1 Copyright 2017 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station

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1 Optimizig Compoet Selectio i Sychroous Motor Compressor Trais Based O Techical ad Fiacial Cosideratios Marti D. Maier Pricipal Rotor Dyamic Aalysis Egieer Research ad Developmet Busiess Uit Dresser-Rad busiess, part of Siemes Busiess Power ad Gas Olea, New York, USA mmaier@siemes.com Garry Studley Process Simulatio Egieer Olea Operatios Dresser-Rad busiess, part of Siemes Busiess Power ad Gas Olea, New York, USA gstudley@siemes.com Marti D. Maier is a Pricipal Rotor Dyamic Aalysis Egieer at the Dresser-Rad busiess, part of Siemes Power ad Gas. He has 40 years of experiece with Dresser-Rad i torsioal ad lateral rotor dyamic aalysis, couplig, bearig ad seal desig, ad machiery vibratio aalysis as it relates to product developmet ad productio support. His experiece icludes program automatio, egieerig stadards developmet ad vibratio troubleshootig. Mr. Maier received a B.S. degree i Physics i 1977 ad a B.S degree i Mechaical Egieerig i 1990, both from the Rochester Istitute of Techology. He is a licesed Professioal Egieer i New York State, sice 1991, ad is a member of the Vibratio Istitute with a Level IV, Machiery Aalyst Certificatio. He has received a umber of U.S. patets i bearig, seal ad aerodyamic desig. Garry Studley is a Process Simulatio Egieer at the Dresser-Rad busiess, part of Siemes Power ad Gas. He has ie years of experiece with Dresser-Rad as a Product Desig Egieer, Project/Packagig Egieer ad his curret positio i Process Simulatio. Garry graduated from the Rochester Istitute of Techology i 2008 with a B.S. degree i Mechaical Egieerig ad a Masters of Egieerig. 1 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

2 ABSTRACT Compressor trais drive by costat speed sychroous motors eed to be desiged to withstad high levels of oscillatig torque durig trasiet startup coditios whe motors are started across-lie. The importace of accurately predictig peak torque levels at resoace is critical for compoet selectio to produce a techically acceptable desig i the most cost effective maer. This process cosists of three phases - (1) a prelimiary torsioal vibratio evaluatio performed i the proposal developmet phase based o available data usig a simplified calculatio method; (2) a traditioal trai torsioal vibratio aalysis performed i the productio phase whe more detailed iformatio becomes available based o a fixed value of assumed modal dampig; ad (3) a special coupled torsioal-lateral aalysis which provides more accurate results for geared systems. This procedure is illustrated usig a 6 MW, 4-pole, sychroous motor trai as a example where the peak torques durig startup were foud to approach 10.2 Per Uit Torque throughout the shaft lie. Numerous meas were ivestigated to reduce the peak torques ad associated stress levels which iclude the followig: (1) icrease the size of all major trai compoets; (2) step dow trasformer to reduce the termial voltage ad correspodig motor air gap torques; (3) elastomeric couplig; (4) grid style couplig; (5) slip clutch couplig; (6) viscous rotatioal damper; (7) hydraulic clutch to disegage the drive compoets durig startup; (8) poy motor plus hydraulic clutch to soft start the trai; (9) VFD starter; (10) reducig compressor load torque; (11) custom motor with more favorable startup torque characteristics. The beefits ad tradeoffs of each optio are evaluated from both fiacial ad techical perspectives. All cost data preseted i this paper have bee ormalized to the base cost of the major bought-out equipmet determied at the proposal stage (i.e. base cost = motor + gear + coupligs = 1.0). The results of the prelimiary evaluatio, traditioal torsioal aalysis, ad special coupled torsioal-lateral aalysis are compared ad discussed i detail. The coupled aalysis, though more complex, provides more precise startup torque levels ad ofte show higher levels of system dampig compared with the traditioal torsioal aalysis. The effects of gear bearig desig ad system parameters o the effective system dampig are quatified from the coupled aalysis for the subject example for two gear bearig sizes. The cost evaluatio preseted i this paper applies to the cited example oly ad is iteded to demostrate the selectio process recogizig that other applicatios may produce differet results. INTRODUCTION High levels of torsioal vibratio are experieced durig direct-o-lie starts of sychroous motor trais which eed to be thoroughly evaluated to esure a reliable desig. Twice-slip frequecy (2 x sf) pulsatig torque is geerated at the motor airgap durig startup due to the saliecy (i.e. o-uiformity) of the motor rotor. This excites the torsioal atural frequecies betwee twice electrical supply frequecy ad the static coditio as the rotor accelerates to sychroous speed. The magificatio of the system respose depeds o the deceleratio rate of the motor twice slip air gap frequecy ad the torsioal dampig preset i the system. API 617, eighth editio, sectio requires that motor drive trais be desiged for the startup coditio as well as steady state operatio to avoid resoace with oe ad two times rotatioal speed(s) ad electrical frequecies. Electrical fault aalyses are also performed depedig o the applicatio requiremet. The desig cosideratios relatig to the motor startup characteristics herei described deals exclusively with costat speed sychroous motors started across-lie. Iductio motors do ot demostrate high peak torque characteristics durig startup largely due to their more symmetric rotor desig. Iductio motors are typically less expesive tha sychroous motors but the operatioal cost is higher due to the lower power factor (typically 0.75 to 0.90) where the utility cost is based o apparet power rather tha the actual power. As sychroous motors typically possess a uity power factor, the operatioal cost is lower as the utility cost is based o actual power cosumed. For this reaso, iductio motors are typically selected for low power applicatios while sychroous motors are typically selected for high power applicatios. For itermediate power levels, it is a judgmet call based o the tradeoff betwee up-frot purchase price ad log term operatioal cost. For sychroous motors, there are two major types of rotor costructio: lamiated pole ad solid pole. Lamiated pole motors geerate lower levels of pulsatig air gap torque tha solid pole motors which results i lower startup torques ad associated stress levels. However, lamiated pole motors are subject to mechaical stress limitatios which limit them to low speed applicatios (6- 1,200 RPM for 60 Hz supply). The tred i idustry is to select less expesive motors that operate at higher speeds 1,800 RPM ad 3,600 RPM for 60 Hz supply curret). Ofte times, the lower motor cost for solid pole motors is offset by higher costs for the drive equipmet (gear, coupligs, etc.) ecessary to trasmit the higher startup torques. 2 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

3 I a startup simulatio for sychroous motors, four mai aspects of the mechaical desig eed to be evaluated: The peak torque capacity of the coupligs; more specifically, the torque capacity of the flexible elemets which represet the couplig s weak lik. The torque capacity of the shaft-to-hub jucture (itegral flage, hydraulic fit, keyed fit,etc.) The fatigue life of the shaftig; both the shaft diameter ad stress cocetratio eed to be cosidered to determie the weak lik locatios alog the shaft lie. Gear teeth cotact stresses API 671 requires a miimum peak torque service factor of 1.15 relative to the couplig peak torque ratig ad the shaft-to-hub jucture. A fatigue aalysis is usually required to determie the umber of allowable starts. For sychroous motors started across-lie, keyed shaft eds are usually avoided due to fatigue cosideratios. Hydraulic fit shaft eds are frequetly limited by slip capacity. Itegral flaged shaft eds are best suited for the motor ad gear shafts as they provide adequate torque capacity with miimal fatigue cocers. Particular attetio eeds to be paid to the size ad positioig toleraces of the flage bolt holes to esure uiform load sharig by the bolts. Ideally, bolted joits should be desiged to trasmit torque through flage frictio rather tha through the bolts i shear but this is ot always possible. The followig optios are available to the desiger to reduce the peak startup torques ad associated stress levels i sychroous motor trais: Reduce pulsatig motor air gap torque by modifyig the motor electrical parameters Reduce air gap excitatio by reducig termial voltage Reduce startup load by activatig the surge cotrol (recycle) valve, suctio throttlig, etc. Icrease system dampig Icrease shaft diameters ad reduce stress cocetratios to reduce localized stress levels Icrease material stregth Adjust system parameters (iertias ad torsioal stiffesses) Motor startup curves are provided by the motor supplier typically for ifiite bus (100 percet termial voltage) ad reduced voltage (typically 80 percet termial voltage). The mea ad pulsatig air gap torques ad load torque are ormalized relative to the rated motor torque ad expressed i terms of Per Uit torque or P.U. New istallatios geerally possess strog electrical grids ad experiece voltage dips less tha 10 percet. Old istallatios which are ofte ecoutered with field upgrades ad revamps frequetly have weak electrical grids where voltage dips ca be as high as 30 percet. To validate assumptios relative to electrical grid stregth ad load for existig equipmet, the termial voltage, speed ad gearbox vibratio should be recorded as a fuctio of time durig startup. Nevertheless, it is prudet to desig the system to withstad startup torques based o ifiite bus as worst case as the electrical grid could be upgraded i the future or existig equipmet o the same electrical supply could be removed from service. A sychroous motor s electrical desig is dictated by API 546 Brushless Sychroous Machies-500 KVA ad Larger, Third Editio, stadards. Desig guidelies that ifluece motor startup characteristics iclude the followig: Sectio states that the motor should be able to start at 80 percet termial voltage. As air gap torque varies with voltage-squared, the air gap torque is reduced to a factor of (0.80)^2 or 64 percet. Sectio states that a 10 percet margi eeds to be maitaied betwee the mea motor torque ad load torque for all speeds betwee zero ad sychroous speed. Sectio a states that the locked rotor (irush) curret should ot exceed 500 percet of the full load curret. 3 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

