws the other out of whack. You might also be better to drill a hole in the center of that bar, and setting your tool a bit high so that you don't have to swing through the exact centerline and can get a full cup. I'll draw that out after I get Thing #2 on the bus in a bit. Cutting the balls will require a different setup altogether.

Another gotcha, is how do you plan on cleaning up the uncut portion from op1? You'll have to recut a new pocket at the new diameter, and readjust everything again. Not impossible, but might be tough to match them up. I'm just thinking out loud through this operation at this point. Sounds like a fun one. Glad I get to watch from my couch . I've only thought of doing this operation once, to make some balls on the end of rods so I can make some variable fixturing bars for the weld table. Not a high accuracy task though.

 

[Mike R]

Note that the cutter needs to pass under the overhang created by the part being held at 45°. So In essence a fly cutter arrangement or the boring bar being held in a horizontal plane.

 

[Susquatch]

I had a look at Tom Lipton's book. What I totally missed in @mjautek's description of the process is that the boring head is not cutting full arcs through the work. Rather, it is cutting small circles within (or on) the work. That is a totally different paradigm - both physically and mathematically.

In my minds eye, I was imagining the red cutting path. A natural outcome of the photo itself. This path is (and must be) a circle outlined by the mills tool cutting radius and an ellipse on the surface of the work. This may also be the initial cuts until a reasonable depth of cut is achieved.



However, the final cuts are within the body of the work as shown by the green and yellow arcs. In this case, there are specific intersects where the cut surface can be spherical. These are defined by the math as outlined in the book.

Basically, cross-sections of inclined work must be eliptical, but within the work, there is no angle of intersection - to the cutter, the work has no boundaries and has no angle of inclination.

With that constraint removed, the process is almost identical to using a ball cutter on a lathe. The work is being turned by the table (analogous to the lathe spindle), and the cutter being turned by the mill (analogous to the manual handle on the ball cutter).

Why you wouldn't just use a lathe and ball cutter to do this is not clear to me.

 

[PeterT]

Yes this is a brain twister to me. If the part is orientated 90-deg to cutter axis then things make intuitive sense but difficult to machine in the real world. As the cutter spins about vertical axis (red arrow) and as part rotates (green line depiction) we get a resultant internal hemispherical shape. This sketch shows conditions to be exactly half a sphere (axis coincident to end). If axis is positioned to the left, it will be same spherical diameter but only a partial sphere internal cutout. Varying the BH bar stick-out changes the radius. I'm not sure if half a sphere is even required for the real part.

But in real life its hard or impossible to set up the boring head & cutter with coincident axis, which is why I think the work is tilted to some angle? So the question is - is there some mathematical happy point of axis displacement & cutter radius where the same cutting/rotation operation yields a spherical socket? Now I'm second guessing my sectional plane method yielding elliptical line a 'proof'. The section through a perfect spherical socket yield a different shape curve of socket depending on where the plane goes through. I just assumed it always has to be an ellipse just like any plane through a cylinder at any angle other than perpendicular results in an ellipse. I've never heard of this cutting method but if its in a book.... maybe a specific setup recipe? Interesting. Keep us posted.