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# CSS Formula

#### EmanuelGoldstein

##### Diamond

oookay, let's say the part is 3.25" diameter. If you want to do in your head (22)(3.25) / 7 = 10.2142857142857 or 10.2 in short.

Or if you want to be picky 3.14159 x 3.25 = 10.2101675 also can be rounded off to 10.2 for our purposes.

Let's say 400 ft/min equals (4800 inches/min)(1 revolution/10.2 inches) = inches top and bottom cancel out so you are left with 470.58823594118 rev/min or probably 471 if you want to get really picky.

I'm certainly not a math wizz but that's pretty simple. And oh yeah, css on a real control (I don't know fanuc) runs in sfm not rpm so you'd run up to the part in g97 at s470 (or 471 if you are anal) then kick it to g96 s400 for the 400 ft/min end of things. If you want to be nice you can calcuate the and-of-pass speed and when you drop back to g97, use that speed for an s #.

Is that too difficult ? Even I can do it ... personally, being a NOT g96 fan for roughing passes, I set my rpm at the speed for the cut and leave it there for the pass. Then also leave it until the tool pulls out in x, change speed for the next pass as the slide returns in z, then when you drop down in x to the next pass diameter the spindle is already there, no wackadoodle g96 uppy-downy going on. Makes for a nice program, easier on the lathe. But people can do what they want, eh ?

#### sinha

##### Titanium
The approximate formula for RPM is
N = 4V/D where V is in ft/min and D is in inch.
= 4 x 400 / 3.25 = 492
Is it not simple enough?

The exact formula for RPM is
N = 12V/(pi x D)
=
470
Don't you realize that you are doing exactly the same thing?
And, when the logic behind the formula is explained from the basic principles, you consider it nonsense!

#### EmanuelGoldstein

##### Diamond
The approximate formula for RPM is
N = 4V/D where V is in ft/min and D is in inch.
= 4 x 400 / 3.25 = 492
Is it not simple enough?

The exact formula for RPM is
N = 12V/(pi x D)
=
470
Don't you realize that you are doing exactly the same thing?
And, when the logic behind the formula is explained from the basic principles, you consider it nonsense!

Your method is dumb. You're making a simple multiplication and division problem into a big deal. I know some people like that but it's counterproductive. Take the circumference and divide it into the desired surface footage and logic's your uncle, no silly "formulas" required. "N = 12V/(pi x D)" screw that nonsense.

There's no point to make mountains out of molehills.

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#### angelw

##### Diamond
Take the circumference and divide it into the desired surface footage and logic's your uncle
Well, no, that's not right; unless you're calculating the circumference in feet.

But Sinha did what you're suggesting, only he converted the FPM to IPM (approximately)

In an earlier Post you converted 400FPM into IPM by multiplying by 12, then dividing that answer by the Circumference. That's what Sinha did.

He qualified that his method was approximate. The 4 in his method comes from canceling out Pi by dividing the 12 used to convert FPM to IPM, by Pi. The closer answer is 3.82 and Sinhas has rounded that up to 4. So, by multiplying FPM by 4 and dividing by the part diameter, its the approximation of converting FPM to IPM and dividing by the Circumference.

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#### sinha

##### Titanium
Well, no, that's not right; unless your calculating the circumference in feet.

But Sinha did what you're suggesting, only he converted the FPM to IPM (approximately)

In an earlier Post you converted 400FPM into IPM by multiplying by 12, then dividing that answer by the Circumference. That's what Sinha did.

He qualified that his method was approximate. The 4 in his method comes from canceling out Pi by dividing the 12 used to convert FPM to IPM, by Pi. The closer answer is 3.82 and Sinhas has rounded that up to 4. So, by multiplying FPM by 4 and dividing by the part diameter, its the approximation of converting FPM to IPM and dividing by the Circumference.
He indirectly called me stupid.
I am afraid, your number is the next

#### Ox

##### Diamond
I'm sure that we didn't doo Pi here until at least 4th grade...

-------------------

Think Snow Eh!
Ox

#### goooose

##### Hot Rolled
There is no way there's machinists out there who don't know and use the formula CS*4/D.
Using 22/7 to approximate pi?? He has to be trolling.

#### guythatbrews

##### Hot Rolled
There is no way there's machinists out there who don't know and use the formula CS*4/D.
Using 22/7 to approximate pi?? He has to be trolling.
22/7 is not an uncommon way to approximate pi.

#### EmanuelGoldstein

##### Diamond
22/7 is not an uncommon way to approximate pi.

The nice part is, you can do it in your head for a quick reality check. Kinda sooprised anyone doesn't know that. It's within 1 in the third place, not so bad.

