The application of extended permutation-inversion groups to internal rotation of a symmetric rotor top in a symmetric or asymmetric rotor molecule

1983 ◽  
Vol 98 (2) ◽  
pp. 375-391 ◽  
Author(s):  
Jon T Hougen ◽  
Benjamin M DeKoven
Keyword(s):  
Internal Rotation ◽  
Symmetric Rotor ◽  
Asymmetric Rotor

Nonparametric Stochastic Modeling of Uncertainty in Rotordynamics

2009 ◽  
Author(s):  
Raghavendra Murthy ◽  
Marc P. Mignolet ◽  
Aly El-Shafei
Keyword(s):  
Stochastic Modeling ◽  
Dynamic Systems ◽  
Stiffness Matrix ◽  
Physical Structure ◽  
Mode Shapes ◽  
Rational Approach ◽  
Structural Dynamic ◽  
Symmetric Rotor ◽  
Asymmetric Rotor ◽  
Rotor Stiffness

A systematic and rational approach is presented for the consideration of uncertainty in rotordynamics systems, i.e. in rotor mass and gyroscopic matrices, stiffness matrix, and bearing coefficients. The approach is based on the nonparametric stochastic modeling technique which permits the consideration of both data and modeling uncertainty. The former is induced by a lack of exact knowledge of properties such as density, Young’s modulus, etc. The latter occurs in the generation of the computational model from the physical structure as some of its features are invariably ignored, e.g. small anisotropies, or approximately represented, e.g. detailed meshing of gears. The nonparametric stochastic modeling approach, which is briefly reviewed first, introduces uncertainty in reduced order models through the randomization of their system matrices (e.g. stiffness, mass, and damping matrices of nonrotating structural dynamic systems). Here, this methodology is first extended to permit the consideration of uncertainty in symmetric and asymmetric rotor dynamic systems. Its application is next demonstrated on a symmetric rotor on linear bearings and uncertainties on the rotor stiffness (stiffness matrix) and/or mass properties (mass and gyroscopic matrices) are introduced that maintain the symmetry of the rotor. The effects of these uncertainties on the Campbell diagram, damping ratios, mode shapes, forced unbalance response, and oil whip instability threshold are analyzed. The generalization of these concepts to uncertainty in the bearing coefficients is achieved next. Finally, the consideration of uncertainty in asymmetric rotors is addressed and exemplified.

Study on the Dynamic Response of an Unbalanced Rotor System Supported by Ball Bearings

2019 ◽  
Author(s):  
Bin Fang ◽  
Jinhua Zhang ◽  
Ke Yan ◽  
Jun Hong
Keyword(s):  
Dynamic Model ◽  
Ball Bearing ◽  
Great Influence ◽  
Rotor System ◽  
Dynamic Responses ◽  
Ball Bearings ◽  
Motion Patterns ◽  
Symmetric Rotor ◽  
Asymmetric Rotor ◽  
Restoring Forces

Abstract This paper proposed a new four-degree-of-freedom dynamic model of the bearing-rotor system based on ball bearing without Raceway Control Hypothesis, and both the inertia forces of balls and the tilting motions of rotor are fully considering in the calculation of restoring forces and moments of ball bearings. Then the dynamic model are solved by the fourth-step Runge-Kutta method, and the dynamic responses of rotor system including the displacement, velocity and center orbits are obtained, and the influences of rotating speeds, eccentricity and symmetry of rotor are studied and analyzed. The results show that both the varying compliance of ball bearing and rotor eccentric force have a great influence on the dynamic responses and motion patterns of bearing-rotor system, and the titling motion of bearing-rotor should be considered in the analysis of asymmetric rotor or the symmetric rotor under some specific conditions.

