|
|
|
Global sensitivity analysis for peak response of a cantilevered rotor with single disc during start-up |
| ZHOU Shengtong1, ZHANG Pei1, XIAO Qian1, LI Hongguang2, ZHOU Xinjian1, WANG Di1 |
1.School of Mechatronics & Vehicle Engineering, East China Jiaotong University, Nanchang 330013, China;
2.State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China |
|
|
|
|
Abstract The global sensitivity of peak response (such as, the maximum peak and its occurrence time) during start-up is an important basis for dynamic design and evaluation of flexible rotor systems.Here, based on Timoshenko beam rotor theory and the finite element method, and considering the randomness of input parameters, the deterministic and stochastic dynamic equations of a cantilevered rotor with a single disc during transient start-up were established.Then, with the limited number of test design samples, the calculation process of the asPC-Sobol sensitivity was given by combining adaptive sparse polynomial chaos (asPC) expansion and Sobol global sensitivity.Finally, based on the analysis of deterministic results of the mean operating condition and the verification of effectiveness of the asPC model, effect laws of start-up acceleration, parametric variability and response measurement point position on the maximum peak value and its time variance of the cantilevered rotor with a single disc passing through the first order positive whirl critical speed were discussed in detail.Example results showed that (1) under the condition of ± 3σ truncated Gaussian distribution, the maximum peak and its time distribution more accord with the lognormal normal distribution, disc diameter D, thickness T, material density ρ, elastic modulus E and unbalance f are the main contribution parameters of the peak response variance; (2) the starting acceleration can more obviously affect the total sensitivity of the maximum peak, but its influence on the total sensitivity of the maximum peak occurrence time is much smaller; (3) when the variability of some main contribution parameters (D, T and ρ) decreases individually or simultaneously, the total sensitivity of the other main contribution parameters can increase obviously, while the increase of the total sensitivity of those non main contribution parameters is limited very much; (4) the influence of the position of response measuring point on the total sensitivity of the maximum peak value and its occurring time is very small, especially, at non-bearing positions.
|
|
Received: 09 November 2020
Published: 15 June 2021
|
|
|
|
［1］ZHANG L, XU H, ZHANG S, et al.A radial clearance adjustable bearing reduces the vibration response of the rotor system during acceleration［J］.Tribology International, 2020, 144: 106112.
［2］CHANDRA N H, SEKHAR A S.Damping identification in rotors from run-up beat responses using Hilbert transforms［J］.Journal of Mechanical Science and Technology, 2014, 28(2): 419-427.
［3］DIDIER J, SINOU J J, FAVERJON B.Study of the non-linear dynamic response of a rotor system with faults and uncertainties［J］.Journal of Sound and Vibration, 2012, 331(3): 671-703.
［4］YANG Y F, WU Q Y, WANG Y L, et al.Dynamic characteristics of cracked uncertain hollow-shaft［J］.Mechanical Systems and Signal Processing, 2019, 124: 36-48.
［5］周生通，祁强，周新建，等.轴弯曲与不平衡柔性转子共振稳态响应随机分析［J］.计算力学学报, 2020, 37(1): 20-27.
ZHOU Shengtong, QI Qiang, ZHOU Xinjian, et al.Stochastic analysis of resonance steady-state response of rotor with shaft bending and unbalance faults［J］.Chinese Journal of Computational Mechanics, 2020, 37(1): 20-27.
［6］ZHOU S T, WU X, LI H G, et al.Critical speed analysis of flexible rotor system with stochastic uncertain parameters［J］.Journal of Vibration Engineering & Technologies, 2017, 5(4): 319-328.
［7］ZHANG Y M, WEN B C, LIU Q L.Reliability sensitivity for rotor-stator systems with rubbing［J］.Journal of Sound and Vibration, 2003, 259(5): 1095-1107.
［8］苏长青，张义民，勾丽杰，等.油膜振荡故障转子系统的可靠性灵敏度排序［J］.兵工学报, 2010, 31(6): 759-764.
SU Changqing, ZHANG Yimin, GOU Lijie, et al.Reliability sensitivity sequencing of rotor system with oil whip fault［J］.Acta Armamentarii, 2010, 31(6): 759-764.
［9］SOBOL’ I M.Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates［J］.Mathematics and Computers in Simulation, 2001, 55(1/2/3): 271-280.
［10］聂祚兴，于德介，李蓉，等.基于Sobol’法的车身噪声传递函数全局灵敏度分析［J］.中国机械工程, 2012, 23(14): 1753-1757.
NIE Zuoxing, YU Dejie, LI Rong, et al.Global sensitivity analysis of autobodies’ noise transfer functions based on Sobol’ method［J］.China Mechanical Engineering, 2012, 23(14): 1753-1757.
［11］邵永生，李成，成明.基于Sobol’法的轨道车辆平稳性的全局灵敏度分析［J］.铁道科学与工程学报, 2018, 15(3): 748-754.
SHAO Yongsheng, LI Cheng, CHENG Ming.Global sensitivity analysis on ride quality of railway vehicle based on the Sobol’ method［J］.Journal of Railway Science and Engineering, 2018, 15(3):748-754.
［12］陈秉智，汪驹畅.基于Sobol’法的轨道车辆前端吸能结构灵敏度分析［J］.铁道学报, 2020, 42(3): 63-68.
CHEN Bingzhi, WANG Juchang.Global sensitivity analysis of energy-absorbing structure for rail vehicle based on Sobol’ method［J］.Journal of the China Railway Society, 2020, 42(3): 63-68.
［13］周生通，李鸿光，张龙，等.基于嵌入式谱随机有限元法的转子系统随机不平衡响应特性分析［J］.振动与冲击, 2016, 35(19): 45-49.
ZHOU Shengtong, LI Hongguang, ZHANG Long, et al.Stochastic unbalance response characteristics of rotor systems based on intrusive spectral stochastic finite element method［J］.Journal of Vibration and Shock, 2016, 35(19): 45-49.
［14］BLATMAN G, SUDRET B.Adaptive sparse polynomial chaos expansion based on least angle regression［J］.Journal of Computational Physics, 2011, 230(6): 2345-2367.
［15］FU C, XU Y D, YANG Y F, et al.Response analysis of an accelerating unbalanced rotating system with both random and interval variables［J］.Journal of Sound and Vibration, 2020, 466: 115047.
［16］SUDRET B.Global sensitivity analysis using polynomial chaos expansions［J］.Reliability Engineering & System Safety, 2008, 93(7): 964-979.
［17］BLATMAN G, SUDRET B.Efficient computation of global sensitivity indices using sparse polynomial chaos expansions［J］.Reliability Engineering & System Safety, 2010, 95(11): 1216-1229.
［18］FRISWELL M I, PENNY J E T, GARVEY S D, et al.Dynamics of rotating machines［M］.Cambridge: Cambridge University Press, 2010.
［19］MARELLI S, SUDRET B.UQLab: a framework for uncertainty quantification in MATLAB［C］//2nd International Conference on Vulnerability, Risk Analysis and Management.Liverpool：ICVRAM, 2014.
|
|
|
|
