Nonlinear Response Characteristics of a Cracked Rotor in Maneuvering Aircraft

2003 ◽  
Author(s):  
Fu-Sheng Lin ◽  
Guang Meng ◽  
Eric Hahn
Keyword(s):  
Fault Diagnosis ◽  
Constant Velocity ◽  
Nonlinear Response ◽  
Nonlinear Behavior ◽  
Rotor System ◽  
Parameter Range ◽  
Cracked Rotor ◽  
Periodic Response ◽  
Response Characteristics ◽  
Cracked Rotor System

This paper investigates numerically the nonlinear response of a simple cracked rotor in moving supports, as may occur in aircraft rotors when the aircraft is maneuvering with constant velocity or acceleration. Of particular interest is the influence of the aircraft climb angle. Results show that the climb angle can markedly affect the parameter range for which the system is stable; and over which there results bifurcation, quasi-periodic response or chaotic response. It is shown that aircraft acceleration can also significantly affect the nonlinear behavior of the cracked rotor system, illustrating the possibility for online rotor crack fault diagnosis.

Shooting With Deflation Algorithm-Based Nonlinear Response and Neimark-Sacker Bifurcation and Chaos in Floating Ring Bearing Systems

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Sitae Kim ◽  
Alan B. Palazzolo
Keyword(s):  
Nonlinear Response ◽  
Nonlinear Behavior ◽  
Rotor System ◽  
Operating Conditions ◽  
Fluid Film ◽  
Stable Limit ◽  
Bifurcation And Chaos ◽  
Chaotic Motions ◽  
Response Characteristics ◽  
Computation Efficiency

The double-sided fluid film force on the inner and outer ring surfaces of a floating ring bearing (FRB) creates strong nonlinear response characteristics such as coexistence of multiple orbits, Hopf bifurcation, Neimark-Sacker (N-S) bifurcation, and chaos in operations. An improved autonomous shooting with deflation algorithm is applied to a rigid rotor supported by FRBs for numerically analyzing its nonlinear behavior. The method enhances computation efficiency by avoiding previously found solutions in the numerical-based search. The solution manifold for phase state and period is obtained using arc-length continuation. It was determined that the FRB-rotor system has multiple response states near Hopf and N-S bifurcation points, and the bifurcation scenario depends on the ratio of floating ring length and diameter (L/D). Since multiple responses coexist under the same operating conditions, simulation of jumps between two stable limit cycles from potential disturbance such as sudden base excitation is demonstrated. In addition, this paper investigates chaotic motions in the FRB-rotor system, utilizing four different approaches, strange attractor, Lyapunov exponent, frequency spectrum, and bifurcation diagram. A numerical case study for quenching the large amplitude motion by adding unbalance force is provided and the result shows synchronization, i.e., subsynchronous frequency components are suppressed. In this research, the fluid film forces on the FRB are determined by applying the finite element method while prior work has utilized a short bearing approximation. Simulation response comparisons between the short bearing and finite bearing models are discussed.

On the Modeling of Open and Breathing Cracks of a Cracked Rotor System

2010 ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Eric A. Butcher
Keyword(s):  
Finite Element ◽  
Crack Detection ◽  
Linear Time ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Crack Model ◽  
Open Crack ◽  
Cracked Rotor ◽  
Critical Rotational Speed ◽  
Cracked Rotor System

The modeling of a cracked rotor system with an open or breathing transverse crack is addressed here. The cracked rotor with an open crack model behaves as an asymmetric shaft. Hence, the time-varying area moments of inertia of the cracked section are employed in formulating the periodic finite element stiffness matrix for both crack models which yields a linear time-periodic system. The harmonic balance method (HB) is used in solving the finite element (FE) equations of motions for studying the dynamic behavior of the cracked rotor system. The unique behavior of the whirl orbits during the passage through the subcritical rotational speeds and the sensitivity of these orbits to the unbalance force direction can be used for early crack detection of the cracked rotor for both crack models. These whirl orbits were verified experimentally for the open crack model in the neighborhood of 1/2 of the first critical rotational speed where a good match with the theoretical whirl orbits was observed.

