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Thruthefence
07-05-2011, 11:45 AM
Is there a tool, or workaround to machine a fairly accurate concavity in the end of a solid cylinder? A depression where a sphere could rest. (think "egg cup".)

Maybe describe it an opposite of a ball turning fixture.

The diameter of the "sphere" is 1.5".

I have an Emco-Maier super 11, with the milling attachment.

winchman
07-05-2011, 11:50 AM
Most any ball turning fixture will also cut concave recesses. You simply position the cutting tool differently.

Like this:

http://bedair.org/Ball/CONCAVE1.JPG

Of course, you may need to relieve the support under the tip to clear the work on deep recesses.

Evan
07-05-2011, 11:53 AM
My ball turning tool will turn either way. It all depends on where you mount the post.


http://ixian.ca/pics8/ballturn2.jpg

Thruthefence
07-05-2011, 12:13 PM
I have one of those OMW tool post ball turners; I suppose I could turn the handle & cutting tool 180 degrees, and try that? As long as I don't get in a hurry.

Thanks, guys!

Dan Dubeau
07-05-2011, 02:31 PM
Rotary table tilted on angle, and a boring head in the mill spindle. I've never done it, but remember seeing it posted here before with a few pictorial descriptions

adatesman
07-05-2011, 02:33 PM
Can't get much easier than plunging with a ball mill. I had to do something similar years back when setting up a screw machine to churn out golf tees out of aluminum (which then got stamped with the school's name and handed out at the open house) and it worked exceedingly well.

Jaakko Fagerlund
07-05-2011, 02:44 PM
Can't get much easier than plunging with a ball mill. I had to do something similar years back when setting up a screw machine to churn out golf tees out of aluminum (which then got stamped with the school's name and handed out at the open house) and it worked exceedingly well.
Sure puts a lot of strain on that cutter as the center is non-cutting and the surface contact becomes large so it will try to move to some direction and chatter like hell, especially if trying to do R20 concave surface.

Weston Bye
07-05-2011, 02:44 PM
Rotary table tilted on angle, and a boring head in the mill spindle. I've never done it, but remember seeing it posted here before with a few pictorial descriptions

I've done it, both convex and concave, but used a flycutter with mill spindle tilted and the rotary table flat on the milling table.

adatesman
07-05-2011, 04:50 PM
Sure puts a lot of strain on that cutter as the center is non-cutting and the surface contact becomes large so it will try to move to some direction and chatter like hell, especially if trying to do R20 concave surface.

True, but I can't imagine a 1.5" diameter ball mill having much problem with rigidity. Plus there's no reason he couldn't rough it in first with a drill/boring bar and then simply slow things down and use the ball mill as a form tool to finish. Lots of ways to skin this cat...

form_change
07-05-2011, 04:57 PM
Last night I posted some pictures of a button die holder I made in the shop tools sticky using the coordinate method for spherical turning. There is no reason that using a boring bar you couldn't do the same thing for a concave cavity.
For those not familiar with the method a spreadsheet (or something) is used to calculate the coordinates, and then you step the cross slide and compound dials according to the calculated values. While surface finish will not be as fine as with a ball turning device it works and a little emery paper will take out any lumps and bumps. For a one off item it is worth considering.

Michael

justanengineer
07-05-2011, 05:02 PM
I simply swing the compound. Never saw a need for a fancy ball turning tool, but then again, I dont do many curves manually.

Forestgnome
07-05-2011, 05:09 PM
I simply swing the compound. Never saw a need for a fancy ball turning tool, but then again, I dont do many curves manually.
I recently saw an old photo of a variation on that. There was a solid link between the operator end of the compound and a fixed point on the lathe bed. The compound was parallel to the lathe axis. As the cross-slide was advanced or retreated the linked end of the compound stayed in one place, so it would pivot the cutting tool to form the recess.

Weston Bye
07-05-2011, 05:12 PM
See post #8 above.

http://img.photobucket.com/albums/0803/Weston/DSCN4041.jpg

The Artful Bodger
07-05-2011, 05:17 PM
That looks very nice Weston. Do you always get a portion of a true sphere? I am thinking a parabola could be machined by careful positioning of the rotary table?

