Forced Wave Motion of Liquid Partially Filling a High-Speed Rotor

1985 ◽  
Vol 107 (4) ◽  
pp. 446-452
Author(s):  
J. Inoue ◽  
Y. Jinnouchi ◽  
Y. Araki
Keyword(s):  
High Speed ◽  
Wave Motion ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Rotor Vibration ◽  
Liquid Motion ◽  
Large Wave ◽  
Main Emphasis ◽  
Two Dimensional Flow ◽  
Theoretical Results

Wave motion of a liquid in a partially filled hollow cylindrical rotor, which rotates at a high speed and is forced to vibrate, is theoretically and experimentally investigated. Main emphasis is placed on the analysis of a large wave motion in the liquid which may cause self-excited vibrations of the rotor. Assuming a thin liquid layer, simplified equations of motion are derived by integration of the governing equations for a two-dimensional flow. Nonlinearity and viscosity are taken into account in the analysis. A large wave motion with a broken wavecrest is analyzed by applying a theory of hydraulic jump. Illustrating typical examples of the theoretical results together with the experimental ones, the dynamic behavior of the liquid motion and the basic relations between the liquid force and the rotor vibration are discussed.

scholarly journals WAVES GENERATED BY A PISTON-TYPE WAVEMAKER

1970 ◽  
Vol 1 (12) ◽  
pp. 36 ◽  
Author(s):  
Ole Secher Madsen
Keyword(s):  
Mathematical Model ◽  
Finite Number ◽  
Wave Height ◽  
Finite Amplitude ◽  
Governing Equations ◽  
Approximate Evaluation ◽  
Large Wave ◽  
Wave Heights ◽  
The Waves ◽  
Theoretical Results

When a wavemaker generates a finite number of waves, it has been found that one of the first and one of the last waves in such a burst is considerably larger than the average A mathematical model, based on the linearized governing equations, is used for the particular problem of the waves generated by a sinusoidally moving piston-type wavemaker starting from rest Theoretical results for the magnitude of the large wave relative to the average agree fairly well with experiments, however, the actual wave height is smaller in the experiments than predicted by theory It is shown, by extending the classical wavemaker theory to second order, that finite amplitude effects do not offer an explanation However, pistons rarely fit the tank dimensions exactly, and an approximate evaluation indicates that the discrepancy between predicted and observed wave heights can be attributed to the effects of leakage around the piston.

Influences of Assault Blocks on Rotor Vibrations in AMB System

2015 ◽  
Vol 9 (1) ◽  
pp. 496-503
Author(s):  
Zhu Yili ◽  
Zhang Yongchun
Keyword(s):  
High Speed ◽  
Dynamic Models ◽  
Dynamic Stiffness ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Control Methods ◽  
Rotor Vibration ◽  
Dynamic Simulations ◽  
Amb System ◽  
Theoretical Results

In an active magnetic bearing (AMB) system, the rotor always rotates at extremely high speed which always accompany with huge vibrations and noises. Most of the former researches associated with reducing the rotor vibrations are mainly focused on the control methods of AMB. A new method of installing series of assault blocks in the rotor is proposed to reduce the rotor vibrations. Firstly, the dynamic models of rotor supported by AMB considering the influences of assault blocks are established. Then, both dynamic simulations with and without assault blocks are carried out separately using the real-time AMB support dynamic stiffness. The rotor vibration displacements are mainly analyzed. Finally, relevant experiments are made to verify the theoretical results. Both theoretical and experimental results validated the advantages of using assault blocks.

