Study on Scaling Laws of Nonlinear Vibration for Rod Fastening Rotor-bearing System
-
摘要: 针对重力对系统原型、模型滑动轴承处振动相似性影响的问题，采用量纲分析法推导了考虑重力影响的组合转子-轴承系统非线性振动相似律表达式。理论分析了考虑重力对缩比模型建立的限制，并提出补偿方案满足完全相似关系。在此基础上，考虑尺寸畸变的影响，采用优化理论推导了轮盘尺寸畸变相似关系。分别建立考虑重力影响和同时考虑重力和尺寸畸变影响的数值仿真模型对相似关系进行验证，并与未修正模型进行对比。结果表明，考虑重力影响和同时考虑重力和尺寸畸变影响建立的修正模型均能对原型轴承处振动响应及油膜涡动过程进行准确预测；而未修正模型的预测误差很大，不能指导非线性振动试验。Abstract: The effect of gravity on the similarity of vibration of sliding bearing of prototype and model was discussed. The scaling laws of nonlinear dynamical systems considering gravity of rotor were established by dimensional analysis. The limitation of gravity law on the design of completely similitude scale model was analyzed, and the compensation scheme was proposed to satisfy the scaling laws. The distorted scaling law was established on the basis of considering geometric distortion by using optimization theory. Finally, the numerical simulation models only considering gravity and simultaneously considering gravity and geometric distortion were established to verify the derived scaling laws. The simulation results were compared with those of the models unmodified. It's shown that the modified model can accurately predict the vibration response of prototype, while the prediction results of the unmodified models have large errors, and they cannot be used in nonlinear vibration test.
-
Key words:
- rotor /
- nonlinear dynamical systems /
- scaling laws /
- gravity /
- distortion /
- optimization
-
表 1 系统量纲矩阵
D1 E ρ d1 D2 b l e B d δ F t Ω α μ Z N ω u M 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 L 1 -1 -3 1 1 1 1 1 1 1 1 1 0 0 -1 0 0 0 0 1 T 0 -2 0 0 0 0 0 0 0 0 0 -2 1 -1 -1 0 0 0 -1 0 
下载: 导出CSV
表 2 原型及模型主要参数
名称 原型 完全相似模型 转轴(l×D2)/mm 500×80 250×40 轮盘(D1×D2×b)/mm 160×80×80 80×40×40 轴承(N×d×δ)/mm 50×80×0.18 25×40×0.09 拉杆直径d1/mm 10 5 轮盘数目Z 4 4 拉杆数目N 12 12 泊松比μ 0.3 0.3 弹性模量E/GPa 210 210 密度ρ/(kg·m-3) 7 800 7 800 润滑油黏度α/(Pa·s) 0.03 0.015 重力加速度g/(m·s-2) 9.8 9.8(未修正模型)19.6(修正模型(考虑重力))
下载: 导出CSV
-
[1] Coutinho C P, Baptista A J, Rodrigues J D. Reduced scale models based on similitude theory:a review up to 2015[J]. Engineering Structures, 2016, 119:81-94 doi: 10.1016/j.engstruct.2016.04.016 [2] 罗忠, 陈晓兵, 于清文, 等.轴承-转子系统中滚动球轴承的动力学相似设计[J].东北大学学报, 2013, 34(9):1296-1299 doi: 10.3969/j.issn.1005-3026.2013.09.019Luo Z, Chen X B, Yu Q W, et al. Dynamic similarity design of rolling ball bearing in bearing rotor system[J]. Journal of Northeastern University, 2013, 34(9):1296-1299(in Chinese) doi: 10.3969/j.issn.1005-3026.2013.09.019 [3] Young Y L. Dynamic hydroelastic scaling of self-adaptive composite marine rotors[J]. Composite Structures, 2010, 92(1):97-106 doi: 10.1016/j.compstruct.2009.07.001 [4] Wu J J. Prediction of lateral vibration characteristics of a full-size rotor-bearing system by using those of its scale models[J]. Finite Elements in Analysis and Design, 2007, 43(10):803-816 doi: 10.1016/j.finel.2007.05.001 [5] 王艾伦, 黄礼坤.