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.

Optimization of Nonlinear Unbalanced Flexible Rotating Shaft Passing Through Critical Speeds

2021 ◽  
Author(s):  
Sadegh Amirzadegan ◽  
Mohammad Rokn-Abadi ◽  
R. D. Firouz-Abadi
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Oscillations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Angular Acceleration ◽  
Beam Theory ◽  
Rotor System ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Applied Torque

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for this work. The shaft is modeled as a beam and the Euler–Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6 degrees of freedom. In order to solve these equations numerically, the finite element method (FEM) is used. Furthermore, for different bearing properties, rotor responses are examined and curves of passing through critical speeds with angular acceleration due to applied torque are plotted. Then the optimal values of bearing stiffness and damping are calculated to achieve the minimum vibration amplitude, which causes to pass easier through critical speeds. It is concluded that the value of damping and stiffness of bearing change the rotor critical speeds and also significantly affect the dynamic behavior of the rotor system. These effects are also presented graphically and discussed.

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.

A Minimum Strain Energy Approach for Obtaining Optimal Unbalance Distribution in Flexible Rotors

1982 ◽  
Vol 104 (4) ◽  
pp. 875-880 ◽  
Author(s):  
T. F. Conry ◽  
P. R. Goglia ◽  
C. Cusano
Keyword(s):  
Strain Energy ◽  
Critical Speed ◽  
Optimization Problem ◽  
Equations Of Motion ◽  
Rotor System ◽  
Quadratic Program ◽  
Unique Minimum ◽  
Flexible Rotors ◽  
Minimum Strain Energy ◽  
Selection Of

A method is developed to design for optimal unbalance distribution in a rotor system which has elements that are assembled on the shaft and operates above the first critical speed. This method can also be used for computing the optimal selection of balance weights in specified planes for a rotor with a known distribution of unbalance—the classic balancing problem. The method is an optimization problem where the strain energy of the rotor and its supports are minimized subject to the constraints of the equations of motion of the rotor system at a particular balancing speed. The problem is a quadratic program that has a unique minimum.

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.

The Dynamic Analysis of SFD-Sliding Bearing Flexible Rotor System Based on Optimization Design

2012 ◽  
Vol 159 ◽  
pp. 355-360
Author(s):  
Ji Yan Wang ◽  
Rong Chun Guo ◽  
Xu Fei Si
Keyword(s):  
High Speed ◽  
Optimization Design ◽  
Critical Speed ◽  
Structural Parameters ◽  
Rotor System ◽  
Flexible Rotor ◽  
Optimization Analysis ◽  
Sliding Bearing ◽  
Critical Speeds ◽  
Design Variables

The paper establishes the mechanical model of SFD-sliding bearing flexible rotor system, adopting Runge-Kutta method to solve nonlinear differential equation, thus acquiring the unbalanced response curve and then gaining the first two critical speeds of the system. Meanwhile, the paper analyzes the sensitivity of the system on the first two critical speeds towards structural parameters, offering design variables to optimization analysis. Based on sensitivity analysis, genetic algorithm is employed to give an optimization analysis on critical speed, which aims to remove critical speed from working speed as much as possible. The critical speed ameliorates after the optimization which supplies theoretical basis as well as theoretical analysis towards the dynamic stability of high-speed rotor system and provides reference for the design of such rotor system.

On the Critical Speeds of a Continuous Rotor

1969 ◽  
Vol 91 (4) ◽  
pp. 1180-1188 ◽  
Author(s):  
R. L. Eshleman ◽  
R. A. Eubanks
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Transverse Shear ◽  
Critical Speed ◽  
Equations Of Motion ◽  
Analytical Investigation ◽  
Relative Importance ◽  
Rotatory Inertia ◽  
Critical Speeds

An analytical investigation was made on the effect of axial torque on the critical speeds of a continuous rotor whose motion was described by a set of partial differential equations including the effects of transverse shear, rotatory inertia, and gyroscopic moments. The equations of motion and associated boundary conditions for long and short bearings were cast in nondimensional form to facilitate the study of the influence of the aforementioned effects on a torque-transmitting rotor’s critical speeds. The results of this study were compared to classical results of Bernoulli-Enter and Timoshenko to determine the relative importance of the rotor’s “secondary phenomena” in a critical speed calculation.

Effect of Temperature Distribution on Critical Speeds of a Dual-Rotor System

2014 ◽  
Vol 709 ◽  
pp. 21-24
Author(s):  
Gui Yu Xin ◽  
Ke Ming Wang ◽  
Mei Jiao Qu ◽  
Tian Yin Wang
Keyword(s):  
High Pressure ◽  
Temperature Distribution ◽  
Critical Speed ◽  
Axial Direction ◽  
Calculation Model ◽  
Rotor System ◽  
Effect Of Temperature ◽  
Critical Speeds ◽  
Calculation Results ◽  
The Impact

A dual-rotor calculation model which can expand freely in the axial direction is established in this paper, and the effects of one-dimensional axial temperature distribution on critical speeds of the dual-rotor system are analyzed with finite element method. The temperature distribution of the dual-rotor system is given referring to that of similar aero-engine rotor system. Assuming that the left end temperature remains at 0 °C, and the highest temperature on the section of the high-pressure turbine disk is 0 °C, 200 °C, 400 °C, 600 °C, and 800 °C respectively, the critical speeds of the dual-rotor system are calculated, analyzed and compared. Calculation results show that, with the increase of the highest temperature of the dual-rotor system, the reduction percentage of the critical speeds increases, and the impact on the first critical speed is most obvious. When the highest temperature is 800 °C, the first critical speed of the rotor system excited by the low-pressure rotor reduces 13.13%, and that excited by the high-pressure rotor reduces 13.49%.

