夏亞磊,楊建剛,張曉斌
(1.東南大學(xué) 火電機(jī)組振動(dòng)國(guó)家工程研究中心,南京 210096;2.華北電力科學(xué)研究院有限責(zé)任公司,北京 100045)
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柔性轉(zhuǎn)子轉(zhuǎn)軸彎曲與不平衡耦合振動(dòng)分析
夏亞磊1,楊建剛1,張曉斌2
(1.東南大學(xué) 火電機(jī)組振動(dòng)國(guó)家工程研究中心,南京 210096;2.華北電力科學(xué)研究院有限責(zé)任公司,北京 100045)
針對(duì)某660 MW超臨界汽輪機(jī)高中壓轉(zhuǎn)子上發(fā)生的不穩(wěn)定振動(dòng)問(wèn)題,建立了轉(zhuǎn)子彎曲與不平衡耦合動(dòng)力響應(yīng)有限元計(jì)算模型,并通過(guò)現(xiàn)場(chǎng)實(shí)例驗(yàn)證模型的準(zhǔn)確性.結(jié)果表明:高轉(zhuǎn)速運(yùn)行時(shí),汽輪機(jī)高壓轉(zhuǎn)子因配重面與失衡面不重合所引起的彎曲變形會(huì)導(dǎo)致振動(dòng)的不穩(wěn)定和持續(xù)爬升;動(dòng)平衡試驗(yàn)應(yīng)盡量在轉(zhuǎn)子失衡面上進(jìn)行;高壓轉(zhuǎn)子環(huán)境溫度高,在外力作用下易發(fā)生蠕變,該現(xiàn)象在大型汽輪機(jī)高壓轉(zhuǎn)子上表現(xiàn)得更為明顯.
柔性轉(zhuǎn)子; 彎曲變形; 不平衡; 振動(dòng); 響應(yīng)
旋轉(zhuǎn)機(jī)械轉(zhuǎn)軸彎曲會(huì)引發(fā)大幅度振動(dòng),對(duì)機(jī)組安全穩(wěn)定運(yùn)行的影響很大.羅挺等[1]建立了具有初始彎曲的多圓盤(pán)轉(zhuǎn)子系統(tǒng)有限元計(jì)算模型,分析了不同平面模態(tài)振型初始彎曲情況下對(duì)多圓盤(pán)轉(zhuǎn)子系統(tǒng)不平衡響應(yīng)的影響.Kang等[2]分析了彎曲轉(zhuǎn)子振動(dòng)特性,指出初始彎曲的大小和角度對(duì)一階臨界轉(zhuǎn)速處振動(dòng)影響巨大.吳文青等[3]以某1 000 MW汽輪機(jī)低壓轉(zhuǎn)子為例,對(duì)轉(zhuǎn)子不平衡和彎曲引發(fā)的振動(dòng)特征進(jìn)行了對(duì)比分析.Song等[4]指出當(dāng)偏心率和阻尼比相對(duì)小時(shí),彎曲將會(huì)嚴(yán)重影響轉(zhuǎn)子振動(dòng).何國(guó)安等[5-6]對(duì)彎曲故障平衡處理方法進(jìn)行了研究.Deepthikumar等[7]提出用傳遞矩陣法平衡同時(shí)具有不平衡和彎曲故障的轉(zhuǎn)子軸承系統(tǒng).轉(zhuǎn)軸彎曲大多是因轉(zhuǎn)軸截面存在不對(duì)稱溫差所引起的[8-9],如動(dòng)靜部件之間的摩擦[10-12].卓明等[13]分析了轉(zhuǎn)子熱彎曲變形的機(jī)理,計(jì)算了熱彎曲變形轉(zhuǎn)子啟動(dòng)時(shí)的振動(dòng)響應(yīng).Baldassarre等[14]提出一種自然冷卻轉(zhuǎn)子熱彎曲變形計(jì)算方法,預(yù)測(cè)轉(zhuǎn)子再啟動(dòng)過(guò)程的振動(dòng)響應(yīng).肖小清等[15]結(jié)合現(xiàn)場(chǎng)實(shí)例對(duì)轉(zhuǎn)子彎曲情況下的不平衡響應(yīng)及熱彎曲變化情況進(jìn)行了分析.近年來(lái),軸承內(nèi)Morton效應(yīng)引發(fā)的熱變形現(xiàn)象逐漸引起重視.研究表明,軸承內(nèi)潤(rùn)滑油的不均勻黏度剪切效應(yīng)會(huì)使轉(zhuǎn)子產(chǎn)生徑向溫度梯度,導(dǎo)致轉(zhuǎn)子產(chǎn)生熱變形[16].
