torsional and electrical dynamic interactions of

1

assignSouthHe alfrom Brandwhereelectr

MSMregist

B

ExxonMo

Consultant to

ABB IRa

nments. Brandhern Universitylso holds a M.SPurdue Univerdon has produce his research fronics, and gen

ME Degrees fromtered Professio

Com

Brandon CassimEngineering S

obil Upstream Houston, Tex

B. Fred EvaMachinery E

o ExxonMobil DHouston, Tex

Don E. MExecutive Co

Inc. Power Sysaleigh, North C

Brandon CasEngineering SUpstream ResTexas. He is research and technologies fapplications. Operating CoCorporation t

don received hisy A&M CollegeS. degree (2003rsity in Electricced journal & focus was elec

netic algorithm

B. Fred Evanmachinery enproviding mato various ongExxonMobil. Mfor Shell GlobSouthwest Resfield technicaproblems. Mr

m Texas Tech onal Engineer

Donald E. Mapower systemutilities and inExecutive Coninvolved in a consulting incfailure analys

Copyright

Torsiompressor Driv

mere, Ph.D. Specialist Research Com

xas, USA

ans. P. E. Engineer Development Cxas, USA

Martin onsultant stems Consultin

Carolina, USA

ssimere is presSpecialist for thsearch Companresponsible fordevelopment ofor ExxonMobiBrandon also s

ompanies of thethrough resears B.S. degree (e in Electrical 3) and Ph.D. dcal & Computeconference pu

ctrical machinems.

ns is a consultingineer responschinery enginegoing upstreamMr. Evans prebal Solutions, Bsearch Institutl services on dy

r. Evans receivUniversity (19in the State of

artin is currentm analysis consu

ndustrial systensultant for ABbroad range ofcluding reliabisis and special

t© 2013 by Tu

nal and Electrve Motors and

mpany

Company

ng

ently an he ExxonMobiny in Houston,r applied

of new electricail Upstream supports the e ExxonMobil rch application(2001) from Engineering.

degree (2008) er Engineeringblications

es, power

ng rotating sible for eering servicesm projects for eviously workedBP, and te, providing dynamics ed BSME and 74), and is a Texas.

tly providing ulting for ms as an

BB Inc. He is of studies and ility analysis, problems.

urbomachinery

rical Dynamicd Gas Turbine

l

al

n

g.

d

activeresponstanda ABST

Lmotorto inteElectrwere etorsiongeneratorsionelectridomai

Pro

Laboratory, T

c Interactions e Driven Powe

DPain

SoSa

e member on sensible for the cards and is a re

TRACT

Load induced por driven reciproeract with a gasrical current puevaluated to denal systems anator drive gear nal mechanicalical model of thin analysis of t

oceedings of the

Texas A&M En

of er Generators

E. Martin HPrincipal En

Dresser-Rand nted Post, New

Danny F. Sm

Manager Gearolar Turbines Inan Diego, Calif

Martin Hinchat Dresser-RaMartin has bevariety of Engcurrently a mforce and theCommittee.

Danny F. Smin MechanicaUniversity ofManager of Gis responsibleturbomachineand utilized aIncorporatedcontributionsconsulting an

everal AGMA tcreation of inteegistered profe

ower fluctuatioocating compres turbine driven

ulsations predicetermine the rend the potentialr teeth. The coml systems werehe interconnecthe dynamic in

e Forty-SecondOcto

ngineering Exp

inchliff ngineer Company

w York, USA

ith, P. E. r Systems ncorporated fornia, USA

hliff is a Principand in Paintedeen at D-R for gineering func

member of the Ae GMRC Projec

mith received hal Engineeringf California, SaGear Systems Ee for all of the ery gear systemat Solar Turbind. Mr. Smith has in the area ofnd forensic anatechnical commernational gearfessional engine

ons in a pair ofessor trains havn power genercted at the geneesponse of bothl for micropittinmpressor and ge modeled aloncting power systeractions.

d Turbomachinober 1-3, 2012,

periment Station

ipal Engineer d Post, NY. r 30+ years in actions. He is API688 task ct Supervisory

his B.S. degree g from the an Diego. As Engineering, h

ms designed nes as made f design, alysis. He is anmittees r design eer.

f synchronous ve been shownation source. erator terminalh mechanical ng of the

generator ng with an stem in a time

nery Symposiu, Houston, Tex

n

a

e

n

s

um xas

2

Copyright© 2013 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station

INTRODUCTION

A natural gas cycling facility is being constructed as an initial production system at the Point Thomson field on Alaska’s North Slope. Condensate produced from the reservoir will be sent by pipeline to join an existing pipeline at Badami and from there to the well-known Trans-Alaska oil pipeline. Approximately 200 MMCSFD of natural gas will be returned to the reservoir at 10,000 psi via two parallel, two stage, 10,000 HP reciprocating gas injection compressors. Power generation for the site is provided by four gas turbine driven generators. Two gas fueled units are rated at 7.9 MWe while the other two dual fuel units are fitted with waste heat recovery and produce slightly less power due to additional exhaust losses. The compressor trains consume approximately two thirds of the facility’s electrical load from the power generation system that is isolated from a power grid due to the remoteness of the site and operates in island mode.

Initial engineering reviews indicated the potential for large electrical current pulsations on the 13.8 kV bus due to the normal torsional characteristics of the reciprocating compressor trains. These current pulsations could interact with the generator and potentially exciting torsional natural frequencies of the gas turbine driven trains. One of the main concerns was the generator drive’s epicyclic gearing being exposed to torsional variations that could cause micropitting of the gear teeth. As part of the initial engineering for the compressor trains, the motor manufacturer performed initial screening calculations for current pulsation. It was predicted that the current pulsation amplitudes could exceed 20 percent under some operating conditions. Later, revised analyses by the motor manufacturer showed reduced values. Further analyses were required using a more refined calculation method to examine the expected interactions with the gas turbine generator trains.

Various compressor operating conditions were simulated via marriage of electrical and mechanical systems into a single digital model to determine the worst case scenario for evaluation and risk assessment. Results showed excitations imposed upon the generator torsional system at frequencies of compressor speed and its harmonics. Employing the refined methods, overall current and torque oscillations of approximately 4 percent of average values were predicted with the dominant frequency being 6 Hz, which is equal to compressor speed of 360 rpm. This is significantly lower than original predictions that exceeded 20 percent.

This paper describes the studies, results and recommendations the project team used to quantify the electrical current pulsation induced excitations and design precautions implemented to assure long-term reliable operation. The first part below provides the groundwork for understanding the concern for micropitting the generator drive train’s gear teeth. The second part discusses the typical individual torsional analyses of the compressor and generator trains. The third part illustrates the combined electrical and mechanical model and results derived for the interactions of two separate torsional systems coupled by an electrical bus.

