Finite element calculation of critical speeds of rotation of shafts with gyroscopic action of discs
About: This article is published in Journal of Sound and Vibration.The article was published on 1987-09-22. It has received 4 citations till now. The article focuses on the topics: Rotation & Finite element method.
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TL;DR: In this paper, a lumped mass model is proposed to study the parametric instability of a cantilever shaft-disk system subjected to axial and follower loads, respectively.
30 citations
TL;DR: In this paper, the authors tried to lump gyroscopic matrix in complex co-ordinates and found that the gyroscope matrix becomes symmetric but non-diagonal.
5 citations
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Dissertation•
01 Jan 2016
TL;DR: In this article, the authors used a 3-layer perceptron neural network model to model the dynamic response of a dual-disc rotor model subjected to parametric nonlinear bearing loads under the action of various external forces and controller design aspects applicable to this rotor.
Abstract: Aero-engines have high speed rotors carrying multi-stage turbine and compressor discs Such systems need continuous monitoring during the operating regime These rotors are mounted on ball bearings supported with squeeze film dampers and connected to stator casings The motions of bearings and rotor are influenced by each other and therefore such a system requires structural dynamic studies These rotors involve several nonlinear factors including contact forces, varying compliance vibration of ball bearing, nonlinear oil-film force of squeeze film damper etc Solving such nonlinear dynamic problems using the traditional transfer matrix method, modal synthesis approach, finite element method or impedance coupling technique is therefore a challenging task
Present work focuses on modelling of rotors using ball bearing nonlinearities along with nonlinear secondary transient excitations using finite element modelling In order to validate the finite element model, preliminary dynamic analysis is carried out using linear spring-damper bearing elements Results are illustrated both for LP rotor model and twin-spool rotor Initially, the natural frequencies obtained from the computer program based on Timoshenko beam elements are validated with ANSYS results Further, the results are also validated with those obtained from impact hammer tests on a scaled dual disk rotor-bearing system To utilize this finite element model, the time and frequency-domain response studies are conducted with double-row ball bearing forces, rub-impact forces, Muszynska’s gas transients along with squeeze-film forces In all the cases, differences from simple rotor supported by single-row ball bearings with only unbalance excitations have been reported Using the fundamental frequency and its amplitude, an inverse modelling approach is applied to predict the parameters of rotor bearing system such as increased bearing clearance, changes in disc unbalances and the centralizing spring constants in squeeze-film damper In this regard, a trained model of 3-layer perceptron neural network model is employed In the second study, changes in dynamic response due to waviness and race-way defects in ball-bearings are first studied using modified contact force relations Using this data, type of bearing fault is estimated from the statistical parameters of the time-domain signal by training an unsupervised Kohenen’s neural network model Here, the simulated data is collected from the rotor over an operating speed range In the third study, the additional stiffness of rotor due to rub-impact forces is identified from optimization modelling Such identification of rotor stiffening effect using finite element modelling is a new concept
Two types of control studies are proposed to minimize the amplitudes of rotor during the critical operating conditions Semi active electromagnetic damper design helps in reducing vibration amplitudes of the LP rotor over a frequency range of interest Here, the damper comprises of an electro-magnet and a spring The required current and spring stiffness are identified from the basic relations and the results of control are illustrated with a two-disc LP rotor model In active controller design, an electromagnetic actuator model is employed The nominal gap maintained between the rotor and actuator coils is used in computing the actuator force A proportional derivative (PD) control strategy is used to estimate the required forces A neural network based alternate control scheme also proposed to compute the required actuator forces
In overall, the work focussed on the dynamic analysis of dual disc rotor model subjected to parametric nonlinear bearing loads under the action of various external forces and some controller design aspects applicable to this rotor
2 citations
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TL;DR: In this article, a FORTRAN IV algorithm is presented for determining sets of dominant eigenvalues and corresponding eigenvectors of symmetric matrices, which is also extended to the solution of the natural vibration of a structure for which symmetric stiffness and mass matrices are available.
Abstract: A FORTRAN IV algorithm is presented for determining sets of dominant eigenvalues and corresponding eigenvectors of symmetric matrices. It is also extended to the solution of the equations of natural vibration of a structure for which symmetric stiffness and mass matrices are available. The matrices are stored and processed in variable bandwidth form, thus enabling advantage to be gained from sparseness in the equations. Some of the procedures may also be used to solve symmetric positive definite equations such as those arising from the static analysis of structures loaded within the elastic range.
162 citations