具有干摩擦阻尼的汽轮机叶片振动分析
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摘要
汽轮机叶片是汽轮机的关键零件,对于汽轮机的安全运行至关重要。叶片可能在因气流的周期性扰动力作用下发生异常振动,从而导致高周或低周疲劳失效。利用叶冠之间的干摩擦力产生的阻尼,是一种有效抑制叶片振动、降低叶片动应力的有效手段。因此研究叶冠干摩擦阻尼的减振机理十分必要。本文围绕汽轮机中带阻尼减振装置(此处指叶冠)叶片的固有振动特性及动力响应特性,开展了以下工作:
(1)用有限元法计算了平行冠叶片的固有振动特性。计算了某汽轮机中压第一级和第十三级动叶片在不同载荷条件下的固有频率。在工作载荷下,这两种叶片的周向一弯固有频率分别为:1027.2Hz和199.66Hz,计算结果同实验结果非常接近。
(2)计算了锯齿冠叶片的固有振动特性。利用ANSYS软件非线性接触的功能,计算了锯齿冠在不同转速下的接触应力和接触区域的变化。计算结果表明:在零转速和100%工作转速下的周向一弯固有频率分别为100.9Hz和139.7Hz,在35%工作转速附近叶冠之间开始发生接触,叶片可能在此转速以后呈现整圈振动特性。
(3)建立了带冠叶片的干摩擦阻尼模型,将叶冠接触面之间的干摩擦力变换为等效刚度和等效阻尼。根据该模型进行了算例验证,本文计算结果同相关文献的计算结果对比表明:本文建立的干摩擦阻尼模型和计算方法是正确有效的。
(4)计算了平行冠和锯齿冠叶片的谐响应特性。编制fortran程序和命令流文件,可用于自动构造接触区域的阻尼矩阵和刚度矩阵,并计算了考虑干摩擦阻尼作用下叶片动应力,与未考虑干摩擦阻尼的计算结果相比,动应力下降了约50%。
Turbine blade is the key component of the steam turbine. It is very important to the safety of the steam turbine. Turbine blade will vibrate under the periodic exciting force of the steam, which will lead to the high frequency and low frequency fatigue failure. The dry friction damp between the shroud of the blades could restrain the vibration of the blades and reduce the dynamic stress of the blade, so it is necessary to research the principle of the dry friction damper. The main contents are as following:
(1) Finite element method is used to study the modal of the turbine blade with parallelogram shroud. Under the working conditions, the first natural frequency of the 1st and 13th stage turbine are 1027.2Hz and 199.66Hz respectively, which meets the experiment result very well.
(2) Finite element method is also used to study the modal of the turbine blade with zigzag shroud. The contact stress and the variation of contact zone between the zigzag shroud is studied by using the contact analysis function of the ANSYS software. The result shows that the first natural frequency of this blade is 100.9Hz and 139.7Hz under zero and 100% working rotation speed respectively. The shroud begins to contact at the rotation speed about 35% working rotation speed.
(3) Mathematic model of the dry friction damper between shroud is built to transfer the dry friction force to equivalent stiffness and damp. A test case is calculated by using this model, and the result meets good with that of some reference, which shows the validity of this model.
(4) Harmonic response of the two types blade are carried out. Fortran language and ANSYS parametric design language are used to develop a program which could construction the damp matrix and stiffness matrix automatically and then calculate the dynamic stress of the blade under periodic exciting force. The result shows that the dynamic stress value reduces about 50% compared to that without dry friction damp.