Weston Bye
07-05-2011, 05:34 PM
Thanks, John. Honestly, I never measured to determine sphere vs. parabola. My work of this nature was always for decorative excersize, so accuracy or geometry wasn't a consideration. Perhaps someone else here can shed some light.

Evan
07-05-2011, 07:19 PM
Assume that the head isn't tilted so that the plane of the fly cutter is coplanar with the bed.

Assume that the rotary table is tilted at 90 degrees so that the surface of the work is perpendicular to the plane of the cutter.

If the cutter is set to cut through the centre of rotation it will produce a cut that is an orthodrome, a segment of a great circle, with the diameter equal to the diameter the cutter cuts. Rotating the work will then produce a section of a sphere with the same diameter.

If the table and work are tilted to some intermediate angle and the cutter still cuts through the center of rotation the path of the cutter will then be a segment of a small circle of a sphere with the diameter equal to the tangent of the angle of tilt. It will still cut a section of a sphere but with a larger diameter.

As the table tilt approaches coplanarity to the plane of the cutter the tangent approaches infinity at which point the diameter of the sphere approaches infinity. When it is coplanar the tangent and the sphere size are infinite and it cuts a flat surface.

The Artful Bodger
07-05-2011, 08:39 PM
Thanks Evan. I assume then that if the cutter does not cut through the centre of rotation there would be some sort of 'peak' produced in the middle of the work?

PeteM
07-05-2011, 08:44 PM
Oops, double post.

PeteM
07-05-2011, 08:46 PM
The classic store-bought solution is a Holdridge Radii Cutter:

http://cgi.ebay.com/HOLDRIDGE-RADII-CUTTER-Model-4-/200620227178?pt=LH_DefaultDomain_0&hash=item2eb5e5ba6a

The size (4" in the above) indicates it will cut a perfect sphere or socket to that diameter. Larger sockets can also be made with an extended tool. The "S" model is a sort of bare bones set. The "D" is "deluxe."

Sphere tools are pretty easy to make, but getting the rigidity and ease of use right takes a bit of planning.

Evan
07-05-2011, 09:34 PM
I assume then that if the cutter does not cut through the centre of rotation there would be some sort of 'peak' produced in the middle of the work?



Yes. I will have to give it some thought to figure out the curve produced. It is probably still a sphere but with a circular column at the centre.

darryl
07-05-2011, 10:37 PM
I set up to cut a large radius concave in some aluminum plate once. I mounted a pivot on the tailstock ram, then from that ran a sturdy bar towards the chuck. Mounted a cutter on the bar, also mounted a support piece on the bed near the chuck. The support is like what wood lathes have for the chisels- the height is such that the bar rests on it and the cutting tool is on center. I worked the bar back and forth manually as I slowly brought the tailstock ram in. The radius of the concave produced was about 16 inches or so, the most distance I could put between the pivot point and the surface of the workpiece.

Getting the pivot point directly in line with the spindle axis gave me a 'proper' concave. If you offset the pivot, you would get a deviation from that.

Then I tried to wrap my head around a method of producing a parabola on the lathe, and I kind of got lost with it. It would have required having the pivot point move in or out as the bar with the cutting tool on it was worked back and forth along the rest.

Evan
07-06-2011, 12:22 AM
This is the one I made. I don't know of a way to turn a parabola. I did some searching and the best I could find was a close approximation using a double bar linkage. I have given it some thought but I cannot think of a mechanical way to produce an exponential curve. There probably is a way but it probably isn't simple. (the red is from my power on warning lamp)

http://metalshopborealis.ca/pics5/radius1.jpg

The Artful Bodger
07-06-2011, 12:51 AM
Yes. I will have to give it some thought to figure out the curve produced. It is probably still a sphere but with a circular column at the centre.


Hmmmm, seems like it would be a variation of a torus.

darryl
07-06-2011, 01:37 AM
I can see a way to make a linkage that would change the distance from the pivot point to the chuck as the cutting tool bar was moved- I have no way of knowing what kind of curve it would end up generating. I was going to mock it up using cardboard and pins, then try to make it follow a curve generated by the string method of drawing a parabola. I might get it close, but if the need was to produce a true parabola, close probably wouldn't count.