4 Thus, if the trai load torque (iclusive of the compressor power, gear power loss ad dissipative power at all bearigs, widage, etc.) at the poit where the load torque curve is at closest proximity with the mea torque curve is, say, 0.58 P.U., the the mea motor torque eeds to be at least 0.58/(0.80)^2/0.90 = 1.0 P.U. at this coditio to satisfy these requiremets. A higher load torque ecessitates icreasig the mea torque. The electrical desig of the motor is such that the pulsatig torque ad mea torque vary i a similar maer. Thus, a high load potetially icreases both the mea torque ad pulsatig torque which reduces the acceleratio rate at resoace thereby icreasig the magificatio factor Q. All three cosideratios icrease peak torque levels alog the shaft lie durig startup. The average ad pulsatig motor air gap torque ad load torque are of primary iterest at the istat whe the twice slip frequecy mometarily coicides with the predomiat torsioal atural frequecy. The predomiat torsioal atural frequecy is the oe which produces the greatest system respose from motor iduced excitatio. The predomiat torsioal atural frequecy for sigle eded motors is the first (fudametal) atural frequecy whereas the predomiat torsioal atural frequecy for doubled eded motor is typically the secod torsioal atural frequecy. The speed at which resoace occurs is give from the followig expressio: I sigle eded motor trais, resoace with the first torsioal atural frequecy typically occurs at 80 percet to 92 percet sychroous speed for 60 Hz electrical supply ad 65 percet to 78 percet sychroous speed for 50 Hz electrical supply, regardless of pole umber. With regard to shaft stress evaluatios, there are may fatigue life predictio methods used throughout the idustry. They are divided ito two mai categories: stress-based ad strai-based methods. Stress-based methods are typically used whe the calculated strai is primarily elastic which occurs for life predictios greater tha 50,000 starts. Strai-based methods are typically used whe the calculated strai is largely plastic which is the case for life predictios less tha 5,000 starts. The traditioal stress-based S-N method uses the ultimate tesile stregth to determie a material s ability to withstad cyclic stresses. The strai-based methods evaluate both the elastic ad plastic compoets of strai which cosiders both the material s stregth ad beeficial ifluece of the material s ductility. Strai-based methods are geerally cosidered more precise ad provide more favorable fatigue life predictios tha traditioal stress-based methods. Oe of the mai parameters that ifluece peak torque levels at resoace is the system dampig which is typically expressed as modal dampig either as a dampig ratio (i.e. 0.02) or percetage of critical dampig (i.e. 2 percet). Corbo (2002) reports that for geared systems, dampig ratios ragig from 0.02 to 0.05 are commoly used i the idustry. This is based o work published by Che (1983), Awar ad Colsher (1979), Mruk (1978), Write (1975). The reaso for this variatio relates largely to dampig cotributed by coupled torsioal-lateral dampig i parallel axis gearboxes. Torsioal dampig i a gearbox is produced by three mai sources: Lateral motio which occurs withi the bearig oil films due to the couplig of the torsioal-lateral degrees of freedom at the gear mesh. More specifically, the torque that is trasmitted across the gear mesh gives rise to lateral gear loads. This torque has both steady ad alteratig compoets. The resultig lateral motio withi the gearbox bearigs dissipates eergy which is torsioally iduced. I this respect, the bearig desig of the gear has a direct ifluece o the magitude of torsioal dampig. 4 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

5 Gear backlash which occurs whe the alteratig torque exceeds the mea torque as the gear teeth move i ad out of mesh. The impact load at the poits of tooth cotact as well as the squeeze film actio that occurs whe the oil is squeezed out of the cavity formed by adjoiig teeth dissipates eergy. No-liearities associated with the gear backlash chage the system dyamics as the teeth repeatedly egage ad disegage. Highly o-liear systems do ot display a discrete atural frequecy ad exhibit what is commoly cosidered a form of pseudo-dampig although eergy is ot dissipated, i the classic sese. To better quatify the amout of dampig preset i the system durig quasi-resoace coditios, a coupled torsioal-lateral aalysis ca be performed. I such istaces, the bearig characteristics of the gearbox eed to be kow ad a program capable of modelig torsioal-lateral coupled systems is required. Pradetto ad Bauma (2015) preseted the results of coupled torsioal-lateral aalyses of three geared trais ad foud that the effective dampig ratios, as determied by field testig, raged from to which were substatially greater tha the ratio commoly used i the idustry. The cotributio to overall system dampig from the gearbox bearig characteristics as a fuctio of load were discussed, as well as the cotributio from mode shape as iflueced by the system parameters (iertia ad torsioal stiffess) were discussed by the authors. Adjustig the system parameters chaged the mode shape ad shifted the resoace coditio to a speed where the motor torques ad load torque produced a lower system respose. A simple calculatio method is icluded i Appedix 1 which is a closed form solutio for a multiple degree of freedom system based o the assumptio that all of the torsioal deflectio occurs betwee the motor ad gear ad that the gear ad compressor(s) oscillate i uiso. This is geerally valid for commo systems. Empirical costats Alpha, Beta, ad Gamma are used to accout for deviatio from this assumptio arisig from relative deflectio elsewhere i the trai. Typical values for Alpha rage from 0.85 to Typical values for Beta ad Gamma rage from 0.95 to Figure A-1 cotaied i Appedix 1 gives the dyamic magifier (Q-Factor) as a fuctio of both system dampig ad acceleratio rate of the twice slip frequecy relative to the first torsioal atural frequecy. The acceleratio rate is a fuctio of the followig parameters: Motor mea torque Load torque Total trai iertia The load torque durig startup is applicatio specific. If it is ot kow, the for compressor trais, it ca be approximated based o the fa law, speed squared, relatioship. As resoace with the first torsioal atural frequecy typically occurs at 85 percet rated speed for 60 Hz electrical supply, the load torque at resoace would be approximately (0.85)^2 = 0.72 rated compressor torque. This is a highly pessimistic estimate as compressors are typically uloaded by suctio throttlig or startig with the recycle (surge cotrol) valve fully ope. This gives coservative results as a higher compressor load will reduce the acceleratio rate through resoace yieldig a higher, less favorable, value for the dyamic magifier Q. As show i Appedix 1, the acceleratio rate of the twice slip frequecy relative to the first torsioal atural frequecy is defied as q which is used to determie magificatio factor Q from Figure A-1. There are two oteworthy limitig cases show i this figure. The first is the case of zero dampig where Q = 3.67*SQRT(q) which ca be used to provide a worst case estimate for rapid acceleratio rates. The secod is the case for steady state coditios where Q = 1/(2* dampig ratio) which ca be used as a worst case estimate for slow acceleratio rates. It ca also be used for highly damped systems where magificatio factor is less iflueced by acceleratio rate. A illustrative example show i Figure 1 is represetative of a typical sigle body compressor trai which shows the ifluece of iertia distributio o shaft torque. I this example, the motor comprises 33.3 percet of the total trai iertia ad load iertia comprises 66.7 percet of the total trai iertia distributed to the gear ad compressor by varyig amouts. Typical motor startup characteristics are assumed for Mea Torque (1.10 P.U.), Pulsatig Torque (0.65 P.U.) ad Load Torque (0.35 P.U.) at resoace. The left portio of the curve is represetative of trais that ivolve low speed, low gear ratio (GR~2), large frame size compressors. The 5 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

