Proceedings of ME Turbo Expo 0 GT0 June -5, 0, openagen, Denmark GT0-6806 ON TO-PLNE BLNING OF YMMETRI ROTOR Jon J. Yu, P.D. GE Energy 63 Bently Parkway out Minden, Nevada 8943 U Pone: (775) 5-5 E-mail: jon.yu@ge.com BTRT en rotor balancing is performed in te field, minimum trial weigt runs would significantly reduce te downtime in power generation and oil-gas industries. Typically two trial weigt runs would be required in order to obtain bot static and couple influence coefficients. Te current paper demonstrates ow bot static and couple influence coefficients can be evaluated wit ig accuracy troug merely one trial weigt run on symmetric rotors. It is sown troug real cases tat, for symmetric rotors suc as double-flow low-pressure (LP) turbine and generator rotors, cross effects between static weigts (placed in-pase at two ends) and couple response (te same vibration amplitude but 80 degrees out-of-pase at two ends) are minimal and can be neglected. Te same olds true for coupled weigts (placed 80 degrees out-of-pase at two ends) and static response (te same vibration amplitude inpase at two ends). Real cases sow tat static and couple influence coefficients for symmetric rotors obtained from te one trial weigt run are very close to te true values from te two trial weigt runs or te classical static/couple approac. From te calculated static and couple influence data troug one trial weigt run, final balance weigts for reducing static or couple response only or teir combination can be determined successfully. INTRODUTION In rotating macines, most ig vibration problems are caused by mass unbalance. itout reducing vibration levels troug balancing, te life span of te macine could be reduced as a result of excessive stresses on te rotor, bearings and casing. Te source of unbalance may include assembly variation and material non-omogeneity. Tis can appen on new macines or macines after rotor repair or overaul. Toug rotors are often low-speed or sometimes ig-speed balanced by manufacturers or worksops before tey are installed for service, unbalance may still occur afterwards due to various reasons. Tese include deposits on or erosion and sifting of rotating parts as well as termal effects. Terefore, in many cases, field balancing is required to reduce syncronous vibration level. Balancing as been of great interest to rotor dynamic researcers as well as practicing engineers [, ]. Vibration readings are typically obtained and monitored by a pair of proximity probes installed on teir bearing caps. steam turbine or generator rotor is typically supported by its two bearings wit adjacent macine rotors connected to eac oter via couplings. Tis often requires two-plane balancing of te rotor. References [3] and [4] discussed two-plane balancing wit amplitude or pase only, wic would often require more trial weigt runs in te field. Te influence coefficient metod is typically used in te field for trim balancing wit two approaces. Te first metod is to andle te trim balancing as a multi-plane balance problem involving a x matrix of complex influence coefficients [5]. In tis approac, two direct influence coefficients along wit two cross-effect influence coefficients are generated so tat correction weigts at two balance planes can be determined. Te second metod is to andle it as two single-plane balance problems using static and couple vibration components along wit static and couple weigts, respectively [6, 7]. Te static and couple components are actually referred to as in-pase and 80 degrees out-of-pase components, respectively. Te static component is usually due to first and/or
tird modes tat are almost symmetric about te rotor mass center wile te couple component is typically due te second mode tat is almost anti-symmetric. tatic weigts are defined as tose placed in-pase at two ends wit te same amount wile couple weigts are defined as tose placed 80 degrees out-of-pase. Terefore, te current static and couple vibration or weigt vectors are really referred to as in-pase and 80 degrees out-of-pase, respectively. tatic and couple terms ave teir origin from rigid rotor balancing, and ave been extended to flexible rotors for balancing te first, te second, and/or even te tird modes. Tese terms are well defined in te standards of balancing, and ave been widely accepted and used in te field. Terefore, tese terms are used trougout tis paper so tat practicing engineers may apply te solutions from te paper by convention. In 009, te autor indicated te relationsip of influence coefficients between static-couple and multiplane metods on two-plane balancing [8]. Tus, Te autor, owever, as found tat one trial weigt run can yield bot static and couple influence coefficients wit ig accuracy In tis paper, te one trial weigt run metod is introduced based on previously proposed static-couple balance model [8] along wit te relationsip of influence coefficients between static-couple and multiplane metods. TEORY aft Probe view Probe aft 7 9 eigt plane eigt plane 7 9 8 aft aft 8 7 9 7 9 8 8