#### CarbideBob

##### Diamond
Did someone say pi?
Would this be apple, cherry or pumpkin.
"in walks her daddy standing 6 foot four saying your not gonna swing with my daughter no more" ... why does this make think of OX?
Bob

Ox

#### goooose

##### Hot Rolled
22/7 is not an uncommon way to approximate pi.
I think most are able to memorize 4 or 5 places quite easily if you need that accuracy. 3.1415 is pretty easy to remember and more accurate then 22/7 if simply using 3 is not accurate enough.Heck, who doesn't have a pi button on their calculator now if that's what you're really after?

Point being, if you want to get into a math debate on formulas and what works vs what doesn't, maybe 22/7 in your formula isn't a good starting point.

#### EmanuelGoldstein

##### Diamond
I think most are able to memorize 4 or 5 places quite easily if you need that accuracy. 3.1415 is pretty easy to remember and more accurate then 22/7 if simply using 3 is not accurate enough.Heck, who doesn't have a pi button on their calculator now if that's what you're really after?

Let me see you multiply by 3.14159 in your head. You can do 22/7 easily and quickly. It's useful for standing at the machine going "wtf ? Is that really correct ?" It's useful for all kinds of quick calculations, in fact. Try (4/3)(3.14159) (r x r) in your head sometime.

Point being, if you want to get into a math debate on formulas and what works vs what doesn't, maybe 22/7 in your formula isn't a good starting point.

Point being, don't be an idiot. 22/7 is accurate to 1 in the third place and simple to do mentally ... if you have a mental. Are you one of those people who can only make change with a point of sale touchscreen and can't count back the remainder properly ? Fractions are good, if you can handle the extreme pressure.

Besides, the debate isn't about what works or not, it's about making a mountain out of a molehill. It's simple to figure the circumference. It's simple to know the surface speed you want. The rest is a trivial and logical division. Why make it into a textbook challenge ?

#### goooose

##### Hot Rolled
Let me see you multiply by 3.14159 in your head. You can do 22/7 easily and quickly. It's useful for standing at the machine going "wtf ? Is that really correct ?" It's useful for all kinds of quick calculations, in fact. Try (4/3)(3.14159) (r x r) in your head sometime.

Point being, don't be an idiot. 22/7 is accurate to 1 in the third place and simple to do mentally ... if you have a mental. Are you one of those people who can only make change with a point of sale touchscreen and can't count back the remainder properly ? Fractions are good, if you can handle the extreme pressure.

Besides, the debate isn't about what works or not, it's about making a mountain out of a molehill. It's simple to figure the circumference. It's simple to know the surface speed you want. The rest is a trivial and logical division. Why make it into a textbook challenge ?
If you want to do mental math that's close enough for SFM, CS*4/D is as basic and easy as it gets. There's no need to do your formula of CS*12*(1/(D*22/7)). Its not 'wrong', its just not easy nor is it necessary.

RPM does not need to be exact in SFM calculations but if you wanted extra accuracy, CS*3.82/D is still easier, quicker, and more accurate than what you are using.

Example, calculate the RPM for a cutting speed of 500 with a diameter or 5", and again for a diameter 0.5".
Use both formulas, CS*4/D and yours. Heck, even try using mental math on both, let me know which formula you can actually do in your head.

#### EmanuelGoldstein

##### Diamond
Example, calculate the RPM for a cutting speed of 500 with a diameter or 5"

A picnic. 500' = 6000", 5 times 22 is 110, 110 over seven is almost 16, 16 into 6000 is 375. Took thirty seconds maybe ? And the best part, there's no bee ess 'formula'. Just remember that you are dividing the surface speed by the length of one circumference. Which is, in fact, what surface speed is.

.5" is even easier, that's 1/2, the 2's cancel out to 11/7, do (6000)(7/11) and I can tell immediately that no way in hell is any lathe I own ever going to go 42,000/11 rpm so finished with engines, I'm done !

Again tho, this is what you are really doing with constant surface speed. Take the speed you want and divide it by a circumference. THAT is your rpm. No need to remember doodly-shoot. Simple arithmetic.

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#### goooose

##### Hot Rolled
A picnic. 500' = 6000", 5 times 22 is 110, 110 over seven is almost 16, 16 into 6000 is 375. Took thirty seconds maybe ? And the best part, there's no bee ess 'formula'. Just remember that you are dividing the surface speed by the length of one circumference. Which is, in fact, what surface speed is.

you do you man lol

#### EmanuelGoldstein

##### Diamond

you do you man lol

Yeah, well coming from someone who doesn't even know that 22/7 is a common and quick way to use pi, sorry that I can't take your comment here too seriously.

