The Influence of Internal Friction on the Stability of High Speed Rotors With Anisotropic Supports

1969 ◽  
Vol 91 (4) ◽  
pp. 1105-1113 ◽  
Author(s):  
E. J. Gunter ◽  
P. R. Trumpler
Keyword(s):  
Internal Friction ◽  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Analog Computer ◽  
Three Dimensional Model ◽  
Stiffness Properties ◽  
Stiffness Characteristics ◽  
The Stability ◽  
Internal Rotor

This paper evaluates the stability of the single mass rotor with internal friction on damped, anisotropic supports. The paper shows under what conditions the rotor stability may be improved by an undamped support with anisotropic stiffness properties. A three dimensional model is presented to show the influence of rotor and support stiffness characteristics on stability. Curves are also presented on how support damping may also improve or even reduce rotor stability. An analog computer solution of the governing equations of motion is presented showing the shaft transient motion for various speed ranges, and also plots of the rotor steady state motion are given for various speeds up to and including the stability threshold. The analysis is used to explain many of the experimental observations of B. L. Newkirk concerning stability due to internal rotor friction.

On the Stability of Rotation of a Rotor With Rotationally Unsymmetric Inertia and Stiffness Properties

1961 ◽  
Vol 28 (4) ◽  
pp. 567-570 ◽  
Author(s):  
S. H. Crandall ◽  
P. J. Brosens
Keyword(s):  
Three Dimensional ◽  
The Body ◽  
Uniform Rotation ◽  
Stiffness Properties ◽  
Principal Axes ◽  
Rotationally Symmetric ◽  
Speed Range ◽  
Stiffness Characteristics ◽  
The Stability ◽  
Gyroscopic Coupling

The stability of uniform rotation of a rigid body about a principal axis of inertia is analyzed for the case where there is a diametral inertia inequality and there is an elastic restoring mechanism with a diametral stiffness inequality which rotates with the body. This model is an idealization for systems such as a two-bladed propeller rotating on a flexible shaft whose stiffness characteristics are not rotationally symmetric. It is found that many such systems possess unstable speed ranges. The instability may be due to either type of asymmetry alone or due to the interaction of the two. Quantitative analytical results are obtained which relate the unstable speed range to the gyroscopic coupling, the inertia inequality, the stiffness inequality, and the relative orientation of the principal axes of inertia with respect to the principal axes of stiffness. Three-dimensional stability surfaces are plotted to give a qualitative overview of the interplay of the various parameters.

CFD Simulation of Particle Transport and Dispersion in Indoor Environment by Human Walking

2012 ◽  
Author(s):  
Iman Goldasteh ◽  
Goodarz Ahmadi ◽  
Andrea Ferro
Keyword(s):  
Particulate Matter ◽  
High Speed ◽  
Cfd Simulation ◽  
Three Dimensional ◽  
Study Data ◽  
Turbulent Dispersion ◽  
Experimental Chamber ◽  
Indoor Environments ◽  
Three Dimensional Model ◽  
Particle Resuspension

Particle resuspension is an important source of particulate matter in indoor environments that significantly affects the indoor air quality and could potentially have adverse effect on human health. Earlier efforts to investigate indoor particle resuspension hypothesized that high speed airflow generated at the floor level during the gate cycle is the main cause of particle resuspension. The resuspended particles are then assumed to be dispersed by the airflow in the room, which is impacted by both the ventilation and the occupant movement, leading to increased PM concentration. In this study, a three dimensional model of a room was developed using FLUENT™ CFD package. A RANS approach with the RNG k-ε turbulence model was used for simulating the airflow field in the room for different ventilation conditions. The trajectories of resuspended particulate matter were computed with a Lagrangian method by solving the equations of particle motion. The effect of turbulent dispersion was included with the use of the eddy lifetime model. The resuspension of particles due to gait cycle was estimated and included in the computational model. The dispersion and transport of particles resuspended from flooring as well as particle re-deposition on flooring and walls were simulated. Particle concentrations in the room generated by the resuspension process were evaluated and the results were compared with experimental chamber study data as well as simplified model predictions, and good agreement was found.

scholarly journals Numerical Analyses on the Stability of a Deep Coalmine Roadway Passing through a Fault Zone: A Case Study of the Gugui Coalfield in China