I did my project for fun- I don't even know where it is now. Might still be attached to a face plate-hmm.

Evan
07-06-2011, 02:12 AM
Hmmmm, seems like it would be a variation of a torus.

That is what I first thought too but it won't be. The cutter will cut a straight sided column when the work is perpendicular to the table which will vary to an inverted cone with increasing angle assuming that the work is brought closer to the cutter by moving the table to increase depth of cut.

On further consideration it depends on the direction that the cutter is offset from centre. Both are possible and combinations of both are also possible.

DATo
07-06-2011, 03:44 AM
I can see a way to make a linkage that would change the distance from the pivot point to the chuck as the cutting tool bar was moved- I have no way of knowing what kind of curve it would end up generating. I was going to mock it up using cardboard and pins, then try to make it follow a curve generated by the string method of drawing a parabola. I might get it close, but if the need was to produce a true parabola, close probably wouldn't count.

I did my project for fun- I don't even know where it is now. Might still be attached to a face plate-hmm.

Don't mean to butt in but I'm fascinated by the problem. I've never done this but I'm sort of intuiting that a combination ball turner coordinated with a cam action might produce the parabola with the f of x : y movement linked to the rotational movement of the radius turner. Perhaps a second (upper) stage to the ball turning attachment linked to an outboard pin fixed the lower plate which runs along a slotted bar on the upper stage with an offset center point?

Weston Bye
07-06-2011, 06:09 AM
I remember seeing how to generate a 2D parabola in Mother Earth News magazine. They were doing it for a solar collector. I have the magazine, but it's buried so deep...

Might be a lead for someone to research on the web.

form_change
07-06-2011, 06:33 AM
An ellipse can be generated by a thing called an Archimedes trammel and a quick search on parabolic trammel turned up an mechanism (Child's Parabolic Trammel) - whether they can be adapted to a lathe to produce a concave surface is another matter.
According to Wikipedia, a parabola is an ellipse with one foci out at infinity. I once did the calculations for the difference between a spherical surface and a parabolic one and noted that the difference in surface profiles was not great, particularly for shallow arcs.
Something must be possible...

Michael

Ian B
07-06-2011, 07:23 AM
Evan,

In the setup you show, I'm guessing that the pivot point at the tailstock end is locked to the bed, and the saddle is free to move under the influence of the radius bar.

If you look at the drawings here: http://www.mamikon.com/USArticles/Trammel.pdf
(scroll down a bit to figure 3), I think that you could reproduce the mechanism simply by locking the saddle and letting the tailstock end pivot move back & forth along the bed.

Would that give a parabola?

Ian

The Artful Bodger
07-06-2011, 07:29 AM
Deleted by me....................brain fade.

The Artful Bodger
07-06-2011, 07:39 AM
Evan,

In the setup you show, I'm guessing that the pivot point at the tailstock end is locked to the bed, and the saddle is free to move under the influence of the radius bar.


Ian


Ian, are you referring to the sketch I deleted?

rohart
07-06-2011, 07:50 AM
Everyone (well...) knows that a light source at the focus of a parabola produces a parallel beam by reflection.

Most know that a light source at one focus of an ellipse will get its output reflected to the other focus, and back again.

What has always intrigued me, and I have never found a practical use for it, is that any ray of light that does not travel through the focus of an ellipse (but is coplanar with the major axis) will get repeatedly reflected closer to the major axis. Thus, if we're talking about an ellipse of revolution, and a light source on the axis, and there's a tiny hole at one end of the axis, eventually all, absolutely all, the reflected light will come out of that hole, the beam being more parallel the smaller the hole is.

But back to the parabola, maybe Evan could tell us if an approximate machining of a parabola would be better than working at distorting a spherical mirror into a parabola - and I'm talking shallow telescope-mirror profiles here ?

Ian B
07-06-2011, 08:39 AM
AB,

No, I was referring to the photograph that Evan showed of his lathe, about a dozen posts ago.

