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.
Key words
overhung rotor system /
peak response /
Sobol global sensitivity /
adaptive sparse polynomial chaos (asPC) expansion
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