() () () () (3) () () () () () relationsip of influence coefficients between static-couple and multiplane metods developed in 009 [8] (see ppendix), (a) (b) and are defined as static and couple components, respectively. imilarly, static weigts are placed in-pase at two ends wit te same amount wile couple weigts are placed 80 degrees out-of-pase. Te static-couple balance approac fits to bot rigid and flexible rotors. (4) (5a) (5b) Probe view Probe 7 aft 9 eigt plane eigt plane 7 aft 9 8 7 aft couple weigts 9 7 aft 9 8 8 static weigts 8
() () () () (7) () () () () (8) E ONE () () () () (9) () () () () () (). supported by two journal bearings, numbered in order from te turbine to te generator. en viewed in Fig. 3 from te turbine towards te generator, te macine train is seen to be rotating in te clockwise direction. Bot te steam turbine and te generator vibrations are measured by XY pairs of noncontacting proximity probes mounted at 45-degree left (Yprobe) and 45-degree rigt (X-probe) relative to te 0 degree vertical reference at eac bearing from Bearing # to #6. Its macine train diagram is sown in Fig. 3. Te data in tis case were presented by using View P-IP LP Brg # Brg # Brg #3 Brg #4 Generator Brg #5 Brg #6 Brg # to #6 Radial Proximity Probes Y 45 L 45 R X Brg#3Y eigt access port Brg#4X eigt access port Brg#3X Brg#4Y
0.54 mil pp 03.04 mil pp 65.37 mil pp 53.835 mil pp 00 Existing weigts Existing weigts (a) Resultant weigt at plane 3: 9.48 oz 7.5 deg (b) Resultant weigt at plane 4: 0
() () 9.48 oz 7.5, 0 wit te corresponding vibration vectors () () 3.57 mil pp 56.647 mil pp 77 0.0896 mil pp /oz 58 0.390 mil pp /oz 68 To offset bot static and couple vibration components, te required static and couple weigts would be Tis would require weigt placement on ole 3 at balance plane 3, wic ad an existing weigt inside already. ince it was not feasible to place te above weigts, an alternative needed to be found. Te main vibration was composed of te couple component, and sensitivity of couple influence data was about to 3 times iger tan tat of static influence data. Terefore, placement of te couple weigts appears to be more effective if it could be implemented. Tis also will demonstrate to see if suc estimated was accurate and effective enoug to offset te couple vibration component. To offset te couple vibration component based on te estimated influence data, te desired couple weigt placement 8.5 oz 7 would need insertion of a weigt on ole 5 or 6 at balance plane 3 plus a weigt on ole 3 or 4 at balance plane 4. owever, since oles 5 and 6 at balance plane 3 were already occupied wit te existing weigts, two available weigts (5.6 ounces on ole and 8.36 ounces on ole 7) were placed as sown in Fig. 7, resulting in an equivalent weigt of 0.073 ounces at 3.6 degrees relative to te Y-probe at balance plane 3. weigt plug of 9.95 ounces was placed on ole 3 at balance plane 4. Tus, te correction weigts were as follows: () () 0.073 oz 3.6, 9.95 oz 87.5 wic were approximately equivalent to te couple weigt 0 oz 6. Te corresponding vibration vectors wit te above weigts were () () 0.87 mil pp 8 0.895 mil pp 0 6.0 oz 5, 8.5 oz 7, () 0.586 mil pp 4 wic are equivalent to te weigts at two planes as below: 4.3 oz 336, 4. oz 09 Existing weigts dded weigts () 0.34 mil pp Existing weigts dded weigts (a) Resultant weigt at plane 3: 0.073 oz 3.6 deg (b) Resultant weigt at plane 4: 9.95 oz 87.5 deg
Fig. 8 sows syncronous X orbits at bearings #3 and #4 before and after balancing. Large outer orbits indicate syncronous vibrations before balance wile small inner orbits indicate syncronous vibrations after balance. t suc a low vibration level, no furter balancing would be needed. Its multiplane influence coefficients can be computed as below () () () () () () () () 0.76 90 0.0975 mil pp / oz 0.68 0.305 97 It can be seen tat Using te conversion formulas (see ppendix), te corresponding influence coefficients for static-couple balance model can be computed as sown below tatic and couple influence coefficients obtained from one trial weigt metod versus te true values via te two trial runs for symmetric LP rotor 0.096349 0.05367 mil pp / oz 0.0 37 0.87 7 Te above static and couple influence data can be considered as true values. Te are very small compared wit direct static and couple influence coefficients. Table sows static and couple influence coefficients using te one trial weigt metod versus te true values via te two trial runs. Te influence data from te one trial weigt metod is very close to te true values wit less tan 0% difference in sensitivity and less tan 0 degrees in pase. Tis can be considered to be well acceptable for field balancing. s can be seen in tis case, using te estimated influence data from te one trial weigt metod yields satisfactory balancing results. In tis example, only one trial weigt was applied at one of te two balance planes to obtain bot static and couple influence coefficients for tis symmetric rotor. E TO, a Bently Nevada RK-4 Rotor Kit was BRG# Vertical (0 ) Mid-span spring BRG# Vertical (0 ) View BRG# orizontal (90 R) eigt plane eigt plane BRG# orizontal (90 R)
