Fundamental Specifications for Eliminating Resonance on Reciprocating Machinery (13)

8/6/2019 Fundamental Specifications for Eliminating Resonance on Reciprocating Machinery (13)

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Presented at 73rd

Annual GPA ConventionMarch 7 9, 1994, in New Orleans

Fundamental Specifications for Eliminating Resonanceon Reciprocating Machinery

Frank Fifer, P.Eng.Beta Machinery Analysis Ltd.

Houston, Texas

Introduction

Question: What is the purpose of performing anacoustical analysis?

Answer: To ensure a smooth running compres-sor package.

Question: Why do you want a smooth runningcompressor?

Answer: To avoid component failure leading toworker injury or equipment loss.

Knowing what unbalanced forces and moments arepresent in a separable reciprocating compressorpackage, and avoiding coincident mechanical naturalfrequencies, will greatly increase your chances ofhaving a smooth running compressor.

Beginning with the fundamental equation of vibration:

1- we will explore what forces are in a reciprocatingcompressor and at what frequencies they occurat, and

2- we will develop a mechanical guideline to avoid

resonance with these high forcing functions.

Vibration Definition

Is the periodic movement of a body about anequilibrium position?

Vibration amplitude is a function of an applied force andthe dynamic stiffness at a given frequency:

Vibration = Dynamic ForceDynamic Stiffness

In controlling vibration, both aspects of the vibrationequation must be considered.

Forcing Functions

Several main forcing functions (ie: dynamic forces) arefound in reciprocating machinery. Most are a functionof the machine make and model rather than operatingconditions. Pulsation induced shaking forces are morea function of operating conditions and piping geometry.

The forcing functions of concern in a reciprocatingcompressor installation are given in the following table

along with the frequency at which the forces are largestand what can be done, if anything, to minimize theforce.

Abstract

When performing acoustical studies,companies have asked for

accompanying mechanical analysis.Presently, no specific mechanicalguideline exists in API Standard 618,which is the most commonly usedstandard for acoustical studies. APIStandard 618 concentrates on theaffects of pulsations only. There aremany more forces associated with areciprocating separable compressor,other than just pulsations, that canresult in unacceptable vibrations.This paper discusses the mainsources of forces and presents amechanical guideline which will helpto avoid mechanical resonance due

to these sources.


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ForcingFunction

Dominant Frequency(Multiple of Run

Speed)

How to MinimizeResponse

Mass Unbalance 1X, 2X Minimize opposing mass unbalance (eg: 0.5to 1 lbs for 1000 RPM, 6 stroke unit).

Moment/Couple 1X, 2X Inherent in design.

Alignment 1X, 2X Check angular and parallel alignment.Pulsation * 1X, 2X, 3X, 4X, . Control pulsations using acoustical simulation

techniques.

Cylinder Stretch * 1X. 2X, 3X, 4X, . Inherent in design but check that cylinderassembly bolts are properly torqued.

Coincidence of torsionaland acoustical natural

frequency

At torsional naturalfrequency

Avoid coincidence of torsional and acousticalor mechanical natural frequencies.

Torque Fluctuations * .5X, 1X, 1.5X, 2X, . Minimize torsional vibration using/replacingtorsional dampener. Keep engine balancedproperly.

NOTE: * - On average these forcing functions decrease with increasing multiples.- The most significant forcing functions occur at 1X and 2X compressor run speed.

Terminology

Mass Unbalance: Mass unbalanced in opposingreciprocating components androtating component unbalance.

Moment/Couple: Created by the offset ofopposed reciprocatingcomponents.

Alignment: Angular and parallel alignmentof driver and compressor shafts.

Pulsation: Pulsation induced shakingforces.

Cylinder Stretch: Elongation/shortening ofcylinder assembly due tointernal gas forces.

Coincidence of Coincident acoustical andtorsional and torsional naturalacoustical natural frequencies feed on onefrequencies: another to produce

frequencies: additional cylinder stretchvibrations and pulsations

Torque Fluctuations: Changes in torque loading.Frequencies to beconcerned with:

-.5X,1X,1.5X.. for 4 cycleengines

-1X,2X,3X.. for 2 cycle engines,motors and compressors.

If engine power cylinder pressures are perfectlybalanced, then the highest torque input frequency willbe N/2 times run speed for a 4 cycle engine and Ntimes run speed for a two cycle engine, where N is thenumber of power cylinders.