6 right portio of the curve is represetative of trais that ivolve high speed, high gear ratio (GR~9), small frame size compressors. The followig treds are oted: 1. For trais with a relatively low gear iertia, the shaft torque betwee the motor ad gear is 7.5 P.U. while the shaft torque betwee the gear ad compressor is 7.5 p.u. idicatig little atteuatio across the gear mesh. Note that 1 p.u. (high speed) = 1 P.U. (low speed) / gear ratio, where 1 P.U. refereces rated motor torque. 2. The shaft torque betwee the motor ad gear is costat based the assumptio that all of the torsioal deflectio occurs betwee the motor ad gear. I reality, shaft deflectio will occur, i some measure, elsewhere i the trai causig the peak torque at the low speed ed to tred dowward with decreasig gear iertia ratio. 3. The shaft torque betwee the gear ad compressor varies from approximately 7.5 p.u. to 1.0 p.u. depedig o the iertia distributio. 4. For a uiform iertia distributio (i.e. motor: 33.3 percet; gear: 33.3 percet; compressor: 33.3 percet), the shaft torques are 7.5 P.U. betwee the motor ad gear ad 4.0 p.u. betwee the gear ad compressor. Figure 1- Illustrative Example of the Peak Startup Torques i a Typical Sigle Body Compressor Trai This example clearly shows that the peak torque levels o the high speed ed are a strog fuctio of iertia distributio. This demostrates that the commo practice of usig service factors to size shaft eds, coupligs ad gear meshes for all trai arragemets is wholly iadequate. Iertia distributio ad startup load eeds to be cosidered as well. For this example, usig a service factor for 6 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

7 the high speed shaft based o a peak trasiet torque of, say, 4.0 P.U. will result i oversizig the coupligs i some istaces ad udersizig the coupligs i other istaces. Oversized coupligs icrease cost, egatively impact the lateral rotordyamics of the drive equipmet, promotes iterferece coditios with casig ad pipig, ad icrease widage ad associated couplig guard temperature. Udersized coupligs ad shaft eds, whe discovered late i the productio phase, seriously impact the productio schedule ad results i cost overrus associated with scrap charges ad expedited delivery charges for both the couplig(s) ad shaft forgigs. The sizig of trai compoets i sychroous motor trais is ofte times a iterative process. Iitially, service factors may be applied to the rated motor torque to size the coupligs, shaft eds ad hub-to-shaft iterfaces; however, a torsioal evaluatio is subsequetly ecessary to make whatever adjustmets are eeded to comply with idustry stadards. The simple closed form solutio cotaied i Appedix 1 ca easily be coded ito a spreadsheet program such as MS Excel. A more precise method for determiig peak torque levels is cotaied i Appedix 3 which is based o a ormal mode sythesis approach. This method is commoly described i vibratio texts. This is more complicated tha the method used i this study but ca be coded ito a solver such as MATLAB. To illustrate the method herei described, a case study is preseted below which exhibited uusually high peak torque levels durig startup ad warrated a thorough ivestigatio of available optios to provide the best solutio from both techical ad commercial perspectives. BACKGROUND The compressor trai which is the subject of this study ad illustrates the selectio process is show i Figure 2. It is a sigle body compressor trai for Alkylatio Refrigeratio Service with the etire trai arragemet ad the dry gas seal system set o a commo baseplate. The driver is a 6 MW, 4-pole, costat speed sychroous motor drivig through a double helical gearbox with a gear ratio of 2.107, to a straight-through, cetrifugal, barrel type compressor. The ceterlie-to-ceterlie distace of the origial gearbox was 16 iches but was later icreased to a larger frame size with a ceterlie-to-ceterlie distace of 22 iches. The compressor ilet pressure is ear atmospheric with a ilet capacity of 36,000 ACFM. Figure 2 Trai Arragemet 7 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

8 The customer specified additioal requiremets over ad above API stadards: The closed loop desig did ot allow the case pressure to be reduced followig shutdow by vetig or flarig the gas due to evirometal cosideratios. This resulted i relatively high startup loads. The settleout pressure ad associated startup load characteristic was determied pre-quote with a dyamic simulatio study. This high load was particularly challegig to the motor supplier from a electrical desig stadpoit. Limited physical floor space to fit withi the prescribed footprit. A simple trai arragemet with othig superfluous added. Budgetary costraits which did ot allow for cost overrus. As this is for a refiery/petrochemical applicatio, the miimum required umber of starts was 10 starts per year. This is i cotrast to 20 starts per year typically specified for other lad based applicatios. The coupligs eeded to be a sigle diaphragm desig with a preferece for a supplier with log lead times. Spare coupligs, bearigs ad dry gas seals were required. I the pre-quotatio phase, the respective OEM s used fixed service factors to size the coupligs, shaft eds ad related compoets. It was subsequetly determied that the shaft lie possessed isufficiet torque capacity promptig the eed to cosider other optios to reduce peak startup torque. Figure 3 is a motor startup curve for the origial motor which shows curves for the average motor torque, twice slip pulsatig motor torque ad compressor load torque plotted as a fuctio of speed. These torques are ormalized relative to rated motor torque (1 P.U.). Curves are show for 100 percet termial voltage (ifiite bus) ad 90 percet termial voltage. Figure 3 Startup Curve For Origial Motor 8 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

9 Resoace with the first torsioal atural frequecy durig startup occurs at 84 percet sychroous speed. The compressor load at this poit i time is 0.58 P.U. motor torque. The electrical parameters of the motor were selected to produce the required torque level i a attempt to comply with API requiremets. The poit of closest proximity betwee the mea motor torque ad load occurs at 60 percet ad at 97 percet speeds. Although API 546, sectio ad requires a miimum separatio of 10 percet at 80 percet voltage, this requiremet is satisfied oly at 90 percet termial voltage. The customer accepted this deviatio from API as the electrical grid was cosidered quite stiff ad the curret draw for the relatively small motor will ot result i a substatial drop i termial voltage. It should be oted that both the load torque ad pulsatig air gap torque are approximately 1.5 times higher tha typical applicatios. The motor startup torque curve for the fial, as maufactured, motor is show i Figure 4. This is a customized desig to address the uusually high startup load. The pulsatig motor torque at resoace (84 percet motor speed) is 0.65 P.U. compared with 0.96 P.U. for the origial motor. I both istaces, the mea torque is cosistet with what is cosidered typical. I additio to the uique motor startup characteristics ad load torque, the trai iertia distributio is of particular iterest where iertia of the compressor comprised 66 percet of the total trai iertia. As previously discussed, a high load iertia serves to icrease peak startup torque levels, particularly o the high speed ed of the trai. Figure 4 Startup Curve For Fial Motor The closed form solutio previously described was used to determie the peak torque levels at resoace. Appedix 2 cotais calculatios for the base offerig that was iitially quoted as well as for alterate trai cofiguratios ad desig optios. For the base offerig, estimated peak torque levels were foud to be 10.2 P.U. ad 10.2 p.u. at both the low speed ad high speed shafts, respectively. The followig observatios are made from this calculatio: The alteratig torque is the mai torque compoet at resoace. Little atteuatio occurs across the gearbox as the gear makes up a relatively small fractio of the total trai iertia. The high air gap pulsatig torque ad high load iertia are major cotributors to the high alteratig torque. The elevated magificatio factor is the direct result of a slow acceleratio rate through resoace due to the relatively large startup load. 9 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