转子变态模型与原型的动力相似研究[J].机械设计, 2013, 30(10):11-15 http://d.old.wanfangdata.com.cn/Periodical/jxsj201310003Wang A L, Huang L K. Research on dynamic similarities between abnormal model and the prototype of rotor[J]. Journal of Machine Design, 2013, 30(10):11-15(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/jxsj201310003 [6] 殷杰, 王艾伦, 陈杰.燃气轮机拉杆转子畸变相似问题研究[J].中国机械工程, 2013, 24(22):3066-3070 doi: 10.3969/j.issn.1004-132X.2013.22.017Yin J, Wang A L, Chen J. Distortion similarity analysis of gas turbine rod-fastening rotors[J]. China Mechanical Engineering, 2013, 24(22):3066-3070(in Chinese) doi: 10.3969/j.issn.1004-132X.2013.22.017 [7] 刘恒, 陈丽.周向均布拉杆柔性组合转子轴承系统的非线性动力特性[J].机械工程学报, 2010, 46(19):53-62 http://d.old.wanfangdata.com.cn/Periodical/jxgcxb201019008Liu H, Chen L. Nonlinear dynamic analysis of a flexible rod fastening rotor bearing system[J]. Journal of Mechanical Engineering, 2010, 46(19):53-62(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/jxgcxb201019008 [8] Capone G. Descrizione analitica del campo di forze fluidodinamico nei cuscinetti cilindrici lubrificati[J]. L'Energia Elettrica, 1991, 68(3):105-110 [9] Sonin A A. The physical basis of dimensional analysis[M]. 2nd ed. Cambridge, MA:Department of Mechanical Engineering, MIT, 2001 [10] 鲍培德.浅谈相似理论与模型试验在机械设计中的应用[J].机械设计与制造工程, 2000, 29(6):27-28 doi: 10.3969/j.issn.1672-1616.2000.06.013Bao P D. Introduction on application of similarity and model tests for mechanical design[J]. Machine Design and Manufacturing Engineering, 2000, 29(6):27-28(in Chinese) doi: 10.3969/j.issn.1672-1616.2000.06.013 [11] 林皋, 朱彤, 林蓓.结构动力模型试验的相似技巧[J].大连理工大学学报, 2000, 40(1):1-8 doi: 10.3321/j.issn:1000-8608.2000.01.001Lin H, Zhu T, Lin B. Similarity technique for dynamic structural model test[J]. Journal of Dalian University of Technology, 2000, 40(1):1-8(in Chinese) doi: 10.3321/j.issn:1000-8608.2000.01.001 [12] 罗先启, 毕金锋.地质力学磁力模型试验原理及其在工程中的应用[J].岩土力学, 2018, 39(1):367-374 http://d.old.wanfangdata.com.cn/Periodical/ytlx201801043Luo X Q, Bi J F. Principle and engineering application of geomechanics magnetic model test[J]. Rock and Soil Mechanics, 2018, 39(1):367-374(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/ytlx201801043 [13] Adams C, Bös J, Slomski E M, et al. Scaling laws obtained from a sensitivity analysis and applied to thin vibrating structures[J]. Mechanical Systems and Signal Processing, 2018, 110:590-610 doi: 10.1016/j.ymssp.2018.03.032 [14] 赵书兰.MATLAB编程与最优化设计应用[M].北京:电子工业出版社, 2013Zhao S L. MATLAB programming and optimization design application[M]. Beijing:Publishing House of Electronics Industry, 2013(in Chinese) [15] Dakel M, Baguet S, Dufour R. Nonlinear dynamics of a support-excited flexible rotor with hydrodynamic journal bearings[J]. Journal of Sound and Vibration, 2014, 333(10):2774-2799 doi: 10.1016/j.jsv.2013.12.021 -
点击查看大图
图(9) / 表(3)
计量
- 文章访问数: 292
- HTML全文浏览量: 187
- PDF下载量: 26
- 被引次数: 0
