# How do concave disk--e.g. very shallow spherical bowl?



## Bill Kahn (Nov 21, 2018)

I have a commercial Euler's Disk.  



 is one of a zillion youtube videos if you have not seen it.  Yes, have made alternative disks to the 3"X.5" steel one it comes with. (Same general effect, but slightly different sounds, timing, visuals, and ending accelerations) But now I want to make my own base--the one it comes with is not as strong/stable as I'd like to try (it is not rigid steel).

(If you spin a disk on a flat metal plate the disk tends to wander a-ways, and as these are pretty heavy and energized pieces of spinning metal when they come off the steel plate they knock stuff around and dent normal household items (don't ask))

So, I want to put a gentle concave curve (think a telescope mirror shape, but I don't need anything near that sort of precision, a section of a sphere, a very shallow bowl) into an 8" diameter (by .5") steel base disk.  I can make the disk (I use a 2" diameter by 1" long stub screwed in from the back to grab with the three-jaw.) This concave bowl shape keeps the heavy spinning Euler's disk safely spinning freely in a constrained space.

I have measured the sagitta from a 6" ruler, and it being .082" indicates I need a radius of like 55".  I have a PM1040V lathe (and PM25MV mill).

My question--any ideas how I make a steel part like this? Geometrically I do want the shape to be a section of a sphere.

Thanks for any pointers as to where this may have been discussed before too.

-Bill


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## RJSakowski (Nov 22, 2018)

I have made concave spherical mirrors in a past life by mounting a long boring bar on the the compound rest and loosening the set screws on the compound pivot. However, my mirrors had a radius of curvature of 7.5" which is a long way from 55".  

Perhaps you could make a special extension for your lathe bed with a pivot point at the required distance.  A stout bar with appropriate cutting bit would do the actual cutting.  The cross feed/compound could be set up to provide support for the bar and to control the feed rate.  Your pivot point axis and cutting plane will have to be set up to intersect the spindle axis in order to cut a spherical profile.

It would be an interesting and challenging project but I think it is doable.


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## mmcmdl (Nov 22, 2018)

Any way of rigging up some sort of tracing unit on your carriage ? I would think you could lay out a template close enough to what you're looking for and maybe rig an air cylinder and stylus up to your carriage somehow . You may have to do some polishing as that surface speed is really going to change over that distance . Seems like a cool little project to experiment around with . I'm interested to hear some other ideas other than a buying a cnc .


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## mmcmdl (Nov 22, 2018)

Another way to rough that puppy out would be to trig out that radius and full depth with a ball mill , then bore in your z axis slightly shallower as you move your x axis out . Think of a G71 roughing cycle on a cnc . Still gonna need polishing and I'll bet that thing will be ringing !!  

Just did a quick calc in my head , difference in the z axis would only be .146 , definitely do-able . But time consuming also .


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## P. Waller (Nov 22, 2018)

Easy to program but difficult to do manually.

Think about how a taper attachment works, the Z axis moves along the ways and the taper attachment slide forces the X axis to generate the taper.
A large radius attachment would work similarly, a rod the length of the radius is attached to the carriage and terminated in a position often beyond the length of the machine, when the X axis is moved toward center this forces the Z axis to generate a radius.

This may be more work then you want to do unless you are making many parts.


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## Mitch Alsup (Nov 22, 2018)

I think the easiest way to do this kind of stuff is to grind the blank like an optician grinding a mirror blank.


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## whitmore (Nov 22, 2018)

Bill Kahn said:


> I have a commercial Euler's Disk...
> 
> I want to put a gentle concave curve (think a telescope mirror shape, but I don't need anything near that sort of precision, a section of a sphere, a very shallow bowl) into an 8" diameter (by .5") steel base disk.
> 
> ...



One way is to get two quarter-inch plates, cut 'em circular, and weld the edges.  Anneal.   Hydraulic oil hand pumps can get
to about 10kpsi, if you can weld a suitable boss onto the assembly.   Pump oil into the interior, until the center bulges appropriately.