Ian

Evan
07-06-2011, 08:53 AM
There is very little difference between a spherical mirror and a parabolic mirror. It is so small for long focal lengths that the spherical abberation is nearly insignificant. Most low cost small telescopes up to six inches or so use spherical mirrors for F8 or longer mirrors.

This question has direct application to the making of mirrors since they are commonly roughed to a spherical shape with diamond tooling now. This has replaced grinding for the majority of stock removal and is responsible for the large decrease in prices since the only grinding now required is parabolization and final figuring.



What has always intrigued me, and I have never found a practical use for it, is that any ray of light that does not travel through the focus of an ellipse (but is coplanar with the major axis) will get repeatedly reflected closer to the major axis. Thus, if we're talking about an ellipse of revolution, and a light source on the axis, and there's a tiny hole at one end of the axis, eventually all, absolutely all, the reflected light will come out of that hole, the beam being more parallel the smaller the hole is.


That is called a "Crab's eye reflector". It has a very important application as a concentrator for solar cells and solar heating. It can be made in a linear form to direct all incoming solar energy on a small diameter pipe.

rohart
07-06-2011, 05:24 PM
Thanks Evan.

So the light enters the Crab's eye reflector through any part of the 'top' half of the ellipsoid, and then gets reflected internally due to some coating, ending up going out of a small hole at the 'bottom' onto the solar cell. Is that it ?

Evan
07-06-2011, 05:55 PM
Yeah, that's it. Look it up on Google, I am sure you will find many examples.

The Artful Bodger
07-06-2011, 08:27 PM
Everyone (well...) knows that a light source at the focus of a parabola produces a parallel beam by reflection.

Most know that a light source at one focus of an ellipse will get its output reflected to the other focus, and back again.

What has always intrigued me, and I have never found a practical use for it, is that any ray of light that does not travel through the focus of an ellipse (but is coplanar with the major axis) will get repeatedly reflected closer to the major axis. Thus, if we're talking about an ellipse of revolution, and a light source on the axis, and there's a tiny hole at one end of the axis, eventually all, absolutely all, the reflected light will come out of that hole, the beam being more parallel the smaller the hole is.




I have failed to find a picture on-line but I know that c1930 there were luxury car headlamps that had some form of enclosed reflector with the light all coming out a very small hole, it is reputed that one could light a cigarette by holding it in front of the aperture.

Weston Bye
07-06-2011, 09:09 PM
I did some playing around with some geometric construction. I think I came up with a method of mechanically generating a parabola. I'm sure that this has been done before, but it is new to me.

http://img.photobucket.com/albums/0803/Weston/Parabola.jpg

Evan
07-06-2011, 10:38 PM
It's only an approximation since if you run it through a full revolution it generates a closed curve.

Black_Moons
07-07-2011, 02:23 AM
Yeah, that's it. Look it up on Google, I am sure you will find many examples.

I can't find any examples of a 'crab's eye reflector' on google, Quoted brings no results, and unquoted is a mess of unrelated results, with the odd one relating to eyes or other types of reflectors. Can you find a basic webpage about em and post the url? Or post better search terms I could use.

Also, I just realised this method on the mill, Could'nt it to be also used to mill spheres? At least, spheres on the ends of rods. I guess rod length would be seriously limited due to rigidity on a rotary table with no large pass through hole, but sphere size could be huge with a large boring head.

The Artful Bodger
07-07-2011, 05:20 AM
Deleted by me, wrong end of the stick!

Lew Hartswick
07-07-2011, 07:01 AM
OK, I took a look at my old LORAN notes which was a navigation system producing parabolic lines of position.:rolleyes:
Those lines are hyperbolas not parabolas.
...lew...

