Parametric resonances for torsional vibration of excited rotating machineries with nonconstant velocity joints

2017 ◽  
Vol 24 (15) ◽  
pp. 3262-3277 ◽  
Author(s):  
Masoud SoltanRezaee ◽  
Mohammad-Reza Ghazavi ◽  
Asghar Najafi
Keyword(s):  
Torsional Vibration ◽  
High Speed ◽  
Power Transmission ◽  
Equations Of Motion ◽  
Monodromy Matrix ◽  
Parametric Instability ◽  
Constant Input ◽  
Inertia Moment ◽  
Disk Model ◽  
Shaft System

The shaft system is a rotating machinery with many applications due to its high speed. The angle between shafts may not be zero. So the shafts can be connected to each other through a nonconstant velocity U-joint, which transforms a constant input angular velocity into a periodically fluctuating velocity. Consequently, the mechanism is parametrically excited and may face resonance conditions. Herein, a power transmission system including three elastic shafts is considered. The polar inertia moment of each shaft is modeled as a dynamic system with two discrete disks at the shaft ends. The equations of motion consist of a set of Mathieu–Hill differential equations with periodic coefficients. The dynamic stability and torsional vibration of the shaft system are analyzed. The system geometry and inertia moment effect are the main issues in this contribution. Parametric instability charts are achieved via the monodromy matrix technique. The graphical numerical results are validated with the frequency analytical results. Finally, the stability regions are shown in the parameter spaces of velocity, misalignment angles and the inertia of disks. The results demonstrated that by changing the system inertia and geometry, stabilizing the whole system is possible. Moreover, to check the precision of the model, the results are compared with a basic single-disk model, which is prevalent in two-shaft systems.

Basic Study on the Seismic Response of the High-Speed Rotational Body Supported by Fluid Film Bearings

2011 ◽  
Author(s):  
Masayoshi Hatta ◽  
Atsuhiko Shintani ◽  
Tomohiro Ito
Keyword(s):  
High Speed ◽  
Seismic Waves ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Fluid Film ◽  
Basic Study ◽  
Fluid Forces ◽  
Shaft System ◽  
Fluid Film Bearings ◽  
Response Behaviors

In this study, the seismic responses of a disk and a shaft are evaluated analytically. In an analytical model, the disk-shaft system is treated as an elastic shaft with a rigid disk, and the shaft is supported by fluid film bearings. Furthermore, the gyroscopic effect of a disk and the fluid forces due to fluid film bearings are considered. The equations of motion are derived for the translational and rotational motions when the floor is subjected to horizontal and vertical excitations. The displacements of the centers of the disk and the shaft are evaluated by numerical simulations. At first, the response behaviors of a rotating disk without base excitation are evaluated, and at second, the effects of sinusoidal base excitations are investigated. Finally, the response behaviors of this system are subjected to seismic waves of varying frequencies. The results of the different seismic wave input are studied.

Torsional Vibration of a Damped Shaft System Using the Analytical-and-Numerical-Combined Method

2001 ◽  
Vol 38 (04) ◽  
pp. 250-260
Author(s):  
Jong-Shyong Wu ◽  
Mang Hsieh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Torsional Vibration ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Combined Method ◽  
Rotating Shaft ◽  
Shaft System ◽  
Element Method

Torsional vibration analysis of the propulsive shaft system of a marine engine—one of the most important tasks in preliminary ship design—is carried out today by either the Holzer method, the transfer matrix method (TMM), or the finite-element method (FEM). Of the three methods, Holzer is the most popular and is adopted by shipyards worldwide. The purpose of this paper is to present an analytical-and-numerical-combined method (ANCM) to improve the drawbacks of existing methods. In comparison with the Holzer method (or TMM), the presented ANCM has the following merits: the mass of the rotating shaft is inherently considered, the damping effect is easily tackled, and the forced vibration responses due to various external excitations are obtained with no difficulty. Since the order of the overall property matrices for the equations of motion derived from the ANCM is usually lower than that derived from the conventional finite-element method (FEM), the CPU time required by the former is usually less than that required by the latter, particularly in the forced vibration analysis. Besides, the sizes (and the total number) of the elements for the FEM have a close relationship with the locations of the disks and the dampers and so does the accuracy of the FEM, but various distributions (or locations) of the disks and the dampers will not create any problems for the ANCM.

