液体火箭POGO振动缩聚模型研究
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摘要
针对液体火箭POGO模型中推进系统模型难以降阶的问题,提出了一种POGO模型缩聚的方法。利用广义逆迭代法只对输送管路的有限元模型模态分解,选取管路任意阶次模态方程与其余部件的方程组合得到推进系统的缩聚模型,进而与结构系统模态方程耦合得到POGO振动缩聚模型。当蓄压器作为纯柔性元件或非纯柔性元件时,缩聚模型的维度由管路的模态变量、结构模态变量再加1或2组成。模型的维度大大降低且算例表明其具有很高的精度。基于缩聚模型研究了某液体火箭蓄压器能量值和惯性对POGO稳定性的影响。研究得出,对于纯柔性或非纯柔性的蓄压器设计,能量值和惯性对不同时刻耦合模型稳定性具有不同的、非单调的影响规律。当耦合而导致结构系统频率大幅降低时,合理的调节蓄压器的能量值或惯性可以显著的增大结构耦合阻尼比,增强结构的稳定性。
Aiming at the order of the propulsion system model being difficult to be reduced in liquid rockets' POGO model,a POGO reduced model method was proposed. The generalized inverse iterative method was used to do modal decomposition only for the transfer pipeline's finite element model to choose the any order modal equation of the transfer pipeline combined with other parts' equations to obtain the reduced model of the propulsion system. The POGO vibration reduced model was obtained by coupling the structure system's modal equations and the propulsion system reduced model. When the accumulator was taken as a pure flexible element or a non-pure flexible one,the dimension of the POGO vibration reduced model was composed of the transfer pipeline 's modal variables,the structure 's modal variables plus 1 or 2. The model's dimension was largely and the calculation examples showed that the POGO vibration reduced model has a high precision. Based on this reduced model,the effects of the accumulator's energy value and inertia of a certain liquid rocket on its POGO stability were studied. The results showed that for a pure flexible accumulator or a non-pure flexible one,its energy value and inertia have different and non-monotonic influences on the coupled model's stability at different time instants; when the structure system's frequency drops obviously due to the coupling effect,a reasonable adjustment of the accumulator's energy value or inertia can significantly increase the structure's coupled damping ratio to enhance the structure's stability.
Aiming at the order of the propulsion system model being difficult to be reduced in liquid rockets' POGO model,a POGO reduced model method was proposed. The generalized inverse iterative method was used to do modal decomposition only for the transfer pipeline's finite element model to choose the any order modal equation of the transfer pipeline combined with other parts' equations to obtain the reduced model of the propulsion system. The POGO vibration reduced model was obtained by coupling the structure system's modal equations and the propulsion system reduced model. When the accumulator was taken as a pure flexible element or a non-pure flexible one,the dimension of the POGO vibration reduced model was composed of the transfer pipeline 's modal variables,the structure 's modal variables plus 1 or 2. The model's dimension was largely and the calculation examples showed that the POGO vibration reduced model has a high precision. Based on this reduced model,the effects of the accumulator's energy value and inertia of a certain liquid rocket on its POGO stability were studied. The results showed that for a pure flexible accumulator or a non-pure flexible one,its energy value and inertia have different and non-monotonic influences on the coupled model's stability at different time instants; when the structure system's frequency drops obviously due to the coupling effect,a reasonable adjustment of the accumulator's energy value or inertia can significantly increase the structure's coupled damping ratio to enhance the structure's stability.
引文
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[7]谭述君,王庆伟,吴志刚.临界阻尼比法在POGO振动稳定性分析中的适用性[J].宇航学报,2015,36(3):284-291.TAN Shujun,WANG Qingwei,WU Zhigang.Applicability of critical damping ratio method on POGO stability analysis[J].Journal of Astronautics,2015,36(3):284-291.
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[11]唐冶,方勃,李明明,等.液体火箭推进系统频率特性的灵敏度分析[J].宇航学报,2014,35(8):878-883.TANG Ye,FANG bo,LI Mingming,et al.Sensitivity analysis of frequency characteristic for propulsion system in liquid rocket[J].Journal of Astronautics,2014,35(8):878-883.
[12]OPPENHEIM B W,RUBIN S.Advanced POGO stability analysis for liquid rockets[J].Journal of Spacecraft and Rockets,1993,30(3):360-373.
[13]WANG Q W,TAN S J,WU Z G,et al.Improved modelling method of POGO analysis and simulation for liquid rockets[J].Acta Astronautica,2015,107:262-273.
[14]张青松,张兵.大型液体运载火箭POGO动力学模型研究[J].中国科学:技术科学,2014,44(5):525-531.ZHANG Qingsong,ZHANG Bing.POGO dynamic model research for liquid launch vehicles[J].Science China:Technological Sciences,2014,44(5):525-531.
[15]赵治华.液体火箭POGO振动的多体动力学建模及稳定性分析[D]:北京:清华大学,2011.
