Natural Frequency Analysis of a Jeffcott Rotor Having Stepped Shaft

2021 ◽  
Vol 6 (3) ◽  
pp. 170-172
Author(s):  
Ahmed A. Alahmadi ◽  
Khalid A. Alnefaie ◽  
Hamza Diken
Keyword(s):  
Natural Frequencies ◽  
Lagrange Equations ◽  
Shaft Length ◽  
Variable Diameter ◽  
Stepped Shaft ◽  
Disc Position ◽  
Jeffcott Rotor ◽  
Mechanical Elements ◽  
Natural Frequency Analysis ◽  
Rotor Model

The Rotating shafts are mechanical elements used to transmit power or motion. A shaft with a step or steps is widely used instead of a shaft with a fixed (non-variable) diameter when operating at high speeds. The aim of this research is to study the effect of the step amount and its location in the shaft on the natural frequencies of the Jeffcott rotor model. Analytical methods are used to find an approximate formulation to obtain the natural frequencies of the Jeffcott rotor model neglecting the shaft mass. Lagrange equations are used to develop dynamic equations assuming elastic shaft with steps carrying a disk. The finite element method by using ANSYS is used to validate and compare the results obtained in the analytical method. The results obtained analytically and numerically were compatible and in good agreement. In addition, some parameters such as the step amount and the stepped shaft length are changed to check its effects on the natural frequencies. the results showed that the natural frequencies increase with an increase in the amount and length of the stepped part, while they decrease the closer the disc position to the center.

scholarly journals Effect of Coupled Torsional and Transverse Vibrations of the Marine Propulsion Shaft System

2021 ◽  
Author(s):  
Akile Neşe Halilbeşe ◽  
Cong Zhang ◽  
Osman Azmi Özsoysal
Keyword(s):  
Numerical Model ◽  
Cross Section ◽  
Transverse Vibration ◽  
Energy Functional ◽  
Lagrange Equations ◽  
Shaft Length ◽  
Numerical Predictions ◽  
Shaft System ◽  
Jeffcott Rotor ◽  
Rotor Model

AbstractIn this study, the coupled torsional–transverse vibration of a propeller shaft system owing to the misalignment caused by the shaft rotation was investigated. The proposed numerical model is based on the modified version of the Jeffcott rotor model. The equation of motion describing the harmonic vibrations of the system was obtained using the Euler–Lagrange equations for the associated energy functional. Experiments considering different rotation speeds and axial loads acting on the propulsion shaft system were performed to verify the numerical model. The effects of system parameters such as shaft length and diameter, stiffness and damping coefficients, and cross-section eccentricity were also studied. The cross-section eccentricity increased the displacement response, yet coupled vibrations were not initially observed. With the increase in the eccentricity, the interaction between two vibration modes became apparent, and the agreement between numerical predictions and experimental measurements improved. Given the results, the modified version of the Jeffcott rotor model can represent the coupled torsional–transverse vibration of propulsion shaft systems.

scholarly journals Effect of intermediate supports location on natural frequencies of multiple cracked continuous beams

2018 ◽  
Author(s):  
Do Nam ◽  
Nguyen Tien Khiem ◽  
Le Khanh Toan ◽  
Nguyen Thi Thao ◽  
Pham Thi Ba Lien
Keyword(s):  
General Solution ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Continuous Beam ◽  
Cracked Beam ◽  
Continuous Beams ◽  
Simplified Method ◽  
Rigid Supports ◽  
Natural Frequency Analysis ◽  
Eigenfrequency Spectrum

The present paper deals with free vibration of multiple cracked continuous beams with intermediate rigid supports. A simplified method is proposed to obtain general solution of free vibration in cracked beam with intermediate supports that is then used for natural frequency analysis of the beam in dependence upon cracks and support locations. Numerical results show that the support location or ratio of span lengths in combination with cracks makes a significant effect on eigenfrequency spectrum of beam. The discovered effects of support locations on eigenfrequency spectrum of cracked continuous beam are useful for detecting not only cracks but also positions of vanishing deflection on the beam.

