Long blade vibration model for turbine-generator shafts torsional vibration analysis

Transcription

1 Avalable ole Joural of Checal ad Pharaceutcal Research, 05, 7(3): Research Artcle ISSN : CODEN(USA) : JCPRC5 Log blade vbrato odel for turbe-geerator shafts torsoal vbrato aalyss ezheg J ad Yuog Gu North Cha Electrc Power Uversty, Chagpg Dstrct, Beg, Cha ABSRAC he ubrella type vbrato of the last stage blade dsk of the low pressure turbe ca be duced by the exteral exctato whch caused by the torsoal vbrato of the turbe-geerator shafts. However, there s o applcable odel for aalyzg the blade dsk vbrato due to shft torsoal vbrato. Accordg to the characterstc of ubrella type blade dsc vbrato, a blade odel for aalyzg the vbrato of the log blades durg the torsoal vbrato of the shafts s gve ths paper. A paraeter adustg ethod based o sestvty aalyss s preseted so as to ake the heret characterstc of the blade dsc odel close to that of the real blade dsc. Keywords: Blade dsc vbrato odel; Paraeter Adustet; urbe-geerator; orsoal vbrato. INRODUCION At preset, splfed odel for shaft-blade cobed vbrato s to cosder the shafts of the stea turbe geerator ut as a ass-sprg odel. I ths case, the turbe blades are cosdered as the brach structures of the shafts odel ad ther radal oveets are gored. o accout the teracto of the blades durg vbrato, the fluece of the shroud has bee aalyzed [-5], ad the shroud s cosdered as sprgs [6]; or cosdered as dapg [7-8]. Durg shaft lateral vbrato, blades dfferet posto have dfferet vbrato states, therefore, these kds of odel ca effectvely sulate the teractos aog dfferet blades durg lateral vbrato. However, durg torsoal vbrato, blades dfferet posto receve the sae exteral torque fro the turbe shft. herefore, the characterstc of the last stage blade dsk vbrato due to shaft torsoal vbrato s ubrella type vbrato wthout radus. here s o relatve oveet aog the blades these two odels uder ubrella type vbrato. Hece, these two odels caot stulate the pact caused by the shroud o the blade durg shaft vbrato. herefore, t s ecessary to establsh a ew vbrato odel for sulatg the vbrato of the log blades durg the torsoal vbrato of turbe-geerator shafts. Log Blade Vbrato Model o aalyze the pact caused by the blade shroud o the log blades durg torsoal vbrato aalyss, a ass-sprg odel ca be establshed accordg to the followg ethods: durg shaft torsoal vbrato, the blade vbrato ca be cosdered as lateral vbrato relatve to the blade root. he, each blade ca be cosdered as a ass-sprg odel wth oe ed fxed o the shaft, whch has oly x drecto vbrato. he ass-sprg odel ca be show the followg Fg.. Fg. Blade vbrato equvalet odel 39

2 ezheg J ad Yuog Gu J. Che. Phar. Res., 05, 7(3): Paraeter Adustet. urbe blades ca be odeled to luped ass torsoal vbrato odel wth degrees of freedo, the u-daped free torsoal vbrato dfferetal equato s as follows: I θ & + Kθ 0 & () Where I ad K are the oet of erta atrx ad stffess atrx, respectvely; θ ad && θ are ass dsplaceet atrx ad accelerato atrx, respectvely. Substtutg θφs (ωt+ψ) to Eq. (), the atural frequecy ω ad vbrato odes φ ca be obtaed fro: ( K I ) φ 0 ω () Based o vbrato echacs, the relatoshps betwee atural frequecy ad vbrato odes are as follows: K ω I φ (3) ( ) 0 [ I ] φ φ (4) Where ω ad φ are the atural frequecy ad vbrato ode after regularzato of the tch order, respectvely. Multply Eq. (3) by φ fro left ad dfferetatg t, followg relatos are obtaed: ϕ I ω ϕ K I + I + K I 0 (5) x x x x x ( ω ) ϕ ϕ ( ω ω ) ϕ ϕ ( ω ) Isertg Eqs. (3) Ad Eq. (4) to Eq. (5), the atural frequecy sestvty of structure paraeter s obtaed by: φ ω x x I ω x ω φ (6) Where x stads for the elastc stffess K. he sestvty of ω to the th sprg s gve by: φ φ ω K ω [( φ ) ( φ ) ] ω + (7) All the sestvtes of each order atural frequeces ca be calculated based o Eq.(7). he value of the sestvty reflects the rate of chage of atural frequecy wth the torsoal rgdty varato. he atural frequecy of torsoal vbrato ω ca be expressed by the oet of erta I ad torsoal stffess K as follows: ( I I K L K ) ω f (8) L, Wth aylor seres expaso Eq. (8) ca be wrtte whe gorg the secodary ad ts above odfed ters: ω ω ω ωo ω I + K (9) I Eq. (9) descrbe the relatoshp betwee the varato of torsoal vbrato atural frequecy ω ad structure paraeters I K. he relatoshp s cosdered to be lear due to the the varato of structure paraeters are 330