Chaotic Vibration and Internal Resonance Phenomena in Rotor Systems: Part I — Theoretical Analysis

2003 ◽  
Author(s):  
Tsuyoshi Inoue ◽  
Yukio Ishida
Keyword(s):  
Internal Resonance ◽  
Critical Speed ◽  
Rotor System ◽  
Nonlinear Phenomena ◽  
Combination Resonance ◽  
Critical Speeds ◽  
Rotor Systems ◽  
Gyroscopic Moment ◽  
Chaotic Vibration ◽  
Resonance Phenomena

Naturally, the gyroscopic moment is small for the many practical rotating machineries. In addition, some mechanical elements of a rotor system make various types of nonlinearity such as clearance in a ball bearing (Yamamoto, 1955)(Yamamoto, 1977), oil film in a journal bearing (Tondl, 1965), geometrical nonlinearity due to the shaft elongation (Shaw, 1988),(Ishida, 1996), etc. In such rotor systems, the natural frequencies of a forward whirling mode pf and a backward whirling mode pb almost satisfy the relation of internal resonance pf : pb = 1 : (−1). And then, the critical speeds of a backward harmonic oscillation and a supercombination oscillation are near from the major critical speed. Similarly, in the vicinity of two times of the major critical speed, the critical speeds of the forward and the backward subharmonic resonances of order 1/2 and the combination resonance are close to each other. Therefore, the internal resonance phenomena may occur at the major critical speed and two times of the major critical speed. However there are few studies on the nonlinear phenomena of the rotor systems due to the influence of internal resonance. In this study, we use a 2DOF rotor model and investigate the dynamic characteristics of nonlinear phenomena, especially the chaotic vibration, due to the internal resonance at the major critical speed and the critical speed of two times of the major critical speed. The following are clarified theoretically: (a) the Hopf bifurcation and consecutive period doubling bifurcations possible route to chaos occur at the major critical speed and at two times of the major critical speed, (b) another chaotic vibration from the combination resonance occur at two times of the major critical speed. The results demonstrate that the chaotic vibration is common nonlinear phenomena in the nonlinear rotor system when the effect of the gyroscopic moment is small.

Critical Speeds Analysis for Dual Rotor Turbofan Engine Using Finite Element Method

2019 ◽  
Author(s):  
Kai Sun ◽  
Zhao Wan ◽  
Huiying Song ◽  
Shaohui Wang
Keyword(s):  
Finite Element ◽  
Rotational Speed ◽  
Critical Speed ◽  
Fixed Number ◽  
Rotor System ◽  
Speed Ratio ◽  
Aircraft Engines ◽  
Campbell Diagram ◽  
Critical Speeds ◽  
Rotor Model

Abstract Intershaft bearing is widely adopted in dual rotor turbofan aircraft engines. Since this kind of dual rotor system has two different rotor speeds and the intershaft bearing leads to the coupling between HP rotor and LP rotor, the calculation of the critical speeds is much more complicated than that of the rotor systems without intershaft bearing. Compared to a single rotor system, the dual rotor system has more critical speeds which can be classified as critical speeds excited by HP rotor and that by LP rotor. In the paper, a finite element rotor model of a high-bypass turbofan jet engine with intershaft bearing is established for the study of critical speeds analysis. The general axisymmetric element is used to model the shafts and disks, and the blades are simplified to mass points. The main bearings including the intershaft bearing are set up with spring element. Assuming that the rotational speed ratio of the two rotors for the dual rotor system is a fixed number, the critical speeds are calculated using three methods based on the finite element rotor model. For the first method, the system critical speeds are obtained directly by Campbell diagram based on QR damped solution method. Then the synchronous unbalance response analyses are carried out and the rotor critical speeds are derived from the amplitude-frequency curves. For the last method, multiple group Campbell diagram analyses are conducted. With one rotor speed fixed at constant rpm N, we can change the speed of the other rotor to obtain one group of critical speeds. By varying speed N of the two rotors, a critical speeds data set can be obtained and plotted as a dual rotor critical speed map. The critical speeds can be easily extracted from the critical speed map according to the rotational speed curve of the engine. The study shows that the dual rotor system critical speeds calculated from above three methods are identical. For the first two methods, the rotational speed ratio of two rotors must be a known and fixed number, which is impossible in reality. The third proposal has no rotation speed relation restriction for rotors, and therefore is recommended for analyzing the critical speeds of aircraft engines with intershaft bearing.

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