单盘悬臂转子启动过程峰值响应全局灵敏度分析

Global sensitivity analysis for peak response of a cantilevered rotor with single disc during start-up

启动过程峰值响应(如最大峰值及其发生时间)的全局灵敏度是柔性转子系统动力学设计和评价的重要依据。基于Timoshenko梁转子有限元理论并考虑输入参数的随机性建立某单盘悬臂转子瞬态启动过程的确定性和随机动力学方程;在有限试验设计样本数限制下,联合自适应稀疏多项式混沌(adaptive sparse polynomial chaos,asPC)展开和Sobol全局灵敏度给出了asPC-Sobol(adaptive sparse polynomial chaos-Sobol)灵敏度计算流程;在均值工况确定性结果分析以及asPC模型有效性验证基础上,详细探讨了启动加速度、参数变异性以及响应测点位置对单盘悬臂转子过第1阶正涡动临界转速时最大峰值及其时间方差的影响规律。算例结果表明:在±3σ截尾高斯分布设定下最大峰值及其时间分布更符合对数正态分布,而且圆盘直径D、厚度T、材料密度ρ、弹性模量E以及不平衡量F是峰值响应方差的主要贡献参数;启动加速度能够较明显地影响最大峰值的总灵敏度结果,但相比之下其对发生时间总灵敏度的影响则小很多;随着某些主要贡献参数(D,T和ρ)变异性的单独或同时减小,其余主要贡献参数的总灵敏度将明显增加,而那些原先非主要贡献参数的增加则非常有限;响应测点位置对最大峰值及其时间总灵敏度的影响非常小,尤其是在非轴承位置处。

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(adaptive sparse polynomial chaos-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±3σtruncated Gaussian distribution,the maximum peak and its time distribution more accord with the lognormal normal distribution,disc diameter D,thickness T,material densityρ,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 andρ)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.