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.

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.

scholarly journals An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

2015 ◽  
Author(s):  
Marijn Nijenhuis ◽  
J. P. Meijaard ◽  
Just L. Herder ◽  
Shorya Awtar ◽  
Dannis M. Brouwer
Keyword(s):  
Three Dimensional ◽  
Beam Element ◽  
Element Analysis ◽  
Cross Sectional ◽  
Flexure Mechanism ◽  
Stiffness Properties ◽  
Spatial Beam ◽  
Discrete Nature ◽  
Stiffness Characteristics

A flexure strip has constraint characteristics, such as stiffness properties and error motions, that limit its performance as a basic constituent of flexure mechanisms. This paper presents a framework for modeling the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear and torsion deformation. The formulation is based on a finite strain discrete spatial beam element with refinements to account for plate-like behavior due to constrained cross-sectional warping. This framework is suited for analytical calculations thanks to the accuracy of the beam element, while its discrete nature allows for easy implementation in numeric software to serve as calculation aid. As case study, a closed-form parametric analytical expression is derived for the lateral support stiffness of a parallel flexure mechanism. This captures the deteriorating support stiffness when the mechanism moves in the intended degree of freedom. By incorporating relevant geometric nonlinearities and a warping constraint stiffening factor, an accurate load-displacement and stiffness expression for the lateral support direction is obtained. This result is verified by nonlinear finite element analysis.

A Model of Kinematic Variables Determining Height Achieved in Water Polo Boosts

1999 ◽  
Vol 15 (3) ◽  
pp. 270-283 ◽  
Author(s):  
Ross H. Sanders
Keyword(s):  
Three Dimensional ◽  
Knee Extension ◽  
Multiple Regression Model ◽  
The Body ◽  
Lower Limbs ◽  
Maximum Height ◽  
Water Polo ◽  
Foot Motion ◽  
Speed Range ◽  
Drag And Lift

A boost is a skill used in water polo to raise the body for the purpose of shooting for goal or passing, or defending against these. The purpose of this study was to investigate kinematic variables contributing to height achieved in a boost. The kinematics of the vertex, shoulders, and lower limbs of 16 players ranging in ability from novice to elite were quantified using three-dimensional videographic techniques. Maximum height of the vertex with respect to water level ranged from 0.50 m to 0.90 m. A multiple regression model comprising the squared maximum resultant foot speed, range of knee joint extension, and initial trunk angle with respect to the horizontal accounted for 74% of the variance in height achieved. Anteroposterior and medio-lateral motions assisted in maintaining foot speed throughout the period of knee extension. The foot orientations and direction of foot motion of the elite players suggested that effective technique involves the use of both drag and lift forces.

scholarly journals Stability of rigid body motion through an extended intermediate axis theorem: application to rockfall simulation

2021 ◽  
Author(s):  
Remco I. Leine ◽  
Giuseppe Capobianco ◽  
Perry Bartelt ◽  
Marc Christen ◽  
Andrin Caviezel
Keyword(s):  
Rigid Body ◽  
Direct Method ◽  
Lateral Spreading ◽  
The Body ◽  
Body Motion ◽  
Numerical Schemes ◽  
Stability Properties ◽  
Principal Axes ◽  
Rockfall Simulation ◽  
The Stability

AbstractThe stability properties of a freely rotating rigid body are governed by the intermediate axis theorem, i.e., rotation around the major and minor principal axes is stable whereas rotation around the intermediate axis is unstable. The stability of the principal axes is of importance for the prediction of rockfall. Current numerical schemes for 3D rockfall simulation, however, are not able to correctly represent these stability properties. In this paper an extended intermediate axis theorem is presented, which not only involves the angular momentum equations but also the orientation of the body, and we prove the theorem using Lyapunov’s direct method. Based on the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints. In particular, we show how this scheme is incorporated in an existing 3D rockfall simulation code. Simulations results reveal that the stability properties of rotating rocks play an essential role in the run-out length and lateral spreading of rocks.

scholarly journals Design, analysis, and control of a cable-driven parallel platform with a pneumatic muscle active support

Robotica ◽  
2015 ◽  
Vol 35 (4) ◽  
pp. 744-765 ◽  
Author(s):  
Xingwei Zhao ◽  
Bin Zi ◽  
Lu Qian
Keyword(s):  
Screw Theory ◽  
Sliding Mode ◽  
The Body ◽  
Sliding Mode Controller ◽  
Pd Controller ◽  
Pneumatic Muscle ◽  
Parallel Platform ◽  
Stiffness Characteristics ◽  
The Stability ◽  
And Control

SUMMARYThe neck is an important part of the body that connects the head to the torso, supporting the weight and generating the movement of the head. In this paper, a cable-driven parallel platform with a pneumatic muscle active support (CPPPMS) is presented for imitating human necks, where cable actuators imitate neck muscles and a pneumatic muscle actuator imitates spinal muscles, respectively. Analyzing the stiffness of the mechanism is carried out based on screw theory, and this mechanism is optimized according to the stiffness characteristics. While taking the dynamics of the pneumatic muscle active support into consideration as well as the cable dynamics and the dynamics of the Up-platform, a dynamic modeling approach to the CPPPMS is established. In order to overcome the flexibility and uncertainties amid the dynamic model, a sliding mode controller is investigated for trajectory tracking, and the stability of the control system is verified by a Lyapunov function. Moreover, a PD controller is proposed for a comparative study. The results of the simulation indicate that the sliding mode controller is more effective than the PD controller for the CPPPMS, and the CPPPMS provides feasible performances for operations under the sliding mode control.