10 It was subsequetly determied that all trai compoets, as origially selected, were uable to hadle these torque levels icludig the coupligs, shaft ed iterfaces, gear mesh tooth stresses ad fatigue life of all shafts. A iitial attempt was made to beef up the shaft desig util it was leared that the torque levels withi the motor rotor exceeded the maufacturer s desig limits based o the stated applicatio requiremets. Cosequetly, various desig optios were cosidered to reduce the magitude of the peak torque levels to produce a torsioally acceptable desig. The cost impact for each desig optio is discussed below. Peak torque calculatios for each case appear i Appedix 2. Empirical costats Alpha, Beta ad Gamma were back-calculated from full aalysis results to demostrate the rage of values. Case 1 ivolves a larger motor frame size. Cases 2 through 10 ivolve the origial, as-quoted motor. The last optio discussed is for the fial desig (Case 11) ivolvig a customized motor. Cost data was compiled for 11 differet optios to provide a solutio that was both cost effective ad techically acceptable. This cost data was the ormalized relative to the base cost of the major bought-out equipmet that was determied at the proposal stage (i.e. base cost = motor + gear + coupligs = 1.0). These desig optios are briefly discussed below. Case 1: Icrease Compoet Sizes The motor frame size eeded to be icreased as the torque capacity of oe of the motor rotor compoets was exceeded. The icrease i frame size icreased the motor iertia from 28 percet to 48 percet of the total trai iertia. The pulsatig air gap torque at resoace decreased from 0.96 to 0.83 P.U. Both factors resulted i a substatial reductio i peak torque levels. The estimated peak torques o the low ad high speed shaft dropped to 7.0 P.U. / 6.5 p.u., respectively. Nevertheless, the gearbox, coupligs ad shaft ed diameters of all trai compoets eeded to be icreased. The tooth profile of the gear mesh required modificatio to reduce cotract stresses ad higher stregth material was selected. Icreased compoet sizes icreased the size of the trai which was ufavorable to the customer as the available footprit was limited. The cost factor associated with the major buyouts was 1.37 relative to the as-quoted, base offerig of Case 2: Step Dow Trasformer to Reduce Termial Voltage ad Motor Air Gap Torque Levels A step dow trasformer is used oly durig startup. Oce up to speed, the trasformer is switched out of the circuit. A speed squared relatioship exists betwee the motor air gap torque (both mea ad pulsatig compoets) ad termial voltage. A trasformer ca potetially be selected to reduce the termial voltage dow to 80 percet durig startup. However, i this istace, a termial voltage of 90 percet is ecessary to accelerate the trai to speed to preclude stall. This reduces the motor air gap torques to (0.90)^2 -> 81 percet of the ifiite bus values. This effect is offset, i part, by the icreased magificatio factor at resoace which chages from 14.3 to 16.3 due to the slower acceleratio rate through resoace. The et result is that the peak torque levels o the low ad high speed shafts reduce to 9.1 P.U. ad 9.1 p.u., respectively. The gear ad low speed couplig eeded to icrease by oe size icremet. The high speed couplig eeded to be icreased by two size icremets. The compressor shaft ed diameter, joural bearigs ad dry gas seals eeded to icrease to the ext stadard sizes. The tooth profile of the gear mesh required modificatio to reduce cotact stresses ad higher stregth material was ecessary. I this istace, a step dow trasformer provides miimal beefit due to the high startup load which limits the voltage reductio. A advatage of a step dow trasformer is that it reduces the impact of startup o other equipmet o the same electrical supply. Disadvatages iclude possible loger wait times betwee successive hot (re)starts ad icreased real estate to accommodate the trasformer. The lead time for a trasformer is typically 20 to 24 weeks. The cost factor for this optio is Case 3: Elastomeric Couplig Betwee Motor Ad Gear Elastomeric coupligs (a.k.a. Holset style or rubber block coupligs) are frequetly used i the idustry betwee the motor ad gear for sychroous motor applicatios to icrease system dampig. The rubber blocks are typically wedge-shaped or have a cylidrical profile ad trasmit the torque from hub-to-sleeve i compressio. The elastomeric half is usually o the motor side ad a covetioal flexible elemet (diaphragm or disk style) is typically o the gear side. For uusually severe applicatios, a tadem block arragemet may be used without a flexible elemet. Published magificatio factors rage from 3.0 to 4.0 for high dampig SBR block material, depedig o block hardess. The effective system dampig is determied based o the cosideratio that relative deflectio occurs both withi the elastomer blocks (high dampig) ad the steel compoets (low dampig) elsewhere i the trai. 10 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

11 For elastomeric coupligs, the effective magificatio factor is approximately 1.6x to 2.0x the published block magificatio factor (i.e. Qeff = 1.7 x 3.0 = 5.1). I this istace, the peak startup torques o the low ad high speed eds are reduced to 4.5 P.U. ad 4.4 p.u., respectively. This eables the origial motor ad gear to be used. However, the high speed couplig eeded to be icreased to the ext larger size. The advatage of the elastomeric couplig optio is prove reliability as they have bee i commo use i sychroous motor trais over the last 50 years. They also hadle high peak trasiets associated with electrical faults which make the trai desig more torsioally robust. Although they are a tried ad true optio, the disadvatage of elastomeric coupligs is that they are viewed as high maiteace as the blocks eed to be replaced approximately every 5 years. Elastomeric coupligs are also temperature sesitive, dimesioally larger, heavier ad produce more widage compared to covetioal flexible elemet coupligs. The lead time for elastomeric coupligs is typically 24 to 28 weeks, depedig o size ad availability of block material. The cost factor for this optio is 0.99 cosiderig that there is a customer requiremet for oe set of spares. Case 4: Grid-style Couplig Betwee Motor ad Gear Grid-style coupligs are frequetly see i field upgrades ad revamps. They were commoly used i the 1960 s ad 1970 s particularly i electric motor applicatios. The shaft ed separatios were typically less tha oe ich. Torque is trasmitted through a circumferetial, serpetie, sprig elemet which is iterwove betwee adjoiig slots i the couplig hubs. The early versios required cotiuous lubricatio but have sice chaged to grease packed lubricatio. Dampig is provided at the cotact iterface betwee the sprig elemet ad retaiers. Atteuatio also results from the sprig characteristics of the serpetie sprig, which is highly o-liear. The magificatio factors typically rage from 9 to 11. They are ot as favorable as elastomeric coupligs but are better tha what covetioal flexible elemet coupligs provide. As with elastomeric coupligs, the magificatio factor eeds to be adjusted to accout for compliace elsewhere i the trai. The effective magificatio factor is approximately 1.0x to 1.5x the published values (i.e. Qeff = 1.0 x 9 = 9.0). I the subject applicatio, the peak torque levels o the low speed ad high speed eds are reduced to 6.4 P.U. ad 6.8 p.u., respectively. This is based o a sigle elemet desig although dual elemet desigs are better suited for typical shaft separatio distaces. The larger frame gearbox was eeded ad the high speed couplig eeded to icrease by two stadard sizes. Grid-style coupligs are compact, require less radial space tha elastomeric coupligs ad ca accommodate short shaft ed separatios. The serpetie sprig elemet ca be replaced without removig the hubs. They also have a relatively high peak torque capacity. A disadvatage is that the sprig elemet requires a fresh applicatio of grease at every major turaroud. They are ot cosidered API compliat although they have a log history of satisfactory use. The lead time for grid style coupligs is typically weeks. The cost factor for this optio is This cosiders the customer requiremet for spares although it could be argued that spares are ecessary oly for the sprig elemet, which is the low cost item. Case 5: Slip Clutch Couplig Covetioal flexible elemet coupligs ca be fitted with a additioal member that trasmits torque through frictioal forces betwee itermediate aular surfaces that are pressed together with a prescribed amout of iterferece. Whe the torque limit is exceeded, relative motio occurs betwee the cotact surfaces ad the surfaces slip relative to oe aother. The torque dowstream of the slip iterface is thereby limited as evideced by the clipped or shaved peaks see i the time-torque sigatures. Slip clutch coupligs are typically applied o the low speed ed, but i some istaces ca be used at the high speed ed. A good discussio of slip clutch couplig applicatios is provided by Hutto (2014). If a higher tha expected torque overload were to occur, the cotact surfaces disegage ad the drive compoet drops oto a bushig or rollig elemet bearig util the trai comes to rest. Durig a slip evet, eergy is dissipated at the cotact surface which traslates ito (coulomb) dampig. Vibratio is also atteuated due to the highly o-liear ature of the device whereby the dyamics of the system mometarily chages followig each slip evet. As the system is highly o-liear, the simple closed form solutio used i the preset study is ot recommeded. However, to establish a frame of referece relative to the other optios evaluated i this study, the effective dyamic magifier which was back-calculated from the clipped torque levels provided by the coupligs maufacturer was foud to be 4.4. I this applicatio, the peak torque levels with the slip couplig at the low ad high speed eds are 3.8 P.U. ad 3.6 p.u., respectively which allowed the use of the origial motor, gear ad coupligs. The compressor, bearigs ad seals could also be reduced i size. The advatage of slip coupligs is that the torque limit is adjustable based o the hydraulic pressure used to activate the device. Additioally, the slip elemet ca be reused ad reactivated followig a major torque overload. Oe disadvatage is that the desig is cosidered proprietary ad the slip characteristics are ot geerally kow ad are difficult to aalyze with covetioal rotor dyamic codes. The lead time for slip clutch coupligs is typically weeks. The cost factor for this optio is This cosiders the customer requiremet for spares. 11 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

