Modeling a two-span rotor system based on the Hamilton principle and rotor dynamic behavior analysis

Journal of Zhejiang University-SCIENCE A, Nov 2014

A nonlinear dynamic model of a two-span rotor system is constructed based on the Hamilton principle and the finite element method. The Musznyska model and the short bearing model are employed to describe the nonlinear seal force and oil-film force. The fourth-order Runge-Kutta method is used to calculate the numerical solutions. The bifurcation diagrams, time-history diagrams, phase trajectories, and Poincare maps are presented to analyze the dynamic behavior of the bearing center and the disk center in the horizontal direction. The numerical results indicate that the rotational speed, the nonlinear seal force, the oil-film force, and the stiffness of the coupling have a significant effect on the stability of the rotor system. The dynamic behavior of the two-span rotor system is more complicated when impacted by the nonlinear seal force and oil-film force.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1631%2Fjzus.A1400100.pdf

Modeling a two-span rotor system based on the Hamilton principle and rotor dynamic behavior analysis

Li et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 1673-565X and rotor dynamic behavior analysis* Wei LI 0 De-ren SHENG 0 Jian-hong CHEN 0 Yong-qiang CHE 0 0 (Department of Energy Engineering, Zhejiang University , Hangzhou 310027 , China) A nonlinear dynamic model of a two-span rotor system is constructed based on the Hamilton principle and the finite element method. The Musznyska model and the short bearing model are employed to describe the nonlinear seal force and oil-film force. The fourth-order Runge-Kutta method is used to calculate the numerical solutions. The bifurcation diagrams, time-history diagrams, phase trajectories, and Poincare maps are presented to analyze the dynamic behavior of the bearing center and the disk center in the horizontal direction. The numerical results indicate that the rotational speed, the nonlinear seal force, the oil-film force, and the stiffness of the coupling have a significant effect on the stability of the rotor system. The dynamic behavior of the two-span rotor system is more complicated when impacted by the nonlinear seal force and oil-film force. Hamilton principle; Two-span rotor system; Nonlinear seal force; Dynamic characteristic doi; 10; 1631/jzus; A1400100 Document code; A CLC number; TK14 - The field of rotor dynamics is concerned with the research of dynamic and stability characteristics of rotating machinery, and it plays an important role in improving the safety and performance of the entire systems. The modeling of rotor systems and dynamic characteristics analysis are the fundamental research content in the field of rotor dynamics. The rotor system is usually supported by bearings and influenced by internal phenomena that rotor rotates around a single axis. Recently the multi-disk and multi-span rotor system is becoming an important field for rotor dynamics research (Chen, 2009). Many studies have been conducted on rotor modeling and dynamic characteristics analysis. The Muszynska model highlights the seal force nonlinear characteristics with clear physical meaning (Muszynska and Bently, 1990). Al-Nahwi et al. (2003) analyzed the principle and interaction of steam excitation on the Jeffcott rotor system combining it with the Moore-Greitzer flow field model. Luo et al. (2007) built a periodical time-variable high-dimensional dynamic rotor system based on the rotor’s finite element model and investigated the stability of the system. Cheng et al. (2008) studied the nonlinear dynamic behaviors of a rotor/bearing/seal coupled system with Muszynska’s seal forces and Capone’s oil-film forces. The influence of the rotation speed, seal clearance, and eccentricity of the rotor were analyzed. de Castro et al. (2008) modeled a flexible rotor with a central disk under unbalanced excitation and validated a complete nonlinear solution to simulate the fluid-induced instability during run-up and run-down. Wang et al. (2009) established a nonlinear mathematical model for orbital motion of the rotor under the influence of leakage flow through an interlocking seal and used the fourth-order RungeKutta method to solve it. Particular attention was placed on the serpentine flow path by spatially separating the aerodynamic force on the rotor surface into two parts, e.g., the seal clearance and the cavity volume (Wang et al., 2009). Okabe and Cavalca (2009) developed an analytical model of a tilting pad bearing based on the short bearing assumption with the turbulence effect included. They found that the bearing model with turbulent flow effect generated higher hydrodynamic forces when compared to the one without this effect, which highlights the importance of considering such phenomenon during the analysis of high speed hydrodynamic bearings. Li et al. (2011a; 2011b) applied the Hamilton principle and the finite element method (FEM) to construct a novel nonlinear model of a rotor/bearing/seal system. The dynamic behavior of the system is illustrated by bifurcation diagrams, large Lyapunov exponents, phase trajectory diagrams, and Poincare maps. Li et al. (2012) presented the effects of journal misalignment on the transient flow of a finite grooved journal bearing using a new 3D computational fluid dynamics analysis method. Based on the FEM and the Lagrange equation, Zhou et al. (2014) proposed a novel nonlinear model of a double disc rotor-seal system, including the coupled effects of the gravity force of the discs, Muszynska’s nonlinear seal fluid dynamic force, and the mass eccentricity of the discs. Other researchers focused on the dynamic analysis of rotor systems supported by gas bearings. Půst and Kozánek (2007) calculated the dynamic characteristics of bearings at different revolutions, which took into account the inertia properties of tilting pads. Ertas et al. (2010) tested a rotor system using a 70-mm diameter damped gas bearing reaching ultra-high speeds of 50 000 r/min and experimentally evaluated the ability of the damped gas bearing to withstand large rot (...truncated)


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1631%2Fjzus.A1400100.pdf

Wei Li, De-ren Sheng, Jian-hong Chen, Yong-qiang Che. Modeling a two-span rotor system based on the Hamilton principle and rotor dynamic behavior analysis, Journal of Zhejiang University-SCIENCE A, 2014, pp. 883-895, Volume 15, Issue 11, DOI: 10.1631/jzus.A1400100