Plasma and Electrospray Deposition to Improve the Biocompatibility of Stents

2007 ◽  
Vol 539-543 ◽  
pp. 529-534 ◽  
Author(s):  
Michael Tatoulian ◽  
Enrico Gallino ◽  
R. Jafari ◽  
Farzaneh Arefi-Khonsari ◽  
L. Tatoulian ◽  
...  
Keyword(s):  
Stainless Steel ◽  
Three Dimensional ◽  
Film Coating ◽  
Polymer Coatings ◽  
The Body ◽  
Metallic Ions ◽  
Ion Release ◽  
Three Dimensional Objects ◽  
Intravascular Stents ◽  
The Stability

Metallic Intravascular stents are medical devices used to scaffold a biological lumen, mostly diseased arteries, after balloon angioplasty. They are commonly made of 316L stainless steel or Nitinol, two alloys containing Nickel, an element classified as potentially toxic and carcinogenic. Although they are largely implanted, the long-term safety of such metallic elements is still controversial, since the corrosion processes may lead to the release of several metallic ions. In order to avoid the metallic ion release in the body and to improve the biocompatibility of metallic stents with their biological environments, polymer coatings have been deposited by two different technologies, i.e. plasma surface modifications and Electrospraying. The role of the polymer coating is then to encapsulate the stainless steel device, and to favour the chemical grafting of Phosphorylcholine, a molecule known for its hemocompatible properties.1 In this talk, the state of the art on low pressure and atmospheric pressure plasmas for deposition of organic coatings will be given and we will present the advantages and drawbacks of each process. Then, we will present an original technology that combine a Dielectric Barrier Discharge and an electrospraying system to deposit well-defined Polyacrylic acid and Polyallylamine films. The advantage of such system is the possibility to limit the extent of the monomer fragmentation and to give rise to rapid deposition of a highly functionalised plasma polymer layer, and also the possibility to cover three dimensional objects, such as stents. Thus, the theory of EHDA technology will be explained: special attention has been paid to define the Electrospray parameters (Voltage, flow of precursor, nozzle-substrate distance…) which control the size distribution of the charged droplets and as a consequence, the structure of the film coating. The film coatings have been analysed with XPS and by ATR. Moreover, special attention will be paid on the stability of the coating which is related to both spraying conditions as well as to the preliminary plasma treatment. The potentiality and the features of the EHDA process will be then presented.

scholarly journals Numerical Modeling and Stability Analysis of Surrounding Rock of Yuanjue Cave

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zhigang Meng ◽  
Fangzheng Fan ◽  
Xuebin Cui ◽  
Shu Tao ◽  
Yi Cao
Keyword(s):  
Numerical Simulation ◽  
Rock Mass ◽  
Lower Layer ◽  
Three Dimensional ◽  
Surrounding Rock ◽  
The Body ◽  
Adjacent Area ◽  
The West ◽  
Monitoring Point ◽  
The Stability

Yuanjue Cave, located in Big Buddha Bay, Mount Baoding, Dazu Rock Carvings Area, has extremely high historical, artistic, and religious value and is an important grotto cultural relic in China. Due to the cutting action of the fissures and weak interlayers, the South Cliff of Big Buddha Bay where Yuanjue Cave is located showed signs of instability. In order to fully evaluate the stability of the rock mass around the cliff where Yuanjue Cave is located, a three-dimensional geological model of the surrounding rock of Yuanjue Cave was established by using FLAC3D software, combined with three-dimensional scanning, fissure investigation, and indoor tests. The stability of the surrounding rock mass adjacent to Yuanjue Cave has been studied by precise numerical simulation, and the results of numerical simulation and monitoring have been compared and analysed. The results show the following: (1) The west of J10 fissure, above the mudstone interlayer, is the main deformation area. The cliff displacement increases gradually from the east to the west. The independent block above the corner has the largest free space displacement, and there is a risk of independent collapse. Special attention should be paid to the stability of this block. The displacement of the upper monitoring point of the cliff wall is significantly greater than that of the lower layer. (2) In the surrounding rock block in the adjacent area, the various concentrated stresses of the body are mainly located at the entrance of Yuanjue Cave, the height of the chest of the Zhengjue Buddha statue, and the lower mudstone erosion and reinforcement zone. Among them, the stress concentration in the erosion and reinforcement area under the Zhengjue Buddha statue is the largest. The conclusions obtained can provide a useful reference for the stability assessment of the surrounding rock of Yuanjue Cave.