12 Case 6: Viscous Rotatioal Damper A ew device recetly itroduced to the API idustry is a torsioal damper which imparts viscous dampig to the torsioal system. It is a drop-i replacemet for a spacer i a covetioal flexible elemet couplig ad requires o special cosideratio with regard to operatio or maiteace as it is a hermetically sealed assembly. The magificatio factor of the viscous rotatio damper is approximately 3.0 to 3.5 which is comparable to that of a elastomeric couplig. I the subject case study, the device reduced the peak torque levels o the low ad high speed eds to 3.1 P.U. ad 2.9 p.u., respectively. Cosequetly, the origially quoted bought out compoets were foud to be satisfactory from a torque trasmissio ad fatigue life perspective. Moreover, the lower peak torque levels at the compressor allowed ot oly the shaft ed diameter to be reduced but also the joural bearig ad dry gas seal to be reduced as the shaft ed diameter, i this istace, dictates bearig ad seal sizes. This results i a cost reductio which helps to offset the cost of the torsioal damper. The disadvatage of this device is its lack of experiece i API idustry although versios of it have bee i widespread use i low speed reciprocatig equipmet. The lead time for a viscous rotatioal damper (spool piece portio) is weeks. The cost factor is This cosiders the customer requiremet for spares. Case 7: Hydraulic Clutch Precedig Gearbox A hydraulic clutch, torque coverter or fluid couplig ca be positioed at the iput shaft of the gear which ucouples the drive compoets from the driver durig startup. Oce up to speed, hydraulic fluid is itroduced ito the device which slowly accelerates the drive equipmet up to speed. Some varieties cotai oil durig startup but disegage the drive compoets through various meas. I this way, the oly compoet that is coected to the driver durig startup is the low speed couplig ad ½ clutch. As the drive iertia is reduced by a order of magitude, the peak startup torque o the low speed ed is reduced to very low levels. The electrical desig of the motor becomes much simpler particularly for high startup loads as a large margi ow exists betwee the mea motor torque ad the load torque, which is miimal durig startup. This may result i a lower cost motor desig. The high speed couplig sees o peak torque durig startup i this sceario. Oce the clutch is filled with fluid ad brigs the drive equipmet up to speed, a optioal lockig mechaism egages across the hydraulic clutch which precludes relative motio. For the subject applicatio, the origial compoet sizes could be used. Although the peak torque levels o the motor shaft are low (0.4 P.U. o this istace), a steady state calculatio is recommeded durig the early productio phase as the first torsioal atural speed for this portio of the trai durig startup ca be i proximity with electrical supply frequecy which ca be excited by curret irush. It is a good desig practice to maitai a 20 percet separatio margi betwee the first torsioal atural frequecy of the low speed brach (i.e. motor + ½ clutch) ad electrical supply frequecy by adjustig the torsioal sprig rate of the low speed couplig. Hydraulic clutches are frequetly itegrated ito the gearbox case requirig little additioal real estate. Variable speed operatio ca also be provided over a desigated speed rage although heat dissipatio ad associated lube oil requiremets icrease substatially. The lube oil reservoir is frequetly located uder the gearbox. Be aware that the cost of the oil system is cosiderable ad is ofte ot icluded i the quoted cost of the clutch/gear. I the subject applicatio, there is potetial to dowsize the compressor shaft ed, bearigs ad dry gas seals which result i a cost savigs that serves, i some measure, to offset the cost of the clutch. The lead time for a itegrated hydraulic clutch & gearbox is typically 26 to 32 weeks. The cost factor is Case 8: Poy Motor + Hydraulic Clutch Precedig Gearbox This is a adaptatio of the previous case (7) cosistig of the additio of a small fixed speed iductio motor (a.k.a helper or poy motor) to the free ed of the primary motor which accelerates the primary motor up to speed while the drive equipmet is ucoupled from the trai. Oce up to speed, the widigs of the primary motor are eergized ad the poy motor disegages from the trai. As the twice slip excitatio is o loger preset i the primary motor air gap, this elimiates the peak startup torques that would otherwise occur durig startup. As a result, for the subject applicatio, the origial compoet sizes could be used with the potetial to dowsize the compressor shaft ed, joural bearigs ad dry gas seals. The poy motor is sized to accelerate the primary motor ad ½ clutch up to 97 percet rated speed withi the time dictated by the thermal limits of the poy motor stator widigs (typically 10 percet-20 percet of the rated power level of the primary motor). This method greatly reduces the impact o the electrical grid durig startup, which is a particular cocer whe the curret draw is high for high power applicatios. The disadvatage of this arragemet is that it icreases footprit size ad adds cost. The lead time for a poy motor is typically weeks, depedig o size. The cost factor for this optio is Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

13 Case 9: Variable Frequecy Drive (VFD) Starter VFD starters are used to soft start motors to elimiate the high trasiet torque levels. The VFD starters are sized such that they ca provide the ecessary torque to overcome the drive load durig startup. Oce up to speed, they are switched out of the circuit ad the motor ow operates o electrical supply curret (60 Hz or 50 Hz). As the power level is usually less tha what covetioal VFD drives require durig steady-state operatio, the excitatio levels of the iteger ad o-iteger harmoics durig startup are relatively small ad do ot effect hardware selectio. As the power level is a fractio of the rated motor power, the cost is less tha a covetioal VFD which provides variable speed operatio at full load. A added beefit of a VFD starter is that the motor cost may be lower as less copper is required to satisfy the API requiremets relative to curret irush at startup. VFD starters, typically LCI drives, ca be cofigured to start multiple trais i a istallatio i successio. The mai disadvatage is that it is a electroic device that has the potetial to malfuctio which may ot be acceptable for critical applicatios. It also requires physical space to accommodate the electroics module which is a major cosideratio particularly for offshore use. The lead time for a VFD starter is typically 18 to 24 weeks. The cost factor for this optio is Case 10: Compressor Startup Load Reductio Startup load i compressor trais is directly related to process coditios, specifically, settleout pressure. Settle-out pressure is the case pressure that is attaied after the pressurized gas cotaied betwee the mai suctio ad discharge valves equalizes followig shutdow. It is a desig cosideratio whe it is ot possible to vet or flare the gas due to evirometal cocers. Settleout pressure is a fuctio ot oly of the pressure differetial across the case immediately prior to shut-dow but also the volumes of the itake ad discharge process pipig ad valve placemet. Oe method to reduce settleout pressure is to icrease the pipig volume o the suctio side through meas of a pressure vessel of a prescribed size. The disadvatage of doig this is cost as well as the additioal real estate eeded to accommodate the pressure vessel. This optio was iitially cosidered for the subject applicatio but was dismissed o the basis of cost. However, the origial motor could have bee redesiged for lower startup load resultig i more favorable motor air gap torque characteristics. The calculated peak torque levels were 6.2 P.U ad 6.2 p.u. o the low speed ad high speed eds, respectively. Nevertheless, the size of the gearbox ad coupligs would eed to be icreased to hadle the elevated torque levels. The cost factor for this optio was Case 11: Customized Motor Fial Desig A customized motor desig was developed which provides more favorable startup characteristics. The iertia of the ew motor was greater (iertia fractio chaged from 0.28 to 0.37) ad the pulsatig air gap torque was reduced from 0.96 P.U. to 0.65 P.U.. Both factors serve to reduce peak torque levels. The peak torque levels at the low-speed ad high-speed eds were 6.1 ad 5.9 P.U., respectively. The gearbox ad coupligs eeded to be icreased to the ext stadard size. The gearbox bearig diameters likewise icreased which altered the lateral dyamic bearig coefficiets pertiet to the coupled aalysis discussed later i this tutorial. The fial desig was both commercially viable ad techically acceptable based o the applicatio requiremets ad met with the customer s approval. The cost factor for the fial desig was Figure 5 is a summary of the cost evaluatio study. For this job, there is a customer requiremet for spare coupligs, bearigs ad seals so data is preseted both with ad without spares. The higher cost optios show i this figure are ofte selected if there is a eed to reduce the impact o the electrical grid durig startup, particularly for high power applicatios (P > 20 MW). For a relatively small motor such as this, electrical grid cosideratios are ot sigificat. For some applicatios, the eed for variable speed operatio drives the decisio. For the subject applicatio, Case 6 ivolvig the Viscous Rotatioal Damper was foud to be the most cost effective but was perceived to ivolve higher risk due to its limited experiece i the API idustry. The other alterate couplig desigs that were examied (elastomeric, slip clutch, grid) were foud to be cost competitive but were dismissed by the cliet based o the desire to avoid uecessary complexities. I the ed, Case 11 with the customized motor was viewed as the most favorable choice from the customer s ad OEM s perspectives so the decisio was made to move forward o that basis. 13 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