3 ezheg J ad Yuog Gu J. Che. Phar. Res., 05, 7(3): relatvely sall. So the secodary ad secodary above odfed ters the aylor expaso were gored. he torsoal oet of erta has bee olded accurately eough ad the dapg coeffcet has lttle fluece o the torsoal vbrato heret characterstcs whe adustg the torsoal vbrato odel. herefore, oly cosderg the torsoal rgdty varato Eq. (9) ca be splfed as: ω K ω (0) orsoal vbrato atural frequecy devato ω ca be acheved based o the actual value ω by otorg ad aalyss ad the calculato result ω o by the torsoal vbrato odel. Ad the the torsoal rgdty of adaptve adustet quatty K ca be solved by a equato set based o Eq. (0), whch ca ake the orgal vbrato odel becoe ore accurate. he equato set ca be wrtte as atrx expresso [A] [X] [B]: ( ) ω L ω B () ( ) X () K L K ω ω L A M L M (3) ω ω L he soluto of ths equato set whch s torsoal rgdty adustet quatty K desred to kow ca be obtaed fro atrx trasforato equatos, that s XA/B. Fro the above, the paraeter adustg procedure s show Fg.. Fg. he logc schee of torsoal vbrato odel ole adaptve adustet Aalyss ad Applcato ake a last stage blade the low pressure turbe of a 000MW turbe-geerator ut as a research obect. Assue the actg stress at the blade tp posed by the shroud were proportoal to the dsplaceet of blade tp relatve to ts root, show Fg.3. Based o fte eleet aalyss results of the ature characterstcs of blade vbrato, the ature characterstcs of ass-sprg odel ca be show Fg.4 ad table. Fg.3 Mass-sprg equvalet odel 33

4 ezheg J ad Yuog Gu J. Che. Phar. Res., 05, 7(3): x ode(orgal) ode(orgal) ode(strg-mass Model) ode(strg-mass Model) R() Fg.4 Mass-sprg odel vbrato odel Let kg able Mass-sprg vbrato odel ature characterstcs ω ω / H z 6 0 / H z ω ω ( ) X ( X) ( X) ( X) k N calculate ass-sprg odel paraeters through paraeter odfcato ethod show the fg. Ad the calculato value s show the followg table. k 3 able ass-sprg odel calculato value ω ω ( ) k / X ( X) It ca be see fro the table, after 4 tes of calculato, the odel ature frequecy rato odel s alost the sae wth blade vbrato characterstcs. Ad the, t s oly requred to adust ad k to ake the odel rotatoal erta relatve to shaft ceterle be the sae wth that of actual blade. Ad the st phase ature frequecy of the odel s the sae wth that of blade. So, the ass paraeter ad rgdty paraeter of sgle blade odel ca be calculated. I-addto, oe crcle has 85 blades. he paraeters of the whole crcle blade ass-sprg odel ca be calculated. he ass ad rgdty values of sgle blade ad oe crcle blades s show the followg table 3. able 3 Mass-sprg odel paraeter k k k3 3.35kg 84.75k g 9.0kg k g N/.46 09N/ CONCLUSION N/ N/ N/ N/ It has bee proved that the heret characterstcs of the log blade ubrella type vbrato due to torsoal vbrato of turbe-geerator shafts ca be accurately sulated usg the blade odelg ethod ad the paraeter adustg ethod. Whch ca sure the accuracy of the blade vbrato respose aalyss. REFERENCES []D. Cha, A.Sha. Joural of Egeerg for Gas urbes ad Power, 003, 5 (4): p [] K. H. Koh, J.H.Grff, S.Flpp, et al. Gas urbes Power, 005, 7 (4): p

5 ezheg J ad Yuog Gu J. Che. Phar. Res., 05, 7(3): [3] Eder Cgeroglu, H.Nevzat Ozguve. Joural of Soud ad Vbrato, 006, 95 (3-5): p [4] Aldo A.Ferr, Waye E.Whtea. Joural of Soud ad Vbrato, 007, 306 (3): p [5]Eder Cgeroglu, NgA, Cha-Hsag, et al. Nolear Dyac, 007, 50. [6]J.H.Grff,.M.Hoosac. Joural of Vbrato, Acoustcs, Stress ad Relablty Desg. 984, 06(): p. 04~0. [7]S..We, C.Perre. Joural of Vbrato, Acoustcs, Stress ad Relablty Desg.988, 0(4): p.49~438. [8]S..We, C.Perre. Joural of Vbrato, Acoustcs, Stress ad Relablty Desg.988, 0(4): p.439~