(1)用有限元法计算了平行冠叶片的固有振动特性。计算了某汽轮机中压第一级和第十三级动叶片在不同载荷条件下的固有频率。在工作载荷下,这两种叶片的周向一弯固有频率分别为:1027.2Hz和199.66Hz,计算结果同实验结果非常接近。
(2)计算了锯齿冠叶片的固有振动特性。利用ANSYS软件非线性接触的功能,计算了锯齿冠在不同转速下的接触应力和接触区域的变化。计算结果表明:在零转速和100%工作转速下的周向一弯固有频率分别为100.9Hz和139.7Hz,在35%工作转速附近叶冠之间开始发生接触,叶片可能在此转速以后呈现整圈振动特性。
(3)建立了带冠叶片的干摩擦阻尼模型,将叶冠接触面之间的干摩擦力变换为等效刚度和等效阻尼。根据该模型进行了算例验证,本文计算结果同相关文献的计算结果对比表明:本文建立的干摩擦阻尼模型和计算方法是正确有效的。
(4)计算了平行冠和锯齿冠叶片的谐响应特性。编制fortran程序和命令流文件,可用于自动构造接触区域的阻尼矩阵和刚度矩阵,并计算了考虑干摩擦阻尼作用下叶片动应力,与未考虑干摩擦阻尼的计算结果相比,动应力下降了约50%。
Turbine blade is the key component of the steam turbine. It is very important to the safety of the steam turbine. Turbine blade will vibrate under the periodic exciting force of the steam, which will lead to the high frequency and low frequency fatigue failure. The dry friction damp between the shroud of the blades could restrain the vibration of the blades and reduce the dynamic stress of the blade, so it is necessary to research the principle of the dry friction damper. The main contents are as following:
(1) Finite element method is used to study the modal of the turbine blade with parallelogram shroud. Under the working conditions, the first natural frequency of the 1st and 13th stage turbine are 1027.2Hz and 199.66Hz respectively, which meets the experiment result very well.
(2) Finite element method is also used to study the modal of the turbine blade with zigzag shroud. The contact stress and the variation of contact zone between the zigzag shroud is studied by using the contact analysis function of the ANSYS software. The result shows that the first natural frequency of this blade is 100.9Hz and 139.7Hz under zero and 100% working rotation speed respectively. The shroud begins to contact at the rotation speed about 35% working rotation speed.
(3) Mathematic model of the dry friction damper between shroud is built to transfer the dry friction force to equivalent stiffness and damp. A test case is calculated by using this model, and the result meets good with that of some reference, which shows the validity of this model.
(4) Harmonic response of the two types blade are carried out. Fortran language and ANSYS parametric design language are used to develop a program which could construction the damp matrix and stiffness matrix automatically and then calculate the dynamic stress of the blade under periodic exciting force. The result shows that the dynamic stress value reduces about 50% compared to that without dry friction damp.
引文
[1]王玉武. 200 MW机组中压转子末级叶片拉筋改进[J].汽轮机技术, 2002,44(4):242-243, 245.
[2] Ci?ero?lu E, ?zgüven H N. Nonlinear vibration analysis of bladed disks with dry friction dampers[J]. Journalof Sound and Vibration, 2006,295(3):1028-1043.
[3]丛佩红,张连祥,刘廷毅,航空发动机涡轮转子叶片锯齿形叶冠紧度的最佳选择,航空发动机,2000,4:9-12.
[4]李辛毅,季葆华,孟庆集,采用整体围带或翅翼形凸肩提供摩擦阻尼的叶片典型结构,汽轮机技术,1996,38(4):217-220。
[5] Cottney D.J., Ewins D.J. , Towards the Efficient Vibration Analysis of Shrouded Bladed Disk Assemblies , ASME Design Engineering Technical Conference , Vo1.2, 1973
[6] Cottney D.J.,Ewins D.J. , On Predicting the Natural Frequencies of Shrouded Bladed Disks , ASME Paper , No.75-DET-113 , Sept.1975
[7] Griffin J.H., Menq C-H. , Friction Damping of Circular Motion and Its Implication to Vibration Control , Journal of Vibration and Acoustics,April 1991 , Vol.113 , pp225-229
[8] Menq C-H. , Griffin J.H. , Bielak J . , The Forced Response of Shrouded Fan Stages, Translation of the ASME , Vol.108 , January 1986 , pp50-55
[9] Wang J.H., Yan H.L., Design of Shrouded Interface Angle to Minimize the Forced Vibration of Blades, The Gas Turbine and Aeroengine Congress and Exposition, June 11-14, 1990, Brussels,Belgium
[10]夏松波,段剑波,武新华,金介荣,非连续整圈带冠叶片振动分析,第三届全国振动理论及应用学术会议论文集,1988
[11]张锦等人,轴流式和离心式叶轮通用模态分析技术和软件包,科研报告,1991.7
[12]王建明,整级带凸肩叶片-盘系统的振动特性分析,硕士学位论文,指导教师:张锦,许锷俊,北京航空航天大学动力系,1995
[13]任勇生,朱德懋,具有干摩擦阻尼的叶片组振动的理论与实验研究,航空学报,1994,第15卷,第11期,pp1306-1314
[14]胡寻峰,带凸肩叶片与轮盘耦合系统振动特性研究,硕士学位论文,指导教师:张锦,刘晓平,北京航空航天大学动力系,1998
[15]漆文凯,涡轮转子叶片叶根阻尼装置减振特性分析及实验研究,[博士学位论文],南京,南京航空航天大学,2005。
[16]孙艳红,多频激励下干摩擦阻尼叶片的共振响应,[硕士学位论文],天津,天津大学机械工程学院,2004。
[17]白鸿柏,黄协清,干摩擦振动系统响应计算方法研究综述,力学进展,2001,31(4):527-534。
[18]侯志强,李跃,迟滞系统受随机激励的响应计算,应用力学学报,2003,20(4):101-104。
[19] WANG Qin meng, ZHANG Jin, MA Xiao qiu, DONG Ben han. Hybrid Method to Analyze ContactStress Distribution on Dry Friction Interfaces.CHINESE JOURNAL OF AERONAUTICS, 2002, 5:77-81.