Zur Störung der Rotationsenergie des asymmetrischen Kreisels durch in den Drehimpulskomponenten lineare Glieder, insbesondere bei interner Rotation

1966 ◽  
Vol 21 (6) ◽  
pp. 694-696 ◽  
Author(s):  
Heinz Dieter Rudolph
Keyword(s):  
Angular Momentum ◽  
Fine Structure ◽  
Internal Rotation ◽  
Second Order ◽  
Absorption Lines ◽  
Methyl Groups ◽  
Rigid Rotor ◽  
Asymmetric Rotor ◽  
Line Strengths

Attention is drawn to the fact that perturbing terms to the HAMILTONian of the asymmetric rigid rotor molecule which are linear in the operators of angular momentum components may be evaluated to second order in the asymmetric rotor basis with the help of published line strengths tables. The usefulness is demonstrated by means of an example where the hindering potential for the internal rotation of the two methyl groups in acetone is calculated from a certain splitting in the quartet torsional fine structure of rotational absorption lines.

scholarly journals Millimeter Wave Spectroscopy of Ne-CO

2000 ◽  
Vol 55 (9-10) ◽  
pp. 754-758 ◽  
Author(s):  
D. A. Roth ◽  
I. Pak ◽  
L. A. Surin ◽  
B. S. Dumeshb ◽  
G. Winnewisser
Keyword(s):  
Millimeter Wave ◽  
High Sensitivity ◽  
Data Set ◽  
Pulsed Jet ◽  
Wave Measurements ◽  
Millimeter Wave Spectroscopy ◽  
Symmetric Rotor ◽  
Type Spectrum ◽  
Asymmetric Rotor ◽  
Global Fit

Abstract The pure rotational b-type spectrum of the van der Waals complex Ne-CO has been measured using a pulsed jet, intracavity millimeter wave spectrometer. The millimeter wave generation is based on the OROTRON principle. The high sensitivity of the spectrometer allowed measurements of R(J), K = 1 ← 0 transitions between 108 and 150 GHz of the Ne isotopomers 20 Ne-CO and 22 Ne-CO. This new millimeter wave data set together with the microwave data in the literature, i.e. a-type microwave transitions, yield in a fit to an asymmetric rotor a reliable set of ground state constants. These are for 20 Ne-CO: A = 107127.021(14) MHz, B = 3479.6597(95) MHz, and C = 3039.5387(93) MHz. For both 20 Ne-CO and 22 Ne-CO, a global fit to a near-symmetric rotor was performed, taking into account the infrared and microwave transition frequencies from the literature and the millimeter wave measurements of the present work.

New Method of Studying Internal Rotation in a Symmetric Rotor

1978 ◽  
Vol 41 (16) ◽  
pp. 1109-1112 ◽  
Author(s):  
W. L. Meerts ◽  
I. Ozier
Keyword(s):  
Internal Rotation ◽  
New Method ◽  
Symmetric Rotor

Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan & Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

Legal Update: North Dakota Supreme Court: Third Edition of Guides is “Most Current”

1999 ◽  
Vol 4 (1) ◽  
pp. 6-7
Author(s):  
James J. Mangraviti
Keyword(s):  
Internal Rotation ◽  
External Rotation ◽  
Measurement Techniques ◽  
Fourth Edition ◽  
Hip Motion ◽  
The Difference ◽  
The Right ◽  
Hip Flexion ◽  
Hip Rotation ◽  
Hip Extension

Abstract The accurate measurement of hip motion is critical when one rates impairments of this joint, makes an initial diagnosis, assesses progression over time, and evaluates treatment outcome. The hip permits all motions typical of a ball-and-socket joint. The hip sacrifices some motion but gains stability and strength. Figures 52 to 54 in AMA Guides to the Evaluation of Permanent Impairment (AMA Guides), Fourth Edition, illustrate techniques for measuring hip flexion, loss of extension, abduction, adduction, and external and internal rotation. Figure 53 in the AMA Guides, Fourth Edition, illustrates neutral, abducted, and adducted positions of the hip and proper alignment of the goniometer arms, and Figure 52 illustrates use of a goniometer to measure flexion of the right hip. In terms of impairment rating, hip extension (at least any beyond neutral) is irrelevant, and the AMA Guides contains no figures describing its measurement. Figure 54, Measuring Internal and External Hip Rotation, demonstrates proper positioning and measurement techniques for rotary movements of this joint. The difference between measured and actual hip rotation probably is minimal and is irrelevant for impairment rating. The normal internal rotation varies from 30° to 40°, and the external rotation ranges from 40° to 60°.

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