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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
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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)