Suspension Bounce Response of Canadian MAGLEV Vehicle Under Guideway Excitations—Part I: Deterministic Analysis

1983 ◽  
Vol 105 (1) ◽  
pp. 104-111
Author(s):  
M. Kotb ◽  
T. S. Sankar ◽  
M. Samaha
Keyword(s):  
Mathematical Model ◽  
High Speed ◽  
Equations Of Motion ◽  
Vehicle Body ◽  
Ride Quality ◽  
Numerical Techniques ◽  
Deterministic Analysis ◽  
Maglev Vehicle ◽  
Main Emphasis

The dynamic bounce response of the Canadian designed high speed magnetically levitated vehicle is investigated when subjected to purely periodic excitations from the guideways. The equations of motion of the system are derived, on the basis of a realistic linear mathematical model, using d’Alembert’s principle of force and moment analysis. Solutions for the system responses in the time and frequency domain are obtained using numerical techniques. Although the main emphasis of this study is focused on the bounce response of the vehicle body as a measure of the ride quality of the vehicle, the vehicle pitching response as well as the bounce responses of the levitation magnets are also given appropriate attention.

Modeling Lubricated Revolute Clearance Joints in Multibody Mechanical Systems

2003 ◽  
Author(s):  
P. Flores ◽  
H. M. Lankarani ◽  
J. Ambro´sio ◽  
J. C. P. Claro
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Hydrodynamic Forces ◽  
Dynamic Loads ◽  
Governing Equations ◽  
Clearance Joints ◽  
Revolute Joints ◽  
System A

This work is concerned with the modeling of lubricated revolute clearance joints in multibody mechanical systems. The existence of the clearance at revolute joints is inevitable in all mechanical systems, and most of them are designed to operate with a lubricant fluid. It is known that the use of lubricant at revolute joints is demonstrated to be an effective way to ensuring better performance of the mechanical systems. The long journal-bearing theory for dynamic loads is used to evaluate the resulting hydrodynamic forces of the pressure distribution in the lubricated revolute joints. These hydrodynamic forces are included into the governing equations of motion of the system. A numerical example is presented in order to demonstrate the efficiency and accuracy of the methodology and procedures adopted. The results are close to those obtained with ideal joints even when simulated in a high-speed mechanism.

scholarly journals Vibration Characteristics of Rotating Mistuned Bladed Disks considering the Coriolis Force, Spin Softening, and Stress Stiffening Effects

2019 ◽  
Vol 2019 ◽  
pp. 1-22
Author(s):  
Shuai Wang ◽  
Chuanxing Bi ◽  
Bin Zi ◽  
Changjun Zheng
Keyword(s):  
Coriolis Force ◽  
High Speed ◽  
Equations Of Motion ◽  
Vibration Characteristics ◽  
Governing Equations ◽  
Bladed Disks ◽  
Reduced Order ◽  
Sector Model ◽  
Effective Component ◽  
Harsh Conditions

Bladed disks of engine rotors usually operate at harsh conditions of high rotating speeds, which may lead to nonnegligible rotordynamic effects, including Coriolis force, spin softening, and stress stiffening effects. These effects on the vibration of mistuned bladed disks are seldom discussed in available investigations. In this paper, the vibration characteristics of rotating mistuned bladed disks are addressed by considering these rotordynamic effects. First, finite element (FE) models of bladed disks are used to obtain the governing equations of motion, and an efficient method for getting the stress stiffening matrix of sector model is developed. Then, the effective component-mode mistuning method (CMM) is employed to create compact, yet accurate, reduced-order models (ROMs). Finally, the models are validated and used to study the influences of Coriolis force, spin softening, and stress stiffening effects on the vibration of bladed disks with frequency mistuning factors. Numerical results show that these rotordynamic effects could significantly affect the vibrations of mistuning bladed disks, especially in the ranges of high speed, and should be carefully considered during analysis.

Model of vortex flow of charge in a vessel with turbine impeller

1987 ◽  
Vol 52 (8) ◽  
pp. 1888-1904
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Theoretical Data ◽  
Eddy Diffusion ◽  
Quantitative Agreement ◽  
Creeping Flow ◽  
Model Parameters ◽  
Mean Flow ◽  
Two Dimensional Flow ◽  
Vorticity Transport

