Analysis of the Non-Linear Dynamic Responses of an Elastic Rotor With a Slant Crack

2012 ◽  
Author(s):  
Xiangmin Zhang ◽  
Changping Chen ◽  
Liming Dai
Keyword(s):  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Dynamic Responses ◽  
Cracked Rotor ◽  
Lagrange Equations ◽  
Linear Dynamic ◽  
Slant Crack ◽  
Non Linear ◽  
Line Spring Model

Considering a rotor system with a slant crack, and using an equivalent line-spring model to simulate the slant crack of the rotor, the flexibility model of the slant-cracked rotor is derived. Then considered the geometric non-linearity and based on the Lagrange equations, the non-linear dimensionless differential equations of motion for the slant-cracked rotor are obtained. Further the non-linear dynamic responses of the single rotor system with a slant crack are discussed by the Galerkin method and the harmonic balance method. It’s detailedly studied that the angle, the depth and the position of the slant crack on the rotor all affect on the non-linear dynamic responses of the rotor system, and the conclusion is very significant to the design of the rotor system in the practical reference aspect.

Numerical Investigation on the Nonlinear Dynamics of Anisotropic Breathing Cracked Rotor Systems

2020 ◽  
Author(s):  
Zhaoli Zheng ◽  
Zixuan Li ◽  
Di Zhang ◽  
Yonghui Xie ◽  
Zheyuan Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Breathing Crack ◽  
Cracked Rotor ◽  
Tangent Stiffness Matrix ◽  
Rotor Systems ◽  
Relative Angle

Abstract The nonlinear breathing crack behaviors and anisotropy of the bearing are important sources of severe vibration of rotor systems. However, the rotor system considering both of these factors has not gained sufficient attention in the existing studies. In this paper, the nonlinear dynamics of such anisotropic breathing cracked rotor system is investigated based on three-dimensional finite element model (FEM). Firstly, the equations of motion of the rotor system are established in the rotating frame to facilitate the modeling of the breathing crack. The fixed-interface component mode synthesis (CMS) is used to reduce the system’s degrees of freedom (DOFs). Then, in the process of solving the equations by harmonic balance method (HBM) and Newton-Raphson method, an original method for fast calculating tangent stiffness matrix is proposed. Finally, the effects of the crack depth, the anisotropy of bearing and relative angle between bearings on the nonlinear dynamics of the system are studied. The results show that the breathing behavior will complicate the vibration and introduce additional transverse stiffness. The increase of crack depth will deteriorate the vibration. The anisotropy and relative angle of bearing will lead to the splitting and merging of the resonant peaks, respectively.

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.

scholarly journals Dynamical analysis of hollow-shaft dual-rotor system with circular cracks

2020 ◽  
pp. 146134842094828
Author(s):  
Yang Yongfeng ◽  
Wang Jianjun ◽  
Wang Yanlin ◽  
Fu Chao ◽  
Zheng Qingyang ◽  
...  
Keyword(s):  
Critical Speed ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Circular Crack ◽  
Rotor System ◽  
Resonance Phenomenon ◽  
Dynamical Analysis ◽  
Dynamical Response ◽  
Critical Speeds ◽  
Hollow Shaft

In this paper, we considered a dual-rotor system with crack in shaft. The influence of circular crack in hollow shaft on dynamical response was studied. The equations of motion of 12 elements dual-rotor system model were derived. Harmonic balance method was employed to solve the equations. The critical speed and sub-critical speed responses were investigated. It was found that the circular crack in hollow shaft had greater influence on the first-backward critical speed than the first-forward critical speed. Owing to the influence of crack, the vibration peaks occurred at the 1/2, 1/3 and 1/4 critical speeds of the rotor system, along with a reduction in sub-critical speeds and critical speeds. The deeper crack away from the bearing affected the rotor more significantly. The whirling orbits, the time-domain responses and the spectra were obtained to show the super-harmonic resonance phenomenon in hollow-shaft cracked rotor system.

Non-linear dynamic behaviour of rotor—bearing system trained by bevel gears

2008 ◽  
Vol 222 (4) ◽  
pp. 617-627 ◽  
Author(s):  
M Li
Keyword(s):  
Equilibrium Points ◽  
Rotor System ◽  
Design Stage ◽  
Oil Film ◽  
Bevel Gears ◽  
Linear Dynamic ◽  
Non Linear ◽  
Rotor Bearing ◽  
Stability And Bifurcations ◽  
Bearing System

The vibrations of parallel geared rotor—bearing system have been intensively discussed; however, little attention has been paid to the dynamic analysis of angled bevel-geared system supported on journals. In the present work, the non-linear dynamics of a bevel-geared rotor system on oil film bearings is studied. First, the dynamic model is developed under some assumptions, such as rigid rotors, short-bearings, small teeth errors, and so forth. Then, the non-linear dynamic behaviours of both the balanced and unbalanced rotor system are analysed, respectively, in which the equilibrium points, limit cycles, their stability, and bifurcations are paid more attention. Numerical results show that in the bevel-geared rotor system under the action of non-linear oil film forces there exists a series of complex non-linear dynamic phenomena of rotor orbits, such as Hopf bifurcation, torus-doubling bifurcation, and jump phenomenon. All these features can help us to understand the dynamic characteristics of bevel-geared rotor—bearing system at design stage and during running period. Finally, some concerned problems during the investigation are also present.

Misalignment Modeling in Rotating Systems

2009 ◽  
Author(s):  
Hassan Bahaloo ◽  
Alireza Ebrahimi ◽  
Mostafa Samadi
Keyword(s):  
Harmonic Balance ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rotating Machinery ◽  
Rotor System ◽  
Common Source ◽  
Series Method ◽  
Coupling Element ◽  
Harmonic Response ◽  
Rotating Systems

Misalignment is a common source of high vibration and malfunction in rotating machinery. Despite its importance and prevalence, no sufficient documentation exists treating this problem. In this paper, a method is introduced for modeling a continuous rotor system which incorporates a misaligned coupling element. It is assumed that both the angular and parallel misalignments are present in the coupling location. The energy expressions are derived and then, applying the Ritz series method, the equations of motion are constructed in matrix form. Because of the special characteristics of the system due to misalignment, a Harmonic Balance Method (HBM) is utilized to obtain the multi harmonic response to an unbalance excitation in disk location. A study on shaft center orbits is also provided and the effect of misalignment type and severity on the orbits is analyzed.

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.

scholarly journals Study of the non-linear dynamic response of a rotor system with faults and uncertainties

2012 ◽  
Vol 331 (3) ◽  
pp. 671-703 ◽  
Author(s):  
Jérôme Didier ◽  
Jean-Jacques Sinou ◽  
Béatrice Faverjon
Keyword(s):  
Dynamic Response ◽  
Rotor System ◽  
Linear Dynamic ◽  
Non Linear
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