MOMENT OF INERTIA ON A CENTRUFUGAL PUMP 7

[robles2713]

HOW CAN FIND THE MOMENT OF INERTIA ON A NEW CENTRUFUGAL PUMP THAT I AM DESIGNING?
I NEED TO SIZE THE MOTOR CORRECTLY BECAUSE IS GOING TO BE A HIGH DOLLAR AMOUNT MOTOR.

 

[Artisi]

electricpete
I must agree completly with your big pump scenario but these installations are rare for the normal day to day pump/motor selections. However,as youself,others and myself are aware, pump installations of this nature need to be engineered from the ground up and certainly entail more complex data than pump inertia which becomes a fairly minor problem in the overal scheme of things.

Like Patricia (vpl) - your effort in this is certainly worth more than 1 star - so another star from me for your effort and detail.

Just hope our budding new pump designer has taken note.

 

[hydtools]

electripete, thank you for the NEMA link. I see the table with the Wk^2 values.

Your approach to the problem is correct, sum the moments of inertia of component elements about the rotation axis.

However, your conclusion is not correct. The values given in the NEMA table for Wk^2 are weight inertia, not mass inertia. W is the weight of the rotating component(s) in lbf. K is the radius of gyration in ft. This weight inertia is used so that easily measured units of weight and distance can be used to calculate moment of inertia.
Using your disk example: the disk weight is 12.27 lb and the radius of gyration is .0313 ft. Wk^2 = .384 lbf-ft^2
It is numerically the same as your lbm approach only because lbf and lbm are numerically equal. For consistant units when you use lbm you must also use the conversion constant gsubc = 32.17 lbm-ft/lbj-sec^2 to convert lbm to consistant mass units. lbf = (lbm/gsubc)*a. Here on earth at sea level a = 32.17 ft/sec^2. So lbf = lbm, numerically.

Mass inertia units are lbf-sec^2-ft. Weight inertia is calculated by multiplying mass inertia by gravitational acceleration g = 32.17 ft/sec^2. The weight inertia units are lbf-ft^2.

Radius of gyration is defined as k = sqrt(I/m). In the case of the disk, k = sqrt((mr^2/2m) or k^2 = r^2/2. For a cylinder, k^2 = (R^2-r^2)/2. To calculate Wk^2, use the weight(lbf) of the component and radius of gyration. Breaking an impeller into disks and cylinders, calculating and summing the Wk^2 for each will result in a figure to be compared to the NEMA chart.

My references are Mark's Standard Handbook for Engineers and Hartman's Dynamics of Machinery.

Ted

 

[electricpete]

To summarize my understanding of your comments:

On 16 Jun 08 11:11, I described the problem and concluded J = .384*lbm*ft^2

You are saying the solution of the same problem should be instead Wk^2 = .384 lbf-ft^2

So, you are saying Polar mass moment of inertia J and this other mysterious quantity WK^2 are not the same thing, and the definitions of the relevant quantities are:
J = m*k^2
and
WK^2 = m*g * k^2 = Weight * k^2

It may be the case, and it would explain what the W in WK^2 stands for. But the quantity WK^2=m*g*k^2 would have absolutely no physical meaning in calculation of rotational acceleration, J=m*k^2 is the only sensible quantity to use for that purpose.

I don't doubt that there may have been bizarre historical reasons similar to your logic that lead to the strange name "WK^2". But I am still skeptical that WK^2 = m*g*k^2 is the current accepted definition of that term. People use this quantity to solve problems using first principles of physics like T = J d^2 theta / dt^2, and this process demands using sensible units lbm*ft^2. Can you please point me to the specific portion of Marke's Handbook of interest?

Regardless of the historical definition W*K^2, the calculation of J as presented above is correct. You can compare the result directly against the NEMA table values labled as "lb-ft^2". (which if interpretted as inertia must be lbm-ft^2, same as J). If you prefer to consider the quantity tabulated is represents m*g*k^2 in lbf-ft^2, then you can divide by g to get the desired quantity J = m*k^2 and then multiply by the unitless conversion g*lbm/lbf to get expected units lbm-ft^2 with the same numerical value.