The fact is, all that surface speed is, is one circumference times the revolutions. That's it, all you have to remember. Don't even have to remember that, because it's plain old logic. Distance per revolution of the wheel.

#### goooose

##### Hot Rolled
Yeah, well coming from someone who doesn't even know that 22/7 is a common and quick way to use pi, sorry that I can't take your comment here too seriously.

The fact is, all that surface speed is, is one circumference times the revolutions. That's it, all you have to remember. Don't even have to remember that, because it's plain old logic. Distance per revolution of the wheel.
Yes I know what 22/7 is. So do the Ancient Egyptians.

500*4=2000.../5=400. That took 5 seconds. Probable 3 seconds using a calc.

The exact answer using the full formula is ~381.98, which if you use 3.82 instead of 4 you'll get 382. Pretty close for such a simple formula.

CSS is an ever evolving RPM calculation based on CS and the current Diameter. It's value is for toolpaths which will cut a large diameter range during a cut, eg facing.
CSS is a calculation done in the background by the control. Doesn't matter what formula you use for RPM, you're giving the control CS, it calculates how it wants, likely using the full formula.

#### guythatbrews

##### Hot Rolled
I think most are able to memorize 4 or 5 places quite easily if you need that accuracy. 3.1415 is pretty easy to remember and more accurate then 22/7 if simply using 3 is not accurate enough.Heck, who doesn't have a pi button on their calculator now if that's what you're really after?

Point being, if you want to get into a math debate on formulas and what works vs what doesn't, maybe 22/7 in your formula isn't a good starting point.
Many ways to come up with the same result. Way back we learned about 22/7, slide rule days before calculators. Haven't used it myself maybe ever but it was a reasonable method. I agree pretty easy to recall pi to several places.

I was in between the slide rule and calculator days. Learned on a slide rule but got a Texas Instruments TI50 "slide rule calculator" as soon as i could.

Very few use logarithims for multiplication any more. But for hundreds of years they were the bomb, and the best starting point . Some of us on PM still use the old ways (probably not logarithims!). And believe it or not, they still work.

Remember, significant figures still matter, even if your calculator can display 9 places. So 22/7 is a practical work around.

#### EmanuelGoldstein

##### Diamond
Yes I know what 22/7 is. So do the Ancient Egyptians.

Cool, you learned something. Five posts ago you didn't seem to know what it was.

500*4=2000.../5=400. That took 5 seconds. Probable 3 seconds using a calc.

Using my HP-41 with the sequence programmed in, took me .5 seconds. Whoop-dee-effing do.

gooose said:
if you wanted extra accuracy, CS*3.82/D is still easier, quicker, and more accurate than what you are using.

More accurate than 382 ? If you don't round off like I did mentally, the answer is 381.8181, the actual number is is 381.9721, your formula comes in at 381.98. Control only takes integers, so at 382, where is all this extra accuracy you are promoting ? Looks like them trolling Ancient Egyptians did fine, at least to my filmy old eyes. Same exact number, ooooh.

The exact answer using the full formula is ~381.98, which if you use 3.82 instead of 4 you'll get 382. Pretty close for such a simple formula.

Using 22/7 you will also get 382. Amazing.

btw, using your quick and dirty the answer is 400. Using my quick and dirty and rounding off in my head the answer was 375. Real number is 382. So who's shortcut is more accurate ?

Answer to that is subtraction, can you do that without a calculator ?

CSS is an ever evolving RPM calculation based on CS and the current Diameter. It's value is for toolpaths which will cut a large diameter range during a cut, eg facing.
CSS is a calculation done in the background by the control. Doesn't matter what formula you use for RPM, you're giving the control CS, it calculates how it wants, likely using the full formula.

Really ? I had no idea ! Damn, and ever since buying an American Tool Eagle 2000 new with a Bendix 5, I thought it was something magic ! The speed really goes up and down ? wow ! Amazing ! thank you so much !

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#### 706jim

##### Stainless
When reading this litany of posts (which method is "better") remember that the actual cutting speed for any material is really a best guess as to what speed won't burn up the tool, really nothing more. Years ago Valenite published a cutting speed chart we had posted in our shop with SFM values for mild steel varying from 250 to 2500sfm depending on the depth of cut and feedrate and also for maximum rate of production and maximum tool life.
So what is the point of calculating rpm to a hundred decimal places anyway?

Ox

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