14 Figure 5 Cost Evaluatio Summary Stadard Torsioal Aalysis Performed i the Productio Phase Oce the fial trai cofiguratio was determied, a stadard trasiet torsioal aalysis was performed to cofirm compoet acceptability. The followig discussio relates to the fial, as maufactured, desig. I the early project phase, little iformatio is geerally available for shaft geometry of the major trai compoets. Ofte time, the opportuity does ot exist to wait for the shaft profiles from the major equipmet suppliers as decisios eed to be made relative to shaft ed sizes as it affects couplig selectio ad shaft forgigs. Also, depedig o the supplier ad the project ship date, the lead time for the coupligs requires that the couplig be ordered withi the first few weeks after a P.O. is received. Chagig shaft ed geometry beyod Week Four ca result i scrap charges ad egatively impact the productio schedule. To address this lack of detailed shaft geometry, the torsioal stiffess of the shaft eds ca be approximated kowig oly the joural bearig diameters for each major body. The equivalet torsioal stiffess of the shaft eds ca be approximated by assumig a legth of shaft which is a fixed multiple of joural diameter. For example, a legth correspodig to two times the joural diameter provides a good estimate for the shaft ed stiffess of the motor, bullgear ad piio shafts. For the drive (o-thrust bearig) ed of compressors, a legth correspodig to three times the joural diameter provides a good estimate for torsioal stiffess. For the drivig (thrust bearig) ed of compressors i drive-thru applicatios, a factor of four is appropriate. This approach provides acceptable results i the early productio phase. Variatios i shaft geometry do ot affect the ed result sigificatly cosiderig that most of the compliace of the torsioal system is cotributed by the coupligs, ot the shaft eds, particularly if the coupligs are a flexible elemet disk pack or diaphragm styles ad the shaft ed separatio distace is at least 18 iches. A prelimiary model is show i Figure 6a usig this approach. The API data sheets for the motor ad gear provide the total rotor iertias. Prelimiary couplig data either from proposal drawigs or data bases provide the torsioal sprig rates of the coupligs. At this poit i the job, oly the lower order, couplig domiat, torsioal atural frequecies are of primary iterest. Figure 6b shows the detailed model used i the fial torsioal report which was created oce the certified vedor drawigs became available. The first two modes are tabulated i Figure 6c which were calculated based o the prelimiary model ad the detailed model. As ca be see, the results differ by less tha 1 percet. However, the estimates for major mass iertias could subsequetly chage durig the early stages of a project so separatio margis i excess of 10 percet should be maitaied, depedig upo the estimated accuracy of the data. 14 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

15 Figure 6a Prelimiary Torsioal Model Figure 6b Fial Torsioal Model Mode Torsioal Natural Frequecies (CPM) # Prelimiary Model Fial Model % Differece 1 1,242 1, ,200 3, Figure 6c Compariso of Aalysis Results It should be oted that i geared systems, speed referecig of the system parameters is required, usually performed relative to driver speed. This is accomplished by multiplyig the torsioal stiffess ad iertia values dowstream of the gear mesh by the gear ratio squared. Usually, this is doe iteral to the program prior to computatios performed by the solver. Oce geometry becomes available, the fial torsioal aalysis ca be pursued. The first step is to determie the torsioal atural frequecies ad their locatios relative to potetial mechaical ad electrical sources of excitatio. This is evaluated o a iterferece diagram, as show i Figures 7 ad 8. API 617, eighth editio, sectio , requires that a miimum separatio margi of 10 percet be maitaied with respect to 1x ad 2x shaft speeds ad 1x ad 2x electrical supply frequecies. Figures 9a ad 9b shows the ormalized torsioal mode shapes for the first two, couplig domiat, torsioal atural frequecies. The relative deflectios across the coupligs ad the amplitude at the major compoets provide the meas to qualitatively assess the sesitivity of the atural frequecies o the system parameters. For typical systems, the first torsioal atural frequecy is a strog fuctio of the low speed couplig stiffess ad the secod torsioal atural frequecy is a strog fuctio of the high speed couplig stiffess. The couplig torsioal sprig rates are adjusted accordigly to achieve proper placemet of the torsioal atural frequecies. 15 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

16 Figure 7 - Iterferece Diagram Relative To Potetial Sources Of Mechaical Excitatio (i.e. 1x ad 2x shaft speed) Figure 8 - Iterferece Diagram Relative To Potetial Sources Of Electrical Excitatio (i.e. 1x ad 2x electrical supply frequecy) 16 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

17 Figure 9a - Mode Shape For First Torsioal Natural Frequecy (1,237 CPM) Figure 9b - Mode Shape For Secod Torsioal Natural Frequecy (3,190 CPM) After the steady state aalysis is completed, a trasiet startup aalysis is performed. It is based o the motor torque curve provided by the motor supplier. The ifiite bus startup curve for the fial, as-built, motor is show i Figure 4. I the fial report, the air gap characteristics were derated slightly to accout for a predicted 3 percet voltage dip i the electrical supply. Note the abrupt jump i the mea ad pulsatig torque at 79 percet sychroous speed. This reflects the custom motor desig aspects that eeded to be implemeted to satisfy the applicatio requiremets relative to startup load. Figure 10 is the plot of motor speed as a fuctio of time. Resoace with the first torsioal atural frequecy occurs at 13.9 secods. The torque reversals at resoace are of sigificat magitude to produce sizable oscillatios i shaft speed as see from this curve. Figure 10 Trai Speed Startup Plot 17 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

18 Figure 11 shows the resposes at the low speed ad high speed couplig locatios whe the twice slip frequecy compoet is i mometary resoace with the secod ad first torsioal atural frequecies durig startup. The jog i the vertical referece lies occurs because the iterferece diagram is speed-based, whereas the torque resposes are time-based. Figure 11 Couplig Torque Respose Dampig is oe of the mai parameters that ifluece peak torque levels at resoace. I the torsioal aalysis, a fixed modal dampig of 2.5 percet critical dampig was assumed, which is cosistet with idustry practice. A value of 1.0 percet is attributed to shaft hysteresis dampig ad 1.5 percet is assumed to be provided by the torsioal-lateral iteractio withi the gearbox. To validate this assumptio, a coupled torsioal-lateral aalysis was subsequetly performed. 18 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