[16]郑铁生,蔡则彪.非对称矩阵结构系统固有特征值分析的广义逆迭代法[J].振动工程学报,1990,3(2):79-84.ZHENG Tiesheng,CAI Zebiao.Generalized inverse interation method for eigenvalue analysis of nonsymmeteric matrix structure systems[J].Journal of Vibration Engineering,1990,3(2):79-84.
[17]ZHENG T S,LIU W M,CAI Z B.A generalized inverse interation method for solution of quadratic eigenvalue problems in structural dynamic analysis[J].Computers&Structures,1989,33(5):1139-1143.
[2]王其政,张建华,马道远.捆绑液体火箭跷振(POGO)稳定性分析[J].强度与环境,2006,33(2):6-11.WANG Qizheng,ZHANG Jianhua,MA Daoyuan.POGOanalysis of cluster liquid rocket[J].Structure Environment Engineering,2006,33(2):6-11.
[3]马道远,王其政,荣克林.液体捆绑火箭POGO稳定性分析的闭环传递函数法[J].强度与环境,2010,37(1):1-7.MA Daoyuan,WANG Qizheng,RONG Kelin.Close-loop transfer function of POGO stability analysis for binding liquidpropellant rocket[J].Structure Environment Engineering,2010,37(1):1-7.
[4]荣克林,张建华,马道远,等.CZ-2F火箭POGO问题研究[J].载人航天,2011(4):8-18.RONG Kelin,ZHANG Jianhua,MA Daoyuan,et al.Research on POGO problem for CZ-2F rocket[J].Manned Spaceflight,2011(4):8-18.
[5]ZHAO Z H,REN G X,YU Z W,et al.Parameter study on POGO stability of liquid rockets[J].Journal of Spacecraft and Rockets,2011,48(3):537-541.
[6]DOTSON K W,RUBIN S,SAKO B H.Mission-specific pogo stability analysis with correlated pump parameters[J].Journal of Propulsion and Power,2005,21(4):619-626.
[7]谭述君,王庆伟,吴志刚.临界阻尼比法在POGO振动稳定性分析中的适用性[J].宇航学报,2015,36(3):284-291.TAN Shujun,WANG Qingwei,WU Zhigang.Applicability of critical damping ratio method on POGO stability analysis[J].Journal of Astronautics,2015,36(3):284-291.
[8]TAN S J,WANG Q W,WU Z G.Effects of damping ratio and critical coupling strength on POGO instability[J].Journal of Spacecraft and Rockets,2016,53(2):370-379.
[9]徐得元,郝雨,杨琼梁,等.液体火箭纵向耦合振动特性的快速求解方法[J].宇航学报,2014,35(1):21-27.XU Deyuan,HAO Yu,YANG Qiongliang,et al.Fast matrix algorithm for POGO instability prediction in liquid rocket[J].Journal of Astronautics,2014,35(1):21-27.
[10]郝雨,徐得元,杨琼梁,等.液体火箭纵向耦合振动建模及动态特性分析[J].振动与冲击,2014,33(24):71-76.HAO Yu,XU Deyuan,YANG Qiongliang,et al.Modeling and dynamic characteristic analysis for longitudinal coupled vibration of a liquid-propulsion rocket[J].Journal of Vibration and Shock,2014,33(24):71-76.
[11]唐冶,方勃,李明明,等.液体火箭推进系统频率特性的灵敏度分析[J].宇航学报,2014,35(8):878-883.TANG Ye,FANG bo,LI Mingming,et al.Sensitivity analysis of frequency characteristic for propulsion system in liquid rocket[J].Journal of Astronautics,2014,35(8):878-883.
[12]OPPENHEIM B W,RUBIN S.Advanced POGO stability analysis for liquid rockets[J].Journal of Spacecraft and Rockets,1993,30(3):360-373.
[13]WANG Q W,TAN S J,WU Z G,et al.Improved modelling method of POGO analysis and simulation for liquid rockets[J].Acta Astronautica,2015,107:262-273.
[14]张青松,张兵.大型液体运载火箭POGO动力学模型研究[J].中国科学:技术科学,2014,44(5):525-531.ZHANG Qingsong,ZHANG Bing.POGO dynamic model research for liquid launch vehicles[J].Science China:Technological Sciences,2014,44(5):525-531.
[15]赵治华.液体火箭POGO振动的多体动力学建模及稳定性分析[D]:北京:清华大学,2011.
[16]郑铁生,蔡则彪.非对称矩阵结构系统固有特征值分析的广义逆迭代法[J].振动工程学报,1990,3(2):79-84.ZHENG Tiesheng,CAI Zebiao.Generalized inverse interation method for eigenvalue analysis of nonsymmeteric matrix structure systems[J].Journal of Vibration Engineering,1990,3(2):79-84.
[17]ZHENG T S,LIU W M,CAI Z B.A generalized inverse interation method for solution of quadratic eigenvalue problems in structural dynamic analysis[J].Computers&Structures,1989,33(5):1139-1143.