An Application of Torsional Wave Analysis to Turbogenerator Rotor Shaft Response

1992 ◽  
Vol 114 (2) ◽  
pp. 149-153 ◽  
Author(s):  
R. Bogacz ◽  
T. Szolc ◽  
H. Irretier
Keyword(s):  
Cross Sections ◽  
High Speed ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Continuous Model ◽  
Rotor Shaft ◽  
Shaft System ◽  
Stepped Shaft ◽  
Angular Velocities ◽  
Turbogenerator Rotor

In this paper transient torsional vibrations of a steam turbogenerator rotor shaft system due to high speed reclosing of the electric network are investigated. The analysis is performed using torsional elastic wave theory applied to a continuous model in the form of a stepped shaft. Wave solutions of the equations of motion are used in order to determine dynamic torsional elastic moments and vibratory angular velocities in cross-sections of the turbine shafts. The results are illustrated in the form of graphs.

Study on the Seismic Response of High-Speed Rotational Disk-Shaft System

2012 ◽  
Author(s):  
Tomohiro Ito ◽  
Masayoshi Hatta ◽  
Atsuhiko Shintani ◽  
Chihiro Nakagawa
Keyword(s):  
Seismic Response ◽  
Seismic Wave ◽  
High Speed ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Seismic Responses ◽  
Shaft System ◽  
High Speed Rotation ◽  
Gyroscopic Effects ◽  
Response Behaviors

Recently, huge earthquakes occurred in the world, such as Great East Japan Earthquake in Japan or huge earthquake in New Zealand in 2011. In Niigata-ken Chuetsuoki earthquake in 2007, turbine blade collisions with the casing were found. Therefore, it is very important to clarify the seismic response behaviors of the high-speed rotational shaft like turbine shafts, because high-speed rotation will cause characteristic dynamic effects, such as gyro moment. In this study, seismic responses of a disk-shaft system are evaluated analytically. The disk-shaft system is treated as an elastic shaft with a rigid disk. In this analysis, gyroscopic effects of a rotating disk are also considered. Equations of motion are derived for the translational and rotational motions when the system is subjected to both horizontal and vertical seismic excitations. Response behaviors of a rotating disk-shaft system are evaluated for sinusoidal excitations and seismic wave excitations. In the sinusoidal excitations, excitation frequencies and rotational speed are varied, and in the seismic wave excitations, seismic responses are evaluated for the waves with various predominant frequencies.

Analysis and enhancement of torsional vibration stopbands in a periodic shaft system

2013 ◽  
Vol 46 (14) ◽  
pp. 145306 ◽  
Author(s):  
Yubao Song ◽  
Jihong Wen ◽  
Dianlong Yu ◽  
Xisen Wen
Keyword(s):  
Torsional Vibration ◽  
Shaft System

Transient Vibration of High-Speed, Lightweight Rotors Due to Sudden Imbalance

1983 ◽  
Vol 105 (3) ◽  
pp. 480-486 ◽  
Author(s):  
M. Sakata ◽  
T. Aiba ◽  
H. Ohnabe
Keyword(s):  
Transient Response ◽  
High Speed ◽  
Rotor System ◽  
Response Analysis ◽  
Transient Vibration ◽  
Flexible Shaft ◽  
Shaft System ◽  
Transient Response Analysis ◽  
Flexible Disk ◽  
Blade Loss

In the field of rotor dynamics, increased attention is being given to the transient response analysis of the rotor, since the effects of impact loading and vibrations of the rotor arising from blade loss can be studied by a time transient solution of the rotor system. As recent trends in rotating machinery have been directed towards lightweight, high-speed flexible rotors, the effect of flexibility on transient response analysis is becoming of increasing importance. In the present paper, a transient vibration analysis is carried out on a flexible-disk/flexible-shaft system or rigid-disk flexible-shaft system subjected to a sudden imbalance that is assumed to represent the effect of blade loss. To solve the basic equation governing a rotating flexible disk the Galerkin’s method is used, and the equation of motion of the rotor system is numerically solved by employing the Runge-Kutta-Gill’s method. Experiments were conducted on a model rotor having a blade loss simulator; the shaft vibrations were also measured. The validity of the anaytical results was demonstrated by comparison with the experimental results.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

