scholarly journals A Class of Wavelet-Based Rayleigh-Euler Beam Element for Analyzing Rotating Shafts

2011 ◽  
Vol 18 (3) ◽  
pp. 447-458 ◽  
Author(s):  
Jiawei Xiang ◽  
Zhansi Jiang ◽  
Xuefeng Chen
Keyword(s):  
Degrees Of Freedom ◽  
Beam Element ◽  
Rotating Beam ◽  
Euler Beam ◽  
Boundary Node ◽  
Six Degrees Of Freedom ◽  
Spline Wavelets ◽  
Rotating Shafts ◽  
Wavelets On The Interval ◽  
Stiffness And Damping

A class of wavelet-based Rayleigh-Euler rotating beam element using B-spline wavelets on the interval (BSWI) is developed to analyze rotor-bearing system. The effects of translational and rotary inertia, torsion moment, axial displacement, cross-coupled stiffness and damping coefficients of bearings, hysteric and viscous internal damping, gyroscopic moments and bending deformation of the system are included in the computational model. In order to get a generalized formulation of wavelet-based element, each boundary node is collocated six degrees of freedom (DOFs): three translations and three rotations; whereas, each inner node has only three translations. Typical numerical examples are presented to show the accuracy and efficiency of the presented method.

Modeling Rotating Shafts Using Axisymmetric Solid Finite Elements with Matrix Reduction

1993 ◽  
Vol 115 (4) ◽  
pp. 484-489 ◽  
Author(s):  
R. W. Stephenson ◽  
K. E. Rouch
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Series Representation ◽  
Element Model ◽  
Beam Element ◽  
Two Dimensions ◽  
Matrix Reduction ◽  
Stiffness Matrices ◽  
Rotating Shafts ◽  
Element Type

An axisymmetric harmonic finite element representation is used to calculate shaft lateral critical speeds and perform stability analysis. Unlike a beam element model, an axisymmetric solid element representation allows the actual rotor geometry to be modeled. A Fourier series representation allows the three-dimensional shaft geometry to be modeled in two dimensions by only considering the radial and axial coordinates. Thus, the degrees of freedom of this element type are different from the usual two translations and two rotations at each node associated with bending of a three-dimensional beam element. A required gyroscopic matrix is also presented for completeness in analysis of rotating shafts. A matrix reduction technique is used to reduce the size of the shaft mass, gyroscopic, and stiffness matrices by condensing out slave degrees of freedom in terms of the retained master degrees of freedom. The formulation is applied to various examples for verification and to investigate the effect of selection of different master degrees of freedom for this element type on the results.

The Rotordynamic Coefficients of Mechanical Seals Having Two Flexibly Mounted Rotors

1991 ◽  
Vol 113 (4) ◽  
pp. 795-804 ◽  
Author(s):  
J. Wileman ◽  
I. Green
Keyword(s):  
Degrees Of Freedom ◽  
Reynolds Equation ◽  
Mechanical Seal ◽  
Mechanical Seals ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Rotating Shafts ◽  
Stiffness And Damping ◽  
Three Degrees Of Freedom ◽  
Degenerate Cases

The Reynolds equation is derived for a mechanical seal in which both elements are flexibly mounted to rotating shafts. Stiffness and damping coefficients for the fluid film are calculated for the three degrees of freedom of each element based upon a small perturbation analysis. The analogous coefficients for simpler configurations (e.g., flexibly mounted rotor, flexibly mounted stator) contained in the literature are shown to be obtainable as degenerate cases of the more general results presented in this work.

