Making tapered flutes with a ball mill

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I believe you could also use this to compute flutes for a tapered column as well. Solve for the angle as if parallel and add the taper angle.
 
John Stevenson said:
Maths is anything with numbers like 3.1416 x 5

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

John i am with you on that, how can you add or subtract or multiply etc letters of the alphabet ????

???

Kind reagards

Malcolm
 
As I expected, "maths" is a codeword for arithmetic. Very confusing and misleading to those of us who weren't raised in the English milieu.

So, you can understand 3.1416 * 5 but you can't grasp the concept of:

c = pi*d

where:

c = circumference
pi = 3.1416
d = diameter

I think you guys are putting me on.

What word do the English use then when they want to refer to the collection of disciplines,

arithmetic
algebra
geometry
trigonometry
calculus
number theory
etc.

that Americans term "mathematics"?
 

What word do the English use then when they want to refer to the collection of disciplines,

COMPLIMICATED..........DOH !

:big: :big: :big: :big: :big: :big: :big:

Kind regards

Malcolm
 
kvom said:
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
Those values give me the correct 0 deg answer. Thanks Marv!

Here's a few thoughts I had.. Others are free to disagree ;)

Poking through the source code, the subtraction for the ATAN is in a different order than the derivation image. ZF-ZS on one, ZS-ZF on the other. I haven't worked out if that really matters or not, but it only changes the sign of the result in most cases.

I would also rather use diameter (or choose which to use) throughout the program for consistency, though I can see some advantages to radius as well (not that it's hard to convert between...). Another personal preference would be to have the defaults be zero. Easier to spot a skipped entry that way.

A zero length flute causes a divide by zero error. Not a big deal, though some might want to (ab)use the program to determine how deep to cut round spots of a desired diameter and not realize that the flute length doesn't matter for that and/or won't believe the previously displayed values are correct if it says 'error'

Likewise various goofy data values also cause incorrect results (-.1 small end .1 big end gives a zero angle..) I can't think of a legitimate reason to have negative values for any of the inputs but am trying to think like somebody that wants a flute to say go to zero halfway along maybe a tapered rod or something and thinks a negative diameter is the way to get there. You can go nuts with input validation, so I'd say it's probably safe to note that silly values will give silly results and drive on.

One more thought-- it appears that the math is unitless so it shouldn't much matter if you use inches, feet or millimeters, as long as you use the same for each, so Our Bretheren of the Meter can play along too.
 
The equation for 'h' is h = zf - zs in both the derivation and in the program. I guess I don't understand your comment.

The only input checking the program does is to verify that the two radii are less than or equal to the radius of the ball mill. I'm not going to waste my time trying to idiot-proof programs. If users are that dumb, they really shouldn't be using a computer, much less a technical program. Sorry, but I've never suffered fools gladly. These programs are meant as an aid to, not substitute for, thought.

If I were specifying a tapered slot on a drawing, I would show the radii, not the diameters of the partial circles. Given this, I had the program ask for the radii. (Hopefully, the user can calculate the radius from the diameter (but don't bet on it).

My thinking on defaults is that, if the user runs the program using only the defaults, he should get an example answer to give him an idea of what the program does. Zero defaults would produce a run-time error here (and in many other of my programs). That would only further confuse him. All this is explained in the downloadable NOTES file on the page. (However, since most people never read the INTRODUCTION, they're not likely to know about, much less read, said file.)

You're right about the units. They don't matter so the user can use any consistent set of units. However, you have to have my appreciation for just how dense some of my 'clients' are.
If I don't indicate units, I get a lot of emails asking what units they should use. If I tell them that units don't matter, they'll mix inches and feet or millimeters and centimeters in the input and expect to get meaningful answers. In programs where it really matters (e.g., DRILL), the program asks for their choice. It's another case of idiot-proofing being a waste of time.

I'm not responsible for the fact that most people slept through every math class they attended. I've made my contribution by doing the derivations and writing the programs. I expect them to contribute a bit of mental effort when they use a tool that's been provided to them at no cost. If that makes me an unsympathetic hard ass, so be it.
 
mklotz said:
The equation for 'h' is h = zf - zs in both the derivation and in the program. I guess I don't understand your comment.
In the initial derivation, H = Zf-Zs but expanded to = Zs-Zf. I highlighted Zf in the attached image for lack of better tools here. I think all that would do is change the direction of the slope, so it's then only a pedantic issue.
You're right about the units. They don't matter so the user can use any consistent set of units. However, you have to have my appreciation for just how dense some of my 'clients' are. .... If that makes me an unsympathetic hard ass, so be it.
Actually I do... ;) I wrote end-user-software for a major computer company for several years... 99% of the work is stupid-user input validation which I wish on nobody.

I've got no problem (and plenty of thanks) if you leave the program as-is-- my comments aren't intended to be change requests, only user observations.

With any luck I will be able to try the program on real metal this weekend..

Capture2.jpg
 
I'd agree that most of these "alternatives" fall into the "doesn't matter" category. I would probably have used diameters rather than radii myself since:

1) The ball mill is specified as a diameter, so consistent

2) When you are computing the width of the flutes and the spaces between, you would compare them to the circumference of the workpiece, and would be less likely to mess up having the diameters to compare with.

Of course there's the old saying, "if you idiot-proof something they'll just invent a better idiot." ;D
 
Shred,

Go back and look at the definitions of zs and zf...

zs = r - sqrt(r^2 - rs^2)
zf = r - sqrt(r^2 - rf^2)

Thus:

zf - zs = r - sqrt(r^2 - rf^2) - r + sqrt(r^2 - rs^2)

zf - zs = sqrt(r^2 - rs^2) - sqrt(r^2 - rf^2)
 
Duh, right. I've forgotten a lot. Sorry.
 
Marv just wanted to say thank you. I finally got back to this thread and noticed you had the program ready to go.:)))

Headed to Toledo for Saturday....have fun all
 
You're welcome. I haven't added anything to my page in a while and it's always fun to concoct something for the ME community.

The program presupposes the use of a ball mill but this technique could be employed with other profile mills, such as:

http://www.use-enco.com/CGI/INSRIT?PMAKA=320-1430&PMPXNO=947390&PARTPG=INLMK32

to produce some unusual bling effects.

Other profiles would, of course, require re-working the math (American usage, Brits!) but that would be very straightforward. In the case of the 90 deg mill above, it would be dead simple...

zs = rs
zf = rf

tan(theta) = (rf-rs)/L
 
zs = rs
zf = rf

tan(theta) = (rf-rs)/L

Oh wow! You speak Klingon as well! A man of many talents.
 

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