叶盘耦合振动转/静子叶片数与节径数关系
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摘要
针对航空发动机中叶盘结构的共振分析问题,通过研究气体激励力和叶盘节径型振动在转子坐标系下的数学表达形式,利用叶盘结构共振时,气体激励力需要对叶盘系统做正功的条件,推导了叶盘发生共振时,节径数与转/静子叶片数应满足的关系式d_m=|kN_v-nN_b|。通过3个数值算例对上述关系式进行了阐述:从气动功和谐响应分析的角度验证了当上述关系存在时,且激励频率等于结构固有频率时,叶盘系统会发生危害共振;同时指出,当上述变量不满足上述关系时,若激励频率等于叶盘结构的固有频率,也会引起部分叶片发生较大振动的可能。
Targeting the resonant analysis of aero-engine bladed-disk structure,by studying the mathematical formula of the gas excitation and nodal diameter vibration in the revolving coordinate and based on the positive work condition when the gas excitation acted on the bladed-disk structure,a relational expression d_m= |kN_v-nN_b| describing the relationship between the number of nodal diameter and rotor/stator was deduced while the structure was in resonance.Three numerical examples were given to illustrate the above relation:from the perspective of aerodynamic work and harmonic response,a bladed-disk structure was in resonance while the above relation existed and the excited frequency was equal to structural natural frequency,and moreover,partial blades may be in serious vibration state while the above-mentioned frequency was equal even if the fore-mentioned relation was not satisfied.
Targeting the resonant analysis of aero-engine bladed-disk structure,by studying the mathematical formula of the gas excitation and nodal diameter vibration in the revolving coordinate and based on the positive work condition when the gas excitation acted on the bladed-disk structure,a relational expression d_m= |kN_v-nN_b| describing the relationship between the number of nodal diameter and rotor/stator was deduced while the structure was in resonance.Three numerical examples were given to illustrate the above relation:from the perspective of aerodynamic work and harmonic response,a bladed-disk structure was in resonance while the above relation existed and the excited frequency was equal to structural natural frequency,and moreover,partial blades may be in serious vibration state while the above-mentioned frequency was equal even if the fore-mentioned relation was not satisfied.
引文
[1]王建军,姚建尧,李其汉.刚度随机失谐叶盘结构概率模态特性分析[J].航空动力学报,2008,23(2):257-262.WANG Jianjun,YAO Jianyao,LI Qihan.Probability characteristics of vibratory mode of bladed disk assemblies with random stiffness mistuning[J].Journal of Aerospace Power,2008,23(3):257-262.(in Chinese)
[2]王延荣,田爱梅.叶/盘结构振动分析中几个问题的探索[J].推进技术,2002,23(3):233-236.WANG Yanrong,TIAN Aimei.Several issues in the implementation of vibration analysis of bladed disk[J].Journal of Propulsion Technology,2002,23(3):233-236.(in Chinese)
[3]孙浩琳,吴娅辉,朱振宇.某航空发动机整体叶盘耦合振动特性分析[J].计测技术,2015,35(5):28-30.SUN Haolin,WU Yahui,ZHU Zhenyu.Coupling vibration characterisitics analysis of holistic bladed disk[J].Metrollogy and Measurement Technology,2015,35(5):28-30.(in Chinese)
[4]孙海,王培屹,郑宁,等.基于非线性谐波法评估压气机转静干涉诱发的强迫响应[J].航空发动机,2015,41(2):40-44.SUN Hai,WANG Peiyi,ZHENG Ning,et al.Evaluating of the forcing response under compressor stator-rotor interaction using NLH[J].Aeroengine,2015,41(2):40-44.(in Chinese)
[5] MOFFATT S,HE L.Blade forced response prediction for industrial gas turbines[J].Journal of Propulsion and Power,2005,18(3):15-19.
