Research On Dynamic Characteristics Of Flexible Rotor System With Uncertain Parameters

Parametric uncertainties are naturally present in flexible rotor systems due to a variety of factors,such as manufacturing and assembling errors,material property dispersions and wear.It is the requirement of both the precise assesement of dynamic characteristics and the modern engineering design.Generally,the uncertainties can be catagorized into two kinds of variables,i.e.random quantities and interval variables,according to their available prior information.The random uncertainties should be described by rigorious probability distribution functions(PDFs)while the interval ones only by lower and upper bounds.Non-probabilistic uncertianty analysis based on the interval arithmetic is a new uncertainty quantificaiton branch which requires little prior information and is suitable for small sample sized problems.It is especially effective in cases where the precise PDFs of the uncertainties are absent or too expensive to derive.In this thesis,the non-intrusive uncertainty quantificaiton technologies are introduced and then developed into uncertain rotordynamics.Applications include the calculation of interval problems of complex rotor systems with multi degrees of freedom and crack fault detection.Hybrid analysis of systems with both the random and interval uncertainties are carried out as well.The methods and results of this dissertation will provide references for the design and dynamics analysis of rotating systems.The main contents are as follows:(1)The deterministic equations of motion of an overhung hollow-shaft rotor system are derived using the finite element method(FEM).Considering the interval uncertainties,the derivative-based Chebyshev interval method is formulated to deal with the interval problem.The uncertain steady-state dynamic responses of the rotor system under different interval parameters with several typical uncertain degrees are studied in detail.In order to investigate the effectiveness of other kinds of orthogonal polynomials in the calculation of interval rotordynamics,the Legendre series are introduced and compared with the Chebyshev method.The Monte Carlo simulation(MCS)and the scanning method are used to verify the accuracy and efficiency of these interval methods.Simulation results show that uncertainties have significant influence on the steady-state dynamics of the rotor under study and phenomenen such as the ‘resonant band’ and the ‘frequency shift’ are observed in some occasions.Different kinds of orthogonal polynomials are applicable in the uncertain rotordynamics investigations and the Chebyshev interval method has higher calculation efficiency than the Legendre method.(2)An interval precise integration method(IPIM)is proposed to solve the uncertain transient dynamic problem of rotor systems.It combines the merits of unconditionally stability and preciseness of the improved precise integration method and the non-intrusiveness and numerical calculation of the Chebyshev inclusion function(CIF).Then,the symbolic computation at those time steps can be avoided to save time.The time-varying deterministic motion equations are deducted based on the transfer matrix method(TMM)and simulations with various uncertain cases are performed.Results show that there are also the peak shifts and resonant bands in some cases,the proposed method has high efficency and accuracy.(3)The nonlinear uncertain dynamics of rotor systems with a crack and interval variables are studied.The FEM and the neutral axis method are employed to construct the local stiffness matrix.Then,the harmonic balance method(HBM)is used to transfom the differential equations with time-variant stiffness terms into a linear algebraic equations with the Fourier coefficients being unknow.A meta-model for the unknown Fourier expansion coefficients are established using the CIF.The uncertain effects of a lot of physical parameters on the super harmonic resonances are investigated.In addition,the polynomial surrogate method is proposed for solving uncertain problems with a large number of interval uncertainties.Simulation results indicate that the meta-model proposed is capable of predicting the nonlinear harmonic responses accurately.Uncertain parameters have different influence patterns on the n ? components and sensitive parameters include Young’s modulus and denstiy,etc.It is recommended that the amplitudes at the sub-critical speeds of the rotor system should be used for early crack fault detection.The indicator of the critical speed variation is not reliable since uncertainties can cause that as well.Simulations also prove that the proposed polynomial surrogate has the same accuracy as the former meta-model but can reduce significant computation cost in multi-dimensinal interval problems.(4)Dual stage non-intrusive uncertainty quantification strategy is incoporated for rotor systems with both random and interval uncertainties.The polynomial chaos expansion(PCE)is used to deal with the random variables and then the improved CIF is employed to serach the bounds of the first two statistic moments.The interval expectation and interval variance are formulated to describe the transient dynamics of an overhung rotor.Combined verification frame by the MCS and the scanning method is adopted to validate the dual stage uncertainty analysis method.Simulation results suggest that the proposed method can effectively predict the interval statistic moments of the rotor under hybrid uncertainties.