scholarly journals On the Role of Nonsynchronous Rotating Damping in Rotordynamics

2000 ◽  
Vol 6 (6) ◽  
pp. 467-475 ◽  
Author(s):  
Giancarlo Genta ◽  
Eugenio Brusa
Keyword(s):  
General Model ◽  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
System Parameters ◽  
Spin Speed ◽  
Rotating Systems ◽  
Jeffcott Rotor ◽  
The Stability ◽  
Rotor Model

Nonsynchronous rotating damping, i.e. energy dissipations occurring in elements rotating at a speed different from the spin speed of a rotor, can have substantial effects on the dynamic behaviour and above all on the stability of rotating systems.The free whirling and unbalance response for systems with nonsynchronous damping are studied using Jeffcott rotor model. The system parameters affecting stability are identified and the threshold of instability is computed. A general model for a multi-degrees of freedom model for a general isotropic machine is then presented. The possibility of synthesizing nonsynchronous rotating and nonrotating damping using rotor- and stator-fixed active dampers is then discussed for the general case of rotors with many degrees of freedom.

Application of the POD Method for Cracked Rotors

2017 ◽  
Author(s):  
Ayesha Al Mehairi ◽  
Mohammad A. AL-Shudeifat ◽  
Shadi Balawi ◽  
Adnan S. Saeed
Keyword(s):  
Covariance Matrices ◽  
Cracked Rotor ◽  
Force Vector ◽  
Highly Sensitive ◽  
Jeffcott Rotor ◽  
Unbalance Force ◽  
Proper Orthogonal ◽  
Integration Response ◽  
Cracked Rotor System ◽  
Rotor Model

The application of the proper orthogonal decomposition (POD) method to the vibration response of a cracked Jeffcott rotor model is investigated here. The covariance matrices of horizontal and vertical whirl amplitudes are formulated based on the numerical integration response and the experimental whirl response, respectively, for the considered cracked rotor system. Accordingly, the POD is directly applied to the obtained covariance matrices of the numerical and experimental whirl amplitudes where the proper orthogonal values (POVs) and the proper orthogonal modes (POMs) are obtained for various crack depths, unbalance force vector angles and rotational speeds. It is observed that both POVs and their corresponding POMs are highly sensitive to the appearance of the crack and the unbalance angle changes at the neighborhoods of the critical. The sensitivity zones of the POVs and POMs to the crack propagation coincide with the unstable zones of the cracked system obtained by Floquets theory.

Rotordynamic Force Prediction of a Shrouded Centrifugal Pump Impeller—Part II: Stability Analysis

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Eunseok Kim ◽  
Alan Palazzolo
Keyword(s):  
Stability Analysis ◽  
Centrifugal Pump ◽  
Forced Response ◽  
Fe Model ◽  
Pump Impeller ◽  
Rotordynamic Coefficients ◽  
Curve Fit ◽  
Jeffcott Rotor ◽  
Ring Seal ◽  
Rotor Model

In Paper I, some test cases of centrifugal pump impellers which showed unconventional impedances curves were reviewed and possible sources of the bump and dip in the impedance curves were investigated by simulating a wear-ring seal pump impeller. In this paper, the unconventional impedances determined in Paper I are converted into a form for inclusion in rotordynamic stability and forced response analyses. First of all, a finite element (FE) rotor model is considered to investigate the influence of the bump and dip in the impedance curves on the rotordynamic stability. With the same FE model, speed-dependent impedances are calculated to obtain unbalance frequency response. Finally, a new linear curve-fit approach is developed to model the fluctuating impedances since the unconventional impedance cannot be expressed by the second-order polynomials with the rotordynamic coefficients (stiffness, damping, and mass). In order to validate the newly developed method, a Jeffcott rotor model with the impeller forces is considered and rotordynamic stability analysis is implemented. The results of the analysis show that the existence of the bump and dip in the impedance curves may further destabilize the rotor system.