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2114
Author(s):  
Yongshui Kang ◽  
Congcong Hou ◽  
Jingyi Liu ◽  
Zhi Geng ◽  
Jianben Chen ◽  
...  
Keyword(s):  
Fault Zone ◽  
Distinct Element ◽  
Three Dimensional ◽  
Tectonic Stress ◽  
Three Dimensional Model ◽  
Support Strategy ◽  
Failure Theory ◽  
Calculation Results ◽  
Pass Through ◽  
The Stability

Massive deformation often occurs when deep coalmine roadways pass through a fault zone due to the poor integrity of rock mass and high tectonic stress. To study deformation characteristics of the surrounding rock in the fault zone of a coalmine, a roadway passing through the FD1041 fault zone in China’s Gugui coalfield was investigated in this research. The geo-stress characteristics of this fault zone were analyzed based on the Mohr failure theory. Furthermore, a three-dimensional model for the experimental roadway in the FD1041 fault zone was built and calculated by a numerical program based on the distinct element method. Stability conditions of the roadway, using several types of support methods, were calculated and compared. Calculation results indicated that pre-grouting provides favorable conditions for the stability of a roadway in a fault zone. Finally, an optimized support strategy was proposed and implemented in the experimental roadway. Monitored results demonstrated that the optimized support strategy is appropriate for this fault zone.

Experiments on the stability of sinusoidal flow over a circular cylinder

2002 ◽  
Vol 457 ◽  
pp. 157-180 ◽  
Author(s):  
TURGUT SARPKAYA
Keyword(s):  
Stokes Flow ◽  
Coherent Structures ◽  
High Speed ◽  
Three Dimensional ◽  
Separated Flow ◽  
Circular Cylinders ◽  
Centrifugal Forces ◽  
Complex Interactions ◽  
Sinusoidal Flow ◽  
The Stability

The instabilities in a sinusoidally oscillating non-separated flow over smooth circular cylinders in the range of Keulegan–Carpenter numbers, K, from about 0.02 to 1 and Stokes numbers, β, from about 103 to 1.4 × 106 have been observed from inception to chaos using several high-speed imagers and laser-induced fluorescence. The instabilities ranged from small quasi-coherent structures, as in Stokes flow over a flat wall (Sarpkaya 1993), to three-dimensional spanwise perturbations because of the centrifugal forces induced by the curvature of the boundary layer (Taylor–Görtler instability). These gave rise to streamwise-oriented counter-rotating vortices or mushroom-shaped coherent structures as K approached the Kh values theoretically predicted by Hall (1984). Further increases in K for a given β led first to complex interactions between the coherent structures and then to chaotic motion. The mapping of the observations led to the delineation of four states of flow in the (K, β)-plane: stable, marginal, unstable, and chaotic.

Internal Rotor Friction Induced Instability in High-Speed Rotating Machinery

1993 ◽  
Author(s):  
James F. Walton ◽  
Michael R. Martin
Keyword(s):  
Internal Friction ◽  
Natural Frequency ◽  
High Speed ◽  
Critical Speed ◽  
Rotating Machinery ◽  
Rotor System ◽  
Analytical Models ◽  
Interference Fit ◽  
Internal Rotor

Abstract Results of a program to investigate internal rotor friction destabilizing effects are presented. Internal-friction-producing joints were shown to excite the rotor system first natural frequency, when operating either below or above the first critical speed. The analytical models used to predict the subsynchronous instability were also confirmed. The axial spline joint demonstrated the most severe subsynchronous instability. The interference fit joint also caused subsynchronous vibrations at the first natural frequency but these were bounded and generally smaller than the synchronous vibrations. Comparison of data from the two test joints showed that supersynchronous vibration amplitudes at the first natural frequency were generally larger for the interference fit joint than for the axial spline joint. The effects of changes in imbalance levels and side loads were not distinguishable during testing because amplitude-limiting bumpers were required to restrict orbits.

scholarly journals Re-Evaluating the Classical Falling Body Problem

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 553 ◽  
Author(s):  
Essam R. El-Zahar ◽  
Abdelhalim Ebaid ◽  
Abdulrahman F. Aljohani ◽  
José Tenreiro Machado ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Body Problem ◽  
Inertial Frame ◽  
Analytic Solution ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Rotating Frame ◽  
Dimensional Model ◽  
Three Dimensional Model

This paper re-analyzes the falling body problem in three dimensions, taking into account the effect of the Earth’s rotation (ER). Accordingly, the analytic solution of the three-dimensional model is obtained. Since the ER is quite slow, the three coupled differential equations of motion are usually approximated by neglecting all high order terms. Furthermore, the theoretical aspects describing the nature of the falling point in the rotating frame and the original inertial frame are proved. The theoretical and numerical results are illustrated and discussed.