筆者所研究的一類轉(zhuǎn)子彎曲故障,與截面溫差無(wú)關(guān),而是由于動(dòng)平衡試驗(yàn)時(shí)配重面與失衡面不重合所引起的.對(duì)于這類故障,如果平衡方法不正確,運(yùn)行一段時(shí)間后轉(zhuǎn)子彎曲加劇,機(jī)組振動(dòng)將會(huì)惡化.Chen等[17]研究了此類現(xiàn)象,對(duì)轉(zhuǎn)子彎曲變化過(guò)程進(jìn)行模擬,指出不均勻蠕變導(dǎo)致轉(zhuǎn)子發(fā)生彎曲變形.這是隨著旋轉(zhuǎn)機(jī)械向大型化方向發(fā)展所出現(xiàn)的一種新型故障現(xiàn)象,突出表現(xiàn)在大型超臨界汽輪機(jī)組上.
筆者針對(duì)某660 MW超臨界汽輪機(jī)高中壓轉(zhuǎn)子發(fā)生的不穩(wěn)定振動(dòng),建立了轉(zhuǎn)子彎曲以及轉(zhuǎn)子彎曲/不平衡力耦合作用下動(dòng)力響應(yīng)有限元模型,分析了動(dòng)平衡試驗(yàn)時(shí)不恰當(dāng)配重所引起的轉(zhuǎn)子彎曲變形現(xiàn)象及其對(duì)振動(dòng)的影響.
1.1 剛性轉(zhuǎn)子平衡
如圖1所示,對(duì)于剛性轉(zhuǎn)子而言,假設(shè)轉(zhuǎn)子中部有一不平衡量F,在轉(zhuǎn)子兩端加重F1和F2,l1和l2分別為兩端截面到中部的距離,如果滿足:
(1)
那么,剛性轉(zhuǎn)子處于平衡狀態(tài).
圖1 剛性轉(zhuǎn)子受力Fig.1 Stress analysis model for the rigid rotor
1.2 外力作用下轉(zhuǎn)子彎曲計(jì)算模型
對(duì)圖1所示的轉(zhuǎn)子模型,在轉(zhuǎn)軸截面突變和葉片等帶有集中質(zhì)量的截面處將其劃分為若干節(jié)點(diǎn),由靜力學(xué)理論可知,外力作用下轉(zhuǎn)子的變形量為
Kq=R
(2)
式中:K為總體剛度矩陣;q為節(jié)點(diǎn)位移矩陣;R為載荷矩陣.
1.3 不平衡與彎曲耦合響應(yīng)分析
由轉(zhuǎn)子動(dòng)力學(xué)理論可知,不平衡與彎曲耦合作用下系統(tǒng)不平衡響應(yīng)動(dòng)力學(xué)方程[18]為
(3)
式中:ω為旋轉(zhuǎn)頻率;M1為整體質(zhì)量矩陣;K1為整體剛度矩陣;G1為整體回轉(zhuǎn)矩陣;cij、kij(i,j=1,2)分別為整體油膜等效阻尼和剛度矩陣;rx、ry為初始彎曲矩陣r在x,y方向的分量;U1、U2為系統(tǒng)位移向量;Q1、Q2為不平衡力向量;下標(biāo)c、s表示不平衡力向量中的余弦和正弦分量.
(4)
其中,θ為截面偏轉(zhuǎn)角.
設(shè)耦合響應(yīng)的穩(wěn)態(tài)解為
(5)
將式(4)、式(5)代入式(3)可得:
(6)
其中,
求解式(6),可得系統(tǒng)在不平衡力和彎曲共同作用下的振動(dòng)響應(yīng).計(jì)算時(shí),純不平衡、純彎曲、不平衡與彎曲耦合工況如下:純不平衡工況,r=0,Q≠0;純彎曲工況,r≠0,Q=0;不平衡與彎曲耦合工況,r≠0,Q≠0.