Stiffness and Mechanical Natural Frequencies

All groups of components, (piping, pulsation bottles,scrubbers, cylinders, etc.) in a reciprocatingcompressor installation will have several mechanicalnatural frequencies below 200 Hz. The mechanicalnatural frequency of a component is the frequency atwhich the component naturally wants to vibrate. Forexample, a spring-mass system will oscillate at aconstant frequency if the weight is pulled down andthen released. Another example is when a guitarstring is plucked it will vibrate at its natural frequencyto produce the sound we hear. The mechanicalnatural frequencies of a pipe or piping systemdepends on lengths, schedules, diameters, elbows,

supports, etc.

The static stiffness of a component helps to determineits mechanical natural frequencies (ie. the frequenciesof the different scrubber modes that are excited whena scrubber is struck once with a hammer). Thedynamic stiffness of the component approaches zeroat its mechanical natural frequencies (ie: the effectivestiffness of a scrubber when it is excited by anoscillating force at its natural frequency).


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Remembering the basic vibration equation, as thedynamic stiffness approaches zero the potential forhigh vibration increases.

Mechanical resonance of a piping component occurswhen a forcing function is applied at a frequency

corresponding to a mechanical natural frequency ofthe component.

If an oscillating force of constant amplitude is appliedto a system over a frequency range, the resultingvibration of the systems will vary. A schematic of atypical suction system is shown in Figure 1. Figure 2 Response of Suction Line Upper Elbow, illustrates theresponse of the suction line.

When the oscillating force is applied at afrequency below the natural frequency of thecomponent there will be some response.

As the frequency of the input forceapproaches the first mechanical naturalfrequency of the component the response ofthe system is greatly amplified. At this pointthe component is resonant.

The shape and the magnitude of theresponse peak is a function of the damping(analogous to electrical resistance) in thesystem. The more damping in the systemthe broader and lower the peak will be.Damping comes from flanged and boltedconnections, clamping, materialcharacteristics, etc.

When the forcing frequency is greater thanthe natural frequency of the component, theresponse of the system drops to very lowlevels.

As the frequency of the input forceapproaches the second mechanical naturalfrequency of the component the response ofthe system may again be greatly amplified.

Considering the typical response curve, componentsof a compressor system will have less response if the

natural frequencies are below compressor speed(components that have their natural frequencies belowcompressor speed are said to be undertuned).However, undertuning is not always possible in caseswhere the static stiffness is high. Also, by undertuningthe first mode, higher modes may become a problem.

As well, the magnitude of the forcing function typicallydecreases as frequency increases. If the componentnatural frequencies are above the frequencies ofgreatest input (ie. one and two times compressorspeed) the vibration levels should be acceptable,assuming the forcing functions are reasonably

controlled.

When a system, or part of a system, is mechanicallyresonant, normal (or even low) pulsation inducedunbalanced force levels can couple with the systemgeometry to produce very high vibration levels.

NOTE: Beta Machinery Analysis field experienceshows that the majority of the vibrationproblems encountered in reciprocatingcompressor installations is related tomechanical resonance, with most of theremaining problems related to acousticalresonance.

Mechanical Guideline

To avoid resonance at the predominant force inputfrequencies, the mechanical natural frequency of anypiping component must not be in the range of 1X or 2Xrun speed. With over 25 years of experience, BetaMachinery Analysis concludes that a minimum naturalfrequency of 30 Hz should be applied to piping closelycoupled to the cylinders (ie: bottles, scrubbers andpiping to the second pipe support). This is due to theinteraction of cylinder stretch, pulsation, torque andtorsional input forces. For all other piping and vessels

there is one of the following two mechanical guidelinesto consider.

Variable Speed Mechanical Guideline:

A mechanical analysis is to be performed on allsystems included in the acoustical models. Afinite element program is to be used todetermine the mechanical natural frequenciesof all vessels and attached piping. Allpredicted mechanical natural frequencies areto be greater than 2.4 times run speed. Theminimum mechanical natural frequency onpiping closely coupled to the cylinders is to be

greater than 30 Hz, or 2.4 times run speed,whichever is higher.


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Fixed Speed Mechanical Guideline:

A mechanical analysis is to be performed on allsystems included in the acoustical models. Afinite element program is to be used todetermine the mechanical natural frequencies

of all vessels and attached piping. Allpredicted mechanical natural frequencies forhigh speed units (900 RPM or over) are to beless than .8 times run speed or between 1.2and 1.6 times run speed or greater than 2.4times run speed. For low speed units, avoidmechanical natural frequencies below 30 Hzthat are within 20% of harmonics of runspeed.

Summary

Avoid resonance, avoid failure! The number one

cause of piping failure in the oil and gas industry todayis mechanical resonance. If you can avoid resonanceat the frequencies that have the highest input forces,then you are well on the way to having a smoothrunning installation. The above guidelines, whenfollowed correctly, do that.


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FIGURE 1


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FIGURE 2

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Fundamental Specifications for Eliminating Resonance on Reciprocating Machinery (13)