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.

 

[electricpete]

J is polar MASS moment of inertia.

From first principles we can calculate it as

J = Sum m * r^2 = Int rho dv
Note the m in m* r^2 stands for MASS.
The m in lbm stands for MASS

If you object to lbm as a unit of mass, then I guess that's a whole 'nother discussion.

Personally, I saw a whole lot of "lb" in the other thread. That is what I would object to. lbm is not ambiguous. (hint: m stands for MASS).

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[electricpete]

Let's go back to the big picture of this thread. The original poster is trying to determine the pump inertia to compare against motor requirements.

Let's say the motor is a general purpose NEMA frame motor with ratings 2hp, 1200 rpm.
Where can we find the max inertia (excluding motor inertia) that can be accelerated by a general purpose NEMA frame motor?

NEMA MG-1 (2003) table 12-7 provides the answer: The value is 30 and the units are given as "lb-ft^2"

One can see here from the context that lb is used as a unit of mass. Like many others, I choose to add "m" to the end (lbm) to make it clear what kind of lb is being talked about without having to analyse the context.

I would like for those in this thread who imply lbm is inappropriate or those in the linked thread who imply that use of lbm represents some misunderstanding to work this same problem above in your preferred units and compare to the NEMA limit.

(A refresher of the problem: solid steel disk with OD = 6", Length = 1.5", rho rho:=500*lbm/ft^3. Find out if it meets the NEMA-specified inertia limit for a 2 hp 1200 rpm motor... namely 30 lb-ft^2)

Then, please compare how many unit conversions were required to finish this task under your preferred unit system to how many I used in my analysis above.

Thanks in advance.

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[electricpete]

By the way, I'm not suggesting my units are best for all situations and context(for example overseas the inertia limit may be given in SI units). But some in this thread and the other thread have suggested that lbm is inappropriate, without even having heard the context. So I choose the context I have provided above (comparing to the NEMA limit). Prove to me it is inappropriate.

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[electricpete]

Another example perhaps would be clearer.

Let's say I have a very thin hollow cylinder. The radius is 1 ft and the mass is 10lbm. (or the weight on the equator of planet earth is 10 lbf, if you prefer).

What is the J?
J = M*R^2 = 10 lbm * 1 ft^2 = 10 lbm-ft^2.

You can compare it directly to the NEMA table which carries the same units and see it is less than their limit of 30. I didn't need any unit conversions to get there.

So you guys are suggesting the correct approach would have been to use slugs or something? I would like to understand.

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[hydtools]

For lack of access to NEMA, I found on an Emerson site reference to load inertia to be consider when applying an electric motor. It appears that Wk^2 is weight inertia not mass inertia. That's why your choice of lbm = lb weight units work out.

Now what?

http://www.emersonct.com/download_usa/techNotesMisc/AC Motors Home Study Course.pdf

Ted

 

[drawoh]

hydtools and electricpete,

There is a system for calculating MOI based on English units and one based on metric units. This is due to the fact that pounds are a unit of weight (force), not mass. The gravitational constant must be accounted for, somehow.

My personal preference, as noted in the thread, above, is to systematically do mass unit calculations, and use m=w/g. You can use the force unit system in English, and the mass unit system in metric. You can refuse to recognize the existence of either English or metric units. A trained professional should be able to interpret the various handbooks and get all this right, especially if they do a unit balance.

Some of us are questioning the OP's level of training. We are, or at least I am, surprised that the impeller inertia is an important factor in a pump design. I do think that a person who understands the fluid density and viscosity and their effect on the impeller would have asked the original question. The pump seal will also use up motor torque.

JHG

 

[drawoh]

I do think that a person who understands the fluid density and viscosity and their effect on the impeller would have asked the original question.

Darn! I hit the Submit button insead of the Preview button.

That should say...

I do not think that a person who understands the fluid density and viscosity and their effect on the impeller would have asked the original question.

 

[electricpete]

Weight inertia is meaningless to me. I am talking about polar mass moment of inertia. Look it up in a textbook. It is the sum of mass times radius squared. It works out because lbm is a unit of mass.


You can get to the MG standards for free. Just give them your email and sign in here:

http://www.nema.org/stds/mg1condensed.cfm#download

You'll get MG-1 2007 condensed version. Table 45 of that document on page 62/76 is the same as NEMA MG-1 Table 12-7.

Take a look at motor OEM sites. They show inertia in units LBF-FT^2 also. For example look here:

http://www.reliance.com/pdf/pdf/aced/E02625-A-A001-V.pdf

Now let's go back to fundamentals. Polar inertia J (as in Torque = J * d^2 theta/dt^2) is the sum of mass times radius squared. Choose a unit for mass and choose a unit for length (radius) and you're done.

In the SI system of units, mass is given in units of kg and distance is given in units of meters, so we would have polar mass moment of inertia in kg*m^2.

In the "American/British Mass (Scientific) System" of units, mass is in units of lbm and distance is in units of feet (Refernce: Applied Dimensional Analysis and Modeling by Thomas Szirtes, Pal Rozsa ISBN: 0123706203), so we would have polar mass moment of inertia in units of lbm*ft^2.

It is really that simple. I have never heard of "weight moment of inertia". I'm sure that some people who use English units are careless about mixing up weight and mass as suggested by the US motors link above. But I cannot be held responsible to defend every misuse of units commited by someone who happens to use English units. Any attempt to introduce weight into discussion of this quantity is in my view completely irrelevant since polar mass moment of inertia depends on mass, not weight (that's what the "mass" stands for). To prove it, send your pump up to the moon and try to accelerate it. Acceleration time will be the same (for the same motor torque profile), even though weight as changed.

I assume the same people who are annoyed by lbm-ft^2 would have no problem with kg-m^2. Now why should that be?

