Putting a big radius on a small part

How is this typically done without CNC equipment?

For example, I think some bucket tappets, while nominally flat, actually have a very large radius on the rubbing surface (40-70" is one set of numbers I've seen mentioned). I can see a small radius being machined/ground with a Holdridge ball turner kind of arrangement, where the machined surface or the tool tip is 2-4" away from the center of arc. I suppose this is how a finger follower with a 2-3" radius is done -- the follower surface is set at the radius on a rotary table and is then swung past the tool, or vice versa.

But that kind of operation seems unlikely if you have a 40,100 or 150" radius. Soon you start needing lever arms that pivot in the next building or a rotary table that can pass as a flying saucer.

Is there some kind of marvelous compound lever mechanism that is used to generate a large radius without needing to actually swing something at that radius?

cheers,
Michael

draw it up in MasterCAM, cut to points and grind, sand, file or polish it down? that's what I do/have done on radii up to like 30" or so but that's on big parts too

Sure, I've done that, but it is not a production/high accuracy procedure.

Perhaps some sort of pantograph linkage is used that would let you turn an accurate small-radius arc into an accurate (but short) big-radius arc? Or maybe running two cams against each other?

Maybe it isn't a common machine, but if someone walks into a grinding shop and says they want a 100" radius put on the part in their hand and they want it ground to a very smooth finish and the radius accurate to a couple ten-thousandths does everyone in the country just say "nope, can't be done"?

cheers,
Michael

Unclear if you are referring to spherical radii, but big SRs are easily executed in lathe on relatively small items with a rod pointed on both ends (the correct length of course) and sitting in center punch marks on bridge of carriage saddle and base of tailstock. You use the carriage hand wheel to hold the carriage against the rod while you crank (or feed) the cross slide across. The tool path is some large radius.

(see post #6 for correction)

johnoder said:

Unclear if you are referring to spherical radii, but big SRs are easily executed in lathe on relatively small items with a rod pointed on both ends (the correct length of course) and sitting in center punch marks on bridge of carriage saddle and base of tailstock. You use the carriage hand wheel to hold the carriage against the rod while you crank (or feed) the cross slide across. The tool path is some large radius.

Click to expand...

OK that's pretty cool. Haven't heard that idea before. Seems like it only works for concave surfaces though, what about convex? I guess we'd have to put the rod against the headstock but typically no room there.

When you run out of room, rig a solid extension for cross slide and put a long rod against something behind headstock.

The above statement (post #4) is incorrect in stating against carriage bridge - it has to go against cross slide - sorry about that.

John, I think I see what you are saying (and will try to remember that if I need it in the future) and I've seen someone who basically made a Holdridge tool (for a lathe) that had about a 3 or 4 foot swing, but what if you need a radius that is much longer than your lathe bed (or your shop building), say by 4-5X?

Let's go back to the bucket tappet in my OP. I bring in a 30mm diameter tappet with the top unfinished, and I tell the shop owner that I want someone to grind or turn a 120" radius (either 2D or 3D) on the end of it. Would I look around to see if they had a lathe with a 12'+ long bed, and if not presume it can't be done there?

I've got a hazy vision of some machine accessory, maybe a couple feet in diameter, that has innards that look like they were pulled out of Baron von Frankenstein's Spirograph (TM)


http://www.iw.net/~nnburk/Presentation1.pdf a discussion of "spirograph math"

where different sets of gears/cams/funny shaped bits are mixed and matched to give whatever radius is needed on some part-holding slide on the top of the machine. If you look in that link some of the arcs that are drawn are much flatter than the radius on the gears being used to generate them.

Don't old-fashioned screw machines use cams to generate different radii? If so, then maybe there is some similar cam mechanism that is used to generate really large radii, (but hopefully without needing the machine to already exist in order to grind that cam).

cheers,
Michael

Some version of this process, using a jig type grinding head?

http://www.practicalmachinist.com/vb/general/video-russian-method-sphere-cutting-248067/

It's too late/I'm too sleepy to work out what the limits might be or whether practical for radii you mention.

If the above won't work & I had to do it for myself, I'd use either a tool & cutter grinder or a surface grinder, and John Oder's method. Bolt a hardpoint/column to the conrete floor, and use a rod between that and the table X, Using Z to traverse. Part in spindex, preferably motorized.

smt

There is a neat bit of geometery known as "euler's line", that can be leveraged to generate big circular arcs from simple linkages.

