WANG Qingwei1, WANG Xiaojun2, ZHANG Qingsong1, PAN Hui1, TAN Shujun3
1.Beijing Institute of Astronautical Systems Engineering, Beijing 100076, China;
2.China Academy of Launch Vehicle Technology, Beijing 100076, China;
3.School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
Abstract: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.
王庆伟 1, 王小军 2, 张青松 1, 潘辉1, 谭述君3. 液体火箭POGO振动缩聚模型研究[J]. 振动与冲击, 2019, 38(1): 8-13.
WANG Qingwei1, WANG Xiaojun2, ZHANG Qingsong1, PAN Hui1, TAN Shujun3. POGO vibration reduced model for liquid rockets. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(1): 8-13.
[1] Rubin S. Longitudinal instability of liquid rockets due to propulsion feedback[J]. Journal of Spacecraft and Rockets, 1966,3(8): 1188-1195.
[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 Qi-zheng, ZHANG Jian-hua, MA Dao-yuan. POGO analysis 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 Dao-yuan, WANG Qi-zheng, RONG Ke-lin. Close-loop transfer function of POGO stability analysis for binding liquid-propellant 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 Ke-lin, ZHANG Jian-hua, MA Dao-yuan, 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 Shu-jun, Wang Qing-wei, Wu Zhi-gang. 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 De-yuan, HAO Yu, YANG Qiong-liang, 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 De-yuan, YANG Qiong-liang, 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 Ming-ming, 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 Qing-song, 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]: 清华大学, 2011.
ZHAO Zhi-hua. Multibody dynamic approach of modeling liquid rocket for POGO stability analysis[D]. Beijing: Tsinghua University, 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 Tie-sheng, Cai Ze-biao. 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.