Inertial loads

[Cronos_2P]

Hello everyone.

I have the natural frequencies of the piping system of a reciprocating pumping unit, I need to verify the separation margin indicated in Annex C of the API 674 standard.

If I have a triplex pump that rotates at 300 rpm, the significant frequency would be f=3*300/60=15 (Hz) as indicated by the standard, but I don't understand how to add inertial loads and how are determined.

I hope you can help me, thank you very much in advance.

 

[GregLocock]

Assuming this is a piston and crank compressor, the inertial loads are a function of the mass of the reciprocating parts, the length of the conrod and the stroke of the piston, and the rpm. Assuming you have 3 parallel 2 stroke cylinders phased at 120 degrees, statically and dynamically balanced, the dominant frequencies are going to be multiple of 1.5 times crankshaft rotation due to inertia (1.5E, 3E, 4.5E etc), and odd multiples of 3E (ie 3E 9E 15E) due to compression and expansion. More details will give a better answer.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[Cronos_2P]

Thank you very much for the help Greg Locock. The data I have about the reciprocating pump are:

- Number of heads: 3
- Bore: 4.5 (in)
- Stroke: 6 (in)
- Rod Length: 16 (in)
- Minimum pump speed: 150 (rpm)
- Nominal pump speed: 240 (rpm)

In your explanation, why are the dominant frequencies going to be multiples of 1.5 times crankshaft rotation? Should this result be added to the calculated 15 (Hz) or is it the total frequency including inertial loads as the code mentions?

I would really appreciate it if you could explain it to me again.

Thanks in advance.

 

[GregLocock]

I think I was wrong on the 1.5E, that's 90 degree V6s. 3 cylinder in line engines have a dominant rocking couple at 1E (piston 1 goes up as piston 3 comes down), but thinking about it they also have 2E 4E 6E etc due to the L/r ratio.

Sorry I don't have any engine design books with me, , but a few observations on your pump - rpm is low so accelerations are low. l/r is high so 2E etc are less important.


Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[electricpete]

I recall Den Hartog's Mechanical Vibrations had a great writeup on reciprocating machine vibration and it used to be available for free / public domain.

I'm going to assume your machine looks something like this (if not let me know)

https://powerzone.com/resources/glossary/triplex

> I don't understand how to add inertial loads and how are determined.

From the quoted standard it doesn't sound like you need to add them, only to determine what the frequencies are and ensure a separation margin from them (the "plus" seems is more like a logic term than a mathematical addition).

Inertial load is load associated with accelerating a mass (F = m*a). Arguably not a true force but it acts like one in many ways.

For that machine I'd say inertial loads are at 1x running speed. Each rod/piston provides an inertial load at 1x running speed. Three rods give three sets of forces spaced at 120 degrees in space and time, which cancels some of the inertial forces but not all (for example the moments created by the forces acting at different points along the crankshaft, or where there are slight differences among the three sets of moving parts).

Many forces can have multiples of the fundamental force frequency created if they are periodic but non-sinusoidal (think Fourier series). I think the pressure and stretching forces fall in that category but to my thinking it wouldn't apply to the inertial forces in this situation. That actually seems problematic for the pressure and stretching forces... if you are allowing for harmonics based on non-sinusoidal behavior, how do you bound them to ensure they are 20% below the resonant frequency. That seems more involved to me.

TLDR to my thinking all you have to worry about for inertial is 1x turning speed for this configuration but the pressure and stretching forces might include harmonics of 1x turning speed (i.e. 2x, 3x etc)

All of that is my take based on my simplistic view of things. I'm not familiar with the standard snippet you cited, and I don't design machines or their applications. So I may be missing something.


=====================================
(2B)+(2B)' ?

 

[Cronos_2P]

Thank you both for the help.

electricpete, what you assume is correct, the pump is similar as show in the link.

As for the inertial loads, it is as you mentioned, these are a function of the equivalent reciprocating mass, ratio of crank radius an connecting rod length, the crank rotation angle and the angular velocity.

The formula I found to calculate this force is:

Fs=ms*r*ω^2(cos Ɵ+λ*cos 2 Ɵ)

where: ms is the equivalent reciprocating mass, λ is the ratio of the crank radius and connecting rod length, θ is the crank rotation angle and ω is the angular velocity.

and the section of the API 688 code that mentions that the amplitude of the inertial load at 2xRPM is approximately 20% of the fundamental.

However, I have not been able to find more information to help me determine that frequency due to extra inertial loads or to justify that this addition mentioned in API 674 is not necessary in this case.