Making tapered flutes with a ball mill

[mklotz]

Roy (Shred) asked me about the mathematics of making a tapered flute with a ball mill by tilting the workpiece along the path of the ball mill. For an example of what we're talking about, look at this old thread

http://www.homemodelenginemachinist.com/index.php?topic=612.msg4066#msg4066

where Bogs used the technique to flute the tapered connecting rod of an engine.

I've derived a mathematical relation for the required tilt of the workpiece as a function of:

the radii at the two ends of the flute
the length of the flute
the diameter of the ball mill

The derivation is very straightforward and the calculation can be done easily on any scientific calculator (the quintessential shop tool) but, if enough people are stupefied by the math, I'll consider putting it together as a program and put it on my page.

 

[shred]

Thanks Marv. :bow: The approach of defining the required end point depths and then determining what angle is needed to connect them somehow escaped me until now. So much easier to see once you see somebody else do it :big:

Thinking about it a little more (and I could be wrong here.. I've not even sketched it out), it seems that if you shimmed directly under the 'deep end' to create the angle, you'd make the shim the same thickness as the depth difference. That has interesting possibilities for the cut-and-try types as well-- you might be able to cut both end points ad-hoc and use the difference in Z to set the tilt for the flute.

 

[mklotz]

A shim of the depth difference would work if the overall length of the part were 'L', but that's not going to be true for most parts because the flute will stop short of the ends of the workpiece.

As you might have guessed, I don't care much for cut-and-try solutions. Math skills aren't developed by avoiding opportunities to practice what you've learned.

 

[shred]

Yeah, you're right.. you'd basically have to make a sine bar out of the part or otherwise hang the small end off something and by that point you might as well get a real sine bar out.

I do need to practice my trig more these days.. I used to be good at that kind of thing, now I'm doing well to just remember old Chief SohCahToa.

Cut-and-try often ends up with my last cut being just a little too mch...

 

[ozzie46]

Marv
I'm sorry, but I am one of those math-a-phobs. I have always struggled with it for over 55 years. Hate math. That post might just as well have been in Russian for all I know.


I'm not knocking you or math, its just frustrating when you see these formulas and can't do anything with them. Not you fault but mine. I have a sister who is a whiz at math.

Ron

 

[tel]

if enough people are stupefied by the math, I'll consider putting it together as a program and put it on my page.

You been peeking through my window again.

 

[kvom]

I'm not stupified by the math, but I have trouble reading the paper. ???

 

[mklotz]

Kvom,

I generally do math with a pencil so mistakes can be corrected as the work is done - it's almost impossible to keep things straight if the page is messy with cross-outs, etc.. Pencil doesn't scan well. I went back and traced over everything with a pen so it should be easier to read now. Now I have to figure out how to get all that ink off my CRT screen.

Ron and Tel,

Many of my mathematical friends have asked me why my page contains some programs that do little more than plug numbers into simple formulae. I tell them my original intent was to simply put the formulae on my page, assuming the user would simply use it with his calculator to get the answer he needed.

It quickly became apparent, however, that a large segment of the ME community can't read or use a formula. Much shop work can be vastly simplified by the application of simple mathematics and I didn't want these folks cut off from such tools by their lack of math skills so I started coding the formulae so that all they had to do was answer a few questions in simple English to get the answer they needed.

From your comments, I guess such a program is needed for the flute computations. I'll get to work on it as time allows. I'll post again in this thread when it's available.

 

[deere_x475guy]

I have to raise my hand at being on the math challenged side of things. I have a dedicated folder to many or your programs already Marv and this would be a great one to add.

TY in advance.

 

[Foozer]

Kvom,


It quickly became apparent, however, that a large segment of the ME community can't read or use a formula. Much shop work can be vastly simplified by the application of simple mathematics and I didn't want these folks cut off from such tools by their lack of math skills so I started coding the formulae so that all they had to do was answer a few questions in simple English to get the answer they needed.

From your comments, I guess such a program is needed for the flute computations. I'll get to work on it as time allows. I'll post again in this thread when it's available.

Still remember some math class, slope intercept stuff, after a month or so of that numbers and angles started to manifest themselves from the objects within my field of vision. Sure fire way to be fitted with a white coat thats got those funny long arms. Never so glad to of been done with that course.

Much rather, for sanity sake, give thanks to those like you, who simplify the math for the rest of us who prefer to remain within the group of knuckle drag'ers

 

[shred]

The cool thing with the programs is it's very easy to play 'what-if' with them. Otherwise plugging into a formula isn't too bad.

A no-math method can be done, but it's sort of a special case do-it-yourself sine bar and how you workhold it may be a challenge.