Grind off the weld, and stack the bowls, then re-weld at the edge.   Polish the concave surface 'til it looks pretty.


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## P. Waller (Nov 22, 2018)

Mitch Alsup said:


> I think the easiest way to do this kind of stuff is to grind the blank like an optician grinding a mirror blank.



I suspect that this is what the OP is trying to avoid (-:

https://ethw.org/Lenses


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## jwmelvin (Nov 23, 2018)

whitmore said:


> One way is to...



Sweet method. Thanks.


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## BGHansen (Nov 23, 2018)

I recall my dad doing this in a shop class but don't recall or have photos of all of the set up.  I was 10 or 11 at the time.  He was making some shallow saucers for some reason.  He mounted a rod with one end attached at the tail stock and supported the other end on the compound.  The radius cut was the distance between the tail stock and the work.  

I don't recall how he attached the tool in the TS.  Could have been a rod slipped through a nut, hole drilled through both and pinned so the rod could rock back/forth in the nut.  The nut was held in the tail stock chuck.

The other end had a tool bit attached to it somehow.  It would have been HSS hand ground.  He might have used a 1/4" rod for the tool holder, made a bushing with set screws in the sides on either end, one to attach the bushing to the 1/4" rod, other to hold the HSS bit.

The compound had a block of steel with a 1/4" hole drilled through on lathe center line.  He probably did that with a drill mounted in the head stock chuck to make sure the hole was dead on center.  The 1/4" tool rod went through the 1/4" hole in the block on the compound.  He probably left the compound nuts loose so it could rotate freely.  Then moved the carriage close to the work (rod would slip through the hole in the block) and moved the cross slide back/forth to do the cut.  Advanced the cut by advancing the tail stock quill, then repeated the cross slide back/forth.

Hope that makes sense, I'll work on a sketch and post it.  My dad was pretty good at coming up with ways of doing these types of odd jobs.

Bruce


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## NortonDommi (Nov 24, 2018)

Take a piece of rod of the length radius you want and make the ends into points. Make a center punch mark on your headstock and another on your cross-slide.  Place the rod between the two and put some pressure on it.  As you wind the cross-slide while maintaining pressure on the rod the tool will describe an arc the radius of the length of rod.
  Very quick and easy for a concave surface.  If you want a convex surface work off the backside of the cross-slide and a stop like the tailstock.  I'll see if I can dreg up an old article showing this.


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## NortonDommi (Nov 24, 2018)

I think all the photo's I took of doing this are on an old computer that is not hooked up   Anyhoo on page 27 of the attached book,(Pg 36 in the PDF),you will see what I mean.
  Sorry I mixed up concave and convex in the above.  Anyway quick and easy.  I forgot to mention center your tool before placing the radius rod.  I make up rods as needed and keep them in a box. I've spot drilled mounting points on my headstock, both side of my cross-slide and my tailstock so no mucking around.


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## Bill Kahn (Nov 24, 2018)

NortonDommi said:


> I think all the photo's I took of doing this are on an old computer that is not hooked up   Anyhoo on page 27 of the attached book,(Pg 36 in the PDF),you will see what I mean.
> Sorry I mixed up concave and convex in the above.  Anyway quick and easy.  I forgot to mention center your tool before placing the radius rod.  I make up rods as needed and keep them in a box. I've spot drilled mounting points on my headstock, both side of my cross-slide and my tailstock so no mucking around.


Hi, OP here.   Wow.  What an amazing book.  Looks like the advanced Object Oriented Programming book analog of the era--material for the genius experts. Well well beyond anything in my league. It continues to fascinate me that things that I have on my mind to make can at times be so very hard to do. (And other times, with a lucky piece of ingenuity, become doabale (well, on the 3rd or try at least)).  -Bill


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## Reddinr (Nov 24, 2018)

This doesn't answer your original question but how about looking online at one of the 7 or 8" magnifying make-up mirrors, take it apart, make a nice wood or metal base and glue it in?  Not sure what concave radius those things have but it might do the trick.   BTW, thanks for the Christmas gift idea!  I just bought one of the Euler's disks for a relative.