以某660 MW超臨界汽輪機(jī)高中壓轉(zhuǎn)子為例進(jìn)行研究,該轉(zhuǎn)子總長(zhǎng)度為7.27 m,總質(zhì)量為20.053 t,材料彈性模量E=2.1×1011Pa.建立有限元模型時(shí),將整個(gè)轉(zhuǎn)子劃分為138個(gè)節(jié)點(diǎn).計(jì)算時(shí),假設(shè)高中壓轉(zhuǎn)子中部存在不平衡量1 180 g·m,兩側(cè)軸承剛度和阻尼系數(shù)矩陣分別?。?/p>
2.1 剛性轉(zhuǎn)子平衡配重計(jì)算
在轉(zhuǎn)子兩端截面上加重,兩端截面到中部的距離l1和l2分別為1.418 m和2.585 m,由式(1)計(jì)算求得兩端截面上的配重量分別為763.4 g·m和418.7 g·m.
不考慮彎曲變形時(shí),轉(zhuǎn)子可視為剛性轉(zhuǎn)子,某一轉(zhuǎn)速下平衡好后,在其他轉(zhuǎn)速下也是平衡的.
2.2 不同轉(zhuǎn)速下轉(zhuǎn)子彎曲變形計(jì)算
考慮彎曲變形時(shí),轉(zhuǎn)子必須看成是柔性轉(zhuǎn)子.隨著轉(zhuǎn)速的升高,不平衡力增大,由此引起的彎曲變形也在增大.
不平衡力引起的離心力為
F=mω2r
(7)
圖2給出了3 000 r/min轉(zhuǎn)速下轉(zhuǎn)子彎曲變形計(jì)算結(jié)果.圖3給出了轉(zhuǎn)子中間截面處的最大彎曲變形量隨轉(zhuǎn)速的變化情況.由圖3可知,500 r/min和3 000 r/min轉(zhuǎn)速下轉(zhuǎn)子最大彎曲變形量分別為2.6 μm和93 μm.圖4給出了3 000 r/min轉(zhuǎn)速下轉(zhuǎn)子最大彎曲變形量隨不平衡量的變化.從圖4可以看出,轉(zhuǎn)子最大彎曲變形量呈線性變化,隨著不平衡量的增大,最大彎曲變形量越來(lái)越大.
計(jì)算結(jié)果表明,低轉(zhuǎn)速和小不平衡力狀態(tài)下的轉(zhuǎn)子彎曲變形量都較小,轉(zhuǎn)子可以視為剛性轉(zhuǎn)子.隨著轉(zhuǎn)速的升高和不平衡力的增大,轉(zhuǎn)子彎曲變形量越來(lái)越大,彎曲變形會(huì)帶來(lái)附加不平衡力,其對(duì)轉(zhuǎn)子振動(dòng)的影響不容忽略.
圖2 3 000 r/min下轉(zhuǎn)子彎曲變形圖Fig.2 Bending deformation of the shaft at 3 000 r/min
圖3 轉(zhuǎn)子中間截面處最大彎曲變形量隨轉(zhuǎn)速的變化Fig.3 Maximum shaft bend vs. rotating speed
圖4 3 000 r/min下轉(zhuǎn)子最大彎曲變形量隨不平衡量的變化Fig.4 Maximum shaft bend vs. unbalance at 3 000 r/min
2.3 耦合響應(yīng)分析
2.3.1 不考慮彎曲變形影響
圖5給出了不考慮彎曲變形時(shí),按剛性轉(zhuǎn)子模型計(jì)算所得配重前后升速過(guò)程中不平衡響應(yīng)隨轉(zhuǎn)速的變化情況.從圖5可以看出,配重前后,臨界轉(zhuǎn)速下1號(hào)軸承、2號(hào)軸承的振幅分別由146 μm和176 μm下降為43 μm和54 μm,平衡配重可以取得較好的減振效果.
2.3.2 考慮彎曲變形影響
圖6給出了考慮彎曲變形時(shí),按剛性轉(zhuǎn)子模型計(jì)算所得配重前后升速過(guò)程中轉(zhuǎn)子不平衡響應(yīng)隨轉(zhuǎn)速的變化情況.
由圖6可知,配重前后,臨界轉(zhuǎn)速下1號(hào)軸承、2號(hào)軸承處轉(zhuǎn)子振幅分別從146 μm和176 μm變?yōu)?96 μm和239 μm;3 000 r/min工作轉(zhuǎn)速下1號(hào)軸承、2號(hào)軸承處轉(zhuǎn)子振幅分別從33 μm和65 μm變?yōu)?8 μm和87 μm.升速過(guò)程中的振動(dòng)反而比配重前還要大,振幅的增大突出表現(xiàn)在臨界轉(zhuǎn)速下.