form_change
07-07-2011, 07:06 AM
As I noted in post 28, there is very little difference between a circle and a parabola when the radius/ focus is way off. The graph below -

http://i1140.photobucket.com/albums/n574/form_change/deltaSmall.jpg

is a plot of the deviation from a parabolic shape for a circular arc and an ellipse. The circle's radius is 1000mm and the arc if turned into a surface of revolution would be 200mm across and around 5mm deep. A couple of interesting things are that the ellipse profile has the lowest overall error, although the circle is the more accurate out to a diameter of say 120mm (as suggested by Evan in post 34). However, the most interesting thing is the size of the error (assuming I haven't fouled up my calculations). For the elliptical profile, the maximum error is just under 0.002mm, or 2 microns (8 100th's of a thou). In machining terms pretty fine, but in optical terms still big. I would suggest that without temperature controlled rooms, equipment and very precise slides/ bearings any mechanism devised to produce a parabolic shape would have errors larger than this and so a spherical surface is probably going to be the best most machinists can realistically achieve with what ever mechanism they can fabricate. A CNC machine could be programmed for a parabola but a typical home shop CNC will have errors of this magnitude or greater, so could not be relied on for an accurate profile. Lots of polishing would be needed to smooth the surface which then has the potential to destroy the form.
(Happy for some one to do it, but it seems to me to be getting beyond the limit of a home shop)

Michael

The Artful Bodger
07-07-2011, 07:44 AM
Those lines are hyperbolas not parabolas.
...lew...


Bugger! Thats true!

Thruthefence
07-07-2011, 11:34 AM
Anyone read Nevel Shute's "Trustee From the Toolroom", where he makes his grieving niece an Egg in his home shop? Didn't take him no time!

I wish I was that sharp!

Evan
07-07-2011, 12:14 PM
Here is an article that mentions the "crab's eye" reflector in Popular Science.

http://books.google.ca/books?id=HwEAAAAAMBAJ&pg=PA97&dq=concentrating+collectors+oct+76+popular+science&hl=en&ei=X9gVTvGYDM6gsQKX6oBw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCkQ6AEwAA#v=onepage&q&f=false

http://ixian.ca/pics9/crabeye.jpg

Evan
07-07-2011, 12:37 PM
A CNC machine could be programmed for a parabola but a typical home shop CNC will have errors of this magnitude or greater, so could not be relied on for an accurate profile

I disagree as I will show below.

I have had pretty good results making mirrors with my CNC mill. It will hold dimensions to an error less than a wavelength of light as I showed by ruling a blaze diffraction grating at 36800 line per inch.

These are some of the mirrors I have machined:

http://metalshopborealis.ca/pics5/mirror2.jpg

In particular, using software I wrote I designed a 4th power parabolic curve that has the property of producing a very wide angle view with far less distortion than a fish eye or other shapes that are available.

Here are the various shapes and the imaging results:

http://metalshopborealis.ca/pics5/mirro1.jpg

http://metalshopborealis.ca/pics5/mirro2.jpg

http://metalshopborealis.ca/pics5/mirro3.jpg

Evan
07-07-2011, 12:41 PM
http://metalshopborealis.ca/pics5/optics2.jpg

Note how straight lines remain straight:

http://metalshopborealis.ca/pics5/optics4.jpg

form_change
07-07-2011, 05:08 PM
Evan,
I did say "typical" home shop CNC - at the time of writing I was thinking of a retrofitted manual machine - either new Chinese or older something else.
I you can get an off tool finish repeatably within 2 micron then you are doing really well, particularly as surface roughness is going to be potentially greater than the tolerance required. If you can machine to tolerances that are less than a wavelength of light so you don't have to polish the surface afterwards then you are doing extraordinarily well.

My current employer has an optics capable lathe. I haven't been near it for some time but from memory it is isolated on a monolithic block, temperature controlled, conditioned electric power as well as being a very solid bit of kit. Next time I see one of the guys I'll have to ask what tolerances they can hold.

We had issues measuring optical form at another employer's facilities - this was for the direct machining of lens surfaces - and if that was required the part was sent off to a multimillion dollar facility for a proper metrology report. When I'm talking about an accurate profile, I'm meaning something dimensionally accurate rather than something that is accurate in a relative way. My involvement in that was to sort out a distortion problem of a few nanometres at the extremes of their surfaces brought about by the post machining polishing they then did.

Michael

Evan
07-07-2011, 05:50 PM
If you can machine to tolerances that are less than a wavelength of light so you don't have to polish the surface afterwards then you are doing extraordinarily well.


Mine isn't that good. I still have to polish but not enough to disturb the figure significantly.