[20]郝燕平,单颖春,朱梓根,缘板摩擦阻尼器的减振实验研究,航空动力学报,2001,16(1):55-58。
[21]武新华,李卫军,自带冠叶片冠间接触碰撞减振研究,汽轮机技术,2005,47(1):41-44。
[22]嵇安森,阻尼结构整圈连接汽轮机叶片频率静态测试的试验研究,电力设备,2005,6(4):76-81。
[23]季葆华,王乐天,李辛毅等,阻尼连接叶片的动力特性研究,汽轮机技术,1996,16(5):45-54。
[24]李锋,孟庆集,谢浩等,阻尼叶片振动特性的优化研究,西安交通大学学报,2001,35(1):33-36。
[25] Awrejcewicz J., Chaos in Simple Mechanical Systems with Friction, Journal of Sound and Vibration, Vol.109, No.l, pp 178-180,1986
[26] Dolezal Z., The Response of The Simple System Damped By Real Dry Friction , ISABE 89-7067 , .pp641-651
[27] Kapitaniak T.,Wojewoda J. , Oscillations of a Quasi-Periodically Forced System with Dry Friction , Journal of Sound and Vibration , Vol.163 , No.2 , 1993 , pp379-384
[28] Kapitaniak T., Analytical Method of Controlling Chaos in Duffing's Oscillator, Journal of Sound and Vibration , 1993 , Vol.163 , pp18 2-187
[29] Ibrahim, R.A., Friction-Induced Vibration, Chatter, Squeal, and Chaos PartII: Dynamics and modeling, Applied Mechanics Reviews., July 1994 , Vo1.47 , No.7 , pp227-253
[30] Popp K., Stelter P., Stick-Slip Vibrations and Chaos, Phil. Trans. Royal Soc., 1990, Vo l.332, pp89-105
[31]刘秉正,《非线性动力学与混沌基础》,东北师范大学出版社,1994.9
[32]褚亦清,李翠英,《非线性振动》,北京理工大学出版社,1996.9
[33] A.H.奈弗,D.T.穆克,宋家啸等译《,非线性振动(上、下)》,高等教育出版社,1990.6
[34] .倪振华,《振动力学》,西安交通大学出版社,1994
[35]清华大学工程力学系固体力学教研组,振动组编,《机械振动(上、中册)》,机械工业出版社,1995
[36] Oancea V.G., Laursen T. A. Investigations of Low Frequency Stick-Slip Motion: Experiments and Numerical Modelling, Journal of Sound and Vibration, 1998, Vo1.213, No.4, pp577-600
[37] Menq C.H.,Grifin J.H., and Bielak J.,The Forced Response of Shrouded FanStages Transactions of the ASME,Vol.108,1996.1,pp50-55
[38] Ferri A.A., Friction damping and isolation systems , Transaction of the ASME, Vol. 117, 1995. No.6, pp196-206
[39] Sanliturk K.Y., Imregun M., Ewins D. J., Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers, ASME Journal of Vibration and Acoustics, January 1997, Vol. 119, pp 96-103
[40] Sinha A and Griffin J.H, Effects of Static Friction on the Forced Response of Frictionally Damped Turbine Blades , ASME Journal of Engineering for GasTurbine and Power 1984,Vol.106,N o.1,pp65-69
[41] Wang J.H, Yau H.L., Design of Shroud Interface-Angle to Minimize the Forced Vibration of Blades , ASME 90-GT-247
