Papers by Author: Yan Jun Lu

Abstract: For description of rotor-bearing system, a symmetrical flexible rotor supported by two turbulent journal bearings is modeled. The analysis of the rotor-bearing system is implemented under the assumptions of turbulent lubricant flow and a long bearing approximation. The bifurcation and chaos behaviors of the system are investigated for various rotational speeds. The motion equations are solved by the self-adaptive Runge-Kutta method. The numerical results show that the bifurcation of nonlinear responses of the system varies with the rotational speed of the rotor. It is found that the rich and complex dynamic behaviors of the system include period-1, period-doubling, quasi-periodic and chaotic motions etc.

Abstract: In this article, the nonlinear dynamic responses of drilling shaft system with hydrodynamic forces of cutting fluid were analyzed in deep slot hole drilling. A numerical method is presented to observe the states of the drilling shaft system. Using the proposed method, the periodic orbit of the drilling shaft motion and its period are calculated when the design parameters of drilling shaft system are subject to change, then the stability for dynamic responses of the drilling shaft system can be determined by the Floquet theory. According to the physical character of cutting fluid, the variational constraint approach is introduced to continuously revise the variational form of Reynolds equation at every step of iteration process. The nonlinear hydrodynamic forces of cutting fluid and their Jacobian are solved simultaneously without the increasing of computing efforts. The numerical examples show that the scheme of this study saves computing efforts but also is good precision, and can make a good reference for the dynamic design of drilling shaft system in deep slot hole drilling.

Abstract: Dynamic model and equation of a nonlinear flexible rotor-bearing system are established based on rotor dynamics. A local iteration method consisting of improved Wilson-θ method, predictor-corrector mechanism and Newton-Raphson method is proposed to calculate nonlinear dynamic responses. By the proposed method, the iterations are only executed on nonlinear degrees of freedom. The proposed method has higher efficiency than Runge-Kutta method, so the proposed method improves calculation efficiency and saves computing cost greatly. Taking the system parameter ‘s’ of flexible rotor as the control parameter, nonlinear dynamic responses of rotor system are obtained by the proposed method. The stability and bifurcation type of periodic responses are determined by Floquet theory and a Poincaré map. The numerical results reveal periodic, quasi-periodic, period-5, jump solutions of rich and complex nonlinear behaviors of the system.

Abstract: The unbalanced response and corresponding bifurcation behavior of the rotor dynamic system supported by gas journal bearings are investigated. A time-dependent mathematical model is used to describe the pressure distribution of gas journal bearing with nonlinearity. The rigid Jeffcott rotor with self-acting gas journal bearing supports is modeled. The finite difference method and the Successive Over Relaxation (S.O.R.) method are employed to solve the time-dependent Reynolds equation of gas journal bearings. The bifurcation of unbalanced responses of the rotor is analyzed by a Poincaré map. The numerical results reveal periodic, period-doubling, quasi-periodic, and chaotic motion of rich and complex non-linear behaviors of the system.

Abstract: In this paper, a numerical method is presented to determine the periodic response of hydrodynamic bearing-rotor system. The observed state information of the system is used to solve inversely the Jacobian matrix, and to trace the periodic response with the change of the control parameter. Jacobian matrix obtained is used to calculate the Floquet multiplier, so the stability of the periodic response can be determined by Floquet theory. The proposed method is applied to a rotor system with the elliptical bearing supports to solve the periodic response and determine its nonlinear stability. Validity of this method is illustrated by comparing numerical results with the traditional method.

Abstract: An analytical method of single field reducing-coupling on dynamic modeling is presented to analyze dynamic behaviors of thin plate structure based on dynamic fundamental solutions. In order to improve systematic modeling precision and efficiency, the method of single field reducing-coupling is introduced to deduce governing equations of thin plate structure dynamics by dynamic boundary element method (DBEM). The scale of matrix and generated time of coefficient matrixes are shortened greatly and dynamic behaviors of thin plate structure is obtained rapidly and accurately. The numerical examples and experiments show that the theory, established method and calculating program are feasible, and it has good precision and high efficiency.