圖5 不考慮彎曲變形時(shí),配重前后轉(zhuǎn)子不平衡響應(yīng)隨轉(zhuǎn)速的變化Fig.5 Unbalance response vs. rotating speed before and after balancing, without consideration of shaft bend
圖6 考慮彎曲變形時(shí),配重前后轉(zhuǎn)子不平衡響應(yīng)隨轉(zhuǎn)速的變化Fig.6 Unbalance response vs. rotating speed before and after balancing, with consideration of shaft bend
如圖1所示,當(dāng)配重面與失衡面不重合時(shí),在3個(gè)力的作用下,轉(zhuǎn)子會(huì)出現(xiàn)彎曲變形,并進(jìn)而產(chǎn)生新的附加不平衡力,而該力無(wú)法被平衡,直接導(dǎo)致振動(dòng)更大.該現(xiàn)象是由轉(zhuǎn)子彎曲變形引起的,與支撐結(jié)構(gòu)形式無(wú)關(guān),對(duì)于柔性轉(zhuǎn)子而言,轉(zhuǎn)子存在彎曲變形的可能性,該現(xiàn)象具有一定的普遍性.對(duì)于剛性轉(zhuǎn)子而言,該現(xiàn)象則可以忽略.
以所研究的超臨界660 MW汽輪發(fā)電機(jī)組出現(xiàn)的不穩(wěn)定振動(dòng)為例進(jìn)行分析,因其具有一定的代表性.該機(jī)組軸系由高中壓轉(zhuǎn)子、低壓轉(zhuǎn)子I、低壓轉(zhuǎn)子II、發(fā)電機(jī)轉(zhuǎn)子和勵(lì)磁機(jī)轉(zhuǎn)子組成,軸系結(jié)構(gòu)布置如圖7所示.
圖7 軸系結(jié)構(gòu)示意圖Fig.7 Arrangement diagram of the shafting system
新機(jī)調(diào)試期間,通過(guò)在轉(zhuǎn)子兩端配重,機(jī)組振動(dòng)達(dá)到優(yōu)秀水平.但是,投運(yùn)一年多以來(lái),高中壓轉(zhuǎn)子振動(dòng)持續(xù)爬升,突出表現(xiàn)在臨界轉(zhuǎn)速下.圖8給出了該機(jī)組歷次停機(jī)過(guò)程中臨界轉(zhuǎn)速下的振動(dòng)變化情況,其中1x、1y、2x、2y分別為1號(hào)軸承、2號(hào)軸承處的轉(zhuǎn)子振幅大小.
圖8 歷次停機(jī)過(guò)程中臨界轉(zhuǎn)速下的振動(dòng)變化Fig.8 Trend of vibration at critical speed during all previous shutdown periods
圖9給出了歷次停機(jī)所測(cè)小軸晃度變化情況.由圖9可知,隨著時(shí)間的延長(zhǎng),小軸晃度逐漸增大,說(shuō)明轉(zhuǎn)子已經(jīng)產(chǎn)生了較大的彎曲變形.
根據(jù)本文模型,懷疑該機(jī)組轉(zhuǎn)子中部存在不平衡力F,如圖10所示.新機(jī)調(diào)試時(shí),由于在轉(zhuǎn)子中部加重比較困難,動(dòng)平衡試驗(yàn)是在轉(zhuǎn)子兩端配重F1、F2的情況下進(jìn)行的.當(dāng)時(shí)雖然取得了較好的效果,但隨著時(shí)間的延長(zhǎng),3個(gè)截面上的不平衡力所引起的轉(zhuǎn)子彎曲變形越來(lái)越大,如虛線2所示.該彎曲變形破壞了新機(jī)調(diào)試時(shí)的平衡狀態(tài).彎曲變形呈現(xiàn)一階振型,導(dǎo)致臨界轉(zhuǎn)速下的振動(dòng)越來(lái)越大.
圖9 小軸晃度變化趨勢(shì)Fig.9 Trend of shaft flutter
圖10 轉(zhuǎn)子彎曲變形示意圖Fig.10 Diagram of rotor bending deformation
根據(jù)上述分析,決定拆除轉(zhuǎn)子兩端的配重塊,改在轉(zhuǎn)子中部加重1 302 g.重新選擇平衡面后,機(jī)組臨界轉(zhuǎn)速下的振動(dòng)明顯減小,結(jié)果如表1所示.4年多以來(lái),機(jī)組振動(dòng)一直很穩(wěn)定,沒(méi)有再出現(xiàn)振動(dòng)爬升現(xiàn)象.說(shuō)明應(yīng)用本文模型很好地解決了發(fā)生在機(jī)組上的不穩(wěn)定振動(dòng)故障.
