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Old November 27th 03, 09:07 AM
natarajan ayyavu
 
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Default 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

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Old November 27th 03, 12:49 PM
Edd
 
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Default why greek "pi" exists in cutting speed calculation?

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:

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


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Old November 27th 03, 04:05 PM
Robert Nichols
 
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Default why greek "pi" exists in cutting speed calculation?

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.

--
Bob Nichols AT interaccess.com I am "rnichols"
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Old November 27th 03, 04:21 PM
Gunluvver2
 
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Default why greek "pi" exists in cutting speed calculation?

I do not understand why greek pi (value = 3.1428) presents in this
formula
when the cutter does not follow a circular motion.


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
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Old November 27th 03, 04:24 PM
Spehro Pefhany
 
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Default why greek "pi" exists in cutting speed calculation?

On Thu, 27 Nov 2003 16:05:44 GMT, the renowned Robert Nichols
wrote:

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.


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
--
"it's the network..." "The Journey is the reward"
Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog Info for designers: http://www.speff.com


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Old November 27th 03, 07:01 PM
Doug Goncz
 
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Default why greek "pi" exists in cutting speed calculation?

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


They are.



Yours,

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

1100 original posts at:
http://groups.google.com/[email protected]
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Old November 27th 03, 08:37 PM
Errol Groff
 
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Default why greek "pi" exists in cutting speed calculation?


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




On 27 Nov 2003 16:21:22 GMT, (Gunluvver2) wrote:

I do not understand why greek pi (value = 3.1428) presents in this
formula
when the cutter does not follow a circular motion.


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


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Old November 27th 03, 10:52 PM
Robin S.
 
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Default why greek "pi" exists in cutting speed calculation?


"Errol Groff" wrote in message
...

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.


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

Regards,

Robin


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Old November 28th 03, 02:37 AM
michael
 
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Default why greek "pi" exists in cutting speed calculation?

"Robin S." wrote:

"Errol Groff" wrote in message
...

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.


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

Regards,

Robin


Bull****! You need ice cream.G

mj


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Old November 29th 03, 07:26 AM
natarajan ayyavu
 
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Default why greek "pi" exists in cutting speed calculation?

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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