On the Choice of Shape Functions of Unsymmetrical Elastic Rotors

2013 ◽  
Vol 332 ◽  
pp. 325-330
Author(s):  
Herbert Parzer ◽  
Hubert Gattringer ◽  
Stefan Hubinger
Keyword(s):  
Permanent Magnet ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Permanent Magnet Synchronous Motor ◽  
Spur Gear ◽  
Gear Pair ◽  
Shape Functions ◽  
Rigid Disks ◽  
Projection Equation

In this paper the effects of rotordynamics under the aspect of the choice of shape functions are discussed. For this purpose a rotor system which consists of a slim shaft and two rigid disks is modeled using the Projection Equation. The shaft is assumed as an elastic Euler-Bernoulli beam, supported by two bearings modeled as radial spring systems. The rotor is driven by a permanent-magnet synchronous motor whose torque is transmitted with a spur gear pair next to one of the bearings. A Ritz approach is used to separate the elastic displacements in position and time, thereby different shape functions are evaluated. Approximated eigenfunctions are computed and used as shape functions as well. For validation, the eigenfrequencies are compared with semi-analytical ones, calculated with the Transfer-Matrix-Method and experimental results. The insights obtained from this work should make it easier to choose the appropriate shape functions for such problems.

Whole Transfer Matrix Method for the Critical Speeds of Skew Gear Transmission System

2011 ◽  
Vol 383-390 ◽  
pp. 5474-5478
Author(s):  
Xian Yue Gang ◽  
Shan Chai
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Transmission System ◽  
Gear Transmission ◽  
Inertia Force ◽  
Gear Pair ◽  
Critical Speeds ◽  
Gear Transmission System ◽  
Six Dof

Whole transfer matrix method is a powerful tool for calculating the critical speeds of multi-rotor system. With vector algebra, the six DOF relative displacement of a skew gear pair is deduced, then exciting force and moment generated by engagement force is calculated. By summing the inertia force and engagement loads, the whole transfer matrix of a skew gear pair is established. A numerical example illustrated the effect of different gear parameters on the critical speeds of the gear transmission system.

The transfer matrix method for lattice proteins—an application with cooperative interactions

Polymer ◽  
2004 ◽  
Vol 45 (2) ◽  
pp. 707-716 ◽  
Author(s):  
Andrzej Kloczkowski ◽  
Taner Z. Sen ◽  
Robert L. Jernigan
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Cooperative Interactions ◽  
Lattice Proteins

A Modified Transfer Matrix Method for Asymmetric Rotor-Bearing Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 309-317 ◽  
Author(s):  
Yuan Kang ◽  
An-Chen Lee ◽  
Yuan-Pin Shih
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Harmonic Balance Method ◽  
Continuous System ◽  
Euler Beam ◽  
Rotating Shaft ◽  
Rotor Bearing ◽  
Asymmetric Rotor ◽  
Steady State Responses

A modified transfer matrix method (MTMM) is developed to analyze rotor-bearing systems with an asymmetric shaft and asymmetric disks. The rotating shaft is modeled by a Rayleigh-Euler beam considering the effects of the rotary inertia and gyroscopic moments. Specifically, a transfer matrix of the asymmetric shaft segments is derived in a continuous-system sense to give accurate solutions. The harmonic balance method is incorporated in the transfer matrix equations, so that steady-state responses of synchronous and superharmonic whirls can be determined. A numerical example is presented to demonstrate the effectiveness of this approach.

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