Optimum Positioning of Tank Mountings in a Fixed Tank Vehicle

Volume 2 ◽  
2004 ◽  
Author(s):  
Dimitris Koulocheris ◽  
Vasilis Dertimanis ◽  
Constantinos Spentzas
Keyword(s):  
Degrees Of Freedom ◽  
Rotational Acceleration ◽  
Six Degrees Of Freedom ◽  
Car Model ◽  
Damping Characteristics ◽  
Geometrical Constraints ◽  
Critical Characteristics ◽  
Stiffness And Damping ◽  
Quasi Newton ◽  
Newton's Methods

This paper aims at optimizing some critical characteristics of a fixed-tank biaxial vehicle, with respect to the lateral performance of the installed tank. For the description of the fixed-tank vehicle, a linear half car model with six degrees of freedom is implemented, subject to many types of road irregularities. The relative position of the tank mountings, with respect to the vehicle frame, as well as their corresponding stiffness and damping characteristics are optimized, such that the maximum values of vertical and rotational acceleration of the tank are minimized, under the geometrical constraints of the vehicle. For the optimization tasks, the BFGS quasi-Newton and the (μ+λ)-Evolution Strategy methods have been implemented. The former outperforms conventional Newton’s methods, due to the secant approximation of the Hessian, while the latter has been shown to perform better in many engineering applications, compared to other categories of EA.

Control of processing at multi-tool two-support setup

2020 ◽  
pp. 67-73
Author(s):  
N.D. YUsubov ◽  
G.M. Abbasova
Keyword(s):  
Degrees Of Freedom ◽  
Factor Model ◽  
Angular Displacement ◽  
Factor Models ◽  
Technological System ◽  
Displacement Control ◽  
Model Accuracy ◽  
Six Degrees Of Freedom ◽  
Angular Displacements ◽  
And Control

The accuracy of two-tool machining on automatic lathes is analyzed. Full-factor models of distortions and scattering fields of the performed dimensions, taking into account the flexibility of the technological system on six degrees of freedom, i. e. angular displacements in the technological system, were used in the research. Possibilities of design and control of two-tool adjustment are considered. Keywords turning processing, cutting mode, two-tool setup, full-factor model, accuracy, angular displacement, control, calculation [email protected]

scholarly journals Magnetic Robots: Small‐Scale Magnetic Actuators with Optimal Six Degrees‐of‐Freedom (Adv. Mater. 23/2021)

2021 ◽  
Vol 33 (23) ◽  
pp. 2170176
Author(s):  
Changyu Xu ◽  
Zilin Yang ◽  
Guo Zhan Lum
Keyword(s):  
Degrees Of Freedom ◽  
Small Scale ◽  
Magnetic Actuators ◽  
Six Degrees Of Freedom

scholarly journals Design and Calibration of a Hall Effect System for Measurement of Six-Degree-of-Freedom Motion within a Stacked Column

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3740
Author(s):  
Olafur Oddbjornsson ◽  
Panos Kloukinas ◽  
Tansu Gokce ◽  
Kate Bourne ◽  
Tony Horseman ◽  
...  
Keyword(s):  
Hall Effect ◽  
Degrees Of Freedom ◽  
Reactor Core ◽  
Degree Of Freedom ◽  
Life Extension ◽  
Scale Model ◽  
Design Development ◽  
Seismic Safety ◽  
Six Degrees Of Freedom ◽  
Six Degree Of Freedom

This paper presents the design, development and evaluation of a unique non-contact instrumentation system that can accurately measure the interface displacement between two rigid components in six degrees of freedom. The system was developed to allow measurement of the relative displacements between interfaces within a stacked column of brick-like components, with an accuracy of 0.05 mm and 0.1 degrees. The columns comprised up to 14 components, with each component being a scale model of a graphite brick within an Advanced Gas-cooled Reactor core. A set of 585 of these columns makes up the Multi Layer Array, which was designed to investigate the response of the reactor core to seismic inputs, with excitation levels up to 1 g from 0 to 100 Hz. The nature of the application required a compact and robust design capable of accurately recording fully coupled motion in all six degrees of freedom during dynamic testing. The novel design implemented 12 Hall effect sensors with a calibration procedure based on system identification techniques. The measurement uncertainty was ±0.050 mm for displacement and ±0.052 degrees for rotation, and the system can tolerate loss of data from two sensors with the uncertainly increasing to only 0.061 mm in translation and 0.088 degrees in rotation. The system has been deployed in a research programme that has enabled EDF to present seismic safety cases to the Office for Nuclear Regulation, resulting in life extension approvals for several reactors. The measurement system developed could be readily applied to other situations where the imposed level of stress at the interface causes negligible material strain, and accurate non-contact six-degree-of-freedom interface measurement is required.

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