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[robles2713]

Thank you all for all valuable input. I now have a better understanding what to look for for this and future inertia calcs on PUMPS. I was succesful getting the LOAD CURVES from my sales guy and I was succefull in getting the inertia calcs. API 541 SPEC required that the motor was capable of starting at 80 v that's how everything starter.

 

[electricpete]

Glad you are still around robles. I thought we scared you off.

Ted - I did find this in "Handbook of Mechanical Engineering Calculations" 2nd ed by Hicks, Tyler

This is the first appearance of the external inertia, WK2. It is merely the weight of the body times the radius of gyration squared. Since the kinetic or ‘‘stored’’ energy in the body is directly proportional to WK2, this expression is commonly known as the ‘‘moment of inertia,’’ although strictly speaking the moment of inertia is WK2 / 32.2. However, in developing the most commonly used formulas, the factor 32.2 disappears or is absorbed in the constants. Hence WK2 itself remains as a convenient medium of calculation and is generally known as ‘‘moment of inertia’’ even though incorrectly.

So, you are right about the definition of WK^2.

But the practical aspect as described in the paragraph are the same as I mentioned above. We can get to the mass moment of inertia J (which is what we need), by using the same numerical value with units changed to lbm-ft^2 instead of lbf-2. It was obviously the intent of whoever concocted WK^2 that it be used this way.

Before the chorus of people telling me to switch to metric chimes in again, NEMA MG-1 is what we are given and what we have to work with. The sensible way to work with it IMO is to treat the values as J in units lbm-ft^2.


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[electricpete]

typo alert:
"units changed to lbm-ft^2 instead of lbf-2"
should be
"units changed to lbm-ft^2 instead of lbf-ft^2"

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[electricpete]

And I vote Ted a star for showing us the bizarre hidden meaning of the term WK2


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[hydtools]

electricpete, thanks.

If it wasn't for bizzare or archaic what would we have to discuss.



Ted

 

[zekeman]

quoteThis is the first appearance of the external inertia, WK2. It is merely the weight of the body times the radius of gyration squared. Since the kinetic or ''stored'' energy in the body is directly proportional to WK2, this expression is commonly known as the ''moment of inertia,'' although strictly speaking the moment of inertia is WK2 / 32.2. However, in developing the most commonly used formulas, the factor 32.2 disappears or is absorbed in the constants. Hence WK2 itself remains as a convenient medium of calculation and is generally known as ''moment of inertia'' even though incorrectly."

Who is Hicks to "decide" that weight moment of inertia is incorrect in favor of mass moment of inertia. I submit that each is equally valid and that mass moment of inertia is only a convenience for making dynamic calculations.
Moreover, why has this thread degenerated into a boring contest of units. I think the answer to the OP question has long ago been made and this tiring overlong discussion where people are overgenerously awarding "stars" for almost no important input should come to a conclusion.

 

[electricpete]

You are free to ignore the thread if it bores you.

I have a question for you, though. What possible purpose would anyone have for calculating polar weight moment of inertia, other than as a means to calculate polar mass moment of inertia ?

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[zekeman]

Electricpete,
FYI, whenever I have done a calculation of polar inertia ,I first sum the WEIGHT moment of inertia and then make the conversion to mass moment of inertia. I have never seen engineering tables of materials of density given in mass units. Have you? Would you do it otherwise?
I still think the subject is boring and anybody who continues to follow this should get a book on basic dynamics,get a day job or spend more time doing the work they are being paid to do.
BTW, I am self employed so this doesn't apply to me.

 

[electricpete]

Sounds like we are in agreement weight moment of inertia WK^2 is simply a means toward determining the mass moment of inertia J. You lost me on the density part (I have always seen density as mass per volume), but that's a typical state of affairs.

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[hydtools]

Uh, the original poster recently said this was all helpful and that is the point. Done.

Ted