A theoretical model is described of the mean two-dimensional flow of homogeneous charge in a flat-bottomed cylindrical tank with radial baffles and six-blade turbine disc impeller. The model starts from the concept of vorticity transport in the bulk of vortex liquid flow through the mechanism of eddy diffusion characterized by a constant value of turbulent (eddy) viscosity. The result of solution of the equation which is analogous to the Stokes simplification of equations of motion for creeping flow is the description of field of the stream function and of the axial and radial velocity components of mean flow in the whole charge. The results of modelling are compared with the experimental and theoretical data published by different authors, a good qualitative and quantitative agreement being stated. Advantage of the model proposed is a very simple schematization of the system volume necessary to introduce the boundary conditions (only the parts above the impeller plane of symmetry and below it are distinguished), the explicit character of the model with respect to the model parameters (model lucidity, low demands on the capacity of computer), and, in the end, the possibility to modify the given model by changing boundary conditions even for another agitating set-up with radially-axial character of flow.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

scholarly journals Hydrodynamic Forces Exerting on an Oscillating Cylinder under Translational Motion in Water Covered by Compressed Ice

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 822
Author(s):  
Yury Stepanyants ◽  
Izolda Sturova
Keyword(s):  
Lift Force ◽  
Wave Motion ◽  
Translational Motion ◽  
Added Mass ◽  
Hydrodynamic Forces ◽  
Wave Resistance ◽  
Translational Velocity ◽  
Damping Coefficients ◽  
Incompressible Ideal Fluid ◽  
Theoretical Results

This paper presents the calculation of the hydrodynamic forces exerted on an oscillating circular cylinder when it moves perpendicular to its axis in infinitely deep water covered by compressed ice. The cylinder can oscillate both horizontally and vertically in the course of its translational motion. In the linear approximation, a solution is found for the steady wave motion generated by the cylinder within the hydrodynamic set of equations for the incompressible ideal fluid. It is shown that, depending on the rate of ice compression, both normal and anomalous dispersion can occur in the system. In the latter case, the group velocity can be opposite to the phase velocity in a certain range of wavenumbers. The dependences of the hydrodynamic loads exerted on the cylinder (the added mass, damping coefficients, wave resistance and lift force) on the translational velocity and frequency of oscillation were studied. It was shown that there is a possibility of the appearance of negative values for the damping coefficients at the relatively big cylinder velocity; then, the wave resistance decreases with the increase in cylinder velocity. The theoretical results were underpinned by the numerical calculations for the real parameters of ice and cylinder motion.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

scholarly journals IV. On the dynamical theory of incompressible viscous fluids and the determination of the criterion

1895 ◽  
Vol 186 ◽  
pp. 123-164 ◽  
Keyword(s):  
Singular Solution ◽  
Physical State ◽  
Theoretical Calculations ◽  
Equations Of Motion ◽  
Dynamical Theory ◽  
Viscous Fluids ◽  
Linear Functions ◽  
Incompressible Viscous Fluids ◽  
Theoretical Results

1. The equations of motion of viscous fluid (obtained by grafting on certain terms to the abstract equations of the Eulerian form so as to adapt these equations to the case of fluids subject to stresses depending in some hypothetical manner on the rates of distortion, which equations Navier seems to have first introduced in 1822, and which were much studied by Cauchy and Poisson) were finally shown by St. Venant and Sir Gabriel Stokes, in 1845, to involve no other assumption than that the stresses, other than that of pressure uniform in all directions, are linear functions of the rates of distortion, with a co-efficient depending on the physical state of the fluid. By obtaining a singular solution of these equations as applied to the case of pendulums in steady periodic motion, Sir G. Stokes was able to compare the theoretical results with the numerous experiments that had been recorded, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved. This was also the result of comparing the flow of water through uniform tubes with the flow calculated from a singular solution of the equations so long as the tubes were small and the velocities slow. On the other hand, these results, both theoretical and practical, were directly at variance with common experience as to the resistance encountered by larger bodies moving with higher velocities through water, or by water moving with greater velocities through larger tubes. This discrepancy Sir G. Stokes considered as probably resulting from eddies which rendered the actual motion other than that to which the singular solution referred and not as disproving the assumption.

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