表1 配重前后臨界轉(zhuǎn)速下1號(hào)軸承、2號(hào)軸承處轉(zhuǎn)子振幅Tab.1 Vibration of bearing 1 and bearing 2 at critical speed before and after balancing μm
(1)高轉(zhuǎn)速運(yùn)行時(shí),汽輪機(jī)高壓轉(zhuǎn)子因配重面與失衡面不重合所引起的彎曲變形不可忽略.
(2)配重面與不平衡面不重合所引發(fā)的轉(zhuǎn)子彎曲變形會(huì)導(dǎo)致振動(dòng)的不穩(wěn)定和持續(xù)爬升,動(dòng)平衡試驗(yàn)應(yīng)盡量在轉(zhuǎn)子失衡面上進(jìn)行.
(3)現(xiàn)場(chǎng)實(shí)例驗(yàn)證了本文模型的準(zhǔn)確性.實(shí)踐表明,該現(xiàn)象更容易發(fā)生在大型汽輪機(jī)高壓轉(zhuǎn)子上.這是因?yàn)楦邏恨D(zhuǎn)子環(huán)境溫度較高,在外力作用下易產(chǎn)生不均勻蠕變.
[1] 羅挺, 劉淑蓮, 鄭水英. 具有初始彎曲的多圓盤(pán)轉(zhuǎn)子系統(tǒng)的動(dòng)力學(xué)特性分析[J]. 振動(dòng)與沖擊, 2010, 29(增刊): 173-175.
LUO Ting, LIU Shulian, ZHENG Shuiying. The dynamic characteristics analysis of the multi-disk rotor system with initial bow[J]. Journal of Vibration and Shock, 2010, 29(S): 173-175.
[2] KANG C H, HSU W C, LEE E K,etal. Dynamic analysis of gear-rotor system with viscoelastic supports under residual shaft bow effect[J]. Mechanism and Machine Theory, 2011, 46(3): 264-275.
[3] 吳文青, 謝誕梅, 楊毅, 等. 具有初始彎曲的1 000 MW汽輪機(jī)低壓轉(zhuǎn)子的振動(dòng)特征分析[J]. 振動(dòng)與沖擊, 2014, 33(17): 150-153.
WU Wenqing, XIE Danmei, YANG Yi,etal. Vibration behavior of a LP rotor with initial bending in a 1 000 MW turbine[J]. Journal of Vibration and Shock, 2014, 33(17): 150-153.
[4] SONG G F, YANG Z J, JI C,etal. Theoretical-experimental study on a rotor with a residual shaft bow[J]. Mechanism and Machine Theory, 2013, 63: 50-58.
[5] 何國(guó)安, 閔昌發(fā), 張學(xué)延, 等. 國(guó)產(chǎn)600 MW汽輪發(fā)電機(jī)組軸系動(dòng)平衡研究[J]. 動(dòng)力工程學(xué)報(bào), 2012, 32(4): 282-288.
HE Guoan, MIN Changfa, ZHANG Xueyan,etal. Dynamic balancing of the shaft system for a domestic 600 MW turbo-generator set[J]. Journal of Chinese Society of Power Engineering, 2012, 32(4): 282-288.
[6] DEEPTHIKUMAR M B, SEKHAR A S, SRIKANTHAN M R. Modal balancing of flexible rotors with bow and distributed unbalance[J]. Journal of Sound and Vibration, 2013, 332(24): 6216-6233.
[7] DEEPTHIKUMAR M B, SEKHAR A S, SRIKANTHAN M R. Balancing of flexible rotor with bow using transfer matrix method[J]. Journal of Vibration and Control, 2014, 20(2): 225-240.
[8] GU Lili, CHU Fulei. An analytical study of rotor dynamics coupled with thermal effect for a continuous rotor shaft[J]. Journal of Sound and Vibration, 2014, 333(17): 4030-4050.
[9] ZIAEI-RAD S, KOUCHAKI E, IMREGUN M. Thermoelastic modeling of rotor response with shaft rub[J]. Journal of Applied Mechanics, 2010, 77(6): 061010.
[10] KHANLO H M, GHAYOUR M, ZIAEI-RAD S. Chaotic vibration analysis of rotating, flexible, continuous shaft-disk system with a rub-impact between the disk and the stator[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16(1): 566-582.