The stability of three-dimensional time-periodic flows with ellipsoidal stream surfaces

1996 ◽  
Vol 324 ◽  
pp. 379-391 ◽  
Author(s):  
G. K. Forster ◽  
A. D. D. Craik
Keyword(s):  
Floquet Theory ◽  
Three Dimensional ◽  
Practical Interest ◽  
Practical Method ◽  
Steady Flows ◽  
Periodic Flows ◽  
Constant Vorticity ◽  
Principal Axes ◽  
The Stability ◽  
Time Periodic

Most steady flows with constant vorticity and elliptical streamlines are known to be unstable. These, and certain axisymmetric time-periodic flows, can be analysed by Floquet theory. However, Floquet theory is inapplicable to other time-periodic flows that yield disturbance equations containing a quasi-periodic, rather than periodic, function. A practical method for surmounting this difficulty was recently given by Bayly, Holm & Lifschitz. Employing their method, we determine the stability of a clas of three-dimensional time-periodic flows: namely, those unbounded flows with fixed ellipsoidal stream surfaces and spatially uniform but time-periodic strain rates. Corresponding, but bounded, flows are those within a fixed ellipsoid with three different principal axes. This is perhaps the first exact stability analysis of non-reducibly three-dimensional and time-dependent flows. Though the model has some artificial features, the results are likely to shed light on more complex systems of practical interest.

scholarly journals An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Marijn Nijenhuis ◽  
J. P. Meijaard ◽  
Dhanushkodi Mariappan ◽  
Just L. Herder ◽  
Dannis M. Brouwer ◽  
...  
Keyword(s):  
Closed Form ◽  
Three Dimensional ◽  
Flexure Mechanism ◽  
Stiffness Properties ◽  
Spatial Beam ◽  
Bearing Stiffness ◽  
Stiffness Characteristics ◽  
Parametric Expression ◽  
Analytical Result ◽  
Analytical Expressions

A flexure strip has constraint characteristics, such as stiffness properties and error motions, that govern its performance as a basic constituent of flexure mechanisms. This paper presents a new modeling approach for obtaining insight into the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear, and torsion deformation. The approach is based on the use of a discretized version of a finite (i.e., nonlinear) strain spatial beam formulation for extracting analytical expressions that describe deformation and stiffness characteristics of a flexure strip in a parametric format. This particular way of closed-form modeling exploits the inherent finite-element assumptions on interpolation and also lends itself for numeric implementation. As a validating case study, a closed-form parametric expression is derived for the lateral support stiffness of a flexure strip and a parallelogram flexure mechanism. This captures a combined torsion–bending dictated geometrically nonlinear effect that undermines the support bearing stiffness when the mechanism moves in the intended degree of freedom (DoF). The analytical result is verified by simulations and experimental measurements.

scholarly journals Kinematic and Aerodynamic Investigation of the Butterfly in Forward Free Flight for the Butterfly-Inspired Flapping Wing Air Vehicle

2021 ◽  
Vol 11 (6) ◽  
pp. 2620
Author(s):  
Yixin Zhang ◽  
Xingjian Wang ◽  
Shaoping Wang ◽  
Wenhao Huang ◽  
Qiwang Weng
Keyword(s):  
High Speed ◽  
Kinematic Model ◽  
Three Dimensional ◽  
Flapping Wing ◽  
The Body ◽  
Main Body ◽  
Free Flight ◽  
Forward Flight ◽  
The Stability ◽  
Generation Mechanisms

To ensure the stability of flight, the butterfly needs to flap its wings and simultaneously move its main body to achieve all kinds of flying motion, such as taking off, hovering, or reverse flight. The high-speed camera is used to record the swing of the abdomen, the movement of the wings, and the pitch angle of the body for butterflies during their free flight; the comprehensive biokinetic observations show that the butterfly’s wings and body are coupled in various flight states. The swing of the abdomen and the flap of the fore wing affect the pitch motion significantly. For theoretical analysis of the butterfly flight, a three-dimensional multi-rigid butterfly model based on real butterfly dimension is established, and the aerodynamic of the butterfly flight is simulated and analyzed via computational fluid dynamics methods to obtain an optimal kinematic model of butterfly forward flight. Moreover, the formation and development of three-dimensional vortex structures in the forward flight are also presented. The detailed structures of vortices and their dynamic behavior show that the wing’s flap and the abdominal swing play a key role in reorienting and correcting the “clap and peel” mechanism, and the force generation mechanisms are evaluated. The research indicates that longitudinal flight performance is mainly related to the kinematic parameters of the wing and body, and it can lead to the development of butterfly-inspired flapping wing air vehicles.

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