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摘要: 提出了一种基于连续梁模型的计算转子支承系统临界转速的方法, 将转轴考虑为等截面自由欧拉梁模型, 轴承对转轴的支承力以及转盘与转轴的作用力均以集中力的形式作用于转轴梁上, 运用模态截断法, 将系统偏微分方程转化为常微分方程组, 运用新型快速显式数值积分方法获取转子系统的响应及其临界转速, 运用ZT-3型多功能转子试验器进行了试验验证。结果表明: 相同参数条件下, 试验临界转速和计算临界转速均在5500r.min-1左右, 表明了计算方法的正确性和有效性。Abstract: A computational method of the critical speed of rotor-bearing system based on the continuous beam model was proposed.Rotor shaft was considered as equisection Euler free beam model.The supporting forces from bearings and the forces between shaft and rotor disks acted on shaft in the form of concentrated force.With modal truncation method, the partial differential equation of the system was transformed into ordinary differential equation set.The system's responses and critical speed were obtained by numerical integral method.ZT-3 type multi-function rotor test rig was used to verify the new method.The calculating critical speed is the same as the actual one, which is about 5 500 r·min-1, so the new method is correct and effective.
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Key words:
- aeroengine /
- rotor-bearing system /
- critical speed /
- continuous beam model /
- modal truncation
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表 1 自由梁函数系数
Table 1. Function coefficients of free beam
n 1 2 3 4 5 ≥6 Cn — — 0.982 502 1.000 777 0.999 966 1.000 000 βnL 0 0 4.730 04 7.853 20 10.995 60 (2n-3) π/2 表 2 ZT-3转子试验台主要计算参数
Table 2. Main computational parameters of ZT-3 type rotor test rig
弹性模量E/Pa 截面惯性矩Iy=Iz/m4 密度ρ/ (kg·m-3) 转轴截面积A/m2 线密度ρA/ (kg·m-1) 转盘质量mrp/kg 转轴长度L/m 2.1×1011 3.998×10-10 7.8×103 7.088×10-5 0.554 3 0.6 0.26 -
[1] 康召辉, 任兴民, 刘婷婷. 一种轴型盘转子系统临界转速的计算分析[J]. 机械科学与技术, 2008, 27 (10): 1177-1180. doi: 10.3321/j.issn:1003-8728.2008.10.012KANG Zhao-hui, REN Xing-min, LIU Ting-ting. Calculation and analyse of the critical speeds of a rotor system with great thickness[J]. Mechanical Science and Technology for Aerospace Engineering, 2008, 27 (10): 1177-1180. (in Chinese) doi: 10.3321/j.issn:1003-8728.2008.10.012 [2] HSIEH S C, CHEN J H, LEE A C. A modified transfer matrix methodfor the couplinglateral and torsional vibrations of symmetric rotor-bearing systems[J]. Journal of Sound and Vibration, 2006, 289 (1/2): 294-333. [3] 贺威, 袁惠群, 朱向哲. 瞬态传递矩阵法分析热弯转子系统的热碰摩故障[J]. 东北大学学报: 自然科学版, 2009, 30 (6): 861-864. https://www.cnki.com.cn/Article/CJFDTOTAL-DBDX200906026.htmHE Wei, YUAN Hui-qun, ZHU Xiang-zhe. Transient transfer matrix method for thermal rub-impact faults in hot bending rotor system[J]. Journal of Northeastern University: Natural Science, 2009, 30 (6): 861-864. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DBDX200906026.htm [4] 孟越, 李其汉. 应用整体传递系数法分析复杂转子系统转静件碰摩振动特征[J]. 航空动力学报, 2003, 18 (1): 146-150. https://www.cnki.com.cn/Article/CJFDTOTAL-HKDI200301026.htmMENG Yue, LI Qi-han. Using WTCMto analyze rub-impact default of a complex rotor system[J]. Journal of Aerospace Power, 2003, 18 (1): 146-150. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKDI200301026.htm [5] 姚红良, 刘长利, 李鹤, 等. 采用瞬态传递矩阵法分析复杂转子系统碰摩故障[J]. 东北大学学报: 自然科学版, 2004, 25 (1): 62-65. https://www.cnki.com.cn/Article/CJFDTOTAL-DBDX200401017.htmYAO Hong-liang, LI U Chang-li, LI He, et al. Transient transfer matrix method for complicated rotor systems with rub-impact fault[J]. Journal of Northeastern University: Natural Science, 2004, 25 (1): 62-65. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DBDX200401017.htm [6] 欧园霞, 李彦. 转子动力特性计算中常用方法的对比分析[J]. 航空动力学报, 1994, 9 (2): 142-146. https://www.cnki.com.cn/Article/CJFDTOTAL-HKDI402.007.htmOU Yuan-xia, LI Yan. Comparison between most used methods for analyzing dynamic characteristics of rotor systems[J]. Journal of Aerospace Power, 1994, 9 (2): 142-146. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKDI402.007.htm [7] 孙红岩, 张小龙. 基于ANSYS软件的转子系统临界转速及模态分析[J]. 机械制造与研究, 2008, 37 (4): 53-54. https://www.cnki.com.cn/Article/CJFDTOTAL-JSGL201003097.htmSUN Hong-yan, ZHANG Xiao-long. Rotor s critical rotation speed and modality analysis based on ANSYS[J]. Machine Building and Automation, 2008, 37 (4): 53-54. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSGL201003097.htm [8] 秦然, 张建伟. 转子临界转速的求解方法比较[J]. 沈阳化工学院学报, 2007, 21 (1): 74-76, 80. https://www.cnki.com.cn/Article/CJFDTOTAL-SYHY200701020.htmQI N Ran, ZHANG Jian-wei. Comparison of rotor critical rotation speeds solution method[J]. Journal of Shenyang Institute of Chemical Technology, 2007, 21 (1): 74-76, 80. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SYHY200701020.htm [9] 陈萌, 马艳红, 刘书国, 等. 航空发动机整机有限元模型转子动力学分析[J]. 北京航空航天大学学报, 2007, 33 (9): 1013-1016. https://www.cnki.com.cn/Article/CJFDTOTAL-BJHK200709004.htmCHEN Meng, MA Yan-hong, LI U Shu-guo, et al. Rotor dynamic analysis of whole aero-engine models based on finite element method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2007, 33 (9): 1013-1016. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-BJHK200709004.htm [10] 翟婉明, 韩卫军, 蔡成标, 等. 高速铁路板式轨道动力特性研究[J]. 铁道学报, 1999, 21 (6): 65-69. https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB199906017.htmZHAI Wan-ming, HAN Wei-jun, CAI Cheng-biao, et al. Dynamic properties of high-speed rail way slab tracks[J]. Journal of the China Rail way Society, 1999, 21 (6): 65-69. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB199906017.htm