Analysis of Models for Torsional Vibration of Shaft System With Planetary Gearing

1997 ◽  
Author(s):  
Jinghui Sun ◽  
Lee Liu ◽  
William N. Patten
Keyword(s):  
Torsional Vibration ◽  
Planetary Gear ◽  
Gear Train ◽  
Mathematical Treatment ◽  
Dynamic Parameters ◽  
Mass Model ◽  
Planar Model ◽  
Shaft System ◽  
Effective Dynamic ◽  
Single Mass

Abstract The kinematics of planetary gearing are complex; thus, making it difficult to build an effective dynamic model. In this paper, a single-mass model of a planetary gear and shaft system is developed to study the torsional vibration of the mechanism. Two new models of the system are proposed: (a) a fictitious co-planar model and (b) an equivalent shaft model. The results from the calculations and analyses using these models indicate that: 1) the single-mass model and the general rotary model are both limited, either mathematically or geometrically; 2) the fictitious co-planar model includes all of the geometric and dynamic parameters of the general rotary model, and it can be connected with the shaft system easily; and 3) using a mathematical treatment, the equivalent shaft model is demonstrated to be the most useful and most effective model for the calculation of torsional vibration of a shaft and planetary gear train.

Investigation of Parametric Resonance Instability in a Flexible Rod Slider Crank Mechanism

1991 ◽  
Author(s):  
David G. Beale ◽  
Shyr-Wen Lee
Keyword(s):  
Potential Energy ◽  
Parametric Resonance ◽  
Variational Approach ◽  
Equations Of Motion ◽  
Monodromy Matrix ◽  
Bending Energy ◽  
Constrained Equations ◽  
Beam Bending ◽  
Floating Frame ◽  
Crank Mechanism

Abstract A direct variational approach with a floating frame is presented to derive the ordinary differential equations of motion of a flexible rod, constant crank speed slider crank mechanism. Potential energy terms contained in the derivation include beam bending energy and energy in foreshortening of the rod tip (which were selected because of the importance of these terms in a pinned-pinned rod parametric resonance). A symbolic manipulator code is used to reduce the constrained equations of motion to unconstrained nonlinear equations. A linearized version of these equations is used to explore parametric resonance stability-instability zones at low crank speeds and small deflections by a monodromy matrix technique.

Vibration-Based Early Crack Diagnosis With Machine Learning for Spur Gears

2020 ◽  
Author(s):  
Fatih Karpat ◽  
Ahmet Emir Dirik ◽  
Onur Can Kalay ◽  
Oğuz Doğan ◽  
Burak Korcuklu
Keyword(s):  
Machine Learning ◽  
Fault Diagnosis ◽  
High Speed ◽  
Crack Detection ◽  
Power Transmission ◽  
Calculated Data ◽  
Design Parameters ◽  
Tooth Stiffness ◽  
Vibration Responses ◽  
Root Crack

Abstract Gear mechanisms are one of the most significant components of the power transmission systems. Due to increasing emphasis on the high-speed, longer working life, high torques, etc. cracks may be observed on the gear surface. Recently, Machine Learning (ML) algorithms have started to be used frequently in fault diagnosis with developing technology. The aim of this study is to determine the gear root crack and its degree with vibration-based diagnostics approach using ML algorithms. To perform early crack detection, the single tooth stiffness and the mesh stiffness calculated via ANSYS for both healthy and faulty (25-50-75-100%) teeth. The calculated data transferred to the 6-DOF dynamic model of a one-stage gearbox, and vibration responses was collected. The data gathered for healthy and faulty cases were evaluated for the feature extraction with five statistical indicators. Besides, white Gaussian noise was added to the data obtained from the 6-DOF model, and it was aimed at early fault diagnosis and condition monitoring with ML algorithms. In this study, the gear root crack and its degree analyzed for both healthy and four different crack sizes (25%-50%-75%-100%) for the gear crack detection. Thereby, a method was presented for early fault diagnosis without the need for a big experimental dataset. The proposed vibration-based approach can eliminate the high test rig construction costs and can potentially be used for the evaluation of different working conditions and gear design parameters. Therefore, catastrophic failures can be prevented, and maintenance costs can be optimized by early crack detection.

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