19 Special Coupled Torsioal-Lateral Aalysis The program used i this study was recetly upgraded to hadle time trasiet, coupled torsioal-lateral systems; however, at the date of this publicatio, it did ot possess a speed-based startup aalysis capability for coupled torsioal-lateral systems. This shortcomig was addressed i the curret study by usig a time-based excitatio table which was geerated usig the acceleratio rate that matched the stadard torsioal startup aalysis. It is see from the startup curve i Figure 9 that the acceleratio rate through resoace is fairly costat. A motor acceleratio rate of 74 RPM/sec traslates ito a twice slip frequecy deceleratio rate of 4.93 Hz/sec. A time-torque tabular listig was the geerated usig a sie swept equatio obtaied from Irvie (1998): Torque (P.U.) = Mea Torque + Pulsatig Torque* Where, f2 fial frequecy f1 iitial frequecy t2 fial time t1 iitial time Sice the first torsioal atural frequecy is of primary iterest, a smaller trai model was geerated to reduce computatioal time of the coupled aalysis. This is show i Figure 12. The shaft ed stiffesses were fie tued to match the first ad secod torsioal atural frequecies. The radial bearigs for each major trai compoet were modeled for sake of completeess although the ifluece of bearigs for the motor ad compressor could probably be igored as they are far removed from the gear mesh. Figure 12 Coupled Torisoal-Lateral Model I the coupled aalysis, the dyamic coefficiets of the bullgear ad piio bearigs evaluated at resoace speed eed to be icluded i the model. The big ukow is the effective bearig load used to geerate the bearig coefficiets recogizig that the bearig coefficiets are a fuctio of eccetricity which is related to istataeous amplitude of vibratio. The rotor dyamic code that was used i this study utilizes (fixed) bearig coefficiets that are ot amplitude depedet. Figure 13 is a sketch of the bullgear ad piio bearigs, which i this istace, are ordiary sleeve type, pressure dam, bearigs. Key parameters relatig to the small bearigs i the origial gearbox ad the large bearigs i the fial, as maufactured, gearbox are also show. The pressure agle of the gear mesh is 20 degrees. At resoace, the gear typically udergoes large torque reversals. The bearig film characteristics are highly o-liear as the shafts trasverse the rage of the full bearig clearace. The maer of modelig bearig loads was discussed i Pradetto (2015). Good correlatio with measured field results was reported by assumig a bearig load of 10 percet of rated load. This makes ituitive sese because the dissipatio of eergy is related to the dampig term times the velocity. Sice the lateral velocity of the shaft is greatest at low joural eccetricities, the effective bearig dampig will be weighted toward the ceter of the bearig. 19 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

20 Origial Gearbox Fial Gearbox w/ Small Bearigs w/ Large Bearigs Bullgear Diameter (I) Legth (I) Uit Loadig (PSI) Surface Speed (Ft/Sec) Sommerfeld Number ( - ) Piio Diameter (I) Legth (I) Uit Loadig (PSI) Surface Speed (Ft/Sec) Sommerfeld Number ( - ) Ceterlie-To-Ceterlie Distace (Iches) Figure 13 Gearbox Bearigs Load Orietatio ad Key Parameters Figures 14 ad 15 show the time trasiet startup torque sigatures from the coupled torsioal lateral aalysis at the low speed ad high speed couplig locatios. Gear backlash effects were ot cosidered i the aalysis as it provides coservative results. These results are comparable to those determied from stadard torsioal aalysis for a fixed value of modal dampig of approximately 2.5 percet. Figure 14 Coupled Trasiet Respose At Low Speed Couplig Figure 15 Coupled Trasiet Respose At High Speed Couplig 20 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

21 Figure 16 shows the calculated steady state respose from the coupled torsioal lateral aalysis at the low speed ad high speed couplig locatios for the large (fial) bearig selectio. Curves are show for three cases which show dampig cotributed by three separate sources: 1. Shaft hysteresis dampig. A value of 1 percet was assumed which is cosistet with idustry practice. 2. Shaft hysteresis dampig plus lateral dampig from the bullgear bearigs 3. Shaft hysteresis dampig plus lateral dampig both from the bullgear ad piio bearigs Figure 16 Coupled Steady State Respose at the Low Speed Couplig For Large (Fial) Gear Bearigs It is see from these results that the bullgear bearigs cotribute the greatest dampig (1.3 percet) to the aggregate dampig of 2.5 percet. These values were determied usig the half power method from the coupled, steady state aalysis. Figure 17 shows a similar plot for the small (iitial) bearig selectio. For the purposes of this study, the gearbox geometry was kept the same, oly the bearig size was chaged. It shows a similar tred where the bullgear provides the greatest amout of torsioal dampig. A uexpected result is that the overall system dampig is higher for the smaller bearigs tha for the larger bearigs (3.4 percet vs. 2.5 percet); however, as is observed with lateral rotor dyamics, for a give set of system parameters, there is a optimum dampig level that produces the most favorable system respose. Although the torque level is lower with the small bearigs, the shaft stresses are higher as torsioal stress varies with diameter cubed. So i this istace, the large bearig selectio results i the lower shaft stresses eve though the torque levels are greater. Figure 17 Coupled Steady State Respose at the Low Speed Couplig For Small (Iitial) Gear Bearigs 21 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

22 A parametric study was performed to determie the effect of couplig (shaft) stiffess o overall dampig levels as show i Figure 18. Coupled respose results were geerated for a rage of couplig stiffess ratios. The couplig stiffess ratio is the ratio betwee the low speed couplig stiffess ad the high speed couplig stiffess relative to driver speed. This is relevat because couplig stiffess is oe variable over which the desiger has cotrol i the early productio phase. The left portio of the plot is for a relatively soft low speed couplig ad the right portio of the plot is for a relatively stiff low speed couplig. Figure 18 Coupled Aalysis Results Showig Ifluece Of Shaft Stiffess Distributio O System Dampig Figure 19 shows the mode shapes for both extremes. Please ote the locatio of the odal poits. As oe would expect, with a relatively soft low speed couplig, the ode is located betwee the motor ad gear. With a relatively stiff low speed couplig, the ode is located betwee the gear ad compressor. For the case of equal couplig stiffesses (while accoutig for gear ratio ifluece), the ode is located at the gear mesh. I this particular istace, it seems that positioig the ode poit at the gear mesh results i the most favorable value of system dampig. The subject applicatio is ear the optimum value of modal dampig of 2.5 percet. Further ivestigatio is required before drawig ay geeral coclusios relative to other trai arragemets. Couplig Stiffess Ratio =.11 (Soft Low Speed Couplig / Stiff High Speed Couplig) NODE 22 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

23 Couplig Stiffess Ratio = 1.0 (Low Speed Ad High Speed Couplig Stiffesses Equal) NODE Couplig Stiffess Ratio = 9 (Stiff Low Speed Couplig / Soft High Speed Couplig) NODE Figure 19 Torsioal Mode Shapes For Various Shaft Stiffess Distributios CONCLUSIONS The potetially high shaft torque levels durig across-lie starts of sychroous motor trais eed to be evaluated i the quotatio phase to properly size trai compoets to preclude cost overrus ad subsequet disruptios i the productio schedule. The severity of the resoace coditio durig a sychroous motor startup is a fuctio of various system parameters. The ifluece of these system parameters o peak torque levels ca be readily evaluated usig the closed form solutio documeted i Appedix 1. This ca be effectively used to assess various desig optios i the pre-quotatio phase of a project to obtai the most favorable desig based o techical ad commercial cosideratios. The followig meas have bee show to reduce peak torque levels durig startup: Decrease pulsatig torque at the motor air gap Decrease motor termial voltage Reduce startup load Icrease motor iertia Icrease system dampig through the use of torsioally resiliet coupligs or torque limitig coupligs Optimize dampig characteristics i the bullgear bearigs ad to a lesser degree i the piio bearigs as dictated by a coupled torsioal-lateral startup aalysis Adjust the stiffesses of the low ad high speed coupligs to positio the dampig ear the optimum value 23 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

24 I the subject example that was evaluated ivolvig a 6 MW compressor trai, a thorough ivestigatio of available optios was performed that resulted i the most favorable solutio based o both techical ad commercial cosideratios. The coupled torsioallateral aalysis was performed which validated the assumed modal dampig value of 2.5 percet used i the traditioal torsioal startup aalysis. Optimizig the bearig characteristics i the gearbox has the potetial to icrease system dampig. The cost evaluatio preseted i this tutorial applies to the cited example oly ad is iteded to demostrate the selectio process recogizig that other applicatios may produce differet results. RECOMMENDATIONS Sice startup load iflueces compoet selectio ad motor desig, a process dyamic simulatio study should be performed i the quotatio phase i istaces where it is ot possible to sufficietly offload a trai durig startup. Wheever possible, joural bearigs i the major trai bodies should be sized at least oe stadard size larger tha the shaft eds i the quotatio phase i the evet it is later discovered that the shaft shear stress or couplig hub slip capacity is later foud to be iadequate. Otherwise, if the shaft ed diameter eeds to be icreased, the resultig icrease i bearig (ad seal) sizes will egatively impact the productio schedule. API-684 should provide guidelies for coupled torsioal-lateral studies for geared systems relative to modelig of gearbox bearigs with respect to equivalet bearig load, gear mesh properties, backlash, etc. A coupled torsioal-lateral aalysis should be performed to validate the assumed dampig level used i the torsioal study for applicatios that are cosidered critical or are margial from a torque trasmissio or fatigue life stadpoit. 24 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