GAS TURBINE DRIVEN GENERATORS – GRID-BASED VERSUS ISLAND-MODE

Gas turbine driven electric generators are installed worldwide to provide power to a variety of markets, but the two main sector divisions are the oil and gas industry and industrial power generation. In both of these markets, turbine generators span a continuum of applications that are bookended at the one end by those that are run against electrical grids and at the other end by those that are run in isolated island mode to provide the complete electrical energy needs for a particular location.

The differences in reactive loads experienced at the generator terminals between grid-based versus island-mode installations can lead to differences in the operating characteristics in terms of dynamic load fluctuations. In general, grid-based installations tend to be more stable, provided the grid is stable, and do not experience much in the way of dynamic loading at steady-state conditions. Island-mode installations run the gamut from stable to dynamic depending upon the equipment and processes at a site, but they generally tend to experience more dynamic loading than grid-based installations. Though these dynamic loads are usually well within the design capabilities of the electrical and mechanical sub-systems of the turbomachinery, they sometimes are significant enough in magnitude, frequency or duration to warrant closer engineering review.

The Point Thomson project is one such program that received additional engineering review. The items that led to this further consideration were: - This is an island-mode application where four gas turbine

generator packages will provide power for the entire site through a main 13.8 kV switchgear electrical bus.

- Two 10,000 hp synchronous motors driving two reciprocating compressors will make up a significant portion of the plant load seen at the electrical bus.

- The two reciprocating compressors will at times run with their mechanical linkages in phase and this is predicted to cause a mechanical torque pulsation that will feed back into the synchronous motors, then to the common electrical bus and then be experienced as torque pulsations by the mechanical components of the generator sets.

- The initial preliminary estimates of the resultant power fluctuations experienced at each generator shaft end indicated that they could be as high as 1.675 MW peak-to-peak at a frequency of 6 Hz – potentially for a significant portion of the equipment’s operating life.

- The site is in a remote, environmentally sensitive location on the North Slope of Alaska.

GAS TURBINE GENERATOR SETS WITH EPICYCLIC REDUCTION GEAR DRIVES

As mentioned above, four gas turbine generator sets were provided to the Point Thomson site (see Figure 1). Each of these features a custom-designed epicyclic reduction gear drive that sits in between the engine and generator. The epicyclic gearbox arrangement is advantageous in that it allows for

3


compact, in-line transmission of power from engine to generator (see Figure 2). Since it is one of the core sub-systems of the drive train, it was important to give it a robust review for this project.

From a gear design perspective, gas turbine generator sets are considered to be one of the smoothest running industrial applications having the smallest and least frequent dynamic excursions from nominal load induced on the gearing by the driving and driven equipment. This is reflected in the design phase by applying low overload/application factors as multipliers to the nominal design loads. The higher and more frequent the typical dynamic loads experienced by a gear unit in various applications, the higher the multipliers are to the nominal design loads. This covers the gross effects of externally induced dynamic loading on common load-dependent failure modes like fatigue (both surface and bending modes) and, to a lesser extent, scuffing and wear. A typical factor for the Point Thomson gas turbine driven generators is 1.1 (Radzevich and Dudley, 1994.)

Figure 1. Schematic of a Gas Turbine Generator Package at

Point Thomson (Courtesy of Solar Turbines)

Figure 2. Schematic of an Epicyclic Reduction Gear Drive at

Point Thomson (Courtesy of Solar Turbines)

In addition to the gross effects of dynamic loading on common load-dependent gear failure modes, if it is severe

enough, dynamic load changes can also disrupt the Elasto-Hydrodynamic Lubrication (EHL) film thickness between the gear teeth. This is particularly true in epicyclic gear units that have floating members that adjust their running positions in response to changing load vectors during dynamic load changes.

Testing of a typical gas turbine with an epicyclic reduction gear drive reveals that this adjustment to running position occurs regularly with instantaneous load step changes during normal operation of the equipment. Figure 3 shows two data plots from one of these tests. The bottom plot shows power versus time for various load steps that occurred during the testing of this package and the top plot shows resulting vibration amplitudes recorded from the reduction gear drive’s case-mounted accelerometer during the same period of testing. Note that for each load change shown on the bottom plot, there is a corresponding spike in acceleration on the reduction gear drive housing shown in the top plot. Over the years, related testing on various epicyclic gear units equipped with proximity probes has verified that these instantaneous changes in accelerometer readings correlate to instantaneous positional shifts of the floating internal gear members in response to changes in load vectors.

Normally, these positional adjustments of the floating gear members are seen as a good thing – floating capability is a mandatory feature that must be part of any sound epicyclic gear design if it is to have any chance at achieving an adequate service life. But experience in various other gear industries indicates that these shifts in loaded gear member position can also be accompanied by disruptions to the EHL film between the mating teeth (Heidenreich and Herr, 2012.) If these disruptions are severe and frequent enough, they can lead to another gear tooth failure mode called micropitting.

CONSIDERATION OF FAILURE MODES – IMPORTANCE OF MICROPITTING

Dynamic loading contributes to gross effects on common load-dependent gear failure modes that are easily accounted for, but dynamic loading can also have effects on more difficult to assess, less load-dependent failure modes like micropitting. Table 1 gives a listing of the five main gear tooth failure modes that could be affected by dynamic load fluctuations with a comparative summary of the mechanisms, the predictability, how they are accounted for in design rating of a gear set, and the probability of occurrence as a primary failure mode. Of all of the failure modes on the list, micropitting was seen as the one that needed the most careful consideration for the Point Thomson Project. The potential to have relatively large magnitude dynamic load fluctuations occurring for significant portions of the operating life of the equipment, along with the related positional adjustments of an epicyclic gear drive’s floating members, meant that there was a high potential for disruption of the EHL film thickness over these periods. This is why micropitting was seen as the failure mode having the most increased probability of occurring: unfortunately it also has the least degree of predictability.

Micropitting is a fatigue failure of the meshing surfaces of

Turbine Exhaust

Turbine Inlet

EpicyclicGearbox

Generator

4


a pair of gears characterized by smaller pits than are experienced when macropitting occurs (Drago, et al. 2010.) Pits on the order of 10 to 20 microinches in size can originate when local lubricant film thickness is insufficient. Localized contact of surface asperities fatigues the gear material. The surface asperities are a function of the gear manufacturing processes and range in size based upon the finishing techniques employed. Typically, it is expected that the EHL film will be thick enough to prevent contact between the asperities on one gear with those on a mating gear. Externally imposed dynamic loads that could disrupt the EHL film thickness was a major concern for the Point Thomson Project.