[42] Wang J.H., Chen W.K., Investigation of the Vibration of a Blade with Friction Damper by HBM, ASME -92-GT-8
[43]戴德沛,《阻尼技术的工程应用》,清华大学出版社,1991.10
[44]何君毅,林样都,《工程结构非线性问题的数值解法》,国防工业出版社,1994.8
[45]邵敏,《有限单元法基本原理和数值方法》,清华大学出版社,1997.3
[46]巴斯K.J.,《工程分析中的有限元法》,机械工业出版社,1991.7
[47]高德平,机械工程中的有限元法基础,西北工业大学出版社,1993
[48]胡海岩,机械振动与冲击,航空工业出版社,1998
[49]肖俊峰,朱宝田,汽轮机叶片振动特性对叶根约束条件敏感性的研究,热力发电,1999.1,p28-32
[50]陈江龙,盛德仁,陈坚红,李蔚,任浩仁,汽轮机T型叶根有限元模态分析边界条件的研究,动力工程,Vo l. 24 No. 4,2004.8
[51]安宁,孟庆集,汽轮机叶片激振因子和阻尼分析,动力工程,Vol.14, No.6,1994
[52]张锦,刘晓平,叶轮机振动模态分析理论及数值方法,国防工业出版社,2001.1
[2] Ci?ero?lu E, ?zgüven H N. Nonlinear vibration analysis of bladed disks with dry friction dampers[J]. Journalof Sound and Vibration, 2006,295(3):1028-1043.
[3]丛佩红,张连祥,刘廷毅,航空发动机涡轮转子叶片锯齿形叶冠紧度的最佳选择,航空发动机,2000,4:9-12.
[4]李辛毅,季葆华,孟庆集,采用整体围带或翅翼形凸肩提供摩擦阻尼的叶片典型结构,汽轮机技术,1996,38(4):217-220。
[5] Cottney D.J., Ewins D.J. , Towards the Efficient Vibration Analysis of Shrouded Bladed Disk Assemblies , ASME Design Engineering Technical Conference , Vo1.2, 1973
[6] Cottney D.J.,Ewins D.J. , On Predicting the Natural Frequencies of Shrouded Bladed Disks , ASME Paper , No.75-DET-113 , Sept.1975
[7] Griffin J.H., Menq C-H. , Friction Damping of Circular Motion and Its Implication to Vibration Control , Journal of Vibration and Acoustics,April 1991 , Vol.113 , pp225-229
[8] Menq C-H. , Griffin J.H. , Bielak J . , The Forced Response of Shrouded Fan Stages, Translation of the ASME , Vol.108 , January 1986 , pp50-55
[9] Wang J.H., Yan H.L., Design of Shrouded Interface Angle to Minimize the Forced Vibration of Blades, The Gas Turbine and Aeroengine Congress and Exposition, June 11-14, 1990, Brussels,Belgium
[10]夏松波,段剑波,武新华,金介荣,非连续整圈带冠叶片振动分析,第三届全国振动理论及应用学术会议论文集,1988
[11]张锦等人,轴流式和离心式叶轮通用模态分析技术和软件包,科研报告,1991.7
[12]王建明,整级带凸肩叶片-盘系统的振动特性分析,硕士学位论文,指导教师:张锦,许锷俊,北京航空航天大学动力系,1995
[13]任勇生,朱德懋,具有干摩擦阻尼的叶片组振动的理论与实验研究,航空学报,1994,第15卷,第11期,pp1306-1314
[14]胡寻峰,带凸肩叶片与轮盘耦合系统振动特性研究,硕士学位论文,指导教师:张锦,刘晓平,北京航空航天大学动力系,1998
[15]漆文凯,涡轮转子叶片叶根阻尼装置减振特性分析及实验研究,[博士学位论文],南京,南京航空航天大学,2005。
[16]孙艳红,多频激励下干摩擦阻尼叶片的共振响应,[硕士学位论文],天津,天津大学机械工程学院,2004。
[17]白鸿柏,黄协清,干摩擦振动系统响应计算方法研究综述,力学进展,2001,31(4):527-534。
[18]侯志强,李跃,迟滞系统受随机激励的响应计算,应用力学学报,2003,20(4):101-104。
[19] WANG Qin meng, ZHANG Jin, MA Xiao qiu, DONG Ben han. Hybrid Method to Analyze ContactStress Distribution on Dry Friction Interfaces.CHINESE JOURNAL OF AERONAUTICS, 2002, 5:77-81.
