Approach for Stability Analysis of a Cracked Rotor With Time-Varying Stiffness

2013 ◽  
Author(s):  
Mohammad A. Al-Shudeifat
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Dynamic Stability ◽  
Coefficient Matrix ◽  
Rotor System ◽  
Time Varying ◽  
Cracked Rotor ◽  
Parametrically Excited ◽  
Time Periodic ◽  
Cracked Rotor System

An approach for dynamic stability analysis of a cracked rotor system with transverse crack is addressed here. The time-varying area moments of inertia of the cracked section are employed in formulating the time-periodic finite element stiffness matrix which yields a linear time-periodic system. The harmonic balance method (HB) is used in solving the finite element (FE) equations of motion for studying the dynamic stability of the system. The sign of the determinant of the scaled coefficient matrix resulting from applying the HB solution to the cracked rotor system is found to be a reliable approach for identifying the major unstable regions of the system in the parameter plane obtained by plotting the shaft speeds of rotation vs. the crack depths. Specifically, the negative values of the determinant of this scaled coefficient matrix identify the unstable regions of the cracked system. This approach is applied here to the parametrically excited Mathieu’s equation, two degree-of-freedom gyroscopic system, and then to the FE model of the cracked rotor system. The results of applying this approach are verified using the Floquet’s theory. Compared with the theory, the sign of the determinant of the scaled coefficient matrix is found here to be an efficient tool for identifying the unstable regions of linear parametrically excited systems, especially the large scale dynamic systems where this approach requires considerably less computational time than the Floquet’s theory.

scholarly journals Dynamic Stability Analysis of Periodically Time-Varying Rotor System with a Transverse Crack

Engineering ◽  
2011 ◽  
Vol 03 (07) ◽  
pp. 719-725 ◽  
Author(s):  
Costin D. Untaroiu ◽  
Alexandrina Untaroiu ◽  
Mihail Boiangiu
Keyword(s):  
Stability Analysis ◽  
Dynamic Stability ◽  
Transverse Crack ◽  
Rotor System ◽  
Time Varying

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.

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.

A novel amplitude-independent crack identification method for rotating shaft

2018 ◽  
Vol 232 (22) ◽  
pp. 4098-4112 ◽  
Author(s):  
Laihao Yang ◽  
Xuefeng Chen ◽  
Shibin Wang
Keyword(s):  
Frequency Analysis ◽  
Instantaneous Frequency ◽  
Vibration Signal ◽  
Rotor System ◽  
Crack Identification ◽  
Fast Time ◽  
Time Varying ◽  
Cracked Rotor ◽  
Time Frequency ◽  
Cracked Rotor System

The shaft crack is one of the most common and serious malfunctions in rotating machines and may lead to catastrophic failure if undetected in time. However, the conventional crack identification methods are amplitude-dependent and thus can be only applied to the crack identification under some specific conditions. In this paper, a novel amplitude-independent crack identification method (AiCIM) is significantly proposed to eliminate the amplitude-dependent property and promote the effectiveness of the crack identification. First and foremost, a fast time-varying vibration phenomenon of the cracked-rotor system is newly found. Through the theoretical analysis, the fast time-varying vibration mechanism of the cracked-rotor system is revealed for the first time. It is indicated that the vibration signal of the cracked-rotor system is modulated by the fast-oscillated instantaneous frequency, which is independent of the amplitude of the vibration signal. AiCIM is then put forward on the basis of the fast time-varying vibration mechanism and matching time–frequency analysis theory. Specially, the amplitude-independent instantaneous frequency of the vibration signal is extracted via the matching time–frequency analysis theory, and the time–frequency representation energy-concentration is enhanced along the instantaneous frequency trajectory. Since instantaneous frequency of the vibration signal carrying the critical fault information is employed to identify the shaft crack, AiCIM is only relevant to the phase of the vibration signal, i.e. amplitude independent. As a result, AiCIM successfully eliminates the dependence on the signal amplitude and is more sensitive to the weak crack. Both the numerical and experimental results demonstrate that AiCIM behaves best to extract the fast-oscillated feature of the fast time-varying vibration induced by the shaft crack in comparison with other time–frequency analysis methods, and AiCIM effectively suppress the effect of noises on the instantaneous frequency estimation because of its amplitude-independent property. Influences of the crack parameters on the nonlinear instantaneous frequency are finally discussed with AiCIM. This study provides a potential way to the online crack identification.

Effects of tip relief on vibration responses of a geared rotor system

2013 ◽  
Vol 228 (7) ◽  
pp. 1132-1154 ◽  
Author(s):  
Hui Ma ◽  
Jian Yang ◽  
Rongze Song ◽  
Suyan Zhang ◽  
Bangchun Wen
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Spur Gear ◽  
Rotor System ◽  
Time Varying ◽  
Frequency Range ◽  
Mesh Stiffness ◽  
Resonance Frequencies ◽  
Vibration Responses

Considering tip relief, a finite element model of a spur gear pair in mesh is established by ANSYS software. Time-varying mesh stiffness under different amounts of tip relief is calculated based on the finite element model. Then, a finite element model of a geared rotor system is developed by MATLAB software considering the effects of time-varying mesh stiffness and constant load torque. Emphasis is given to the effects of tip relief on the lateral–torsional coupling vibration responses of the system. The results show that as the amount of tip relief increases, the saltation of time-varying mesh stiffness reduces at the position of approach action and transition mesh region from the single tooth to double tooth. A number of primary resonances and some super-harmonic of gears 1 and 2 are excited by time-varying mesh stiffness in amplitude frequency responses. As the amount of tip relief increases, some super-harmonic responses change due to the variation in the higher frequency components of time-varying mesh stiffness. After tip relief, the vibration and meshing force decrease obviously at lower mesh frequency range except at some resonance frequencies; however, tip relief is not effective in reducing the vibration at higher mesh frequency range. The amplitude fluctuation of the vibration acceleration reduces evidently after considering tip relief, which is not remarkable with the increase of meshing frequency.

Dynamic Stability of Timoshenko Beams by Finite Element Method

1976 ◽  
Vol 98 (4) ◽  
pp. 1145-1149 ◽  
Author(s):  
J. Thomas ◽  
B. A. H. Abbas
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Shear Deformation ◽  
Dynamic Stability ◽  
Timoshenko Beam ◽  
Dynamic Instability ◽  
Rotary Inertia ◽  
Timoshenko Beams ◽  
Buckling Loads

A Finite Element model is developed for the stability analysis of Timoshenko beam subjected to periodic axial loads. The effect of the shear deformation on the static buckling loads is studied by finite element method. The results obtained show excellent agreement with those obtained by other analytical methods for the first three buckling loads. The effect of shear deformation and for the first time the effect of rotary inertia on the regions of dynamic instability are investigated. The elastic stiffness, geometric stiffness, and inertia matrices are developed and presented in this paper for a Timoshenko beam. The matrix equation for the dynamic stability analysis is derived and solved for hinged-hinged and cantilevered Timoshenko beams and the results are presented. Values of critical loads for beams with various shear parameters are presented in a graphical form. First four regions of dynamic instability for different values of rotary inertia parameters are presented. As the rotary inertia parameter increases the regions of instability get closer to each other and the width of the regions increases thus making the beam more sensitive to periodic forces.

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.

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
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