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Curran919

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I've got a pump train with a AC drive with VFD. It direct drives a booster pump and drives the boiler feed pump through a 4:1 gearbox. The MoI of the entire system was estimated to be 1642 kgm^2. The customer's in situ test claim to measure closer to 2400 kgm^2. I'm not sure what exactly the customer needs this data for (controller? hard start safety factor?), but obviously if this difference is true, our torsional natural frequency predictions are all BS.

I was asked to give a protocol for more accurately determining the MOI in situ. I gave my idea already, but I'm curious what this community would come up with. There is no torque meter. VFD gives speed, current, voltage. An encoder [several pulse/rev] may be possible to install.

If push comes to shove, I'd install a telemetry kit on the spacer to measure torque directly, which would also allow experimental validation of the torsional analysis.
Shurafa2

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Reply with quote  #2 
I never did this before, but I would consider the electric power curves of the motor and online data. I guess one can estimate the torque and moment of inertia during the startup if you have the rest of the details from the datasheets.

In a couple of facilities I worked for, they had high-resolution data collection during the first seconds of startup. I used this online system to identify what causes the motor to trip during crazy cases. Sometimes, it was simply a logic issue while in other cases the current curves indicate a type and amount of an abnormal load on the motor.

It would be nice to let us know your findings.

Regards- Ali M. Al-Shurafa 
Walt Strong

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Reply with quote  #3 
I have never been asked to measure mass moment of inertia on larger machines, but I have measured torque and torsional vibrations. Here is the basic formula that would require a measurement of torque and angular acceleration:

Torque Formula (Moment of Inertia and Angular Acceleration)

 The torque on a given axis is the product of the moment of inertia and the angular acceleration. The units of torque are Newton-meters (N∙m).

torque = (moment of inertia)(angular acceleration)

τ = Iα

τ = torque, around a defined axis (N∙m)

I = moment of inertia (kg∙m2)

α = angular acceleration (radians/s2)

 From <https://www.softschools.com/formulas/physics/torque_formula/59/>

A strain gage telemetry system can be installed to measure torque (I use the Binsfeld system), and shaft speed encoder V-F system (I use the Copp-Tek) can measure angular velocity that could be converted to angular acceleration. The measurements could be made during startup or shutdown, and I suggest both so that friction force can be minimized.

Torsional natural frequency can be measured with the strain gage telemetry system or the encoder with V-F converter method. I have also seen natural frequency on a large ACC fan during startup by measuring the motor current.

Curran, What was your suggested method?

Walt
John from PA

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Reply with quote  #4 
To my knowledge, some studies on water hammer by Wylie and Steeter (1993) resulted in a method that is typically used for this task.  A summary of the method can be found at 

https://neutrium.net/equipment/estimation-of-pump-moment-of-inertia/.

One thought I would add, and it comes from my background in Marine Engineering/Naval Architecture, when you are doing torsional modeling for shipboard power trains, there is a "fudge factor" (for lack of a better term) that accounts for the additional moment of inertia of the water in motion with the propeller.  In large vessels, where propellers can be very large, this increased inertia can be substantial.  Whether something similar should be done in a pump is a consideration.  There is some literature on the web that provides a discussion; see https://www.researchgate.net/publication/276247023_Added_mass_moment_of_inertia_of_centrifugal_dredge_pump_impellers as an example. 


electricpete

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Reply with quote  #5 
From my perspective, the motor should be the easy part.  During a ramp in frequency, you can calculate motor input power (assuming you have the waveforms to determine power factor angle), subtract estimated motor losses (as a function of time) to get motor output power.  Divide by speed to get motor output torque.  A dynamic motor model encompasses all these factors. 