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## RJSakowski (Nov 24, 2018)

Bill Kahn said:


> I have a commercial Euler's Disk.
> 
> 
> 
> ...



It is well known that when the head of vertical mill is out of tram, the path cut will be concave rather than flat.  The radius of the concavity depends on the deviation from vertical of the head and approaches infinite as the head approaches vertical.

To cut a spherical concave surface, the work would be mounted on a rotary table with the lowest point of the cutter arc intersecting the RT spindle axis. A fly cutter set for a diameter bigger than the disk diameter would be needed.  Because the path of the cutter, the cut path will deviate from the spherical at the outside of the disk but will be a good approximation at the center of the disk.

For a 6" disk, it would take a fairly substantial  fly cutter and I would suggest making a custom cutter  using a disk as the basis rather than a typical fly cutter.  This will provide for better balance of the tool.  If you envision increasing the diameter of the typical fly cutter, you are fairly well there.

Here is an article on the process. https://authors.library.caltech.edu/46457/1/1.1752357.pdf


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## Bill Kahn (Nov 24, 2018)

RJSakowski said:


> It is well known that when the head of vertical mill is out of tram, the path cut will be concave rather than flat.  The radius of the concavity depends on the deviation from vertical of the head and approaches infinite as the head approaches vertical.
> 
> To cut a spherical concave surface, the work would be mounted on a rotary table with the lowest point of the cutter arc intersecting the RT spindle axis. A fly cutter set for a diameter bigger than the disk diameter would be needed.  Because the path of the cutter, the cut path will deviate from the spherical at the outside of the disk but will be a good approximation at the center of the disk.
> 
> ...


I may give this a try--make up a 10" steel disk on the mill with the rotary table (maybe could fit on my 1040 lathe?).  Bolt in (need to puzzle just how) a carbide insert, tilt the milling head (a pain to retram) or the rotary table a bit (doing the math provided, which sounds like fun). Mount (well) the 8" steel blank disk.  Find some RPM that doesn't scare the bejeezus out of me. How hard could this be? I can just imagine that 10" disk spinning around right at sternum height. (I can generally stay out of the lathe work piece plane of rotation for stuff like this). Does sound like fun.  Ahh, so many projects.


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## P. Waller (Nov 24, 2018)

RJSakowski said:


> It is well known that when the head of vertical mill is out of tram, the path cut will be concave rather than flat.  The radius of the concavity depends on the deviation from vertical of the head and approaches infinite as the head approaches vertical.



This creates a radius in one axis only, it will not produce a concave spherical shape.
This work may be done in a mill but will require either a tracer or 3 Axis control. It is far more easily accomplished on a lathe since it is a round part to begin with.

A lathe would require a simple attachment as noted above. This is a quick and dirty sketch to show the idea.

If your machine is not long enough this will require building an attachment point beyond the end of the bed which is easily done, this will allow turning any size radius within its range by changing the linkage length.
Short of CNC control the other alternative is to gear the X and Z axes together much like the set up used for the helical milling of gear teeth.


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## RJSakowski (Nov 24, 2018)

P. Waller said:


> This creates a radius in one axis only, it will not produce a concave spherical shape.
> This work may be done in a mill but will require either a tracer or 3 Axis control. It is far more easily accomplished on a lathe since it is a round part to begin with.
> 
> A lathe would require a simple attachment as noted above. This is a quick and dirty sketch to show the idea.
> ...


That is why you would use the rotary table to rotate the part.  The result will deviate from the desired spherical profile at the edges but the the center section would be fairly true to the spherical profile and that is where all of the disk spinning takes place. 

As to using the lathe, you will see in post #2 above, what you are suggesting is what I had proposed.  The big problem, here is that the desired radius is 55" which extends well past the OP's lathe bed.  It makes for a very long cutting arm and will require additional support near the cutting bit.  It isn't impossible; I have done similar things.

edit: looking closer at your drawing, I see that you are attaching the near pivot point to the compound.  This would provide a more stable cutter presentation.  The one comment that I would add is that the far side pivot would need to be offset from the spindle axis  by the same amount that the near side pivot was offset from the cutter in the x direction.