Paul Alciatore
07-08-2011, 01:30 AM
Assume that the head isn't tilted so that the plane of the fly cutter is coplanar with the bed.

Assume that the rotary table is tilted at 90 degrees so that the surface of the work is perpendicular to the plane of the cutter.

If the cutter is set to cut through the centre of rotation it will produce a cut that is an orthodrome, a segment of a great circle, with the diameter equal to the diameter the cutter cuts. Rotating the work will then produce a section of a sphere with the same diameter.

If the table and work are tilted to some intermediate angle and the cutter still cuts through the center of rotation the path of the cutter will then be a segment of a small circle of a sphere with the diameter equal to the tangent of the angle of tilt. It will still cut a section of a sphere but with a larger diameter.

As the table tilt approaches coplanarity to the plane of the cutter the tangent approaches infinity at which point the diameter of the sphere approaches infinity. When it is coplanar the tangent and the sphere size are infinite and it cuts a flat surface.

Re: the comment in bold.

A tool tip that is tilted in this manner will travel in an elliptical path as viewed from the side. If the work is moved past it in a linear manner, it will cut a depression with an elliptical cross section. Not spherical and not a parabolic section.

However, if the work is on a rotary table and the tool tip passes through the center of the RT’s rotation axis, the situation becomes more complex. Although the tool tip is traveling in an elliptical path as viewed from a direction parallel to the original work surface, this tool motion is NOT passing along a diameter of the circular depression being cut as viewed in a normal (perpendicular) direction to the original surface of the work. Instead, this path, as viewed from this normal direction, is also an ellipse. This will introduce a distortion to the elliptical cross section bring cut: the curve produced will actually be flatter at the edges than a true elliptical section would have been. In fact, a quick check using a CAD program seems to confirm that this “distortion” is just enough to produce a true sphere. I find that this is very curious.

Does anybody know of any proper derivation or proof of this? And what limits are there on this? It would seem that if taken to extremes, there must be a variation from this seemingly spherical surface. Or to the contrary, is it only a very good approximation and does anybody know what the actual curve is? A proper mathematical proof would be very nice here.

Evan
07-08-2011, 01:58 AM
A tool tip that is tilted in this manner will travel in an elliptical path as viewed from the side. If the work is moved past it in a linear manner, it will cut a depression with an elliptical cross section. Not spherical and not a parabolic section.


Neither the tool or the work are passing the other. Only the depth of cut changes. Since the work only rotates the shape produced is a surface of revolution of the planar cut.

small.planes
07-08-2011, 03:16 AM
Heres how I made a ball seat, not so long ago:

http://bbs.homeshopmachinist.net/showthread.php?t=43482

The milling offset thing has been much discussed also, there is a set of threads over on PM about it, and also this on here:

http://bbs.homeshopmachinist.net/showthread.php?t=32038

In post 26 Old Tiffee (What happened to him?) does some maths, which I havent checked :confused: ;)

Dave

Evan
07-08-2011, 03:47 AM
Here is a visual proof. The blue disk represents the plane of the fly cutter.

http://ixian.ca/pics9/flycut_sphere.jpg

beanbag
07-08-2011, 05:18 AM
I think Evan is right and it really does cut a perfect spherical section. His drawing is the basis for the "proof" I am about the explain.

First we have to assume that only the very tips of the flycutter teeth cut, so instead, imagine that the cutter is a ring of hot wire.

Find a sphere of whatever diameter you want and press it into the workpiece to make the spherical indentation as shown.

Drop the ring into the sphere and make one part of it touch the very bottom of the indentation. That's the path it will cut for one position of the rotary table. Does the ring contact the surface of the sphere (indentation) at all points? Yes it does, so so far so good.

Turning the rotary table is the same as rotating the ring about an axis that is perpendicular to the workpiece and centered at the bottom of the indentation. As you rotate this ring around, its entire edge still contacts the sphere and you are able to sweep out the indentation.

Evan
07-08-2011, 10:08 AM
BTW, that drawing is somewhat like how I see things in my head.

adatesman
07-08-2011, 11:25 AM
BTW, that drawing is somewhat like how I see things in my head.

Very cool, and good to hear I'm not the only one like that. :)