Finite Element and Modal Analyses of Rotor-Bearing Systems Under Stochastic Loading Conditions

1984 ◽  
Vol 106 (1) ◽  
pp. 80-89 ◽  
Author(s):  
E. Hashish ◽  
T. S. Sankar
Keyword(s):  
Finite Element ◽  
Simple Procedure ◽  
Stochastic Loading ◽  
Rotor Bearing ◽  
Random Disturbances ◽  
Element Technique ◽  
Stiffness And Damping ◽  
The Mathematical Model ◽  
Rotor Dynamic ◽  
Spatial Support

A flexible rotor bearing system is represented in detail utilizing the state of the art finite element technique. The mathematical model takes into account the gyroscopic moments, rotary inertia, shear deformation, internal viscous damping, hysteretic damping, linear as well as nonlinear stiffness, and damping for the finite bearing and the bearing support flexibility. Using a simple Timoshenko element and recognizing an analogy between the motion planes, a procedure is given that requires a construction of only three symmetric 4×4 matrices. As an application, the different effects of the bearing lining flexibility and the bearing support flexibility on the rotor stability behavior is studied and discussed. The necessary relation for general modal analysis is simply restated and integrated into the conventional spectral approach, thus developing a simple procedure for the calculation of the stochastic response of a general rotor dynamic system. An application to a light rotor bearing featuring a general spatial support and subjected to random disturbances is illustrated.

Updating Rotor-Bearing Finite Element Models

1997 ◽  
Author(s):  
Cristinel Mares ◽  
Cecilia Surace
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Parameters Estimation ◽  
Flexible Rotor ◽  
Estimation Errors ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Measured Frequency Response ◽  
Stiffness And Damping ◽  
The Finite Element Model

Abstract In this paper, the possibility of updating the finite element model of a rotor-bearing system by estimating the bearing stiffness and damping coefficients from a few measured Frequency Response Functions using a Genetic Algorithm is investigated. The issues of identifiability and parameters estimation errors, computational costs and algorithm tuning are addressed. A simulated example of a flexible rotor supported by orthotropic bearings is used for illustrating the method.

Rotor Vibration under the Coupled Effects of Mass Unbalance and Asymmetric Bearings

2016 ◽  
Vol 846 ◽  
pp. 199-204 ◽  
Author(s):  
Joseph Patrick Spagnol ◽  
Helen Wu
Keyword(s):  
Critical Speed ◽  
High Energy ◽  
Damping Matrix ◽  
Mass Unbalance ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Stiffness And Damping Coefficient ◽  
Early Fault Detection ◽  
Stiffness And Damping ◽  
Rotor Dynamic

Large unbalance in rotor-dynamic systems is typically responsible for high energy vibrations and the consequent decrease in machine life. This paper presents an analytical model developed using Lagrangian mechanics and partial differential equations (PDEs) for the purpose of early fault-detection in rotor-bearing systems. The model was validated through a Fortran based program, RDA99 developed by Adams (2010), by successfully quantifying the single-peak unbalance response of the simple 8 DOF and 12 DOF rotor-bearing mass stations over two cases. Case I uses bearings with symmetric stiffness and damping matrix. The critical speed for Case I occurred at 1690 rpm and orbital shapes of each mass station was found to be circular with forward-whirl orbits. In Case II asymmetrical bearing stiffness and damping coefficient matrices demonstrate an anisotropic system. Critical speed occurred at 1655 rpm and rotor, bearing and pedestal orbits were seen to be elliptical and changing with shaft speed. Both cases demonstrated a significant shaft bending contribution to the disk displacement.

Unbalance Response of Rotors Considering the Distributed Bearing Stiffness and Damping

1994 ◽  
Author(s):  
A. S. Sekhar ◽  
B. S. Prabhu
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Journal Bearings ◽  
Principle Of Virtual Work ◽  
Unbalance Response ◽  
Tilting Pad ◽  
Bearing Stiffness ◽  
Element Technique ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearings

Usually while modelling rotor-bearing systems the bearings are treated as point supports. In the present paper, using the finite element technique, the unbalance response of rotors is studied by considering distributed bearing stiffness and damping. The bearing stiffness and damping terms are derived by the principle of virtual work. Unbalance responses of rotors with bearing distributed effects are compared with the model using point supports and for different supports Viz., cylindrical journal bearings, tilting pad journal bearings, offset and three lobe journal bearings.

scholarly journals Dynamic Behaviour Analysis of Turbocharger Rotor-Shaft System in Thermal Environment Based on Finite Element Method

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Zhihao Liu ◽  
Renren Wang ◽  
Fang Cao ◽  
Pidong Shi
Keyword(s):  
Finite Element ◽  
Temperature Field ◽  
Tangential Force ◽  
Accurate Prediction ◽  
Internal Damping ◽  
Rotor Shaft ◽  
Shaft System ◽  
Rotor Bearing ◽  
Rotor Dynamic ◽  
Bearing System

The stable operation of a high-speed rotating rotor-bearing system is dependent on the internal damping of its materials. In this study, the dynamic behaviours of a rotor-shaft system with internal damping composite materials under the action of a temperature field are analysed. The temperature field will increase the tangential force generated by the internal damping of the composite material. The tangential force will also increase with the rotor speed, which can destabilise the rotor-shaft system. To better understand the dynamic behaviours of the system, we introduced a finite element calculation model of a rotor-shaft system based on a 3D high-order element (Solid186) to study the turbocharger rotor-bearing system in a temperature field. The analysis was done according to the modal damping coefficient, stability limit speed, and unbalance response. The results show that accurate prediction of internal damping energy dissipation in a temperature field is crucial for accurate prediction of rotor dynamic performance. This is an important step to understand dynamic rotor stress and rotor dynamic design.