[6]孟越,李琳,李其汉.尾流激振情况下叶片强迫响应瞬态分析方法[J].北京航空航天大学学报,2006,32(6):671-674.MENG Yue,LI Lin,LI Qihan.Transient analystical method of vane forcing response under stator-rotor wake influence[J].Journal of Beijing University of Aeronautics and Astronautics,2006,32(6):671-674.(in Chinese)
[7]晏砺堂,朱梓根,李其汉.高速旋转机械振动[M].北京:国防工业出版社,1994.
[8]中国航空工业总公司发动机系统工程局.航空涡喷、涡扇发动机结构设计准则研究报告[M].北京:中国航空工业总公司发动机系统工程局,1997.
[9]航空发动机设计手册总编委会.航空发动机设计手册:第18册叶片轮盘及主轴强度分析[M].北京:航空工业出版社,2001.
[10]张大义,史亚杰,林力,等.带宽弦叶片的盘片耦合振动特性研究[J].北京航空航天大学学报,2004,30(9):808-812.ZHANG Dayi,SHI Yajie,LIN Li,et al.Model analysis of bladed disk coupled system of compressor with low aspect ratio[J].Journal of Beijing University of Aeronautics and Astronautics,2004,30(9):808-812.(in Chinese)
[11]姚建尧.流体激励下谐调和失谐整体叶盘结构响应分析[D].北京:北京航空航天大学,2010.YAO Jianyao.Forced response analysis of bladed disk under fluid excitation[D].Beijing Universtiy of Aeronautics and Astronautics,2010.(in Chinese)
[12]辛建强.航空发动机转自结构的典型振动问题研究[D].北京:北京航空航天大学,2011.XIN Jianqiang.Research on typical problems of blisk rotaor vibration in turbomachinery[D].Bejing:Beijing University of Aeronautics and Astronautics,2011.(in Chinese)
[13]乞征,王建军.叶盘耦合共振条件中激励阶次的确定[J].北京航空航天大学学报,2014,40(7):984-987.QI Zheng,WANG Jianjun.Excitation order verification of bladed-disk coupled resonance condition[J].Journal of Beijing University of Aeronautics and Astronautics,2014,40(7):984-987.(in Chinese)
[14]徐峰,李春松,罗秋生,等.轴流压气机整体叶盘叶片裂纹故障研究[J].燃气涡轮试验与研究,2012,25(4):25-29.XU Feng,LI Chunsong,LUO Qiusheng,et al.Study on the blade crack of an axial flow compressor blisk[J].Gas Turbine Experiment and Research,2012,25(4):25-29.(in Chinese)
[15]吴长波,周拜豪,崔海涛,等.小展弦比带掠风扇转子叶片的耦合颤振[J].航空动力学报,2014,29(12):2887-2890.WU Changbo,ZHOU Baihao,CUI Haitao,et al.Coupling flutter of swept fan rotor blade with small aspect ratio[J].Journal of Aerospace Power,2014,29(12):2887-2890.(in Chinese)
[16]李琳,马浩然,王培屹.转静干涉流畅的激励特征与叶盘结构的共振设计[J].航空动力学报,2016,31(6):1368-1376.LI Lin,MA Haoran,WANG Peiyi.Excitation characteristics of rotor/stator-interaction flow field and resonant design of blaed disk[J].Journal of Aerospace Power,2016,31(6):1368-1376.(in Chinese)
[2]王延荣,田爱梅.叶/盘结构振动分析中几个问题的探索[J].推进技术,2002,23(3):233-236.WANG Yanrong,TIAN Aimei.Several issues in the implementation of vibration analysis of bladed disk[J].Journal of Propulsion Technology,2002,23(3):233-236.(in Chinese)
[3]孙浩琳,吴娅辉,朱振宇.某航空发动机整体叶盘耦合振动特性分析[J].计测技术,2015,35(5):28-30.SUN Haolin,WU Yahui,ZHU Zhenyu.Coupling vibration characterisitics analysis of holistic bladed disk[J].Metrollogy and Measurement Technology,2015,35(5):28-30.(in Chinese)
[4]孙海,王培屹,郑宁,等.基于非线性谐波法评估压气机转静干涉诱发的强迫响应[J].航空发动机,2015,41(2):40-44.SUN Hai,WANG Peiyi,ZHENG Ning,et al.Evaluating of the forcing response under compressor stator-rotor interaction using NLH[J].Aeroengine,2015,41(2):40-44.(in Chinese)
[5] MOFFATT S,HE L.Blade forced response prediction for industrial gas turbines[J].Journal of Propulsion and Power,2005,18(3):15-19.