Figure 3. Test of Turbine Generator w/ Epicyclic Gear Unit Load Changes vs. Vibration (Courtesy of Solar Turbines) Much has been written about micropitting over the years

and a full treatment of it is beyond the scope of this paper, but there are several summary points that should be made:

- Micropitting is a relatively recent concern for gearing as it

has probably only been recognized as a separate failure mode since the early 1990’s. It occurred in gear applications since the 90’s. In most of these occurrences, it was usually called grey staining or frosting and was incorrectly identified as a

wear mechanism or sometimes confused with the more well-understood failure mode of macropitting.

- Many of the things that influence micropitting are well understood but there is not yet a reliable, internationally recognized method to predict a gear design’s susceptibility to this failure mode. The best approach available today is to compare ways to make a design more robust against this failure mode.

- Micropitting can occur in many different types of applications with completely different operational characteristics, but certain industries see it more frequently than others.

- Turbomachinery applications are not known to be very susceptible to this failure mode, but certain industries (for example, wind energy power generation, where the gear trains are regularly exposed to relatively large magnitude dynamic load fluctuations for significant portions of the operating life) are known to experience a relatively high frequency of micropitting issues.

Table 1. Failure Modes of Gear Teeth

Name Mechanism Predict-ability

Effect of Load Fluctu-ation

Probability of Occurrence

* Tooth Breakage Bending Fatigue Good

Increases Ka

Slightly Increased

Macro pitting

Surface fatigue (sub-surface) Good

Increases Ka

Slightly Increased

Scuffing Adhesion Fair Little Effect

Slightly Increased

Wear Abrasion Poor Disrupts EHL

NOT Increased

Micro pitting

Deformation/ Cracking of Surface Asperities Poor

Disrupts EHL Increased

*As primary mode of failure Taking all of the above into consideration, it was deemed

appropriate for the Point Thomson project to pursue some methods to mitigate risk and reduce the potential of encountering micropitting issues. One of the most important and proven ways to make a gear design more robust against micropitting is to put the finish-ground gear through a final superfinishing stage using a chemically accelerated vibratory process (Arvin, et al. 2002, Bell, et al. 2012, Errichello, 2011, Michaud, et al. 2011, Winkelman, et al., 2010.) SUPERFINISHING – IMPROVING MICROPITTING FACTOR OF SAFETY

Micropitting is known to be influenced by:

- Operating conditions (e.g., load, speed and sliding temperature)

- Lubricant conditions (e.g., viscosity, additive packages and cleanliness)

- Surface conditions (e.g., roughness, lay, texture)

For a given application, any number of the above items cannot be changed (e.g., load or speed or lubrication), but usually some of the items can be improved to reduce the risk of

5


micropitting. And as mentioned above, one of the proven methods of increasing a gear design’s capacity to withstand micropitting is to improve the surface through superfinishing. For a given design that is finish-ground, superfinishing can be used to improve the surface and greatly improve the margin against micropitting. Surface roughness quality is usually described by a Ra value which stands for roughness average and is one of several parameters used in gear tooth machined surface evaluation (Talati, 2011.)

Typically, precision high-speed turbomachinery gearing is case-carburized and finish-ground. The grinding process usually achieves a surface finish with a roughness of between 32 and 20 micro-inches Ra. The surface is characterized by long shallow peaks and valleys in the direction of the grinding wheel travel (see Figure 4) and the carburized peaks represent sharp, discontinuous, brittle asperities that can serve as initiation sites for micropitting.

Chemically accelerated vibratory superfinishing, is a benign finishing process that removes these peaks and leaves the surface of the gear tooth smooth, neutral and free of initiation sites for micropitting. Surface finishes achieved with superfinishing are typically on the order of less than 4 micro-inches Ra; less than 1 micro-inch is readily achievable, depending upon the needs of the application.

Figure 4. Carburized Ground Gear – Micropitting Initiates on

Grinding Mark Peaks (Courtesy of Solar Turbines)

ISO/TR 15144-1 (2010) provides a method for evaluating and calculating a safety factor against micropitting. Equation (1) is as follows:

GF, min, min

GFPS S

(1)

Where, S is the safety factor for micropitting GF,min is the minimum specific lubricant film thickness in

contact area GPF is the permissible specific lubricant film thickness S,min is the minimum required safety factor for micropitting

One thing to note about this calculation is that it assumes that the permissible specific film thickness is known. Thus, it assumes that there is a way to calculate it or to know if a given design is on the cusp of micropitting. However, one can also use this equation to calculate a comparison of micropitting safety factors for gears finished with a superfinishing process versus as-ground finishes. Since the specific film thickness is defined as the actual EHL film thickness divided by the effective mean surface roughness, in a given application where the actual EHL film thickness is the same regardless of finish, the film thicknesses cancels out. What is left is the ratio of the reciprocals of the two different effective mean surface roughness values for before and after superfinishing. This yields a comparative safety factor against micropitting. Another way to look at it would be as a margin of increase. Table 2 compares two typically achievable surface roughness values for superfinishing (e.g. Ra=4 and Ra=1) against two typically achievable surface roughness values for as-ground gears (e.g., Ra=32 and Ra=20).

Thus, if an as-ground gear design at 32 micro-inch surface roughness were on the cusp of micropitting (i.e., the safety factor 1.0), switching to an superfinishing process that achieved a surface roughness of 4 micro-inches would yield a safety factor of 8.0 which is an 8X margin of increase.

Table 2. Micropitting Safety Factor Comparison (ref. ISO 15144-1, 2010)

Compare SF = (1/Ra, SF) / (1/Ra, Ground)

Ratio SF to 32 micro-inches

Ratio SF to 20 micro-inches

@Ra, SF = 10 3.2 2.0

@Ra, SF = 4 8.0 5.0

@Ra, SF = 1 32.0 20.0

MECHANICAL SYSTEMS Reciprocating Compressors

The two parallel, two-stage, four cylinder, natural gas compressors are a four-throw, horizontally-opposed design driven at 360 RPM by direct coupled synchronous motors. The synchronous drive motors are a single bearing design that attaches to the compressor flywheel. First stage suction pressure is approximately 2,600 psi and final discharge pressure is 10,000 psi. Capacity control is achieved via a recycle arrangement capable of 100 percent flow. At design operating conditions, the compressors consume approximately two-thirds of the electrical power being generated on site.