Euler line - Math Open Reference
and
Euler line - Wikipedia, the free encyclopedia

Stephen, I was reading some race engine design articles on camshafts and related components, especially the barely-crowned tappets and got to wondering "hmmm, how did they do this kind of accurate work before CNC?" It isn't something I need for a project.

That Russian hemisphere lathe is basically the same concept as the Holdridge or other ball turner attachments but it doesn't look like it is going to be able to do an arc with a ten foot radius. And that style of lathe seems like overkill if your job is to put a ten foot radius surface on the end of 20-30,000 of a 1 or 2 inch diameter parts.

For many projects John's procedure would be plenty good enough, just as a Holdridge ball turner attachment is plenty good enough for a lot of small radii.

But would someone doing that kind of work on a daily or production basis use it? And if they needed to be able to change to a different radius are they going to rummage through 50-100 or more different precise-length rods (that might be 12' long) and then have some sort of moveable fulcrum point that is adjusted to match the new rod being used? I can see it being possible to use different length links to set an arc for small radii, somewhat like the bull gear on a shaper can be adjusted for stroke. I see that being a cumbersome method for a very large radius, and if something is cumbersome enough some bright person often comes up with something to make it much less cumbersome.

It seems unlikely to me, but maybe that's been the standard way of doing highly accurate and very large radii for most of the last century. I don't know, that's why I'm asking. I'll admit that when I started this thread I was expecting Forrest, or someone who worked at Pratt and Whitney or GM in the 1950s would have posted "oh, you're talking about a radiuscombobulator, I haven't seen one in years but we used to have a factory full of them turning out parts with near-flat radii like that. They were the size of a refrigerator and they had interchangeable dohickeys that let them form a radius from .005" to 50 feet."

<jbc>, do you know if that Euler's line has been incorporated into a radiuscombobulator machine? I figured there must be some sort of linkage/cam way to do it, but I don't know of any machine tools that were built to do the job (though it seems like they must exist).

ETA, is he Euler concept what is used in the Watts drills to drill triangular and other non-circular holes?

cheers,
Michael

something wrong with a form cutter?

Cam followers or flat face tappets usually have around a 90-100" radius. AFAIK the radius is somewhat dependent on the face width of the cam. These are usually ground on a tappet grinder that has the large radius dressed into the flat face of about a 6" diameter plate mounted grinding wheel- the wheel dresser is pretty simple and has the dressing diamond mounted at about a 1" radius on a disc that mounts on the work spindle. By tipping the work spindle, the rotating diamond will generate the large radius on the face of the grinding wheel. Remove the dressing diamond, pop in the tappet and grind the face.

Tobin Arp, Storm Vulcan and Sunnen have all made these grinders and they all work on the same principle. Sunnen purchased all the Tobin Arp designs, so the Sunnen machine is an improved TA. Several years ago, I modeled the dressing of the wheel face in Solidworks and sure enough it works!

Michael- if you need to get some folowers reground, PM me and I'll give you a contact that is pretty local to you.

Dan

How are you going to generate the mythical 10 foot radius on the form cutter? I'm trying to learn how the radius is done, and I don't really care whether it would then be turned with a cutter or ground with a stone, as they both need to get the tool to move on the correct arc.

A radiuscombobulator could be used to generate an arcuate slot that the tool head moves in for a production machine doing one particular radius over and over. I want to learn about the tool that generates the first radius.

cheers,
Michael

Here is a link to an old PM post by Stephen Thomas regarding generating spherical surfaces by the use of a fly cutter.

http://www.practicalmachinist.com/vb/general/generating-spherical-surfaces-139400/

The theory is the same for this application except the flycutter is repalced by the dressing diamond and generates the radius in the face of the grinding wheel.

