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Technical Brief

# A Method for Dynamic Analysis of Three-Dimensional Solid Element Rotors With Uncertain Parameters

[+] Author and Article Information
Yanfei Zuo

College of Mechanical and Electrical Engineering,
Beijing University of Chemical Technology,
Beijing 100029, China;
School of Power and Energy Engineering,
Beijing University of Aeronautics and Astronautics,
Beijing 100191, China
e-mail: zuo_yanfei@163.com

Jianjun Wang

School of Power and Energy Engineering,
Beijing University of Aeronautics and Astronautics,
Beijing 100191, China
e-mail: wangjianjun@buaa.edu.cn

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 29, 2015; final manuscript received October 5, 2016; published online December 1, 2016. Assoc. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 139(5), 054501 (Dec 01, 2016) (4 pages) Paper No: GTP-15-1430; doi: 10.1115/1.4035049 History: Received August 29, 2015; Revised October 05, 2016

## Abstract

Three-dimensional solid element models often with a great number of degrees-of-freedom (DOFs) are now widely used for rotor dynamic analysis. While without reduction, it will cost considerable calculating resources and time to solve the equations of motion, especially when Monte Carlo simulation (MCS) is needed for stochastic analysis. To improve the analysis efficiency, the DOFs are partly reduced to modal spaces, and the stochastic results (critical speeds or unbalance response) are expanded to polynomial spaces. First, a reduced rotor model is got by component mode synthesis (CMS), and the stochastic results are expanded by polynomial chaos basis with unknown coefficients. Then, the reduced rotor model is used to calculate the sample results to obtain the coefficients. At last, the expressions of the result by polynomial chaos basis are used as surrogate models for MCS. An aero-engine rotor system with uncertain parameters is analyzed. The accuracy of the method is validated by direct MCS, and the high efficiency makes it possible for stochastic dynamic analysis of complex engine rotor systems modeled by 3D solid element.

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## References

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## Figures

Fig. 1

Reduction scheme of the rotor system

Fig. 2

Histogram offrequency count of the first F critical speed: (a) first F critical speed by MCS and (b) first F critical speed by PCE

Fig. 3

Histogram of the second F critical speed: (a) second critical speed by CMS and (b)second critical speed by PCE

Fig. 4

Stochastic unbalance response of bearing 2: (a) stochastic response got by MCS and (b) stochastic response got by PCE

Fig. 5

Comparisons of envelopes and mean values of the response got by MCS and PCE

## Errata

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