why greek "pi" exists in cutting speed calculation?

Dear Sirs:

We have installed a Gear Shaping machine (model: similar to Lorenz LS400). We would like to operate at 20 mpm cutting speed while cutting internal splines. The intruction manual says: cutting speed = pi * stroke length * strokes per minute / (1000)

(note, here stroke length = spline length + approach + over travel)

I do not understand why greek pi (value = 3.1428) presents in this formula when the cutter does not follow a circular motion. Here the cutter follows a reciprocatory movement and shifted for relief by about 0.5mm away from cutting surface. To my understand, I think the formula must have been cutting speed = 2 * stroke length * strokes per minute / (1000)

Can anyone explain why "pi" is considered in the formula.

Awaiting your help

with best regards

N. Ayyavu

Reply to
natarajan ayyavu
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The speed of the stroke varies according to where you are in any given revolution. At the ends of the stroke the speed is zero (it's reversing). Maximum speed occurs in the center of the forward and reverse stroke (at

90 and 270). At those points the speed of the stroke is equal to the rotational speed of a circle who's speed is 22/7 ths (pi) times the length diameter of the stroke times the number of revolutions every minute.

I wish I had one!

edd

natarajan ayyavu wrote:

Reply to
Edd

In article , natarajan ayyavu wrote: : :We have installed a Gear Shaping machine (model: similar to Lorenz :LS400). We would like to operate at 20 mpm cutting speed while cutting :internal splines. The intruction manual says: :cutting speed = pi * stroke length * strokes per minute / (1000) : :(note, here stroke length = spline length + approach + over travel) : :I do not understand why greek pi (value = 3.1428) presents in this :formula :when the cutter does not follow a circular motion. Here the cutter :follows a reciprocatory movement and shifted for relief by about 0.5mm :away from cutting surface. To my understand, I think the formula must :have been :cutting speed = 2 * stroke length * strokes per minute / (1000)

For suitable units (stroke length in mm, cutting speed in meters/min), the formula in the manual gives the _peak_ cutting speed for a cutter whose velocity varies sinusoidally. The formula you suggest would be correct for a cutter whose velocity was constant during the stroke and with an instantaneous reversal at each end.

Reply to
Robert Nichols

Logic tells me that your machine is converting circular motion to linear motion and thus "pi" comes into play. I don't want to devote too much time thinking about this because it is Thanksgiving day and the only PIE I am thinking about right now is that wonderful pumpkin pie that I smell from upstairs.

Happy Thanksgiving all, DL

Reply to
Gunluvver2

Or if you'd prefer calculus: If the cutter moves 's' strokes per minute in a simple sinusoidal motion, then the cutter motion can be described as:

x = x0 + 0.5 * stroke * sin(2 * pi * s * t) where t is in minutes

(sin goes +/-1 so, hence the 0.5 factor)

The speed is: dx/dt = 0.5 * stroke * 2 * pi * s) * cos (2 * pi * 1/2 * t).

(since we know d/dx sin(a*x) = a * cos(ax) )

The maximum speed is when cos(...) = 1, or stroke * pi * s.

I think shapers are made asymmetrical so they move faster on the back stroke.

Best regards, Spehro Pefhany

Reply to
Spehro Pefhany

They are.

Yours,

Doug Goncz (at aol dot com) Replikon Research, Seven Corners, VA

1100 original posts at:
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Reply to
Doug Goncz

The other day my wife asked what kind of pie I would like for TurkeyDay. I replied pumpkin or apple would be fine.

After dinner today the choices were chocolate or pineapple cream. I asked what had happened to apple and pumpkin. There was a reason but it is too complicated to recount here.

Errol Groff

Reply to
Errol Groff

Thanksgiving (and Christmas) aren't complete until the person:pie ration reaches 2:1 (twelve people). An you _gotta_ have pumpkin and apple (don't even need anything else).

Regards,

Robin

Reply to
Robin S.

Bullshit! You need ice cream.

mj

Reply to
michael

Dear Sirs

First of all, I am stunned at the response.

Now I understand the formula well.

I thank Mr. Edd Slater for being an opening bats man. I liked his simplistic explanation. I thank Mr. Robert Nichols for the comments on formula of my understanding. I thank Mr. Spehro Pefhany for a in-depth explanation with calculus. My hearthy thanks. I enjoyed out -of-square answers of M/s Doug Goncz, Gunluvver2, Errol Groff, Robin S, .Michael

My special thanks for Google.

Bye

N. Ayyavu

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Reply to
natarajan ayyavu

On Thu, 27 Nov 2003 20:37:15 GMT, Errol Groff wrote something ......and in reply I say!:

I just watched a show about the brain, that postulated that we actually do not really see and hear things, but that the signals get in there and the brain simply "dreams" the result. The show was being narrated by a woman psych specialist....

**************************************************** sorry remove ns from my header address to reply via email

Imagine a _world_ where Nature's lights are obscured by man's. There would be nowhere to go. Or wait a while. Then you won't have to imagine.

Reply to
Old Nick
Reply to
Barry Jarrett

On Sun, 30 Nov 2003 07:00:16 GMT, snipped-for-privacy@rileys-coffee.com (Barry Jarrett) brought forth from the murky depths:

Surely he was using the metric value of pi, Barry. Any Brits out there care to share the Whitworth value?

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Reply to
Larry Jaques

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