scholarly journals A Study of the Influence of Rubbing on the Dynamics of a Flexible Disk Rotor System

1993 ◽  
Author(s):  
Fangsheng Wu ◽  
George T. Flowers
Keyword(s):  
Harmonic Balance ◽  
Dynamical Behavior ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Governing Equations ◽  
System A ◽  
Jeffcott Rotor ◽  
Inertial Moment ◽  
Flexible Disk ◽  
Rotor Model

This study is concerned with investigating the influence of lateral disk flexibility on the dynamics of a rotor system experiencing rub. A rotating, flexible continuous disk/shaft model was developed and the dynamical behavior of this system with and without rubbing was studied. The model developed in this study is similar to the Jeffcott rotor model except that the disk is treated as a laterally flexible continuous circular plate. The motion of the disk was transformed from physical coordinates to a set of generalized coordinates under which the generalized motion was uncoupled and the responses were calculated. Then the inertial moment acting on the shaft was computed and introduced into the governing equations of the shaft motion. Direct integration and the harmonic balance method were used to study the steady state motion of the system. A number of parameter variation studies were performed for varied rub clearances and disk mass influence ratios. The system responses to the rub, its occurrence and development, and the global stability of the observed responses were studied. The results show that rub can be classified into two types: light rub and heavy rub, and the light rub has the forms of forward, backward, or mixed whirling motion. The results also show that the disk flexibility may alter the critical speed to some degree and may also significantly affect the amplitude and stability of the rotor vibration.

Nonlinear vibration characteristics of the rotor bearing system with bolted flange joints

2019 ◽  
Vol 233 (4) ◽  
pp. 910-930
Author(s):  
Yifu Zhou ◽  
Zhong Luo ◽  
Zifang Bian ◽  
Fei Wang
Keyword(s):  
Nonlinear Vibration ◽  
Time Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Vibration Characteristics ◽  
Rotor System ◽  
Rotor Bearing ◽  
Bolted Flange ◽  
Bearing System

As sophisticated mechanical equipment, the rotor system of aero-engine is assembled by various parts; bolted flange joints are one of the essential ways of joints. Aiming at the analysis of the nonlinear vibration characteristics of the rotor-bearing system with bolted flange joints, in this paper, a finite element modeling method for a rotor-bearing system with bolted flange joints is proposed, and an incremental harmonic balance method combined with arc length continuation is proposed to solve the dynamic solution of the rotor system. In order to solve the rotor system with rolling bearing nonlinearity, the alternating frequency/time-domain process of the rolling bearing element is deduced. Compared with the conventional harmonic balance method and the time-domain method, this method has the characteristics of fast convergence and high computational efficiency; solving the rotor system with nonlinear bearing force; overcome the shortcoming that the frequency–response curve of the system is too sharp to continue solving. By using this method, the influence of bearing clearance and stiffness on vibration characteristics of the rotor system with bolted flange joints is studied. The evolution law of the state of the rotor system with bolt flange is investigated through numerical simulation and experimental data. The results indicated that the modeling and solving method proposed in this paper could accurately solve the rotor-bearing system with bolted flange joints and analyze its vibration characteristics.

scholarly journals Theoretical and experimental investigation of a 1:3 internal resonance in a beam with piezoelectric patches

2020 ◽  
Vol 26 (13-14) ◽  
pp. 1119-1132 ◽  
Author(s):  
Vinciane Guillot ◽  
Arthur Givois ◽  
Mathieu Colin ◽  
Olivier Thomas ◽  
Alireza Ture Savadkoohi ◽  
...  
Keyword(s):  
Harmonic Balance ◽  
Internal Resonance ◽  
Harmonic Balance Method ◽  
Mode Shapes ◽  
Governing Equations ◽  
Internal Resonances ◽  
Thin Beam ◽  
Beam Focusing ◽  
Theoretical Results ◽  
Theoretical Developments

Experimental and theoretical results on the nonlinear dynamics of a homogeneous thin beam equipped with piezoelectric patches, presenting internal resonances, are provided. Two configurations are considered: a unimorph configuration composed of a beam with a single piezoelectric patch and a bimorph configuration with two collocated piezoelectric patches symmetrically glued on the two faces of the beam. The natural frequencies and mode shapes are measured and compared with those obtained by theoretical developments. Ratios of frequencies highlight the realization of 1:2 and 1:3 internal resonances, for both configurations, depending on the position of the piezoelectric patches on the length of the beam. Focusing on the 1:3 internal resonance, the governing equations are solved via a numerical harmonic balance method to find the periodic solutions of the system under harmonic forcing. A homodyne detection method is used experimentally to extract the harmonics of the measured vibration signals, on both configurations, and exchanges of energy between the modes in the 1:3 internal resonance are observed. A qualitative agreement is obtained with the model.

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.

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.