The action of the reciprocating mechanisms in the injection

6

compsignifcompangulrevoluvibratdrive back

Icriticafrequtypicaare +/other naturawas wshowand +therefmotiodampcompconsitorsio

F

Acompof fulmachis 66 Thesetargetreasodesigcurrenunderor disMinimits im

pressors producficant amplitudpressor crankshlar variation ofution. The oscition excitation motor and cauinto the power

It is common toal machinery tr

uencies and sysal and worst ca/-10 percent focompressor or

al frequency (Twell situated ben in Figure 5. T

+6.9 percent resfore, the effecton with the inerping is very lowpressor manufadered the comp

onal vibration s

Figure 5. Camp

According to Apressors, the elell load torque f

hines. A limit ispercent for bote values providt for robust manable values fon. Initial predint pulsations cr some operatinscharge pressurmizing the curr

mpact on other s

ces a crank effode variation thrhaft. This, in tuf the drive motoillatory torsionapplied to the

uses electrical cr supply systemo perform a torrains to determtem response t

ase conditions. or compressor srders up to the TNF) was deteetween the 7th aThe calculatedspectively. Thet on current pulrtia helping to

w and thus has acturer performpressor train tostandpoint.

pbell Diagram

API 618 (2007)ectrical currentfor synchronous also publisheth synchronousde compressor achine design, bor the Point Thctions by the mould exceed 20ng conditions (re approachingrent pulsation asystems is desi

Copyright

ort torque that rough one revourn, creates an oor rotor during

nal energy acts hard-coupled

current pulsatiom. rsional analysis

mine torsional nto operating loaRequired sepa

speed and +/-5 tenth. The firsrmined to be 4and 8th compre

d separation mae machine is tolsation is primacontrol the pula negligible ef

med the torsionao be acceptable

for Injection C

for reciprocatit pulsation limi

us and 40 perced in NEMA Ms and inductionand motor venbut do not nece

homson facilitymotor manufact0 percent and c(e.g., crank endg piping relief vat the source anirable.

t© 2013 by Tu

has a olution of the oscillatory

g each as a forced synchronous on that is fed

s for most natural ads under aration marginspercent for t torsional

44.9 Hz which essor orders as argins are -6.4 orsionally stiff;arily rigid bodylsation. Systemffect. The al analysis and e from a

Compressor

ing it is 66 percent

ent for inductioMG1 (2011) and

n machines. ndors with a essarily reflect y’s island modeturer indicatedcould be higherd valve failure valve settings. nd evaluating

urbomachinery

s

y

m

t n

d

e d r

Nreciprodata (nthen cinertia

Mis donobtainthen adetermelectri

Tis smafrequespeed.first foconsidcomprerror waccuratorsion

Aunloadcomprtwo arseverelimitedmainte - Norm- Ope

case- Ope- Ope

Tcalcul4.4; 5.full lovaluesinvestcurrensystem Gas T

Sfour gturbinepicycpercenrecovefour g

Tthe gefreque

Ttorsionare sh

Laboratory, T

Normal practiceocating comprneglecting mas

calculates the ca as a rigid bod

Much later in thne to obtain thened. The displaavailable, and pmine current puical lag (rotor t

The error using all for the normency is well ab. Note that dueour harmonics derations. If theressor train wewould be largeate current pulsnal analysis (ro

A robust designders and there ressor conditiore valve failuree cases that thed period of timenance.

mal full load oeration at final de) eration with a faeration with a fa

The compressorlated current pu.1; 9.3; and 15

oad operation vs predicted by ttigation was want pulsations wm.

Turbine Generaite power for th

gas turbine-drivnes are connectclic gearbox. Unt of the year, fery is employe

generators are cThe turbine manenerator drive tencies shown in

Two areas of intnal natural freq

hown on the Ca

Texas A&M En

e is that currentressor train is dss-elastic effeccurrent pulsatiody to smooth thhe project the ce true torque puacement amplitprovides the moulsation becausto rotating magthe rigid body

mal case that thbove the fourth e to flywheel efthat are of intee first torsiona

ere low (certaine and the only wsation would botor angular di

n is needed. Evare no alternat

ons, (listed beloe cases which ae compressor mme until it can b

operation discharge relie

failed 1st stage dfailed 2nd stage

r manufacturerulsation amplit.9 percent, resp

value of 4.4 perthe motor manarranted to det

with the turbine

ators the Point Thomven electrical gted to the 1800 Under normal ofour generators

ed to provide prconnected to a nufacturer perftrain that revean Table 3.

nterference betwquencies and tyampbell Diagra

ngineering Exp

t pulsation on done with the ccts). The motoron using the enhe current pulsacompressor torsulsation on the tude of the motost accurate mse it accuratelygnetic field). y assumption nohe first torsiona

harmonic of cffect, it is normerest for currenl natural freque

nly if less than way to calculat

be to use the ouisplacement FFen though therte operating conow) were consiare not uncomm

may need to opebe shut down f

ef valve pressur

discharge valvdischarge valv

r’s torsional antudes for these pectively. Whircent was belownufacturer, furthermine the inteand generator

mson facility is generators. The

RPM generatooperating condis are online. Wrocess and buil13.8 kV switch

formed a torsioaled the torsion

ween the seconypical potentiaam in Figure 6.

periment Station

a motor drivencrank effort r manufacturer tire train ation. sional analysismotor shaft is

tor rotor is alsomeans to y represents the

ormal method al natural compressor mally only the nt pulsation ency of the 4x) then the te a reasonably

utput of the FT). re are no nditions, four idered. The lasmon but are erate at for a

for

re (max power

ve ve

alysis includedfour cases of:

ile the normal w the original her eractions of thetorsional

provided by e single shaft ors by an itions for 66

Waste heat lding heat. Thehgear bus. onal analysis ofnal natural

nd and fourth al excitations . The

n

n

o

e

y

t

r

d

e

e

f

7

separwhileForcevendobe acforcintransmfrequ

Ta

T

take iinjectHoweelectrneedemanuscrutianalyrobuscurren

F PRIO

Cmachdynamthe intorsioThompublicof LCal., 202009.

ration margins e the required sed torsional vibor showed the ceptably low. Ing functions ofmitted torque a

uencies.

able 3. TurbineMode

1 2 3 4

The initial torsiinto account extion compressoever, predictedrical system byed to be addresufacturers’ currinized closely.

ysis techniques,st analysis wount pulsations o

Figure 6. Camp

OR MODELIN

Creating couplehinery to study mics during opndustry but is nonal analyses emson gas compcations have de

CI and PWM de008, Rotondo e.) The typical e

were +1.0 and separation margbration analyseshaft stresses dIn these analysf between 0.5 aat 1x and 2x of