[20]郝燕平,单颖春,朱梓根,缘板摩擦阻尼器的减振实验研究,航空动力学报,2001,16(1):55-58。
[21]武新华,李卫军,自带冠叶片冠间接触碰撞减振研究,汽轮机技术,2005,47(1):41-44。
[22]嵇安森,阻尼结构整圈连接汽轮机叶片频率静态测试的试验研究,电力设备,2005,6(4):76-81。
[23]季葆华,王乐天,李辛毅等,阻尼连接叶片的动力特性研究,汽轮机技术,1996,16(5):45-54。
[24]李锋,孟庆集,谢浩等,阻尼叶片振动特性的优化研究,西安交通大学学报,2001,35(1):33-36。
[25] Awrejcewicz J., Chaos in Simple Mechanical Systems with Friction, Journal of Sound and Vibration, Vol.109, No.l, pp 178-180,1986
[26] Dolezal Z., The Response of The Simple System Damped By Real Dry Friction , ISABE 89-7067 , .pp641-651
[27] Kapitaniak T.,Wojewoda J. , Oscillations of a Quasi-Periodically Forced System with Dry Friction , Journal of Sound and Vibration , Vol.163 , No.2 , 1993 , pp379-384
[28] Kapitaniak T., Analytical Method of Controlling Chaos in Duffing's Oscillator, Journal of Sound and Vibration , 1993 , Vol.163 , pp18 2-187
[29] Ibrahim, R.A., Friction-Induced Vibration, Chatter, Squeal, and Chaos PartII: Dynamics and modeling, Applied Mechanics Reviews., July 1994 , Vo1.47 , No.7 , pp227-253
[30] Popp K., Stelter P., Stick-Slip Vibrations and Chaos, Phil. Trans. Royal Soc., 1990, Vo l.332, pp89-105
[31]刘秉正,《非线性动力学与混沌基础》,东北师范大学出版社,1994.9
[32]褚亦清,李翠英,《非线性振动》,北京理工大学出版社,1996.9
[33] A.H.奈弗,D.T.穆克,宋家啸等译《,非线性振动(上、下)》,高等教育出版社,1990.6
[34] .倪振华,《振动力学》,西安交通大学出版社,1994
[35]清华大学工程力学系固体力学教研组,振动组编,《机械振动(上、中册)》,机械工业出版社,1995
[36] Oancea V.G., Laursen T. A. Investigations of Low Frequency Stick-Slip Motion: Experiments and Numerical Modelling, Journal of Sound and Vibration, 1998, Vo1.213, No.4, pp577-600
[37] Menq C.H.,Grifin J.H., and Bielak J.,The Forced Response of Shrouded FanStages Transactions of the ASME,Vol.108,1996.1,pp50-55
[38] Ferri A.A., Friction damping and isolation systems , Transaction of the ASME, Vol. 117, 1995. No.6, pp196-206
[39] Sanliturk K.Y., Imregun M., Ewins D. J., Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers, ASME Journal of Vibration and Acoustics, January 1997, Vol. 119, pp 96-103
[40] Sinha A and Griffin J.H, Effects of Static Friction on the Forced Response of Frictionally Damped Turbine Blades , ASME Journal of Engineering for GasTurbine and Power 1984,Vol.106,N o.1,pp65-69
[41] Wang J.H, Yau H.L., Design of Shroud Interface-Angle to Minimize the Forced Vibration of Blades , ASME 90-GT-247
[42] Wang J.H., Chen W.K., Investigation of the Vibration of a Blade with Friction Damper by HBM, ASME -92-GT-8
[43]戴德沛,《阻尼技术的工程应用》,清华大学出版社,1991.10
[44]何君毅,林样都,《工程结构非线性问题的数值解法》,国防工业出版社,1994.8
[45]邵敏,《有限单元法基本原理和数值方法》,清华大学出版社,1997.3
[46]巴斯K.J.,《工程分析中的有限元法》,机械工业出版社,1991.7
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