A Modified Approach for Torsional Vibration Analysis of Some Rotor Systems Using Holzer and Matlab GUI Techniques

Abstract This paper presents the development of two tapered finite elements for use in torsional vibration analysis of rotor systems. These elements are particularly useful in analysis of systems that have shaft sections with linearly varying diameters. Both elements are defined by two end nodes, and inertia matrices are derived based on a consistent mass formulation. One element assumes a cubic displacement function and has two degrees of freedom at each node: rotation about the shaft’s axis and change in angle of rotation with respect to the axial distance along the shaft. The other element assumes a linear displacement function and has one rotational degree of freedom at each node. The elements are implemented in a computer program. Calculated natural frequencies and mode shapes are compared for both tapered shaft sections and constant diameter sections. These results are compared with results from an available constant diameter element. It is shown that the element derived assuming a cubic displacement function offers much better convergence characteristics in terms of calculated natural frequencies, both for tapered sections and constant diameter sections, than either of the other two elements. The finite element code that was developed for implementation of these elements is specifically designed for torsional vibration analysis of rotor systems. Lumped inertia, lumped stiffness, and gear connection elements necessary for rotor system analysis are also discussed, as well as calculation of natural frequencies, mode shapes, and amplitudes of response due to a harmonic torque input.

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Dynamic Analysis of Geared Rotor-Bearing Systems by the Transfer Matrix Method

Volume 3B: 15th Biennial Conference on Mechanical Vibration and Noise — Acoustics, Vibrations, and Rotating Machines ◽

10.1115/detc1995-0491 ◽

1995 ◽

Author(s):

Siu-Tong Choi ◽

Sheng-Yang Mau

Keyword(s):

Transfer Matrix ◽

Transfer Matrix Method ◽

Matrix Method ◽

Vibration Analysis ◽

Transmission Error ◽

Mode Shapes ◽

Rotor Systems ◽

Gear Mesh ◽

Mass Unbalance ◽

Rotor Bearing

Abstract In this paper, an analytical study of the dynamic characteristics of geared rotor-bearing systems by the transfer matrix method is presented. Rotating shafts are modeled as Timoshenko beam with shear deformation and gyroscopic effects taken into account. The gear mesh is modeled as a pair of rigid disks connected by a spring-damper set and a transmission-error exciter. The transfer matrix of a gear mesh is developed. The coupling motions of the lateral and torsional vibration are studied. In free vibration analysis of geared rotor systems, natural frequencies and corresponding mode shapes, and the whirl frequencies under different spin speeds are determined. Effects of bearing stiffness, isotropic and orthotropic bearings, pressure angle of the gear mesh are studied. In steady-state vibration analysis, responses due to the excitation of mass unbalance and the transmission error are studied. Parametric characteristics of geared rotor systems are discussed.

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Torsional vibration analysis of a geared transmission system of a large scale lathe under gravitational unbalancing torque

2010 IEEE International Conference on Mechatronics and Automation ◽

10.1109/icma.2010.5588083 ◽

2010 ◽

Author(s):

Guo Rui ◽

SungHyun Jang ◽

KwangSeop Sim ◽

YoungHyu Choi

Keyword(s):

Torsional Vibration ◽

Vibration Analysis ◽

Large Scale ◽

Transmission System

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Modelling of multi-bearing rotor systems for vibration analysis and control law synthesis

Active Control in Mechanical Engineering ◽

10.1201/9781003211204-24 ◽

2021 ◽

pp. 221-232

Author(s):

J.M. Krodkiewski ◽

L. Sun

Keyword(s):

Vibration Analysis ◽

Control Law ◽

Rotor Systems ◽

And Control

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Vibration of Bending-Torsion Coupled Resonance in a Rotor

Volume 8: 22nd Reliability, Stress Analysis, and Failure Prevention Conference; 25th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2013-12778 ◽

2013 ◽

Cited By ~ 1

Author(s):

Hiroyuki Fujiwara ◽

Tadashi Tsuji ◽

Osami Matsushita

Keyword(s):

Numerical Simulations ◽

Natural Frequency ◽

Torsional Vibration ◽

Rotational Speed ◽

Coupling Effect ◽

The Other ◽

Resonance Phenomenon ◽

Horizontal Direction ◽

Bending Vibration ◽

Rotor Systems

In certain rotor systems, bending-torsion coupled resonance occurs when the rotational speed Ω (= 2π Ωrps) is equal to the sum/difference of the bending natural frequency ωb (= 2π fb) and torsional natural frequency ωθ(= 2πfθ). This coupling effect is due to an unbalance in the rotor. In order to clarify this phenomenon, an equation was derived for the motion of the bending-torsion coupled 2 DOF system, and this coupled resonance was verified by numerical simulations. In stability analyses of an undamped model, unstable rotational speed ranges were found to exist at about Ωrps = fb + fθ. The conditions for stability were also derived from an analysis of a damped model. In rotational simulations, bending-torsion coupled resonance vibration was found to occur at Ωrps = fb − fθ and fb + fθ. In addition, confirmation of this resonance phenomenon was shown by an experiment. When the rotor was excited in the horizontal direction at bending natural frequency, large torsional vibration appeared. On the other hand, when the rotor was excited by torsion at torsional natural frequency, large bending vibration appeared. Therefore, bending-torsion coupled resonance was confirmed.

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