Dynamic Response Analysis of Rotor System With Uncertain Parameters via Interval Analysis Method

2012 ◽  
Author(s):  
Jie Hong ◽  
Jun Wang ◽  
Meng Chen ◽  
Yanhong Ma
Keyword(s):  
Dynamic Response ◽  
Interval Analysis ◽  
Operating Conditions ◽  
Response Analysis ◽  
Superposition Method ◽  
Uncertain Parameters ◽  
Analysis Method ◽  
Operating Cycle ◽  
Interval Analysis Method ◽  
Modal Superposition

The support stiffness and connecting structure stiffness change with different assembly conditions and operating conditions. The phase and amount of rotor unbalance in different operating cycle changes due to wear of blade tip and connecting structures in different working cycles. These parameters which have significant effect on rotordynamics are “uncertain but bounded”, in another word, the distributions of the parameters are unknown, but the intervals of uncertain parameters are always got easier. An interval analysis method, which solves the dynamic response with these uncertain parameters, has presented. Based on interval mathematics and modal superposition method, interval analysis method simplifies the uncertain parameters to interval vectors so that it can get the intervals within which the dynamic response varies when less information of structure is known. The interval analysis method is efficient under the condition that probability approach cannot work because of small samples and sparse statistics characteristics. The formulation of rotor dynamic response using interval modal superposition analysis method is formulated. A numerical example of comparison between interval analysis method and Monte Carlo method is given, and the results illustrate the interval analysis method.

Interval Analysis Method for Rotordynamic With Uncertain Parameters

2011 ◽  
Author(s):  
Yanhong Ma ◽  
Peng Cao ◽  
Jun Wang ◽  
Meng Chen ◽  
Jie Hong
Keyword(s):  
Perturbation Method ◽  
Interval Analysis ◽  
Operating Conditions ◽  
Small Samples ◽  
Squeeze Film ◽  
Uncertain Parameters ◽  
Analysis Method ◽  
Interval Analysis Method ◽  
Different Temperatures ◽  
Interval Perturbation Method

The support stiffness and connecting structure stiffness which has significant effect on rotordynamics change with different assembly conditions and operating conditions. For example, the squeeze film stiffness changes with different film force, and the elastic support stiffness changes with different temperatures. These parameters are “uncertain but bounded”, in another word, the distributions of the parameters are unknown, but the intervals of the uncertain parameters are always got easier. An interval analysis method, which solves the rotordynamics with these uncertain parameters, is presented. Based on interval mathematics and perturbation method, interval analysis method simplifies the uncertain parameters to interval vectors so that it can get the intervals within which the rotordynamics varies when less information of structure is known. The interval analysis method is efficient under the condition that probability approach cannot work because of small samples and spare statistics characteristics. The formulation of natural frequencies of rotor using interval perturbation analysis method is formulated. A numerical example of comparison between interval perturbation method analysis and monotonic method is given. The rotordynamic analysis of a turbofan rotor is performed with this method, and the test data validates the numerical results.

INTERVAL AND SUBINTERVAL ANALYSIS METHODS OF THE STRUCTURAL ANALYSIS AND THEIR ERROR ESTIMATIONS

2006 ◽  
Vol 03 (02) ◽  
pp. 229-244 ◽  
Author(s):  
Y. T. ZHOU ◽  
C. JIANG ◽  
X. HAN
Keyword(s):  
Interval Analysis ◽  
Taylor Expansion ◽  
Truncation Error ◽  
Estimation Methods ◽  
Uncertain Parameters ◽  
Analysis Method ◽  
Interval Analysis Method ◽  
Analysis Methods ◽  
Second Derivatives ◽  
Error Estimations

In this paper, the interval analysis method is introduced to calculate the bounds of the structural displacement responses with small uncertain levels' parameters. This method is based on the first-order Taylor expansion and finite element method. The uncertain parameters are treated as the intervals, not necessary to know their probabilistic distributions. Through dividing the intervals of the uncertain parameters into several subintervals and applying the interval analysis to each subinterval combination, a subinterval analysis method is then suggested to deal with the structures with large uncertain levels' parameters. However, the second-order truncation error of the Taylor expansion and the linear approximation of the second derivatives with respect to the uncertain parameters, two error estimation methods are given to calculate the maximum errors of the interval analysis and subinterval analysis methods, respectively. A plane truss structure is investigated to demonstrate the efficiency of the presented method.

Interval Analysis on Aero-Engine Rotor System With Misalignment

2015 ◽  
Author(s):  
Cun Wang ◽  
Yanhong Ma ◽  
Dayi Zhang ◽  
Jie Hong
Keyword(s):  
Interval Analysis ◽  
Second Harmonic ◽  
Joint Stiffness ◽  
Element Model ◽  
Rotor System ◽  
Operating Conditions ◽  
Analysis Method ◽  
Interval Analysis Method ◽  
Frequency Components ◽  
Different Characteristics

Misalignment is a usual phenomenon in rotating machines. The rotor centerlines are not collinear at the couplings and the rotors operate in incorrect axial positions in a multi-span rotor. The effects of misalignment of flexible rotor system are summarized as the variation of joint stiffness and additional misalignment excitation force based on the dynamic model established. The variation of joints stiffness is difficult to describe, meanwhile the misalignment excitation and rotor unbalance changes with different assembly and operating conditions. The distributions of these parameters which have significant effect on rotor dynamics are unknown, but the intervals of uncertain parameters are usually easier to get. An interval analysis method based on Taylor expansion and direct integration, which solves the dynamic response of rotor system under complex excitations including misalignment and multi unbalance with different frequencies and excitation points is presented. The differential equation of rotor system is formulated by combination of the matrixes of an actual rotor system finite element model and interval excitation vectors. The responses of a single spool and two spools with misalignment and unbalance are calculated by the interval analysis method. The results indicate that the method is effective and reflects some dynamic influence of misalignment and unbalance on rotor system. Second harmonic frequency appears, and rotor orbit is irregular. The response reflects the uncertain interval distribution characteristics, and the frequency components on different locations of the rotor have different characteristics.

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