[6]孟越,李琳,李其汉.尾流激振情况下叶片强迫响应瞬态分析方法[J].北京航空航天大学学报,2006,32(6):671-674.MENG Yue,LI Lin,LI Qihan.Transient analystical method of vane forcing response under stator-rotor wake influence[J].Journal of Beijing University of Aeronautics and Astronautics,2006,32(6):671-674.(in Chinese)
[7]晏砺堂,朱梓根,李其汉.高速旋转机械振动[M].北京:国防工业出版社,1994.
[8]中国航空工业总公司发动机系统工程局.航空涡喷、涡扇发动机结构设计准则研究报告[M].北京:中国航空工业总公司发动机系统工程局,1997.
[9]航空发动机设计手册总编委会.航空发动机设计手册:第18册叶片轮盘及主轴强度分析[M].北京:航空工业出版社,2001.
[10]张大义,史亚杰,林力,等.带宽弦叶片的盘片耦合振动特性研究[J].北京航空航天大学学报,2004,30(9):808-812.ZHANG Dayi,SHI Yajie,LIN Li,et al.Model analysis of bladed disk coupled system of compressor with low aspect ratio[J].Journal of Beijing University of Aeronautics and Astronautics,2004,30(9):808-812.(in Chinese)
[11]姚建尧.流体激励下谐调和失谐整体叶盘结构响应分析[D].北京:北京航空航天大学,2010.YAO Jianyao.Forced response analysis of bladed disk under fluid excitation[D].Beijing Universtiy of Aeronautics and Astronautics,2010.(in Chinese)
[12]辛建强.航空发动机转自结构的典型振动问题研究[D].北京:北京航空航天大学,2011.XIN Jianqiang.Research on typical problems of blisk rotaor vibration in turbomachinery[D].Bejing:Beijing University of Aeronautics and Astronautics,2011.(in Chinese)
[13]乞征,王建军.叶盘耦合共振条件中激励阶次的确定[J].北京航空航天大学学报,2014,40(7):984-987.QI Zheng,WANG Jianjun.Excitation order verification of bladed-disk coupled resonance condition[J].Journal of Beijing University of Aeronautics and Astronautics,2014,40(7):984-987.(in Chinese)
[14]徐峰,李春松,罗秋生,等.轴流压气机整体叶盘叶片裂纹故障研究[J].燃气涡轮试验与研究,2012,25(4):25-29.XU Feng,LI Chunsong,LUO Qiusheng,et al.Study on the blade crack of an axial flow compressor blisk[J].Gas Turbine Experiment and Research,2012,25(4):25-29.(in Chinese)
[15]吴长波,周拜豪,崔海涛,等.小展弦比带掠风扇转子叶片的耦合颤振[J].航空动力学报,2014,29(12):2887-2890.WU Changbo,ZHOU Baihao,CUI Haitao,et al.Coupling flutter of swept fan rotor blade with small aspect ratio[J].Journal of Aerospace Power,2014,29(12):2887-2890.(in Chinese)
[16]李琳,马浩然,王培屹.转静干涉流畅的激励特征与叶盘结构的共振设计[J].航空动力学报,2016,31(6):1368-1376.LI Lin,MA Haoran,WANG Peiyi.Excitation characteristics of rotor/stator-interaction flow field and resonant design of blaed disk[J].Journal of Aerospace Power,2016,31(6):1368-1376.(in Chinese)