[11] 孫健, 楊建剛, 田永偉. 汽輪發(fā)電機(jī)組摩擦引起的不穩(wěn)定振動(dòng)分析[J]. 振動(dòng)、測(cè)試與診斷, 2013, 33(6): 1084-1088.
SUN Jian, YANG Jiangang, TIAN Yongwei. Analysis on unstable vibration due to rub in turbo generator unit[J]. Journal of Vibration, Measurement & Diagnosis, 2013, 33(6): 1084-1088.
[12] BEHZAD M, ALVANDI M, MBA D,etal. A finite element-based algorithm for rubbing induced vibration prediction in rotors[J]. Journal of Sound and Vibration, 2013, 332(21): 5523-5542.
[13] 卓明, 楊利花, 張巖巖, 等. 重型燃機(jī)轉(zhuǎn)子的熱彎曲變形及振動(dòng)響應(yīng)分析[J]. 機(jī)械工程學(xué)報(bào), 2015,49(6):89-94.
ZHUO Ming, YANG Lihua, ZHANG Yanyan,etal. Analysis of rotor thermal bow and vibration response in gas turbine[J]. Journal of Mechanical Engineering, 2015,49(6):89-94.
[14] BALDASSARRE L, FONTANA M. Modeling of rotor bow during hot restart in centrifugal compressors[C]//Proceedings of the 39th Turbomachinery Symposium. Texas, USA: Texas A&M University, 2010.
[15] 肖小清, 劉石, 馮永新, 等. 發(fā)電機(jī)轉(zhuǎn)子彎曲振動(dòng)問(wèn)題分析與處理[J]. 振動(dòng)、測(cè)試與診斷, 2011, 31(2): 259-261.
XIAO Xiaoqing, LIU Shi, FENG Yongxin,etal. Diagnosis on vibration problem of generator with bending rotor[J]. Journal of Vibration Measurement & Diagnosis, 2011, 31(2): 259-261.
[16] MURPHY B T, LORENZ J A. Simplified Morton effect analysis for synchronous spiral instability[J]. Journal of Vibration and Acoustics, 2010, 132(5): 051008.
[17] CHEN Jingming, JIANG Dongxiang, LIU Chao. Fault analysis and optimal balancing of bowing of steam turbine rotor under long-term service[J]. Journal of Engineering for Gas Turbines and Power, 2015, 137(11): 112503.
[18] 高慶水, 鄧小文, 張楚, 等. 單支撐1 000 MW超超臨界汽輪機(jī)軸系不平衡響應(yīng)分析[J]. 振動(dòng)與沖擊, 2014, 33(14): 201-204.
GAO Qingshui, DENG Xiaowen, ZHANG Chu,etal. Unbalance response of 1 000 MW ultra supercritical turbine with single bearing support[J]. Journal of Vibration and Shock, 2014, 33(14): 201-204.
Analysis of Flexible Rotor Vibration Under Coupled Action of Shaft Bend and Rotor Unbalance
XIAYalei1,YANGJiangang1,ZHANGXiaobin2
(1. National Engineering Research Center of Turbo Generator Vibration, Southeast University, Nanjing 210096, China; 2. North China Electric Power Research Institute Co., Ltd.,Beijing 100045, China)
To solve the problem of unstable vibration occurring in the HP-IP rotor of a 660 MW supercritical steam turbine, a dynamic response model was set up for the system under coupled action of shaft bend and rotor unbalance using finite element method, of which the accuracy was verified with field experiments. Results show that the shaft bend caused by inconsistency between balancing and unbalance plane can not be neglected at high rotating speeds, since it may lead to the instability and increase of vibration. The balancing plane should be chosen on the unbalance plane as far as possible. High-pressure rotor is easy to have creep deformation under the effect of external force due to its high-temperature operation environment; the phenomenon is even more obvious for high-pressure rotors of large steam turbine.
flexible rotor; shaft bend; unbalance; vibration; response
2015-12-14
2016-01-12
夏亞磊(1992-),男,河南開(kāi)封人,碩士研究生,研究方向?yàn)樾D(zhuǎn)機(jī)械振動(dòng)監(jiān)測(cè)及故障治理. 楊建剛(通信作者),男,教授,博士生導(dǎo)師,電話(Tel.):13951988554;E-mail:Jgyang@seu.edu.cn.
1674-7607(2016)11-0877-06
TK113.1
A 學(xué)科分類號(hào):470.30