To convert motor output torque to accelerating torque (which is equal to radian speed ramp rate times inertia), you first need to subtract out any fluid torque (and friction torques) of the driven equipment, which seems like the most challenging part to me.  I can think of a few ways to attack that:
  1. Obviously the fluid torques will depend not only on the pumps characteristic but the system characteristics / lineup.  You have pump curves and system curves to work with. You can measure fluid parameters.  As best I can figure, you have to put all those together for your fluid torque estimate.  If you are confident in those estimates, then use them. 
  2. Let's say you are not very confident in those estimates.  Can you create a situation where the estimates of fluid/friction torques are small / negligible compared to the accelerating torques?  I'm not sure, but if that can be achieved, the best way to achieve it would be by minimizing fluid torque (dead headed condition, for short enough time that pump doesn't overheat) and maximizing accelerating torque (by selecting as high a ramp rate as you can achieve).   The direction of this error of neglecting the fluid / friction torques would be to increase your estimate of inertia. So at least you consider your estimate to be a bounding-high estimate of inertia. If it is reasonably close to your estimate and far below the customer's then it's good enough.  
  3. Let's say you just have a plot of total torque vs time during a ramp acceleration in speed starting at zero. Here is another way to split out the accelerating torque from the other torques.   The accelerating torque would be constant during a ramp acceleration.  Most the other torques are something like speed-squared variation but in any case should be zero at zero speed.  Use the curve of total torque vs speed to project smoothly backwards the most accurate estimate of the torque at zero speed... that should be your estimate of accelerating torque.
  4. 3A. There are some problems problem with #3 that the friction torque doesn't actually go to zero at zero speed due to breakaway torque effects and the also the behavior of vfd at the moment of start is somewhat unpredictable.  You could rotate manually prior to start to minimize breakaway torque effects.  Also when you project the curve smoothly back to zero speed,  you can do that using the data starting above say 100rpm (and ignoring the data at lower speeds which is influenced by breakaway friction and vfd stabilization). 

I think most vfd's only display output frequency and only a few give you and estimated motor speed based on an internal model that estimates slip. If you are working with output frequency, than obviously motor slip is not accounted for and you'll get better results measuring speed directly.
John from PA

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Reply with quote  #6 
Quote:
Originally Posted by electricpete
From my perspective, the motor should be the easy part


Perhaps easier than you might expect.

In the States, it is common for the OEM of the prime mover of a machine train to do a torsional analysis, if requested by a purchase spec or required by an invoked specification.  Consequently, sometimes just going to the motor manufacturer engineering department will get you the needed number.  In 20 to 30 years of doing torsional modeling, I have always been able to get the needed info in this manner.  That has also included getting info on internal combustion engines, steam turbines, gas turbines.
electricpete

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Reply with quote  #7 
John - just to clarify, my point was that the calculations/modeling involving the motor (input electric power to output torque) are the easy part.  I'm not sure if that falls in the category of "a number" (if you are working with an efficiency number, it is not constant as conditions change and it falls short of a dynamic model).   I wasn't considering any need to estimate motor inertia since that is part of the total train inertia.

I think you raised a critical point earlier that I never thought about in my response above.... separating fluid inertia from mechanical inertia.  That could very well be the most challenging aspect of the whole thing.  How could you separate out mechanical inertia from fluid inertia through in situ testing?    The pump certainly cannot be operated dry at any significant speed.  If you did attempt to test it dry, it would have to be very low-speed low-rotation tests with  specialized equipment (not driving with a vfd). 

Still thinking out loud, maybe the customer doesn't care about separating fluid inertia from mechanical components inertia. In that case, just lump it all together and see what you get.  (do a test as if you were looking for mechanical inertia, recognizing the result will be a combination of mechanical and fluid inertia).
John from PA

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Reply with quote  #8 
Quote:
Originally Posted by electricpete
John - just to clarify, my point was that the calculations/modeling involving the motor (input electric power to output torque) are the easy part.  I'm not sure if that falls in the category of "a number" (if you are working with an efficiency number, it is not constant as conditions change and it falls short of a dynamic model).   I wasn't considering any need to estimate motor inertia since that is part of the total train inertia.

I think you raised a critical point earlier that I never thought about in my response above.... separating fluid inertia from mechanical inertia.  That could very well be the most challenging aspect of the whole thing.  How could you separate out mechanical inertia from fluid inertia through in situ testing?    The pump certainly cannot be operated dry at any significant speed.  If you did attempt to test it dry, it would have to be very low-speed low-rotation tests with  specialized equipment (not driving with a vfd). 