scholarly journals An Algebraic Approach for Identification of Rotordynamic Parameters in Bearings with Linearized Force Coefficients

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2747
Author(s):  
José Gabriel Mendoza-Larios ◽  
Eduardo Barredo ◽  
Manuel Arias-Montiel ◽  
Luis Alberto Baltazar-Tadeo ◽  
Saulo Jesús Landa-Damas ◽  
...  
Keyword(s):  
Rotational Speed ◽  
Algebraic Approach ◽  
Rotational Inertia ◽  
Fe Model ◽  
Rotordynamic Coefficients ◽  
Rotor Bearing ◽  
Identification Technique ◽  
Stiffness And Damping ◽  
The Mathematical Model ◽  
Bearing System

In this work, a novel methodology for the identification of stiffness and damping rotordynamic coefficients in a rotor-bearing system is proposed. The mathematical model for the identification process is based on the algebraic identification technique applied to a finite element (FE) model of a rotor-bearing system with multiple degree-of-freedom (DOF). This model considers the effects of rotational inertia, gyroscopic moments, shear deformations, external damping and linear forces attributable to stiffness and damping parameters of the supports. The proposed identifier only requires the system’s vibration response as input data. The performance of the proposed identifier is evaluated and analyzed for both schemes, constant and variable rotational speed of the rotor-bearing system, and numerical results are obtained. In the presented results, it can be observed that the proposed identifier accurately determines the stiffness and damping parameters of the bearings in less than 0.06 s. Moreover, the identification procedure rapidly converges to the estimated values in both tested conditions, constant and variable rotational speed.

Natural frequency analysis of a functionally graded rotor-bearing system with a slant crack subjected to thermal gradients

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arnab Bose ◽  
Prabhakar Sathujoda ◽  
Giacomo Canale
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Power Law ◽  
Beam Theory ◽  
Functionally Graded ◽  
Thermal Gradients ◽  
Element Analysis ◽  
Rotor Bearing ◽  
Natural Frequency Analysis ◽  
Bearing System

Abstract The present work aims to analyze the natural and whirl frequencies of a slant-cracked functionally graded rotor-bearing system using finite element analysis for the flexural vibrations. The functionally graded shaft is modelled using two nodded beam elements formulated using the Timoshenko beam theory. The flexibility matrix of a slant-cracked functionally graded shaft element has been derived using fracture mechanics concepts, which is further used to develop the stiffness matrix of a cracked element. Material properties are temperature and position-dependent and graded in a radial direction following power-law gradation. A Python code has been developed to carry out the complete finite element analysis to determine the Eigenvalues and Eigenvectors of a slant-cracked rotor subjected to different thermal gradients. The analysis investigates and further reveals significant effect of the power-law index and thermal gradients on the local flexibility coefficients of slant-cracked element and whirl natural frequencies of the cracked functionally graded rotor system.

Tissue necrosis and passage of fluid due to cold stress from the thermally damaged human body peripherals: A mathematical model

2015 ◽  
Vol 04 (02) ◽  
pp. 1550012
Author(s):  
M. A. Khanday ◽  
Fida Hussain ◽  
Khalid Nazir
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Heat Equation ◽  
Cold Stress ◽  
Human Body ◽  
Human Subjects ◽  
Diffusion Equations ◽  
Tissue Necrosis ◽  
Cold Temperatures ◽  
Element Technique

The development of cold injury takes place in the human subjects by means of crystallization of tissues in the exposed regions at severe cold temperatures. The process together with the evaluation of the passage of fluid discharge from the necrotic regions with respect to various degrees of frostbites has been carried out by using variational finite element technique. The model is based on the Pennes' bio-heat equation and mass diffusion equations together with suitable initial and boundary conditions. The results are analyzed in relation with atmospheric temperatures and other parameters of the tissue medium.

2-D electromagnetic modeling by finite‐element method with a dipole source and topography

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 465-475 ◽  
Author(s):  
Yuji Mitsuhata
Keyword(s):  
Finite Element ◽  
Delta Function ◽  
Dipole Source ◽  
Electromagnetic Modeling ◽  
Secondary Field ◽  
Controlled Source ◽  
Transient Electromagnetic ◽  
Isoparametric Finite Element ◽  
Anomalous Bodies ◽  
Element Technique

I present a method for calculating frequency‐domain electromagnetic responses caused by a dipole source over a 2-D structure. In modeling controlled‐source electromagnetic data, it is usual to separate the electromagnetic field into a primary (background) and a secondary (scattered) field to avoid a source singularity, and only the secondary field caused by anomalous bodies is computed numerically. However, this conventional scheme is not effective for complex structures lacking a simple background structure. The present modeling method uses a pseudo‐delta function to distribute the dipole source current, and does not need the separation of the primary and the secondary field. In addition, the method employs an isoparametric finite‐element technique to represent realistic topography. Numerical experiments are used to validate the code. Finally, a simulation of a source overprint effect and the response of topography for the long‐offset transient electromagnetic and the controlled‐source magnetotelluric measurements is presented.

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