Curve fitting units

[jdesai-2]

Hello,

What is the best way to handle units in a curve fitting equation situation.

On line 4 if I leave the ksi in then line 6 does not work, I had to create a unitless line 5 to get line 6 to work. Also I had to text in the word "cycles"  because MC does not take cycles unit in lines 6 & 8. 

 

[Werner_E]

1) To be able to calculate "sigma -23" obviously both must be of same dimension. Itz can't work if sigma has unit ksi and 23 is unitless

2) The arguments of functions like exp, log, sin, etc. must be unitless. Thats not a limitation of Mathcad, though 😉

3) If this is an old empiric formula, you may assign unit ksi to sigma and then use log(sigma/ksi-23) to make it work. No need to create a unitless variable manually.

4) Concerning cycles you may define your own "unit" (its not a unit anyway) for this. Assign cycles:=1 and label the word cycles as "unit".

[ValeryOchkov]

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@Werner_E wrote:

4) Concerning cycles you may define your own "unit" (its not a unit anyway) for this. Assign cycles:=1 and label the word cycles as "unit".

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cycles: = 1

Pi + cycles=4.142 ???

Better use cycles: = mole

[Werner_E]

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wrote:

Pi + cycles=4.142 ???

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Garbage in - garbage out 😉

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Better use cycles: = mole

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Is it really better?

[Fred_Kohlhepp]

why not cycles = 2*pi*rad?  or cycles := rev

"rev" is a built-in unit!

[jdesai-2]

Pure Genius!

[Fred_Kohlhepp]

AWWWW

shucks!

[jdesai-2]

Hmmm! where do you create this unit?

[Fred_Kohlhepp]

on your top row, select cycles and under math/labels select unit.  The font and color will change to match other units on the sheet.

[MJG]

Be careful with this.  Depending on your usage, this may incorrectly change the value of the result.

From the equations provided, I did not interpret "cycles" to be equal to revolutions.  Instead, I interpreted "cycles" to be the number of times an object has been subjected to a design event.  For example, in fatigue design you may be required to design a member for 2M cycles of a given fatigue loading.

I believe OP calculated that a member can undergo the specified stress 3,500 times.  After accounting for a service factor of 6, the member would be rated for only 590 design events.

[ValeryOchkov]

I do sometimes so

[Fred_Kohlhepp]

There are a couple mistakes (I believe) in your note.  MJG is right, this is fatigue (I recognize the MIL-HNDBK-5 equation).  So we need to be careful about how we treat this, and about what the definition of cycles is.  Please look at the attached Prime 3.0 sheet.

[jdesai-2]

Borrowing on Fred's idea how about

cycles=1*Hz*sec

Math/label/unit

seems to work fine. Does anybody see a problem with this?

[Fred_Kohlhepp]

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wrote:

Borrowing on Fred's idea how about

cycles=1*Hz*sec

Math/label/unit

seems to work fine. Does anybody see a problem with this?

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Well, Hz = 1/sec

so Hz sec is unitless. 

Because (for fft's) I need Hz for frequency of vibration due to a rotating shaft, I set "RPM = Hz/60" (note the caps!)  Then I get the correct numerical value for the fft resolved frequency.  I like this answer:

[jdesai-2]

Great. This is the new "DesKohlhepp Equation/Theory"

[AlvaroDíaz]

Hi Fred.

I prefer 1 RPM = 2 Pi / 60 Hz and 1 rev = 2 Pi.

Best regards.

Alvaro.

[Fred_Kohlhepp]

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wrote:

Hi Fred.

I prefer 1 RPM = 2 Pi / 60 Hz and 1 rev = 2 Pi.

Best regards.

Alvaro.

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Hmmm

so RPM =   rpm (already built-in)

And rev is a built-in and equals 2 pi.

Okay!

And cycle?

[AlvaroDíaz]

For cycle I guess that cycle = 1. Because then for the electrical alternating current you have  that 60 cycles/seg = 60 Hz which agrees with the usual frequency.

Best regards.

Alvaro.

[ValeryOchkov]

cycle = 1

cycle  + % = 2 but must be an error

PS

In Mathcad 11

rad + sr = error (!!!)

In Mathcad 15 and Prime

rad + sr = 2 (???)

[Fred_Kohlhepp]

in Prime % is a function, not a unit, so

[jdesai-2]

What is Alvaro trying to say?

Is cycle=Hz*sec wrong?

I checked out Mathcad Prime results with my casio calculator, and then checked the casio calculator results with my Aristo Scholar slide rule, and they all agree

[LucMeekes]

I tend to agree that the statement 'cycle=Hz*s' is wrong. Cycle is (should be) just a number without units (hence it is 1) because it is an occurrence of something...or anything. You can compare 'cycle' with e.g. 'drops of water falling' from a dripping tap. When the circumstances are unchanged, these drops fall with a certain frequency, or a period of time between them. But that does not make 'drops of water falling' a unit. It's their rate of falling that has a unit: Hz.

Mathcad allows you to define cycle as a unit.

If you do, for the above reason, define it as cycle:=1, not as cycle:=Hz*s.

Success!
Luc

[jdesai-2]

So N = 100,000 what?

[LucMeekes]

N=100 000 times the occurrence of one cycle if you will.

Look up the definition of rad and sr in table 3 of the SI brochure at https://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf .

There are more units that are...just 1.

Success!
Luc

[AlvaroDíaz]

I'm, as electromechanical, always use mass basis for thermodynamics, and see molar basis as a simple curiosity. But working between chemicals engineers, must to use it, even at the first understand nothing. Later I see that for chemicals the weight isn't that important, it is more important the quantity of particles, because the reactions are between them, not mases. And, for example, the hydrogen have a very little mass, and in practical calculus it mass disappear in the approximations. But taking their number (moles) in the reactors you get more accurate precision with the less effort.

If I cook bread I know that 2 kg of eggs with 10 kg of flour give me 12 kg of bread plus some humidity (it's an open system for the water). But for a chemical engineer, they use kgmol, and the product isn't the summation of the kgmol. You must to convert they first to kg. So, for things you must to be very clear about the domain of what you are adding. In mathcad for solve problems from the viewpoint of the chemistry I define kgmW, kgmH2O, kgmCl, etc for each compound as the molecular weight  for a supply for steel working with mases, not amount of things.

So, my conclusion of cycles is that it must to be very important. There are a lot of examples where the number of cycles are counting in distinct way at each region. For example, the number of passes in a heat exchange is used for calculus in some places, but in others is the number of "U" 's. It's easy get confusing counting those things. In some places people says "nos vemos en 8 días" (we'll see in 8 days) meaning "say next week". What means "we'll see in 8 days"? A week? That's don't agree my circadian cycle ...

Best regards.

Alvaro.

[Fred_Kohlhepp]

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wrote:

I tend to agree that the statement 'cycle=Hz*s' is wrong. Cycle is (should be) just a number without units (hence it is 1) because it is an occurrence of something...or anything. You can compare 'cycle' with e.g. 'drops of water falling' from a dripping tap. When the circumstances are unchanged, these drops fall with a certain frequency, or a period of time between them. But that does not make 'drops of water falling' a unit. It's their rate of falling that has a unit: Hz.

Mathcad allows you to define cycle as a unit.

If you do, for the above reason, define it as cycle:=1, not as cycle:=Hz*s.

Success!
Luc

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I'd like to point out that Hz sec is (at least in Mathcad) unity.  So you're both right

This horse is no longer breathing, lifeless and bleeding on the floor.  Stop beating him!