Still thinking out loud, maybe the customer doesn't care about separating fluid inertia from mechanical components inertia. In that case, just lump it all together and see what you get.  (do a test as if you were looking for mechanical inertia, recognizing the result will be a combination of mechanical and fluid inertia).


I'm not certain why total system inertia would be desirable without also having the motor inertia.  If I have the total inertia and the motor inertia, then I can readily calculate the load inertia.  That enables me to properly size the motor and also do a crude calculation of the 1-node torsional critical speed.  Many machine trains have the 1st critical node at the coupling so a crude calculation can be made using some relatively simple canned formulas from a textbook and or handbook.  Many purchase specification desire the calculation of the first three torsional modes so that becomes a bit more complicated.  Even here Curran919 needs to account for that 4:1 reducer in the train as that means if we build a model with the motor as a reference then everything from the gear (as opposed to the pinion) needs to have its inertia divided by 16 or the ratio squared.  As an FYI that would be the first thing I would check to possibly explain the discrepancy "The MoI of the entire system was estimated to be 1642 kgm^2. The customer's in situ test claim to measure closer to 2400 kgm^2."

I dug up my copies of Marine Engineering, a textbook/handbook published by the Society of Naval Architects and Marine Engineer (SNAME).  My version is from 1960, the days of slide rules so keep that in mind.  Quoting:

Quote:
For propellers, a certain quantity of water must be considered as attached to the blades and partaking of their motion.  This allowance for entrained water will vary with bladed width, thickness and other factors.  By analysis of trial results it is found that an addition of 25% to the propeller inertia is approximately correct for this factor.

An empirical formula for the propeller inertia is given by the formula J = 0.0046 nD3bt where n = number of blades, D = diameter (inches), b = maximum developed blade width (inches), and t = maximum blade thickness at 1/2 radius (axis to tip) in inches.


Units for the term J are not stipulated.  To be honest, in my modelling efforts, I just used the 25% factor and also found that the propeller manufacture could readily supply the inertia with and without the effects of the water.
Curran919

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Reply with quote  #9 

Quote:
As an FYI that would be the first thing I would check to possibly explain the discrepancy 


That is indeed the first thing that I checked.

Quote:
Whether something similar should be done in a pump is a consideration. 


Yes, water inertia is considered. The calculation is well validated (probably a trade secret). Even if there was significant error in these assumptions, the combined MoI of BFW pump and booster pump (including fluid) make up less than 3% of the total system MoI. So while it could have a significant effect on the dynamic torsional system, it is not affecting this MoI measurement.

Quote:
you first need to subtract out any fluid torque (and friction torques) of the driven equipment,


There are two more obvious methods from what I can tell:

  • It is a VFD, so we can take the quasistatic (no rotor acceleration) trend of the torque with speed. We then subtract that from the ramping data and all we have left should be the accelerating torque, without having to quantify the underlying 'absorbed torque' (fluid/friction).
  • Alternatively, we can ramp up, which will add the accelerating torque, then ramp down, which will subtract the accelerating torque. Half of the difference would be the torque necessary to calculate the inertia.

I recommended the latter. However, we don't have a direct torque measurement and probably won't have the chance to install some gages + telemetry. So we are estimating the torque by using the electrical power and shaft speed measurements. I was having trouble considering the effect of the motor torque curve on the deceleration trace. Did the ramp down have to be slower than the coast down to ensure that the motor would not be braking? I decided it didn't matter, just made the calculations more difficult (negative torque, current OoP). However, my knowledge of power factors is very limited, and I don't know if I'll have to consider this during the ramp down.

Quote:
To my knowledge, some studies on water hammer by Wylie and Steeter (1993) resulted in a method that is typically used for this task.  A summary of the method can be found at 


Interesting, I can't imagine this being very precise, but I will recommend it as an extra validation step.

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