scholarly journals A Study on the Relationship between the Design of Aerotrain and Its Stability Based on a Three-Dimensional Dynamic Model

Robotics ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 96
Author(s):  
Quang Huan Luong ◽  
Jeremy Jong ◽  
Yusuke Sugahara ◽  
Daisuke Matsuura ◽  
Yukio Takeda
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Three Dimensional ◽  
Vehicle Body ◽  
Directional Stability ◽  
Rigid Body Model ◽  
Body Design ◽  
The Stability ◽  
New Generation ◽  
The Relationship

A new generation electric high-speed train called Aerotrain has levitation wings and levitates under Wing-in-Ground (WIG) effect along a U-shaped guideway. The previous study found that lacking knowledge of the design makes the prototype unable to regain stability when losing control. In this paper, the nonlinear three-dimensional dynamic model of the Aerotrain based on the rigid body model has been developed to investigate the relationship between the vehicle body design and its stability. Based on the dynamic model, this paper considered an Aerotrain with a horizontal tail and a vertical tail. To evaluate the stability, the location and area of these tails were parameterized. The effects of these parameters on the longitudinal and directional stability have been investigated to show that: the horizontal tail gives its best performance if the tail area is a function of the tail location; the larger vertical tail area and (or) the farther vertical tail location will give better directional stability. As for the lateral stability, a dihedral front levitation wing design was investigated. This design did not show its effectiveness, therefore a control system is needed. The obtained results are useful for the optimization studies on Aerotrain design as well as developing experimental prototypes.

scholarly journals Safety Evaluation of Underground Caverns Based on Monte Carlo Method

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Qifeng Guo ◽  
Zhihong Dong ◽  
Meifeng Cai ◽  
Fenhua Ren ◽  
Jiliang Pan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Three Dimensional ◽  
Safety Evaluation ◽  
Cumulative Distribution ◽  
Three Dimensional Model ◽  
Maximum Displacement ◽  
The Monte Carlo Method ◽  
Underground Caverns ◽  
The Stability

In order to study the influence of joint fissures and rock parameters with random characteristics on the safety of underground caverns, several parameters affecting the stability of surrounding rock of underground caverns are selected. According to the Monte Carlo method, random numbers satisfying normal distribution characteristics are established. A three-dimensional model of underground caverns with random characteristics is established by discontinuous analysis software 3DEC and excavation simulations are carried out. The maximum displacement at the numerical monitoring points of arch and floor is the safety evaluation index of the cavern. The probability distribution and cumulative distribution function of the displacement at the top arch and floor are obtained, and the safety of a project is evaluated.

Resistive Ballooning Modes in Three-Dimensional Configurations

1982 ◽  
Vol 37 (8) ◽  
pp. 848-858 ◽  
Author(s):  
D. Correa-Restrepo
Keyword(s):  
Growth Rates ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Coupled System ◽  
Small Constant ◽  
Ballooning Mode ◽  
The Stability ◽  
The Magnetic Field ◽  
Symmetric Systems ◽  
The Ideal

Resistive ballooning modes in general three-dimensional configurations are studied on the basis of the equations of motion of resistive MHD. Assuming small, constant resistivity and perturbations localized transversally to the magnetic field, a stability criterion is derived in the form of a coupled system of two second-order differential equations. This criterion contains several limiting cases, in particular the ideal ballooning mode criterion and criteria for the stability of symmetric systems. Assuming small growth rates, analytical results are derived by multiple-length-scale expansion techniques. Instabilities are found, their growth rates scaling as fractional powers of the resistivity

Analysis and Research of High Speed Milling of Thin-Walled Bracket Part Based on UG NX

2010 ◽  
Vol 129-131 ◽  
pp. 256-260
Author(s):  
Yi Shu Hao ◽  
Chuang Hai ◽  
Xin Xing Zhu
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Structural Features ◽  
Milling Process ◽  
Analysis Method ◽  
Three Dimensional Model ◽  
Machining Processes ◽  
Element Analysis ◽  
High Speed Milling ◽  
Tool Paths

Treating high speed milling theory as the guidance, this paper researched high speed milling process of bracket part based on UG NX. Combined with the structural features of bracket part, three dimensional model is built by UG NX CAD and machining processes are worked out after analysis. UG CAM module was applied to fabricate tool paths. At last, finite element analysis method is introduced to study the processing deformation by UG NX NASTRAN module, based on which measures to restrain processing deformations is advanced and processing sequences are optimized.

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