Dynamics of a cracked rotor system with oil-film force in parameter space

2017 ◽  
Vol 88 (4) ◽  
pp. 2347-2357 ◽  
Author(s):  
Xiao-Bo Rao ◽  
Yan-Dong Chu ◽  
Ying-Xiang Chang ◽  
Jian-Gang Zhang ◽  
Ya-Ping Tian
Keyword(s):  
Parameter Space ◽  
Rotor System ◽  
Cracked Rotor ◽  
Oil Film ◽  
Cracked Rotor System

Vibration Analysis and Detection of Rotor Crack in a Multi-Disk Rotor System by Periodic Excitation Using AMB

2007 ◽  
Author(s):  
Tsuyoshi Inoue ◽  
Toshihiro Yamamichi ◽  
Masato Kato ◽  
Yukio Ishida
Keyword(s):  
Rotating Machinery ◽  
Rotor System ◽  
Dynamic Responses ◽  
Periodic Excitation ◽  
Cracked Rotor ◽  
Risk Condition ◽  
Cracked Rotor System ◽  
Two Degree Of Freedom ◽  
Crack Element ◽  
Rotor Model

Operating of rotating machinery with a rotor crack is a risk condition, since the rotor crack grows gradually and may fail causing a catastrophic accident. Therefore, it is very important to detect the occurrence of a crack on rotating machinery in early stages. The authors have used the simple two-degree-of-freedom cracked rotor model, and investigated the usage of periodic excitation for the detection of the rotor crack. This paper constructs a finite element rotor model with breathing crack element, and performs the numerical investigation. The dynamic responses of a cracked rotor system under applied periodical external excitation are investigated. The occurrences of various kinds of nonlinear sub-resonances are observed numerically, and the dynamical characteristics of these sub-resonances are clarified. The influences of the position and depth of the crack are clarified. Furthermore, these sub-resonances due to crack are observed in the experiment. This result made us enable to detect the occurrence of a rotor crack.

Negative Effective Stiffness Content in Cracked Rotors

2018 ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Fatima K. Alhammadi
Keyword(s):  
Equations Of Motion ◽  
Rotor System ◽  
Effective Stiffness ◽  
Cracked Rotor ◽  
Force Vector ◽  
Rotor Systems ◽  
Wide Range ◽  
Unbalance Force ◽  
Time Periodic ◽  
Cracked Rotor System

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.

Roll-Yaw Coupling Effect of Jeffcott Rotor With Breathing Crack

2015 ◽  
Author(s):  
J. Zhao ◽  
H. A. DeSmidt ◽  
M. Peng ◽  
W. Yao
Keyword(s):  
Coupling Effect ◽  
Rotor System ◽  
Crack Model ◽  
Breathing Crack ◽  
Cracked Rotor ◽  
Lagrange Principle ◽  
Jeffcott Rotor ◽  
Vibration Responses ◽  
Cracked Rotor System ◽  
Rotor Model

A new rotor model is developed in this paper to explore the dynamic coupling effect of roll-yaw motion. The rotor model employs a 6 degree-of-freedom Jeffcott rotor with a breathing crack. Based on the energy method and Lagrange principle, equation of motion is derived in yawing coordinate system with consideration of unbalance mass. The breathing crack model is established by Zero Stress Intensity Factor (SIF) method based on the crack released strain energy concept in fracture mechanics. SIF method is used to determine the crack closure line by computing SIF for opening mode. The vibration responses of the cracked rotor system are solved by Gear’s method. The coupling effect of yawing and rolling motion is studied in this paper to investigate vibration response of cracked rotor system. With the yawing motion, the dynamics of the rotor-bearing system is changed by additional stiffness and force terms. The parametric study is conducted to analyze the effect of yawing rate and acceleration on the crack breathing behavior. Finally, the vibration responses of the nominal and damaged rotor systems are analyzed to find out the indication for the damage detection and health monitoring.

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