Generator TorFrequency,

19.15 60.61 116.02 228.70

ional analysis bxcitation from ior drive motorsd current pulsaty the compressossed. The motorent pulsation aWhile no flaw, it was determ

uld be required on the gas turbi

pbell Diagram f

NG HISTORY

ed electrical-mthe effects of s

peration has beenot as common xpected to be pressors and poealt with variabesign (Szolc anet al., 2009, Feexcitations stud

Copyright

-9.5 percent, rgin was +/- 10

es performed bydue to these intses it is commoand 2.5 percentf shaft speeds a

rsional Natural, Hz Fre

by the turbine vinteractions bes and the genertions imposed uors became a cr and compres

amplitude predws were pointedmined that a mo

to assess the imne generator d

for Gas Turbin

Y

mechanical digitsteady state anden performed pa subject as th

performed for twer generatorsble speed drivend Pochanke 2eese and Maxfidied deal with h

t© 2013 by Tu

respectively, percent.

y the turbine terferences to on to assume t of the and line

l Frequencies equency, cpm

1149 3637 6961

13722

vendor did notetween the rators. upon the concern that sor

dictions were d out in the re refined and mpact of the

drive trains.

ne Generator

tal models of d transient previously in he usual the Point s. Several e motors, both 011, Hutten et eld 2008, Sihleharmonics

urbomachinery

t

er

generarespontechnimethothat resystemtechnithat dymodelthree sgeneraresultsorigintorsionselectedifferehandlisystemsimulaoil and ANAL

Inmanufof the mode by comand mcharacEnginmodelphase.one ovfrequefrequemechainertiageneralumpelumpefor theresultsmodeltorsioncompr

Tdrive mapplieoperatfrequecomprbe obsharmoof the withoumanufamplit

Laboratory, T

ated within thense of a single iques include mods of finding sepresent electrim being studiedique was requirynamically couls (compressorsets of electricaator and balancs would illustra

nating in the conal vibration aed analysis tooential equationing multiple elms and their coator used in stud gas industry

LYSIS AND R

nitial torsional facturers emplocompressor anshapes and ste

mmon Eigen anmotor manufactucteristics of the

neering Procureled the balance. All of these inverall system mencies of conceencies of the twanical models wal masses and tator torsional med masses respeed masses (Figue time step anas in the frequenl was exercisednal natural freqressor and turb

The crank effortmotor interface

ed as an excitatting at a normaency seen in thressor running served in the tionic content of

crank effort fout mass elasticfacturer to calctudes. Table 5

Texas A&M En

e power convermechanical sy

modal frequencsolutions to setical and mechad. For the Poinred that wouldupled two mecr train and gas tal models (synce of plant elecate the interact

ompressor and mat the generatorol represents anns in the time dectromagnetic

ontrols. It is anaudying and des(Dommel, 196

RESULTS

modeling by thoyed discrete, nd generator tready state forcenalysis and moturers also modeir machines duement and Cone of plant electrndependent momodel as shownern involved thwo mechanical were reduced ttorsional springmodels originaectively, whichure 8.) This red

alysis without sncy range of ind to verify it prquencies as thebine manufactut torque at the e shown as a tition input to thal steady state che time wave is

speed of 360 rime wave also.f the torque calor each individc effect. This wculate the initiashows the outp

ngineering Exp

rsion electronicystem. The analcy domain and ts of differentiaanical portions nt Thomson mad provide a timehanical torsionturbine generat

nchronous motoctrical system.)tions between emotor and resur drive gear’s snd solves the redomain. It is cap

and electromealogous to a prsigning process69, Wilson, 200

he compressorlumped mass eains. Natural fred responses wodal methods. Tdeled the electruring design. T

nstruction (EPCrical system inodels were inten in Figure 7. S

he lowest torsiosystems, both

to fewer equivags. The comprelly consisted oh were reducedduced the comsacrificing accunterest. The overoduced the same initial analyseurers. compressor flyime wave in Fi

he overall systecondition. Thes 6 Hz which corpm. Higher ha Table 4 illustrculated as a ve

dual compressowas used by theal current pulsaput of the comp

periment Station

cs and the lysis time domain

al equations of the overall

achinery, a e-step solutionnal mass elastictor train) with or, power ) The required excitations ulting forced hafting. The elevant

apable of echanical rocess s units in the 05.)

r and turbine elastic models frequencies, were determinedThe generator rical The project’s C) contractor n its design egrated into Since the onal natural mass elastic

alent lumped essor and

of 18 and 10 d to 4 and 5

mputation time uracy of the erall system me first es by the

ywheel and igure 9 was

em model whilee dominant orrelates to armonics can rates the ector addition or throw e motor ation pressor

n

c

d

e

8

manushaft differlow h(espebetwe

FGen

T

displadegrepoles polesone furotativibratwhichmotorgive aalongrefineat norcompdisplaprimapulsapulsagenerexcita

Cseparvibratof thecompby the

ufacturer’s torson the motor s

rences in Tableharmonics and cially near the een the seventh

Figure 7. Comnerators and Tw

Table 6 shows acement at the ees. Note there in an electrica, there are 20 t

full revolution ong magnetic fitory displacemh equals 4.44 pr is not linear wa good first ord

g with the harmed calculationsrmal operating

pressor torsionaacement harmoarily at 1x motoation at the thirdations in the marator terminals ation of the gasComparison of ration margin btory displaceme gas turbine gepressor was note gas turbine m

ional analysis side of the flywes 4 and 5 due tthe magnificatcompressor fir

h and eighth or

mbined System wo Compressor

the resulting vmotor rotor exare 180 electri

al motor. As thtimes, 180 equaof the motor. Inield by 36 elect

ment is 1.6 deg percent. Cautiowith load and cder approximat

monic content. T revealed a cur load which shal analysis. Froonic strength shor speed but thd and fourth haain 13.8 kV buand its magne

s turbine and gf Tables 3 and 6between the thiment and the fir

enerator train. t considered in

manufacturer. A

Copyright

for the torque iwheel. There arto the flywheeltion of the highrst torsional narders of running

Model for Thrrs Online (Cou

ibratory peak-txpressed in P-Pical degrees beis synchronousals 3,600 electrn this motor, thtrical degrees awhich is 1.6 di

on, the torque vcurrent; howevtion of the currThe motor manrrent pulsation hows good agreom Table 6 the hows that currehere is significaarmonics. The s in turn act at tic field as a fo

generator drive 6 shows a +6.3rd harmonic ofst torsional natThis excitationthe original to

Applying this e

t© 2013 by Tu

in the motor re some l smoothing th

h harmonics atural frequencg speed.)

ee Turbine urtesy of ABB)

to-peak (P-P) P electrical etween adjacens motor has 20 rical degrees inhe rotor lags that full load. Thivided by 36,

vs. lag of the ver, this does rent pulsation nufacturer’s of 4.4 percent

eement with throtor

ent pulsation isant current current the electric

orced torsional train.