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.

Adjustment of a Rotor Model to Achieve Agreement between Calculated and Experimental Natural Frequencies

1979 ◽  
Vol 21 (6) ◽  
pp. 389-396 ◽  
Author(s):  
G. T. S. Done
Keyword(s):  
Mathematical Model ◽  
Natural Frequencies ◽  
Turbine Rotor ◽  
Beam Elements ◽  
Stiffness Properties ◽  
Standard Values ◽  
Lumped Masses ◽  
The Mathematical Model ◽  
Best Fit ◽  
Rotor Model

This paper is concerned with the problem of adjusting the mathematical model of a system such that the computed natural frequencies coincide with those measured experimentally. The particular system considered is a laboratory turbine-rotor model, modelled mathematically by 42 Timoshenko beam elements and lumped masses. Model adjustments are made by assuming, firstly, Young's modulus and the modulus of rigidity to be variable, a change from standard values representing overall stiffness deficiencies in the mathematical model. In this case, a best fit to the lowest six natural frequencies, as measured experimentally, is made. Secondly, stiffness diameters are assumed variable, thereby allowing for deficiencies in the model near discontinuous changes of section, and in this case, the lowest six natural frequencies are matched exactly, but an overall measure of the differences between the actual and the stiffness diameters is minimized. An analysis for the rates of change of natural frequency with the various stiffness properties (i.e. the sensitivities) is presented, and the results of the manipulation discussed.

Natural Frequency Analysis of a Fixed-Fixed Cracked Plate in Bending

2005 ◽  
Author(s):  
Hien Luong Thi Nguyen ◽  
Quang Giang Vuong
Keyword(s):  
Inverse Problem ◽  
Dynamic Response ◽  
Frequency Analysis ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
High Accuracy ◽  
Crack Identification ◽  
Isoparametric Element ◽  
Central Crack ◽  
Natural Frequency Analysis

The paper aims to study the dynamic behavior of a bending thin plate with fixed-fixed ends after crack occurrence. Using the FEM with an 8-node quadrilateral isoparametric element based on the Ressner-Mindlin’ theory of plate, the program CRACK-PLATE is developed to investigate the effect of crack length and position on the dynamic response of plate. The natural frequencies and modes are calculated and analyzed numerically for the non-faulty case and additionally with the edge and the central crack. In order to achieve a high accuracy, a singularity element of Barsoum is combined. The numerical results show that the natural frequencies are very sensitive to the crack presence in bending plate. It provides a basis to carry out the inverse problem for crack identification based on the dynamic characteristics of plates.

1/2-Order Subharmonic Resonances in Horizontally Supported Jeffcott Rotor

2011 ◽  
Author(s):  
Nao Yoshida ◽  
Tomoyuki Takano ◽  
Hiroshi Yabuno ◽  
Tsuyoshi Inoue ◽  
Yukio Ishida
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Vertical Direction ◽  
Support Condition ◽  
Restoring Force ◽  
Rotary Machine ◽  
Jeffcott Rotor ◽  
The Difference ◽  
Subharmonic Resonances

A Rotary machine is a significant component of many mechanical systems. It is important to clarify the dynamic characteristics in several conditions. This study deals with nonlinear dynamics of a horizontally supported Jeffcott rotor. The equations of motion are derived by considering the effects of gravity and the cubic nonlinearity of restoring force by the support condition. These effects produce the difference between the linear natural frequencies in the vertical and horizontal directions and make the stiffness in the vertical direction unsymmetric. It is theoretically and experimentally shown that due to such effects, the 1/2-order subharmonic resonances are produced in the cases when the rotational speed is in the neighborhood of twice the natural frequencies in the horizontal and vertical directions, and the frequency response curve of the resonance near twice the horizontal natural frequency is hardening-type, while near twice the vertical natural frequency is softening-type.

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