On-line Estimation of Nonlinear and Time Varying Effects in Rotor System Using Qr Orderly Recursive Method

This paper investigates the on-line estimation of parameters and the determination of the significance of several nonlinear and time varying linear effects in rotor dynamic systems. These effects include nonlinear spring restoring forces, nonlinear structural damping, and the asymmetric stiffness of the shaft. Since these effects are all linear in the parameter, a linear regression scheme can be formulated to estimate the parameter. To solve this linear regression problem, an orderly recursive QR factorization method is used. Based on the estimated parameters and the residual error energies of a series of models, which are available from the QR orderly recursive method, a partial F-statistic test is used to determine the significance of each effect. The simulation results show that the parameters can be obtained after the resonant peak and the significance of these effects can be determined correctly if the sequence of these effects in the QR factorization matrix is carefully arranged. NOMENCLATURE Cuvw body-fixed coordinate system Cxyz intermediate non-spinning coordinate system between OXYZ and Cuvw OXYZ stationary inertial coordinate system h coefficient of the nonlinear structural damping k average of the stiffness of the shaft in two directions kij coefficient of the nonlinear spring restoring force. i,j=0...3 and i+j=3. It, Ip diametric and polar moment of inertia of the disk. y x θ θ , inclination angle in two directions of the disk y x θ θ , angular velocity of the disk y x θ θ , angular acceleration of the disk φ φ φ , , spinning angle, velocity, and acceleration of the rotor τ dynamic unbalance. It is an angle between the principle moment of inertia and the symmetrical axes. ∆ difference of the stiffness of the shaft in two directions