Nonlinear Dynamics of the Rod-Fastened Jeffcott Rotor

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Qi Yuan ◽  
Jin Gao ◽  
Pu Li
Keyword(s):  
Nonlinear Dynamics ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Operating Parameters ◽  
Flexural Stiffness ◽  
The Finite Element Method ◽  
Jeffcott Rotor ◽  
Unbalance Force ◽  
Contact Surfaces ◽  
Tie Rods

Rod-fastened rotors are composed of some disks clamped together by a central tie rod or several tie rods distributed along the circumference. Due to the nonlinear flexural stiffness of the contact interfaces in disks, especially when the contact surfaces are partially separated, the dynamics of the rod-fastened rotors are potentially different from that of the solid rotors. In this paper, the nonlinear flexural stiffness of a rod-fastened Jeffcott rotor is calculated by the finite element method (FEM). Then the harmonic balance method is adopted to analyze the dynamics of the rotor. The flexural stiffness of a rod-fastened Jeffcott rotor dramatically decreased with the increase of the dimensionless load γ1 from 1 to 2.5. Thus, the dynamics of the rotor were nonlinear when it was subjected to a large unbalance force. The response of the rotating rotor contains a predominantly forward 1X component or both forward 1X component and backward 1X components. However, the rotor may settle in a state depending upon both the operating parameters and its history.

Vibration Analysis of Nano-Beam with Consideration of Surface Effects and Damage Effects

2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Fan Yin ◽  
Chang Ping Chen ◽  
De Liang Chen
Keyword(s):  
Harmonic Balance ◽  
Couple Stress Theory ◽  
Harmonic Balance Method ◽  
Beam Theory ◽  
Governing Equations ◽  
Bernoulli Beam ◽  
Stress Theory ◽  
Beam Thickness ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam

AbstractOn the basis of Euler-Bernoulli beam theory, surface elastic theory, the strain equivalent assumption and modiffed couple stress theory, the nonlinear governing equations of the nano-beam are derived. In addition, the Galerkin method and the Harmonic Balance Method are adopted so as to give a solution to the equations. In the example, the effects of nano-beam length, nano-beam thickness, damage factor and surface efect to curves of amplitude-frequency response of the nano-beam are discussed. The results show that damage effects should be taken into consideration and the frequency can be controlled by load and structure size of nano-beam.

Nonlinear vibration control of a horizontally supported Jeffcott-rotor system

2017 ◽  
Vol 24 (24) ◽  
pp. 5898-5921 ◽  
Author(s):  
M Eissa ◽  
NA Saeed
Keyword(s):  
Multiple Scales ◽  
Perturbation Technique ◽  
Rotor System ◽  
Response Curves ◽  
Restoring Force ◽  
System A ◽  
Jeffcott Rotor ◽  
Before And After ◽  
System Frequency ◽  
Multiple Scales Perturbation Technique

A positive position feedback (PPF) controller is proposed to control the nonlinear vibrations of a horizontally supported Jeffcott-rotor system. A nonlinear restoring force and the rotor weight are considered in the system model. The controller is coupled to the system with 1:1 internal resonance. A second order approximate solution to the system governing equations is constructed by applying the multiple scales perturbation technique (MSPT). The bifurcation analyses of the Jeffcott-rotor system before and after control are conducted. The effects of the different controller parameters on the system frequency–response curves are investigated. Optimum working conditions of the controlled system are extracted to be used in the design of such systems. Numerical simulations demonstrated a good agreement with the approximate results that obtained by MSPT. A comparison is provided with already published work.

Trained Harmonic Balance Method for Parametrically Excited Jeffcott Rotor Analysis

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
Ghasem Ghannad Tehrani ◽  
Chiara Gastaldi ◽  
Teresa M. Berruti
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Periodic Variation ◽  
Balance Method ◽  
Rolling Bearings ◽  
Parametrically Excited ◽  
Axial Forces ◽  
Catastrophic Failures ◽  
Jeffcott Rotor ◽  
The Stability

Abstract Being able to identify instability regions is an important task for the designers of rotating machines. It allows discarding, since the early design stages, those configurations which may lead to catastrophic failures. Instability can be induced by different occurrences such as an unbalanced disk, torsional, and axial forces on the shaft or periodic variation of system parameters known as “parametric excitation.” In this paper, the stability of a Jeffcott rotor, parametrically excited by the time-varying stiffness of the rolling bearings, is studied. The harmonic balance method (HBM) is here applied as an approximate procedure to obtain the well-known “transition curves (TCs)” which separate the stable from the unstable regions of the design parameter space. One major challenge in the HBM application is identifying an adequate harmonic support (i.e., number of harmonics in the Fourier formulation), necessary to produce trustworthy results. A procedure to overcome this issue is here proposed and termed “trained HBM” (THBM). The results obtained by THBM are compared to those computed by Floquet theory, here used as a reference. The THBM proves to be able to produce reliable TCs in a timely manner, compatible with the design process.

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