-- Set your part on two identical rollers positioned exactly underneath the center endpoints of your flute (where the deepest part of the ball stops, not the end of the flute), like a little sine bar.
-- On the 'shallow' end, plunge in Z until you get the flute diameter you want (or use math and work it out since it's otherwise going to be some tricky cut-and-try that's easy to get wrong). Zero Z
-- Drive over to the 'deep' end and plunge until you get the diameter you want there. Record Z.
-- Find / make a roller that's the Z-value larger than the original and replace the original with it, or stick a shim of height 'Z' under the roller
-- Go back to Z zero and cut the flute.

 

[mklotz]

Ok, guys, the program is written and up on my page. The archive name is FLUTE.ZIP.

I haven't validated it in the shop with real metal. Perhaps one of you could do that some time. It's better if someone other than I does the validation anyway. I know what's "supposed" to happen so that makes me a biased validator. Plus we'll be able to see if people understand how to use the program.

 

[ozzie46]

I have to raise my hand at being on the math challenged side of things. I have a dedicated folder to many or your programs already Marv and this would be a great one to add.

TY in advance.

I have a folder for Marv also.

Thanks Marv. Man that was quick!

Ron

 

[tel]

It quickly became apparent, however, that a large segment of the ME community can't read or use a formula. Much shop work can be vastly simplified by the application of simple mathematics and I didn't want these folks cut off from such tools by their lack of math skills so I started coding the formulae so that all they had to do was answer a few questions in simple English to get the answer they needed.

From your comments, I guess such a program is needed for the flute computations. I'll get to work on it as time allows. I'll post again in this thread when it's available.

And for that, many of us are eternally grateful. Quick work on the flute prog - thanks!

 

[kvom]

I tried the program, but something seems odd. By specifying the same start/end radii I expected that the angle would be 0. However, I got this:

Ball mill diameter [0.5 in] ? 1
Flute radius at small end [0.1 in] ? .25
Flute radius at large end [0.2 in] ? .25
Length of flute [3 in] ?

Depth of cut at small end of flute = 0.0670 in
Depth of cut at large end of flute = 0.4330 in
Required workpiece inclination angle = 6.9562 deg = 6 deg, 57 min, 22 sec

 

[mklotz]

Kvom,

Good catch. I can't read my own derivation. I left an "r" out of one of the cut depth calculations.

It's fixed now. Download the new version and try it again. When I tried your input here I got zero for the required inclination.

 

[John S]

I'm not too bad at maths but algebraic formulae gives me a blank mind.

Some while ago I needed to work out the pulleys needed to run a poly vee belt between a set centre distance, so get the poly vee design book out and this are formula's for belt length, centre distance, ratio etc etc but no formulae for the second pulley given belt length and centre distance.

Think 3 step pulley, fixed centre, fixed belt length but you need the same tension on each ratio so the last pulley has to be made to fit.

All it takes is the transposition of the formula in the book.

ZAP --- total blank.

Ring the Poly Vee people up but can't get across what is needed, they keep telling me to alter centre distance, can't it's cast in iron- literally.

Ring friendly professor up but he's at some start wars conference on Jupiter so stumped because I was useless at this when I was at school........school ????

So I sent the following fax to my old school.

Dear ex teachers,
I was a pupil here from 1959 until 1964 and during this time I had problems understanding algebra, problems I still have.
However I can remember my history and in 1948 the year I was born one of our politicians, Aneurin Bevin made a speech announcing the National Health Service in that we would be looked after from the cradle to the grave.

So could you please transpose the following formulae to give me the values of D and d

John Stevenson Ex Form 5B

The following day I received a fax back with the two formula on it.

JS.

 

[mklotz]

"I'm not too bad at maths but algebraic formulae gives me a blank mind."

Curious comment. To me "math" *is*, to a large degree, the manipulation of various algebraic expressions. Math includes arithmetic, algebra, trig, calculus, number theory and a bunch of other esoteric stuff, all of which are expressed and manipulated algebraically.

So what do you mean when you say "maths"? Is that British English for arithmetic?

 

[John S]

Maths is anything with numbers like 3.1416 x 5

x=[a+b] is letters, that English literature

 

[steamer]

Marv,

A fine derivation. I was wondering how Bogs did that. Thanks for that and for writing and posting the program...saves on calculator strokes for sure! :bow: The "Seadog" will be getting that profile!

All
Don't let a few equations bother you....They are your friend in the shop and even the "mean" ones, Like a " bully at the playground" , when push comes to shove, usually fall to pieces pretty easily! .....

Dave