Dynamic behaviors of a geared rotor system under time-periodic base angular motions

The appearance of cracks in rotor systems affects the whirl response in the neighborhood of the critical whirl rotational speeds. The combined effect of the crack depth and the unbalance force vector angle orientation with respect to the crack opening direction on the effective stiffness content of the cracked rotor system in the neighborhood of the critical rotational speed is addressed here. The effective stiffness expression of the cracked system can be obtained from the direct integration of the equations of motion of the cracked rotor system. The cracked rotor equations of motion can be expressed by the Jeffcott rotor or the finite element models. The appearance of cracks in rotor systems converts them into parametrically excited dynamical systems with time-periodic stiffness components. The interaction between the time-periodic stiffness and the external periodic forcing function of the unbalance force significantly alters the effective stiffness content in the system at both transient and steady state operations. For wide range of crack depths and unbalance force vector angles, the effective stiffness has been found to be of negative values. This means that the cracked rotor system tends to have more resistance to deflect towards the center of its whirl orbit and less resistance to deflect away under the unbalance force excitation effect. Consequently, in the negative stiffness content zone of the unbalance force vector angles, the cracked rotor system tends to exhibit a sharp growth in the vibration whirl amplitudes. However, for positive effective stiffness values, the shaft has more resistance to deflect away from its whirl orbit center. Therefore, the cracked rotor system is at higher risk of failure in the negative effective stiffness zone of unbalance force vector angles than the positive effective stiffness zone of these angles.

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Investigation on dynamic behaviors of rotor system with looseness and nonlinear supporting

Mechanical Systems and Signal Processing ◽

10.1016/j.ymssp.2021.108400 ◽

2022 ◽

Vol 166 ◽

pp. 108400

Author(s):

Haopeng Zhang ◽

Kuan Lu ◽

Wei Zhang ◽

Chao Fu

Keyword(s):

Rotor System ◽

Dynamic Behaviors

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Dynamic Modelling and Nonlinear Characteristics of a Cracked Bolt-Disc Combined Rotor System

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4051415 ◽

2021 ◽

Author(s):

Yi Liu ◽

Heng Liu ◽

Yuan Li ◽

Nanshan Wang

Keyword(s):

Stiffness Matrix ◽

Crack Depth ◽

Dynamic Modelling ◽

Rotor System ◽

Correction Coefficient ◽

Local Defect ◽

Open Crack ◽

Rotating Shaft ◽

Dynamic Behaviors ◽

Crack Location

Abstract Different from the crack on the rotating shaft, the crack on the bolt which is a connecting part of the bolt-disc combined rotor is a kind of local defect. The local crack on the bolt under high pretension is always in open state, and it increases the overall vibration of the combined rotor significantly in practice. This paper studies the modelling of the crack on the bolt and nonlinear dynamic behaviors of the cracked bolt-disc rotor system. The circumferential bolts with a transverse open crack are treated as several bar elements under the assumption that each bolt has the same original tensile extension length. The cracked correction coefficient is introduced to describe the decreasing amount of bolt's tension due to crack. After this coefficient is obtained according to finite element method, the stiffness matrix of circumferential bolts with crack is built based on total potential energy. The dynamic model consists of a time-independent stiffness matrix for perfect bolts, a time-variant reductive stiffness and an additional moment. As a result, the crack in bolt reduces rotor's nonlinear stability and leads to greater vibration and fluctuation. In addition, crack depth has much larger influence than crack location on the dynamic behaviors.

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Dynamic Behaviors of Geared Rotor System in Integrally Centrifugal Compressor

Journal of Vibration Engineering & Technologies ◽

10.1007/s42417-019-00117-0 ◽

2019 ◽

Vol 7 (3) ◽

pp. 241-249

Author(s):

Zhang Hao ◽

Yun Xianghe ◽

Han Qingkai ◽

Hao Hai

Keyword(s):

Centrifugal Compressor ◽

Rotor System ◽

Dynamic Behaviors

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Nonlinear Dynamic Analysis of a Rotor-Labyrinth Seal-Bearing-Foundation System

Volume 1: Advances in Aerospace Technology ◽

10.1115/imece2016-65586 ◽

2016 ◽

Cited By ~ 1

Author(s):

Enjie Zhang ◽

Yinghou Jiao ◽

Zhaobo Chen ◽

Wenchao Mo

Keyword(s):

Flow Velocity ◽

Mass Flow ◽

Nonlinear Dynamic ◽

Labyrinth Seal ◽

Rotor System ◽

Inlet Pressure ◽

Mean Flow ◽

Dynamic Behaviors ◽

Oil Film ◽

Mean Flow Velocity

Steam turbine rotors are subjected to various excitation forces originated from inner structure and outer environment. Unbalance forces, nonlinear oil film forces, nonlinear seal forces, and base excitation are drastically influence the dynamic behaviors of the rotor system. A mathematical model of rotor system, including the coupled effects of these excitation forces, is established by applying the Lagrange’s equations. The axial flow velocity and leakage mass flow, which vary with the structure of labyrinth seal and with inlet/outlet pressure ratio, are calculated using the two-control-volume model. The axial mean flow velocity is then introduced into the Muszynska’s nonlinear seal forces model. The nonlinear oil-film forces are also obtained based on the short bearing theory. The equations of motion are solved by Runge-Kutta numerical integration. The influences of inlet pressure and seal strip number on axial mean flow velocity and leakage mass flow are analyzed. The effects of rotational speed, foundation movements and inlet pressure on the nonlinear dynamic characteristics of the labyrinth seal-bearing-rotor system are investigated. The bifurcation diagrams, axis orbits and spectrum cascades are used to analyze the nonlinear dynamic behaviors of the system.

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