39 percent f motor rotor tural frequencyn from the orsional analysiexcitation

urbomachinery

e

y

)

nt

n he e

e

s

y

is

indepemodelshaft s

Soveralcomprvariabof comwinteroperatbest anpulsatoutputvariabundersgenerathe gethe ge

Laboratory, T

Figure 8. RedSolar Turb

endently to thel in the manufastress. Howeveince there are tll compressionressors was incbles studied incmpressors onlinr (7.2 vs. 4.5 Mting conditionsnd worst case stion range. Whts of any calcu

ble as a functiostanding the cuator drive gearenerator terminearbox output a

Gas T

Mo

Texas A&M En

duced Torsionabines and Dress

e gas turbine geacturer’s analyer, the concern two parallel co

n system, the recluded as a varcluded number ne and balance

MW). These vas listed above wscenarios to br

hile the analysisulated electricalon of time, the ourrent pulsationring are the dynnals and the torand generator in

Turbine Gener

otor Compresso

ngineering Exp

al Models (Couser-Rand Comp

enerator forcedsis did not predfor micropittin

ompressors repelative phasing riable in the an

of generators e of plant load iariables along wwere employedracket the antics tool is capabll or torsional moutputs of intern severity and namic signals oque in the shafnput.

rator Reduced

or Reduced

periment Station

urtesy of ABB,pany)

d vibration dict excessive ng of remained

presented in thebetween the alysis. Other online, numbein summer vs. with the four d to determine cipated current le of delivering

mechanical rest for its impact on

of the power atfting between

n

d. e

r

g

t

9

F Table

H

Tab

H

T

operawere cylindCase loadeload epredicseconwave figure(recipvery n18 anand fo

Figure 9. Comp

e 4. Crank EffoHarmonic

1 2 3 4 5 6 7 8

Total

ble 5. CompresTorque a

Harmonic

1 2 3 4 5 6 7 8

Total

The system moating condition in phase, i.e., eder number on1 and is for a w

ed turbine and tequally. Figurected at the gen

nd time period. for the same tes show a domprocating compnoticeable. The

nd 24 Hz by FFfourth harmonic

pressor Crank E

ort Torque HarmFrequency

cpm 360 720 1080 1440 1800 2160 2520 2880

ssor Torsional as Percent of T

Frequency cpm 360 720 1080 1440 1800 2160 2520 2880

odel was exerciwas found to b

each compresse at the same twinter facility two turbines she 10 illustrates nerator terminal

Figure 11 illuime period as s

minant 6 Hz freqpressor speed) e higher harmo

FT analysis whcs of compress

Copyright

Effort Torque T

monic Content4HH

Crank Eff9014203001

34.

Output FFT ofTransmitted To

4HHTorsional S

70152651520

52.

ised and a worsbe when the twor reaches top ime. This is reelectrical load haring the remathe power flucls for this case strates the shafshown in Figurquency componwith higher ha

onics were deteich correlates wsor speed. The

t© 2013 by Tu

Time Wave

t at 360 RPM HE-VLffort FFT, %9.04 0.00 4.56 0.96

3.22 0.00 0.54 1.91 .50 %

f Shaft Motor rque

HE-VLShaft FFT, %7.60 0.91 5.11 6.68

5.64 1.01 5.14 0.50 .75 %

st case normalwo compressors

dead center offerred to as with one fully

aining facility ctuations for a one

ft torque time re 8. Both nent

armonic contenermined to be with the third slight

urbomachinery

s f

y

nt

amplitis due

Tab

Harm

12345678

TotNote: rotor tvector

Tthe moimpactwo covariouphase comprgeneraperceninitial that mcomproscillain-lbf torque

Tsome througarrangonlineamplitcomprthe resOverasystemrelativfor eac

FFinput scompoamplitthe 18conditHz comcould overal144 de

Laboratory, T

tude difference to the unequal

ble 6. CompresVibratory Dis

monic Frequcpm

3602 720

1084 1445 1806 2167 2528 288talHarmonic stre

to magnetic fier addition due t

Table 7 lists somodel for severact of relative phompressors waus response freto out-of-phas

ressors, Case 1ator terminals wnt of the generapredictions us

matches fairly wressor manufacation in the genwhile the trans

e oscillation is Table 7 is separ

data repeated fgh 15.5, and 9)gements of the e. Having two ctude for normaressors there casulting power o

all, the cases inm response to tve phasing for tch compressorFT analyses ofshaft are illustronent is seen totude from in ph

8 and 24 Hz comtion but do notmponent. If thbe accurately cll torque oscillaegrees between

Texas A&M En

es in the three tl loading on th

sor Torsional Osplacement in ency 4H

m RDispl

00804000602080

ength is the rotoeld full load lagto phase angles

me of the resulal of the cases thasing (TDC oas investigated.quencies’ amp

se. For in phase1, peak to peak were predictedator power - cosing other less well with the 4.cturer’s torsionnerator/gear shsmitted torque 3.9 percent of

rated into severfor clarity. The) compares wintwo compressocompressors inal operation. Atan be addition oscillations see

n the first groupthe variation inthe possible phr. f the torque timrated in Figureo have a monohase to out of pmponents are tt show the sam

he relative phascontrolled for ations could ben top dead cent

ngineering Exp

traces in each ohe generators.

Output FFT of P-P Electrical HHE-VL

Rotor P_P lacement, deg

1.230 0.038 0.254 0.282 0.040 0.004 0.024 0.068

1.6 or P-P displaceg; harmonics ars.

lts developed bthat were invesf cylinder num. This demonst

plitudes changee operation of tpower oscillat

d to be 0.28 MWonsiderably lowsophisticated t.4 percent fromnal analysis. Thhafting is shown

is 342,000 in-f the transmittedral groupings oe first group (canter loads for vors with three n phase yields tt different phasor cancelling oen at the generp show the varin the two comphasing between

me waves at thee 12 for these ctonically decrephase operationthe highest for

me decreasing psing between theach motor stae minimized atter of cylinder

periment Station

of these figure

f Motor Rotor Degrees

4HHE-VLHarmonicStrength,

%3.420.110.710.780.110.010.070.19

4.44 %ement/36 deg re added by

by exercising stigated. The

mber 1) of the trated how the ed from in the tions at the W. This is 3.9 wer than the techniques but m the he P-P torque n to be 13,460 lbf. Thus the d torque. of cases with ases 1, 15.1

various phasinggenerators the highest sing of the of harmonics inrator terminals.iation in

pressors’ n motor poles

e first generatocases. The 6 Hzeasing n. However, an in phase attern as the 6

he compressorsart-up, the t an angle of number 1 for

n

s

Lc,

g

n

or z

s

10

the twthat threlativcontin

Figu

Figu

T

loads genergenerthus tvalve

wo compressorhe two compreve phasing so tnually subjecte

ure 10. Power O

ure 11. Torque a

The second gro and four vs. thrators will be orator online casthe controlling e failure scenar

rs. There is not essors always wthe design mused to the worst

Oscillations at for Cas

Oscillations inand Generators

oup in Table 7 chree generatorsonline for 66 pese shows highecase. The third

rios. The higher

Copyright

a reliable methwill operate witst be robust enocase condition

Each Generatose 1

n Shafting betws for Case 1

compares wints online. Whileercent of the timer amplitude red group compar amplitudes sh

t© 2013 by Tu

hod to assure th the same ough to be n (case1).

