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Metalworking (rec.crafts.metalworking) Discuss various aspects of working with metal, such as machining, welding, metal joining, screwing, casting, hardening/tempering, blacksmithing/forging, spinning and hammer work, sheet metal work. 
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#1




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 
#2




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 
#3




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" 
#4




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 
#5




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 
#6




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] 
#7




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 
#8




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 
#9




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 
#10




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 indepth explanation with calculus. My hearthy thanks. I enjoyed out ofsquare answers of M/s Doug Goncz, Gunluvver2, Errol Groff, Robin S, .Michael My special thanks for Google. Bye N. Ayyavu ()()()()()()()()()()()()()()()() 
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