Abstract: In order to research the effects of random variation of steady-state temperature field and centrifugal load on vibration characteristics of turbine bladed disk， the certainty analysis of the vibration characteristics of a turbine bladed disk under the steady-state temperature field was conducted by FEM (Finite Element Method). Based on this， the probabilistic analysis of the vibration characteristics of the bladed disk was performed by adopting quadratic response surface method with cross terms. The probability distribution of the vibration characteristics of the bladed disk under steady-state temperature field was obtained and the influence of random variables such as temperature field and centrifugal load on the modal frequency of the random vibration of the bladed disk was presented. Finally， according to the reference state of resonance and Campbell chart， considering the correlation of speed and rotor vibration frequency， the theory of avoiding resonance analysis of the random vibration of the bladed disk was proposed， and the analysis was carried out under several typical operating conditions. The results show that random parameters of 3% variance will lead to over 50% extension of the resonance speed region of the bladed disk and the overlapping of multiple resonance speed regions.

Key words: Turbine bladed disk；Steady-state temperature field；Quadratic response surface method；Probabilistic analysis；Campbell chart；Avoiding resonance analysis

摘要： 为了研究稳态温度场及离心载荷的随机变化对涡轮叶盘振动特性的影响，利用有限元方法对稳态温度场作用下的涡轮叶盘结构振动特性进行确定性分析。在此基础上，采用含交叉项的二次响应面方法对叶盘结构振动特性进行概率分析，得到稳态温度场下叶盘结构振动特性的概率分布特征，并给出温度场及离心载荷等随机变量对叶盘结构随机性振动的模态频率的影响规律。最后，根据共振考核状态及坎贝尔图，结合转速与频率的相关性提出叶盘随机性振动避共振方法，并在几个典型工况下对叶盘结构随机性振动进行了避共振分析。结果表明，随机参数3%的变化能够导致叶盘共振转速区拓宽50%以上，并造成多个共振转速区重叠现象。

关键词: 涡轮叶盘；稳态温度场；二次响应面法；概率分析；坎贝尔图；避共振分析