Taking your concept one step further, it would be relatively easy to make a tool which would accomplish this task.  A threaded hole for a shoulder bolt for the near side pivot, some means of feeding into the work in the z direction, adjustability in the x direction for the far side pivot come to mind.


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## P. Waller (Nov 24, 2018)

RJSakowski said:


> The result will deviate from the  It makes for a very long cutting arm and will require additional support near the cutting bit.  It isn't impossible; I have done similar things.



It moves the carriage just as a taper attachment moves the cross slide so there is no need for any additional tool support.
This may also be done with a template that forces the carriage to move in relation to the cross slide, this is far easier assuming that you have a way to generate a 55" radius template of the desired accuracy.


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## RJSakowski (Nov 24, 2018)

P. Waller said:


> It moves the carriage just as a taper attachment moves the cross slide so there is no need for any additional tool support.


I got that and it is an obvious improvement over what I had originally suggested.


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## P. Waller (Nov 24, 2018)

RJSakowski said:


> I got that and it is an obvious improvement over what I had originally suggested.


We are on the same page then.
With the template method the difficulty lies with the method of producing accurate partial radius templates that will be within the range of hobby accuracy which often appears to be in the .0001" range here.

Spending a good deal of time making a part to tolerances that you can not measure is pointless. (How would you measure such a part)


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## RJSakowski (Nov 24, 2018)

P. Waller said:


> Spending a good deal of time making a part to tolerances that you can not measure is pointless. (How would you measure such a part)


A spherometer is used to accurately measure the curvature of lenses and mirrors.  A fairly simple one is made with two points a distance apart and an indicator at the midpoint.  The distance above or below the line connecting the midpoints is measured and the radius of curvature can be calculated.  The OP did just that in calculating the radius of curvature needed at 55".  The more sophisticated spherometers use three points in an equilateral triangle with a micrometer at the center of the triangle to measure the distance above or below the plane through the three contact points.

For the OP's purpose though, I would think that the actual radius of curvature isn't that critical.  He got his specification by reverse engineering a commercially available product.


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## rwm (Nov 25, 2018)

Nice diagram Mr Waller. I may try something like this also. I want to make a concave bowl for hammering copper discs.
Question: If the tailstock pivot was offset on the cross slide axis (is that X or Y) what would be the resulting shape? 
Robert


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## Cooter Brown (Nov 25, 2018)

You need a Bridgeport with a Cherrying attachment and a rotary table.....

https://www.ebay.com/itm/Bridgeport...d:g:3eQAAOSwsuNbzvhs:rk:1:pf:1&frcectupt=true


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## P. Waller (Nov 25, 2018)

rwm said:


> Nice diagram Mr Waller. I may try something like this also. I want to make a concave bowl for hammering copper discs.
> Question: If the tailstock pivot was offset on the cross slide axis (is that X or Y) what would be the resulting shape?
> Robert


If the pivot point is off center the tool will reach full depth before or after the center resulting in a radiused groove on the face.


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## homebrewed (Nov 26, 2018)

If you look at the intended purpose of Euler's disk, a conical profile should work just fine to confine the spinner.  There is no particular magic in a spherical surface -- the main thing is to create a radially symmetric inward-pointing bias to the spinner.  If you don't have a mill and RT to create the conical profile, you may be able to set your  lathe compound over far enough to do the job -- or use the taper-attachment idea mentioned earlier in this thread.

Another idea:  go to thinner stock for the disk.  Evenly support it at its perimeter, then apply a pull force to the center (from the back).  It will deform into a curve, the depth of which depends on the thickness  and diameter of the stock, and the magnitude of force applied.  The details on how to apply the force are left up to you .

I personally like the simplicity of a piece that's just turned to produce the desired profile.


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