Dan

I have generated big radia on sheetmetal with a diskgrinder and a long (Say 3mtr )pole with a swiveling point several times
That way you can get a accurate cam you can mount on your lathe to follow
Mount the (hardened) cam between the carriage and the headstock
Have a camfollower mounted on the carriage
Engage the crossfeed and follow the cam manualy with your longfeed (or whatever it is called in Englisch)

Peter from holland

large radius on a lathe sometimes done with a modified taper cutting attachment.
.
instead of a straight bar set at a angle to cut tapers it is a curved bar.
.
i have heard of setups where the bar is curved by pushing in center and retrained by dowel pins on the end. basically if outer pins are 10" apart you could push on the center 0.250" to put a curve in it. depending on the curved bar and the cam followers design you can smooth the curve out. similar to a wood plane straightens a wood board by cutting the high spots and a longer wood plane will in general make a straighter wood board.
.
crowned flat belt pulley were sometimes done this way.

radiuscombobulator

Click to expand...

Could be levers with variable pivot points and could be compounded - more than one pivoting arm in the train

To wit:

A pivoted arm with a cam follower on the LONG end caused to follow a 5.000" female radius (an easy product of v. mill and rotab) with a 1.000" movement in "Y" and made or adjusted to have a 5:1 ratio will describe
a 24.758" male radius on the short end in that same 1.000" of "Y" movement.

Not precisely 5:1, but fairly close.

An incidental is that a 5:1 mechanical advantage is introduced


If instead of guiding a cutting tool, the short end was made to move a secondary pivoted arm with a 5:1 ratio it can be seen that the radius would be in the 120" range and the gender would be reversed - and an over all mechanical
advantage of 25:1 (less frictional losses) would be enjoyed.


Above is merely descriptive - to nail down a radii one would need to fine tune tool path math.

Harry A. Miiler's employee Leo Goosen used much smaller radii on his inverted cam follower buckets on such as the DOHC Miller 91 and apparently these functioned fairly well with the mating rather "pointy" cam lobe profiles they used.
These were not spherical radii.

Radii generators

The machine tool used is a "Generator", a some what contracted term for "radius generator. Often a vertical spindle grinding machine that takes a cup wheel. The wheel spindle can be set at any angle between vertical and nearly horizontal. Horizontal machines are seen from time to time. Refurbished lens generator Coburn 2113

Loh, Strausbaugh, and others are names.

The work is fixed to the motorized (or not) rotary table beneath the spindle. Viola! Small Radii are simple.

These machines are in every optical lens making shop in large numbers. And a bridgeport mill works in a pinch ;-)

Finish surfaces are achieved by lapping with a shaped lap.

Cheers

That Russian hemisphere lathe is basically the same concept as the Holdridge or other ball turner attachments but it doesn't look like it is going to be able to do an arc with a ten foot radius. And that style of lathe seems like overkill if your job is to put a ten foot radius surface on the end of 20-30,000 of a 1 or 2 inch diameter parts.

Click to expand...

Michael, i was referring to the set of options in the post, primarily the boring head set up that Alwyn uses on a mill. (replaced by an offset jig grinding head). It could potentially be arranged on a lathe, too; say jig head in spindex on compound, if lathe is large enough.

The arc generation method is _not at all_ "like a Holdridge...". It depends on the diameter of the tool in the boring head, and the angle of the head to the work.

If r is the radius of he boring head, and R the desired radus of the partial sphere, then the angle between the axes of the work and the rotating cutter = sin^-1 of r/R

My calculator is in the shop, but this looks to make possible very large radii on small parts with small dia swing cutting tools; so long as the section of the large sphere is "quite small" as it would be with your tappets.

Here's another post on the subject. http://www.practicalmachinist.com/vb/general/internal-hemisphere-138401/

smt

Edited: CalG was posting while I was still figuring (smacks self upside head) we've all done some form of this at sometime or another on a grinder with a cup wheel. (usually grinding a faintly hollow non-discriminate "flat" on some tool or surface). It just did not occur to me that if one can dress and measure the diameter of the cup accurately enough for the work, it can apparently be done to relatively high precision on any T & C grinder or even surface grinder with a spindex & sine bar. (rather than using a jig head with adjustable center distance)

This question interests my feeble brain, which came up with this:



The rounds are gears, the horizontals are racks. As the small gears are pulled to the right the tip of the arm will describe an arc, the radius of which is determined by the ratio of the two gears running on the racks. If the necessary slides and pivots were built with enough precision it should do a pretty good job.

I have no idea if this has ever been done, but I doubt that I'm the first to think of it.