Yongfeng Yang

Nonlinear response prediction of cracked rotor based on EMD

Abstract The empirical mode decomposition (EMD) method is introduced, to improve the prediction accuracy of cracked rotor׳s nonlinear response during a long-term period. The EMD method was applied to decompose the nonlinear response into series of intrinsic mode functions (IMF). Consequently, the prediction results of IMF were obtained, based on the maximal local Lyapunov exponent (LLE). By adding all the prediction results of IMF, the nonlinear response of cracked rotor can be predicted, called the IMF prediction method. Compared with the response predicted directly by the maximal local Lyapunov exponent, when the forecasting step is less than the maximal prediction time which is calculated by the multiplicative inverse of maximal Lyapunov exponent, the IMF method has the same prediction accuracy. When the forecasting step is greater than maximal prediction time, the IMF prediction method is more advantageous than the Lyapunov prediction method. Bently RK4 rotor test is used to validate the IMF prediction method׳s advantage.

Rationalize the irrational and fractional expressions in nonlinear analysis

Chebyshev polynomial approximation is an effective method to study the stochastic bifurcation and chaos. However, due to irrational and fractional expressions existing in the denominator of some mechanical systems, the integral process is very complicated. The Taylor series expansion is proposed to expand the irrational and fractional expressions into a series of polynomials. Smooth and discontinuous oscillator was taken as an example, and the results show that the Taylor series expansion method is acceptable. The rub-impact force was taken as another example. Numerical results indicate that the method is suitable for the rub-impact rotor system.

Nonlinear analysis of a rub-impact rotor with random stiffness under random excitation

Stochastic bifurcation and chaos of a rub-impact rotor system with random stiffness under random excitation are studied in this article. Due to the irrational and fractional expressions existing in the denominator of rub-impact force, the integral process is very complicated. Taylor series expansion is used to expand the irrational and fractional expressions into a series of polynomials. Chebyshev polynomial approximation method is applied to reduce the system equations with random parameter to its equivalent deterministic one, and the responses of stochastic system can be obtained by numerical methods. Numerical simulations show that random parameters have a significant effect on the rub-impact rotor system. It may promote the nonlinear response when the rotational speed is near the 1/2 first-order critical speed and may suppress the nonlinear response when the rotational speed is over the first-order critical speed.

Transient Analysis of Speed-Varying Rotor with Uncertainty Based on Interval Approaches

The nonintrusive Chebyshev interval method is used to analyze the transient response of a rotor system. The main idea is to analyze the uncertainty in speed-varying rotor systems and reduce the error in the calculation. The hybrid analysis procedure, which combines the black-box modeling and overestimation controlling, is proposed via the Chebyshev approximation and searching the extreme values of the approximation function for the uncertain response. It can both increase accuracy and improve the computational efficiency of the proposed method. Effects of the uncertain parameters on response bounds and estimation errors of the system are investigated, e.g., supporting stiffness and damping. The accuracy and efficiency of the proposed method are verified via comparing with the scanning method. Overestimation effects caused by the interval arithmetic can be controlled, particularly the sensitive domains near the critical speed. It can provide guidance for general uncertain transient mechanical systems, particularly those that have severe fluctuations near resonances.

Modeling and Nonlinear Response of the Cam-Follower Oblique-Impact System

In order to quickly and accurately analyze the complex behavior of cam-follower oblique-impact system, a mathematical model which can describe separation, impact, and contact was established in this paper. The transient impact hypothesis was extended, and the oblique collision model was established by considering the tangential slip. Moreau time-stepping method was employed to solve the linear complementarity problem which transformed by the oblique-impact equations. The simulation results show that the cam and follower kept permanent contact when the cam rotational speed was low. With the increase of the cam rotational speed, the cam and follower would be separated and then impact under the gravity action. The system performance shows very complex nonlinear characteristics.

Unbalance Identification of Speed-Variant Rotary Machinery without Phase Angle Measurement

As rotary mechanical structure becomes more complicated, difficulty arises in receiving prime correction mass and optimum balancing plane efficiently. An innovative modal balancing process for estimating the residual unbalance from different equilibrium plane of complex flexible rotor system is presented. The method is based on a numerical approach with modal ratio among measurement points (MRMP) coefficient and triple phase method (TPM). The veracity of calculation result is verified by an academic rotor model. The latter study in this paper is subsequently put forward through a power turbine rotor modeled by finite element method. Simulation results show that proper equilibrium plane performs commendably in recognizing residual unbalance and reducing the vibration effect through the critical region. Moreover, the inherent unbalance recognized by experimental data from a turbine rotor with slender shaft is found to be in certain difference under different counterweight combination. Choosing suitable balancing planes will improve the accuracy of unbalance identification.

Analysis of Stochastic Bifurcation and Chaos in a Rub-Impact Rotor System With Random Parameter

Stochastic bifurcation and chaos of a rub-impact rotor system with random parameter is studied in this paper. Due to an irrational and fractional expression existing in the rub-impact force, there is a very complicated integral operation. Then, the Taylor series expansion is proposed, and it expands the rub-impact force into a polynomial. Firstly, take SD oscillator for example, the results show the taylor series expansion method is acceptable. Secondly, expand the rub-impact force, the numerical results indicate that the method is available to the rub-impact rotor system. At last, the Chebyshev polynomial approximation method is applied to reduce the system with random parameter to its equivalent deterministic one, and the responses of stochastic system can be obtained by numerical methods. Numerical simulations show that random parameters have a significant effect on the rub-impact rotor system.Copyright

Rotating machine fault diagnosis based on denoising source separation

The application of denoising source separation (DSS) technology to the mechanical vibration signal processing provides a new technique of mechanical fault diagnosis. The DSS theory is investigated in this paper. The analog signals of the rotating machine are separated and the performance index and correlation coefficient of DSS are better than those of the joint approximate diagonalization of eigen-matrices (JADE). Applying the DSS method to rotating machine fault diagnosis, the measured fault signals are analyzed and the results are found to be in agreement with practice. The results show that the DSS method is efficient in analyzing the fault diagnosis of rotating machine.