() ().3 g 80, 0.8 g 80 Te above weigts are equivalent to () ().05 g 80, 0.5 g 80 Tese weigts yielded te corresponding vibration vectors ().593 mil pp 7 ().08 mil pp 7 ().306 mil pp 7 () 0.88 mil pp 7 3.97 mil pp 40 5.736 mil pp 04.976 mil pp /g 8. mil pp 75 8.0957 mil pp /g 3 4.790 mil pp 3 s sown in te above, after te first trial weigt placement, te couple response was reduced to 0.88 mil pp. Only te static response of.306 mil pp migt need to be offset. Based on te above calculated s.306 mil pp 7 0.5684 g 5.976 mil pp /g 8
tatic and couple influence coefficients obtained from one trial weigt metod versus te true values via te two trial runs for symmetric rotor kit () () 0.8 g 80, 0.3 g 80 Te corresponding vibration vectors wit te above weigts were () 0.43 mil pp 35 () 0.34 mil pp 08 imilar to case one, () () 0.44 mil pp 50 0.07 mil pp 7 Fig. sows syncronous X orbits at bearings # and # before and after balancing. Large outer orbits indicate syncronous vibrations before balance wile small inner orbits indicate syncronous vibrations after balance. Bot static and couple response vibration vectors became very low, and no furter balancing was needed. Its multiplane influence coefficients can be computed as below () () () () () () () () 8.33 33 0.4405 mil pp / g 0.37808 8.5887 35 Using te conversion formulas as presented in ppendix, te corresponding influence coefficients for static-couple balance model can be computed as below.79879 0.4996 mil pp / g 0.8564 8.67930 Te above static and couple influence coefficients can be considered as true values. Te are very small compared wit direct static and couple influence coefficients. Table sows static and couple influence coefficients using te one trial weigt metod versus te true values via te two trial runs. In tis case, te influence data from te one trial weigt metod is even closer tan in case one to te true values wit less tan 3% difference in sensitivity and less tan 3 degrees in pase. Tis accuracy level certainly is considered to be ig enoug for field balancing. Using te estimated influence data from te one
trial weigt metod again yields satisfactory balancing results as in case one. In tis example, unlike case one, one trial weigt placement was implemented at two balance planes to obtain bot static and couple influence coefficients for tis symmetric rotor kit. ONLUION Based on analytical and real case studies presented in tis paper, te following conclusions are stated regarding two-plane balancing of symmetric rotors: () () One trial weigt run can yield bot static and couple influence coefficients close to te true values ( ) from two trial weigt runs. Te accuracy level of tese influence coefficients is ig enoug for field trim balancing. (3) One trial weigt placement can be implemented by adding or removing weigts at one end only, wic generates equal amount of static and couple weigts. Tis can also be alternatively done by weigt placement at two ends, as long as it generates bot static and couple weigt amounts. (4) ensitivity of bot static and couple influence data can ten be evaluated via te one trial weigt run along wit vibration response to see eiter static or couple weigts are more effective. (5) Rotor symmetry can also be seen from te influence data using te multiplane balance model. Tis is indicated by te same diagonal elements (direct term) plus te same off-diagonal elements (cross term). (6) Te effectiveness of using te proposed one trial weigt placement for obtaining bot static and couple influence coefficients as been demonstrated by real examples. KNOLEDGMENT NOMENLTURE syncronous vibration vector measured by probe syncronous vibration vector measured by probe couple vibration vector couple vibration influence vector due to couple weigts couple vibration influence vector due to static weigts (cross effect) static vibration influence vector due to couple weigts (cross effect) static vibration influence vector due to static weigts probe vibration influence vector due to plane weigt probe vibration influence vector due to plane weigt probe vibration influence vector due to plane weigt probe vibration influence vector due to plane weigt static vibration vector weigt vector at balance plane weigt vector at balance plane couple weigt vector static weigt vector GREEK pase lag of pase lag of pase lag of pase lag of UPERRIPT 0 initial status witout weigts. status wit weigts or wit first trial weigts status wit second trial weigts PPENDIX: ONVERION FORMUL OF INFLUENE OEFFIIENT BETEEN TTI- OUPLE ND MULTIPLNE BLNE MODEL () () (3) (4) (5) (6) (7) (8)
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