Critical Speeds of Shaft-Disk Systems Subjected to Longitudinal Forces

1997 ◽  
Author(s):  
Lien-Wen Chen ◽  
Hong-Cheng Sheu
Keyword(s):  
Axial Force ◽  
Longitudinal Force ◽  
Numerical Results ◽  
Follower Force ◽  
Numerical Techniques ◽  
Disk System ◽  
Critical Speeds ◽  
Whirl Speed ◽  
The Right ◽  
Left Portion

Abstract The critical speeds of a spinning Timoshenko shaft with an intermediate attached disk subjected to a longitudinal force are analytically solved. The expressions of whirl speed equations for hinged-hinged, hinged-clamped, clamped-hinged, and clamped-clamped rotors are given respectively. The critical speeds of each shaft-disk system are sought from its corresponding whirl speed equation by using simple numerical techniques. The effects of the disk location and the longitudinal force on the critical speeds of the shaft-disk systems are investigated. Numerical results reveal that if the disk locates in the left portion of the shaft, both the primary forward and backward critical speeds for the rotor subjected to a follower force are larger than those subjected to an axial force with the same magnitude. The results are contrary while the disk locates in the right portion of the shaft.

Additional Investigations Into the Natural Frequencies and Critical Speeds of a Rotating, Flexible Shaft-Disk System

2007 ◽  
Author(s):  
Lyn M. Greenhill ◽  
Valerie J. Lease
Keyword(s):  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Rotor Dynamics ◽  
Axial Position ◽  
Disk System ◽  
Apparent Contradiction ◽  
Critical Speeds ◽  
Shaft Flexibility ◽  
Gyroscopic Effects ◽  
Lumped Masses

Traditional rotor dynamics analysis programs make the assumption that disk components are rigid and can be treated as lumped masses. Several researchers have studied this assumption with specific analytical treatments designed to simulate disk flexibility. The general conclusions reached by these studies indicated disk flexibility has little effect on critical speeds but significantly influences natural frequencies. This apparent contradiction has been reexamined by using axisymmetric harmonic finite elements to directly represent both disk and shaft flexibility along with gyroscopic effects. Results from this improved analysis show that depending on the thickness-to-diameter (slenderness) ratio of the disk and the axial position of the disk on the shaft, there are significant differences in all natural frequencies, for both forward and backward modes, including synchronous crossings at critical speeds.

scholarly journals Modelling Macrophage Infiltration into Avascular Tumours

2002 ◽  
Vol 4 (1) ◽  
pp. 21-38 ◽  
Author(s):  
C. E. Kelly ◽  
R. D. Leek ◽  
H. M. Byrne ◽  
S. M. Cox ◽  
A. L. Harris ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Spatial Structure ◽  
Random Motion ◽  
Numerical Results ◽  
Macrophage Infiltration ◽  
Numerical Techniques ◽  
Model Predictions ◽  
Independent Experimental Data

In this paper a mathematical model that describes macrophage infiltration into avascular tumours is presented. The qualitative accuracy of the model is assessed by comparing numerical results with independent experimental data that describe the infiltration of macrophages into two types of spheroids: chemoattractant-producing (hepa-1) and chemoattractant-deficient (or C4) spheroids. A combination of analytical and numerical techniques are used to show how the infiltration pattern depends on the motility mechanisms involved (i.e. random motion and chemotaxis) and to explain the observed differences in macrophage infiltration into the hepa-1 and C4 spheroids. Model predictions are generated to show how the spheroid's size and spatial structure and the ability of its constituent cells influence macrophage infiltration. For example, chemoattractant-producing spheroids are shown to recruit larger numbers of macrophages than chemoattractant-deficient spheroids of the same size and spatial structure. The biological implications of these results are also discussed briefly.

scholarly journals On the Importance of the Influence of both Velocity and Aspect Ratios on the Occurrence of Bifurcation Phenomena within a Two-Sided Lid-Driven Enclosure

2015 ◽  
Vol 55 ◽  
pp. 160-172
Author(s):  
Fayçal Hammami ◽  
Nader Ben Cheikh ◽  
Brahim Ben Beya
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Left Wall ◽  
Driven Cavity ◽  
Aspect Ratios ◽  
The Stability ◽  
The Right

This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. The stability analysis depending on the aspect ratio, velocity ratios α and the Reynolds number when transition phenomenon occurs is considered in this paper.

Analysis on Dynamic Response of the Foundation Pit Supporting Structure under Vehicle Loads

2013 ◽  
Vol 790 ◽  
pp. 638-642
Author(s):  
Hong Zhi Qiu ◽  
Ji Ming Kong ◽  
Yin Zhang
Keyword(s):  
Dynamic Response ◽  
Axial Force ◽  
Effective Means ◽  
Numerical Results ◽  
Engineering Practice ◽  
Foundation Pit ◽  
Supporting Structure ◽  
Half Wave ◽  
Sinusoidal Load ◽  
Vehicle Loads