or’s Terminals

ween Gearboxe

ter and summere four me, the three esults and is ares compressohown would

urbomachinery

s

r

or

only eT

that ingeneratorsionexcitawas prreferenturbinin anofor thetorsiongearboreducepercen10,100The poresultidue tothe ge

Figu

POTE

Nsystemassessassesseach pthe riswere nconsid

T - Impr

---

- Isola-

Laboratory, T

exist for a shortThe last group cncludes a lowerator train. Sincnal natural freq

ation at 18 Hz predicted becaunced above. Co

ne generator traother remotely e Point Thomsonal stiffness ofox, the first tored to 15.66 Hznt. The torque 0 in-lbf but theower oscillatioing torque osci

o the softer couear by somewha

ure 12. FFT AnFunction of C

ENTIAL SYST

Now that an anam, various systs effectiveness sment was condpotential modifsk assessment wnot deemed feaderable redesig

The potential m

rove gear tolerImproving Increase oilGearbox m

ate oscillatory Increasing p

Texas A&M En

t time until thecompares the or first natural f

ce the gas turbiquency was 19played a role inuse of the insufonsidering tors

ain that are duelocated machinon Project, it isf the coupling brsional natural z yielding a seposcillations in

e power oscillaons were reducillations were rupling transmittat isolating it f

nalyses ResultsCompressor R

TEM MODIF

alysis tool wasem modificatioin reducing thducted with allfication. Due towas performedasible (markedgn of the facilit

modifications w

rance to torsiontooth surface fl film thicknes

modifications – energy within polar mass ine

ngineering Exp

e compressor isoriginal case 1 wfrequency for thine generator sy9.2 Hz, the torsn how severe thfficient separatisional excitatioe to forcing funne is not comms necessary. Bybetween the gefrequency of th

paration marginthat shafting a

ations are almoed by only 1 preduced by 25 pting less oscillfrom the genera

s of Torque TimRelative Crank P

FICATIONS

available to evons could be ine response ampl involved parto the project tim

d, several of thed as NF below) ty.

were categorized

nal oscillationsfinish (superfins on gear teethframe size incrinjection comp

ertia – NF

periment Station

s shut down. with a case he gas turbine ystem’s first ional he response ion margin ons of the gas nctions rooted mon. However,y reducing the enerator and thhat system is n of -12.96 are reduced to st constant. ercent but the percent. This iatory torque toator inertia.

me Wave as a Phasing

valuate the nvestigated to plitudes. A riskies to evaluate meline when e modificationwithout

d as follows:

s by nishing) h rease – NF pressor by

n

e

s o

k

s

11


- Compressor modifications – 6-throw vs. 4-throw crankshaft – NF

- Motor modifications – two bearing motor with torsionally softer shaft; induction motor – NF

- Coupling modifications – torsionally soft and/or damper couplings – NF

- Reducing oscillatory energy in the electrical system by - using VFD motors for compressor drivers – NF - Using static electrical filters to detune frequency – NF

- Isolate oscillatory energy within the generator train (prior to the gearbox) by

- Increasing mass inertia of the generator windings – NF - Generator modifications – flywheel addition – NF - Judiciously torsionally tune coupling between gearbox

and generator - Provide spare gearbox and store on site SELECTED MODIFICATIONS

- Improve gear teeth surface finish with superfinishing

- A margin increase of 8x was achieved (see Figure 13)

- Increase lube oil viscosity to increase EHL film thickness - Change the lube oil for the gas turbine generator from

ISO VG 32 to ISO VG 46 - Increase polar mass inertia of the compressor flywheel which

was implemented early in the project - The flywheel polar mass inertia was increased as much

as possible within the starting constraints of the motor prior to investigating the current pulsations

- Tune the torsional stiffness of the coupling between the gearbox and generator to provide additional separation margin between the first torsional natural frequency and the external excitation at 18 Hz

- The coupling torsional stiffness was reduced from 122E6 in-lbf/radian to 54E6 in-lbf/radian

- Provide a spare gearbox stored onsite - Due to the remoteness of the Point Thomson site on the

North Slope of Alaska, and the long delivery time for a new gearbox, a new spare gear box was purchased. Any anticipated gear failure because of micropitting was considered to be contained within the gearbox casing

Figure 13. Example of Tooth Surface Roughness Before and After Superfinishing (Courtesy of Solar Turbines Figure 13 shows actual measurement examples of one of the Point Thomson epicyclic gear’s tooth surface finish before and after chemically accelerated vibratory superfinishing. The upper trace before superfinishing has an Ra of 19.3 while the lower trace after superfinishing has an Ra of 2.4. This example illustrates an increase in safety factor for micropitting of 8.1x according to a ratio of Equation (1) applied before and after

superfinishing. While the example may not show measurements at exactly the same tooth profile location, sufficient before and after measurements were recorded to confirm the safety margin improvement was achieved. The after trace is on a different vertical scale, such that a more pronounced effect is actually achieved than is evidenced in a visual review of Figure 13.