25 REFERENCES Awar,I., Colsher, R., 1979, Computerized Time Trasiet Torsioal Aalysis of Power Trais, ASME Paper 79-DET-74. API 617, 2014, Axial ad Cetrifugal Compressors ad Expader-Compressors for Petroleum, Chemical ad Gas Idustry Services, Eight Editio, America Petroleum Istitute, Washigto D.C. API 684, 2005, API Stadard Paragraphs Rotordyamic Tutorial: Lateral Critical Speeds, Ubalace Respose, Stability, Trai Torsioals, ad Rotor Balacig, Secod Editio, America Petroleum Istitute, Washigto D.C. API 546, 2008, Brushless Sychroous Machies 500 kva ad Larger, Third Editio, September 2008, America Petroleum Istitute, Washigto, D.C. Che, H.M., McLaughli, D.W., ad Malaowski, S.B., 1983, A Geeralized ad Simplified Trasiet Torque Aalysis for Sychroous Motor Drive Trais, Proceedigs of the Twelfth Turbomachiery Symposium, Turbomachiery Laboratory, Texas A&M Uiversity, College Statio, Texas, pp Corbo, M.A., Cook, C.P., Yeiser, C.W., ad Costello, M.J., 2002, Torsioal Vibratio Aalysis ad Testig of Sychroous Motor- Drive Turbomachiery, Proceedigs of the Thirty-First Turbomachiery Symposium, Turbomachiery Laboratory, Texas A&M Uiversity, Texas, pp Irvi, T., 1998, Sie Sweep Frequecy Parameters, Iteret dowload from tomirvie@aol.com. Used with permissio. Mruk, G., Hallora, J., ad Kolodziej, R., 1978, New Method Predicts Startup Torque- Part 1: Aalytical Model, Hydrocarbo Processig, pp Pradetto, J.C., Bauma, U., 2015, Coupled Torsioal Ad Lateral Aalysis For The Determiatio Of The Dampig Of The First Torsioal Mode Of Sychroous Motor Drive Compressor Trais, Proceedigs of the Forty-Fourth Turbomachiery Symposium, Turbomachiery Laboratory, Texas A&M Uiversity, Texas. Yeiser, C.W., Hutte, V., Ayoub, A., ad Rheiboldt, R., 2006, Revampig A Gas Compressor Drive Trai From 7000 HP To 8000 HP With A New Sychroous Motor Driver Ad A Cotrolled Slip Clutch Mechaism, Proceedigs of the Thirty-Fifth Turbomachiery Symposium, Turbomachiery Laboratory, Texas A&M Uiversity, Texas. Wright,J., 1975, Large Sychroous Motor Drives: A Review of the Torsioal Vibratio Problem ad It s Solutio, Koppers Compay, Ic., Baltimore, Marylad. Wolff, F.H., 1977, Acceleratio through Resoace of Multi-Degree of Freedom Systems, the Shock Ad Vibratio Bulleti, Naval Research Laboratory, No. 47, Part 2, pp Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

26 Appedix 1: Simple Method For Estimatig Peak Shaft Torques I Sychroous Motor Trais For Across-Lie Starts The followig method ca be used to estimate peak shaft torques durig across-lie starts for trais cotaiig costat speed sychroous motors. It serves as a aid i makig decisios relative to the prelimiary sizig of coupligs ad shaft eds. The oly iformatio required to use this method are the iertias of the major trai compoets, a motor startup curve, gear ratio, load distributio ad the Magificatio or Q Factor of the system. J1 J2 J3 J4 T1 T3 Motor L2 Gear L3 Compr. 1 L4 Compr. 2 MEAN TORQUE ALTERNATING TORQUE Defiitio Of Terms: J1,J2,J3,J4 Iertia Fractio Of Major Compoets Refereced To Motor Speed (where J1+J2+J3+J4 = 1.00) T1,, T3 Total Peak Shaft Torque L2,L3,L4 Load Fractio Of Total Load (where L2+L3+L4 = 1.00) Tload Total load at resoace from motor startup torque curve Tmea Mea motor torque at resoace from motor startup torque curve Tpuls Pulsatig motor torque at resoace from motor startup torque curve Mode shape adjustmet factor associated with T1 (typically betwee 0.80 to 1.00) β Mode shape adjustmet factor associated with (typically betwee 0.90 to 1.10) γ Mode shape adjustmet factor associated with T3 (typically betwee 0.90 to 1.10) GR Gear Ratio Q Magificatio Factor 26 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

27 Notes: 1) All torques are expressed i cosistet uits such as P.U. or I-Lbs. 2) Gear Ratio (GR) term is applied to both the mea torque ad alteratig torque, as show. 3) The iertia values dowstream of the gear mesh are refereced to motor speed by multiplyig them by the GR squared. The total gear iertia show o the API 613 data sheets usually reflects this where the Total Gear Iertia = Bullgear Iertia + (Gear Ratio )^2* Piio Iertia. 4) If the motor speed correspodig to the first torsioal atural frequecy is ot kow, the load, mea ad pulsatig torques ca be evaluated at 85 percet rated speed for 60 Hz supply or at 75 percet rated speed for 50 Hz supply. 5) Magificatio factors are a fuctio of dampig ratio ad acceleratio rate. See Figure A-1 below. 6) The major bodies eed to be arraged as show below with the motor i the left most positio. This method caot be used for doubled eded motor applicatios. 7) A complete ad thorough trasiet torsioal aalysis must be performed oce the hardware is selected to cofirm torsioal acceptability. Determiig Magificatio Q Factor The equatios for peak torques show o the previous page predict the trasiet respose of a torsioal system at resoace. The effects of acceleratio are take ito cosideratio by adjustig the magificatio Q factor usig the method obtaied from Wolff (1977) ad summarized below. Durig trasiet coditios, Where, Q = Magificatio Factor q = Acceleratio Factor = (Hz-sec) f1 = First Torsioal Natural Frequecy (Hz) = Electrical Supply Frequecy (60 Hz or 50 Hz) h = Deceleratio Rate Of Twice Slip Frequecy At Resoace Tmea Tload 2* flie h= * TotalTraiIertia N rated / 60 (Hz/Sec) I this equatio, torque is expressed i uits of i-lbs. ad total trai iertia is expressed i uits of lbs-i-sec2. Note that parameter h is the acceleratio rate of the twice slip frequecy relative to the torsioal atural frequecy ot the acceleratio rate of motor speed relative to the torsioal atural frequecy. Oce ξ ad q are determied, the magificatio factor Q ca be obtaied from Figure A-1 below. It is see from this plot that for rapid acceleratio, the dampig ratio has less ifluece o the magificatio factor tha for the case of slow acceleratio. Additioally, for heavily damped systems, the magificatio factor is relatively isesitive to acceleratio rate. 27 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio

28 If the dampig ratio is ot kow, a very coservative estimate for magificatio factor ca be determied based o a dampig ratio of zero. I this istace, the magificatio factor Q becomes purely a fuctio of acceleratio rate: Durig trasiet coditios, At steady state, [Special case for zero dampig] [Special case for zero acceleratio] For applicatios with covetioal all-steel coupligs, the magificatio factor typically rages from 10 to 20. Elastomeric coupligs (a.k.a Holset or rubber block coupligs) are used betwee the motor ad gear to provide higher levels of dampig tha could otherwise be achieved with all-steel coupligs. The published magificatio factors for elastomeric coupligs rage from 3.0 to 4.0 for high dampig, SBR, material depedig o the material hardess. I the prelimiary evaluatio, the equivalet magificatio factor eeds to be estimated based o a weighted average of the relative deflectio of the rubber blocks (high dampig) ad steel elemets (low dampig). Cosequetly, the effective magificatio factor is approximately 1.5x to 2x the published block magificatio factor (ie. Qeff = 1.67 x 3.0 = 5.0). Figure A-1 28 Copyright 2017 by Turbomachiery Laboratory, Texas A&M Egieerig Experimet Statio