Using ABAQUS software analyzed the dynamic response of foundation pit supporting structure under vehicle loads. The vehicle load was simplified as a half-wave sinusoidal load, in order to analyze the influence of internal force and displacement of pile-anchor supporting structure under the vehicle loads, the position of half-wave sinusoidal load and the size of radian frequency were considered. Loading location away from the supporting structure is more nearly and the displacement value of support piles is greater, the greater the axial force of the bolt; with the increasing of radian frequency, the horizontal displacement value of supporting piles increased, on the contrary, the axial force of bolt reduced. A practical engineering was studied here. analysis of the monitoring data and compared with the numerical results, the analysis showed that the experimental results and numerical results are in good agreement, and the numerical method can be used as an effective means of research. The conclusion of the study has significance on engineering practice.

scholarly journals Continuous action right knife unit with ground interaction analysis

2020 ◽  
Vol 17 (4) ◽  
pp. 452-463
Author(s):  
V. A. Nikolayev ◽  
D. I. Troshin
Keyword(s):  
Total Energy ◽  
Soil Layer ◽  
Practical Interest ◽  
Longitudinal Force ◽  
Energy Costs ◽  
Continuous Action ◽  
Action Unit ◽  
The Face ◽  
The Right ◽  
The Impact

Introduction. To solve the problem of accelerating the construction of roads, improving their quality, it is advisable to use a continuous action unit to form a underlying layer. The main working bodies of this unit are buckets, which cut off the soil layer from below and on the side. At the same time, the bottom knife cuts off the ground layer from below, the right knife on the side, and the console knife partially cuts the top layer of soil from below for the next bucket. In particular, the analysis of interaction with the soil of the right knife of the continuous action unit is of theoretical and practical interest. To do this, the right knife is divided into elements and analyzed the interaction of these elements with the ground. The consistent impact on the soil of many right knives, within the width of the grip of the unit, is replaced by the impact on the ground of one conventional right knife at a distance necessary for the development of one cubic meter of soil. The forces of interaction of the conventional right knife with the ground are called conditional forces.The method of research. The method for calculating the energy costs during punching the right knife into the ground is shown: on separating the formation of the ground from its body, on overcoming the ground friction on the edge of the blade, on overcoming the ground pressure on the edge of the blade, on accelerating the ground of the blade by means of the axle, on overcoming the ground friction on the shelf, to overcome the ground friction against the outside surface.The total energy costs of interacting with a soil of one cubic meter are derived from the addition of private energy costs. The method of calculating the horizontal longitudinal force needed to move the right knife is given.Results. On the basis of the methodology developed, energy costs are calculated when introducing the right knife into the ground: on separating the soil from its body, on overcoming the friction of the ground on the edge of the blade, on overcoming the pressure of the ground on the face of the blade, on the acceleration of the ground with a fascia blade, on overcoming the ground friction on the face. The total energy costs of the right knife interact with the soil of one cubic meter. The horizontal long-lived force needed to move the right knife has been determined.Conclusion. As a result of the calculations: the energy needed to cut the ground with the right knives, more than 71 J/cube. The horizontal longitudinal force needed to move the right knife is 730 N. To determine the total energy spent on cutting the ground by buckets of the unit to remove the top layer of soil from the underlying layer of the road, it is necessary to analyze the interaction with the soil of other elements of the bucket.

scholarly journals Analysis of Longitudinal Force of Beam and Rail of Continuously Welded Rails (CWR) on Railway Bridge

2022 ◽  
Vol 2148 (1) ◽  
pp. 012065
Author(s):  
Zhiping Zeng ◽  
Ji Hu ◽  
Qiang Zeng ◽  
Zhibin Huang ◽  
Huatuo Yin ◽  
...  
Keyword(s):  
Element Model ◽  
Longitudinal Force ◽  
Relative Displacement ◽  
Railway Bridge ◽  
Simply Supported ◽  
Maximum Value ◽  
Constant Resistance ◽  
Left And Right ◽  
The Right ◽  
Track Bridge

Abstract To study the longitudinal force of CWR on viaduct, a track-bridge-pier finite element model is established. Taking a multi-span simply supported beam with a maximum span of 32.7m of an elevated CWR as an example, the additional expansion and contraction forces, displacement between rail and beam and the force of pier are calculated, and whether the rail stress meets the requirements when setting constant resistance fasteners is checked. The results show that: (1) For the left and right lines, the maximum additional expansion forces of single strand rail are both 211.13kN, and the maximum relative displacements between beam and rail are both 6.572mm. (2) The maximum value of the additional expansion and contraction forces and the relative displacement between beam and rail of the same line occur at the same position. The left line is at ZFZ29 pier and the right line is at ZFS31 pier. (3) The maximum force of pier in this section is 500.80kN, and the pier numbers are ZFZ27 and ZFS29. (4) The rail stress is less than the allowable stress of 352MPa, and the rail strength meets the requirements.

Critical Speeds, Divergence, and Flutter Instability in High-Speed Planetary Gears

2012 ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Numerical Results ◽  
Planetary Gears ◽  
Critical Speeds ◽  
Flutter Instability ◽  
Divergence Instability ◽  
Translational Mode

The structured properties of the critical speeds and associated critical speed eigenvectors of high-speed planetary gears are given. Planetary gears have only planet, rotational, and translational mode critical speeds. Divergence instability is possible at speeds adjacent to critical speeds. Numerical results verify the critical speed locations. Divergence and flutter instabilities are investigated numerically for each mode type.

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