12


Table 7. Partial Summary of Cases Investigated

Case Facility

Electrical Load

No of Comprs. Online

Two Compressor Phase Angle Shift of

Motor Torque Pulsations degrees

No of Gens. Online

Peak-to-Peak

Generator Power

Oscillation kW

Peak-to-Peak

Generator/Gear

Torque Oscillation

in-lbf

Compressor Operation

1 Winter 2 0 In Phase 3 278 13460 Normal15.1 Winter 2 18 3 249 11933 Normal15.2 Winter 2 36 3 225 8170 Normal15.3 Winter 2 72 3 196 10309 Normal15.4 Winter 2 108 3 159 9959 Normal15.5 Winter 2 144 3 107 5980 Normal

9 Winter 2 180 Out of Phase 3 68 7310 Normal

1 Winter 2 0 In Phase 3 278 13460 Normal2 Summer 2 0 In Phase 3 272 13032 Normal5a Winter 2 0 In Phase 4 220 10470 Normal7 Winter 1 0 In Phase 3 157 7578 Normal

16 Summer 2 0 In Phase 3 380 16500 1st Stage

Valve Failure

16 Summer 2 180 Out of Phase 3 200 11400 1st Stage

Valve Failure

17 Summer 2 0 In Phase 3 540 21500 2nd Stage

Valve Failure

17 Summer 2 180 Out of Phase 3 350 16100 2nd Stage

Valve Failure

1 Winter 2 0 In Phase 3 278 13460 Normal18 Winter 2 0 In Phase 3 275 10100 Normal

CONCLUSIONS Based upon the analysis of the current pulsations for the

combined electrical and mechanical systems the following conclusions can be stated:

- Significant electrical system current pulsations are not

normally present nor a concern in machinery systems similar to those at Point Thomson since reciprocating compressor loads are typically small compared to grid size. Thus they are not normally checked when dynamic analyses such as torsional natural frequency and forced vibration calculations are made. The fact that this phenomenon exists for the Point Thomson Project is unique because this is an electrical island with the reciprocating compressor being the major load on the generator.

- Electrical system pulsations do not normally cause significant torsional vibration, but in this case a torsional resonance condition exacerbated the situation as very little damping is available to control maximum response amplitudes.

- The turbine and gear manufacturer expressed concern for micropitting failure in the gearbox in its drive train due to

power fluctuations imposed upon the generators’ terminals by the injection compressor drive motors.

- Current and power pulsations have been adequately modeled between the injection compressor drive motor and the power generators. The predicted amplitudes are much lower than originally reported by the motor manufacturer but were sufficient to warrant closer engineering review.

- The modeled system’s worst case power pulsation was predicted to be 0.28 MW under normal operating conditions.

- The effects of the predicted 0.28 MW power pulsation could be reduced by generator train coupling stiffness tuning.

- Relative phasing (misalignment of TDC) of the two injection compressors during operation can reduce the power oscillations. However, the degree of misalignment cannot be controlled, so a worst case scenario of in phase operation must be assumed for continuous operation.

- Superfinishing can be used as a benign method to improve gear tooth surface finish and increase the margin of safety against micropitting.

- Operating with all four gas turbine generators online reduces the predicted torsional excitation experienced at the gear

13


teeth. However, maintaining sufficient load on the turbine to achieve emissions requirements must be considered.

REFERENCES API 618, 2007, “Reciprocating Compressors for Petroleum,

Chemical, and Gas Industry Services,” Fifth Edition, American Petroleum Institute, Washington, D.C.

Arvin, J., Manesh, A., Michaud, M., Sroka, G., and Winkelman, L., 2012, “The Effect of Chemically Accelerated Vibratory Finishing on Gear Metrology,” Technical Paper 02FTM1, American Gear Manufacturers Association.

Bell, M., Sroka, G., and Benson, R., 2012, “The Effect of Surface Roughness Profile on Micropitting,” Technical paper 12FTM20, American Gear Manufacturers Association.

Dommel, H. W., 1969, “Digital Computer Solution of Electromagnetic Transients in Single and Multiphase Networks,” Transactions on Power and Power Apparatus and Systems, Institute of Electrical and Electronics Engineers, PAS-88, pp.388-399.

Errichello, R.L., 2011, “Morphology of Micropitting,” Technical Paper 11FTM17, American Gear Manufacturers Association.

Drago, R. J., Cunningham, R.J., and Cymbala, S., “The Anatomy of a Micropitting-Induced Tooth Fracture Failure – Its Causation, Initiation, Progression, and Prevention,” Gear Technology, June 2010, pp.63-69.

Feese, T. and Maxfield, R., 2008, “Torsional Vibration problem with Motor/ID Fan Due to PWM variable frequency Drive,” Proceedings of the Thirty-Seventh Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, Texas, pp. 45-56.

Heidenreich, D. and Herr, D., 2012, “Why Gearboxes Fail and a Solution to Lower Drivetrain Costs,” Windpowerengineering.com, October, 2012.

Hutten, V., Zurowski, R. M., and Hilsher, M., 2008, “Torsional Interharmonic Interaction Study of 75 MW Direct-Driven VSDS Motor Compressor Trains for LNG Duty,” Proceedings of the Thirty-Seventh Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, Texas, pp. 57-66.

Michaud, M., Sroka, G., and Winkelmann, L., 2011, “Chemically Accelerated Vibratory Finishing for the Elimination of Wear and Pitting of Alloy Steel Gears,” Technical Paper 01FTM07, American Gear Manufacturers Association.

ISO TR 15144-1, 2010, “Calculation of Micropitting Load Capacity of Cylindrical Spur and Helical Gears — Part 1: Introduction and Basic Principles,” First Edition, International Organization for Standardization, Geneva, Switzerland.

NEMA MG1, 2011, “Motors and Generators,” National Electrical Manufacturers Association, Rosslyn, VA.

Radzevich, S. P. and Dudley, D. W., 1994, Handbook of Practical Gear Design, Boca Raton, Florida: CRC Press.

Rotondo, P., Andreo, D., Falomi, S., Jorg, P., Lenzi, A., Hattenbach, T., Fioravanti, D., De Franciscis, S., 2009, “Combined Torsional and Electromechanical Analysis of an LNG Compression Train with Variable Speed Drive System,” Proceedings of the Thirty-Eighth Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, Texas, pp. 93-102.

Sihler, C., Schramm, S., Song-Manguell, J., Rotondo, P., Del Puglia, S., Larsen, E., 2009, “ Torsional Mode Damping for Electrically Driven gas Compression Trains in Extended Variable Speed Operation,” Proceedings of the Thirty-Eighth Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, Texas, pp. 81-91.

Szolc, T. and Pochanke, A., 2011, “Dynamic Analysis of Electro-Mechanical Interaction between the Drive Systems and the Electric Motors,” 19th International Conference on Computer Methods in Mechanics, Warsaw, Poland.

Talati, J., 2011, “Surface Roughness – Significance and Symbol Interpretation in Drawing,” Hexagondesign.net, June, 2011.

Wilson, P., 2005, “EMTDC Transient Analysis for PSCAD Power System Simulation, User’s Guide,” Manitoba HVDC Research Center, Winnipeg, Manitoba, Canada.

Winkelmann, L., El-Saeed, O., and Bell, M., 2010, “The Effect of Superfinishing on Gear Micropitting, Part II,” Technical Paper 08FTM10, American Gear Manufacturers Association.

torsional and electrical dynamic interactions of

Documents