I am not telling anyone which units to choose. Choose what you want as long as you apply it correctly and get the right answer. But for someone to suggest that my choise of lbm as a unit of mass is incorrect (when those are in fact the units captured in NEMA/ANSI standard documents) is a little bit wacky imo.

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[electricpete]

my last post was a response to hydtools.

drawoh - I think we are in agreement that any units applied correctly give the correct answer. I assume that means you retract your comment about lbm.



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[electricpete]

An obvious (?) correction to my post of 16 Jun 08 19:38:
"They show inertia in units LBF-FT^2"
should have been
"They show inertia in units LB-FT^2 "

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[electricpete]

And while I am very prepared to move on from the lbm thing (I have beaten that dead horse), I am surprised to see yet another jab at the original poster.

Some of us are questioning the OP's level of training. We are, or at least I am, surprised that the impeller inertia is an important factor in a pump design. I do not think that a person who understands the fluid density and viscosity and their effect on the impeller would have asked the original question. The pump seal will also use up motor torque.

The original poster said he wanted to know pump inertia as an input to motor selection. When you size a motor to match a load, you need to know two distinct characteristics of the load: the load torque-speed curve (which is where the seals and viscosity part comes in) and the rotating inertia. Both are needed. If the inertia is too high, it can drive you toward a larger motor for successful starting, regardless of the level of the load torque speed curve. Picture a tiny motor trying to start a huge flywheel on frictionless magnetic bearings. The motor will be so slow coming up to speed that it will overheat (or trip off-line if properly protected).

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[BillBirch]

electricpete,
Now I know why I prefer the SI system. Isn't the imperial fundamental unit of mass the slug?

 

[electricpete]

Slug is the unit of mass in the "American/British Force (Engineering) System".

Pound-mass is a unit of mass in the "American/British Mass (Scientific) System"

Once again, my reference for the above statements is: "Applied Dimensional Analysis and Modeling" by Thomas Szirtes, Pal Rozsa ISBN: 0123706203).

I am not particularly interested in all the arcane historical twists of unit systems. The simple fact is the industry standard document and vendor documents I cited above give inertia is units lb-ft^2. It doesn't take too much thought to see the lb here is lbm.

If you prefer SI, I can certainly understand that and have no objection. I would never presume to correct anyone based on the fact that their personal preference for a unit system was different than mine.



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[Artisi]

Electricpete

I think the following is a poor analogy for a centrifugal pump, although you are not particularly refering to a pump in this statement - it will probably be read that way by many who haven't followed the discussion.

" Picture a tiny motor trying to start a huge flywheel on frictionless magnetic bearings. The motor will be so slow coming up to speed that it will overheat (or trip off-line if properly protected). "

Your earlier statement is more to the point for a centifugal pump and to my mind fully answers the original poster - who by the way seems to have now vanished :-

"electricpete (Electrical) 13 Jun 08 17:51
For a single stage centrifugal pump, the pump rotating inertia is often relatively insigificant compared to the motor rotating inertia."

In my 30+ years in the pump industry, the only time I have needed pump inertia is to fill in the blank on a data sheet because a consultant thought it should be included - what they did with the info once given is anyone guess.

 

[electricpete]

Artisi - thanks for acknowledging there was a context to those comments. The context was to demonstrate that load inertia and load torque-speed characteristics are two separate and independent inputs to motor DOL starting evaluation. That was an important point to make at that point in the conversation based on the particular post that I was responding to.

Both torque speed and load inertia are needed for motor starting calculation or validation.

For small and medium motors (up to approx 200 hp), it typically amounts to a validation that the inertia is less than the maximum inertia listed in the NEMA tables linked above. Typically would not be a challenge to achieve for a centrifugal pump. For example the example I gave above - 2hp 1200 rpm motor can start a load up to 30 lbm-ft&2 which is pretty darned large - a hollow cylinder of 1' radius (2' diameter) with 30 pounds mass on the circumference which is much bigger than any 1200 rpm 2 hp pump I'd (I'll leave it to others to calculate how many slugs that is).

But for large motors (perhaps 300-500hp and up, depending on speed), NEMA doesn't give us any table of maximum inertia. In that sense each large motor purchased to NEMA specs will be a custom engineered motor. The motor manufacturer will need to know the driven load torque-speed characteristics AND inertia to evaluate starting performance under worst case voltage conditions. He will develop a worst case starting profile (current vs time) and compare it to the motor damage curve (current vs time) and verify there is enough margin to provide protective relay function between those two curves.

And while typically the pump inertia is typically a very small part of that equation, it is not always so. I have in front of me a motor starting calculation for a vertical 3500 hp 324 rpm motor driving a single stage axial pump (power plant circ water pump). The pump impeller is huge like an airplane propeller. The motor inertia is 110,000 lbm-ft^2 and the pump inertia is 20,000 lbm-ft^2. So the pump inertia is more than 15% of the total inertia which is not insignificant. As a result of presence of the pump inertia, it takes the machine 15% longer to accelerate than it would without the pump inertia.


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[electricpete]

Correction:
"The pump impeller is huge like an airplane propeller."
should have been
"The pump impeller is huge like an cruiseship propeller."


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[vpl]

Electricpete, You deserve a star for thoroughly discussing this topic.

Thanks

Patricia Lougheed

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[electricpete]

Thanks, I appreciate that.

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[PeterCharles]

Slug is the unit of mass in the "American/British Force (Engineering) System".

It's years since I've heard that term!
One good thing about metrication was the clear division between FORCE (in Newtons) and MASS (in kilograms)

 

[svanels]

Nice thread Electricpete, when it comes to vibration and inertia the best things to do is to stick with the SI system. In this age of "the computer did it", or "I got it from the Internet" it is good to see that "plain old calculation" by engineering principles still exists.
I what happened to the OP