Reduced-Order Nonlinear Dynamic Model of Coupled Shaft-Torsional and Blade-Bending Vibrations in Rotors

2000 ◽  
Vol 123 (1) ◽  
pp. 82-88 ◽  
Author(s):  
B. O. Al-Bedoor
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Small Deformation ◽  
Nonlinear Dynamic Model ◽  
Bending Vibrations ◽  
Reduced Order ◽  
Lagrange’S Equation ◽  
Multibody Dynamic ◽  
Parametric Studies

In this study, a reduced-order nonlinear dynamic model for shaft-disk-blade unit is developed. The multibody dynamic approach with the small deformation theory for both blade-bending and shaft-torsional deformations is adopted. The equations of motion are developed using Lagrange’s equation in conjunction with the assumed modes method (AMM) for approximating the blade transverse deflection. The model showed strong coupling between the blade bending and shaft torsional vibrations in the form of inertial nonlinearity, modal coupling, stiffening, softening, and parametric excitations. The model is suitable for extensive parametric studies for predesign stage purposes as well as for diagnostics of rotor malfunctions, when blade and shaft torsional vibration interaction is suspected.

Analysis of Tourism Ecology Capacity Based on the Nonlinear Dynamic Model

2009 ◽  
Vol 11 (2) ◽  
pp. 163-168
Author(s):  
Long LV ◽  
Zhenfang HUANG ◽  
Jiang WU
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Model

scholarly journals Rattle dynamics of noncircular face gear under multifrequency parametric excitation

2021 ◽  
Vol 12 (1) ◽  
pp. 361-373
Author(s):  
Dawei Liu ◽  
Zhenzhen Lv ◽  
Guohao Zhao
Keyword(s):  
Dynamic Model ◽  
Parametric Excitation ◽  
Nonlinear Dynamic ◽  
Velocity Ratio ◽  
Harmonic Balance Method ◽  
Transmission Error ◽  
Dynamic Responses ◽  
Discrete Fourier Transformation ◽  
Nonlinear Dynamic Model ◽  
Face Gear

Abstract. A noncircular face gear (NFG) conjugated with a pinion is a new type of face gear which can transmit variable velocity ratio and in which two time-varying excitations exist, namely the meshing stiffness excitation and instantaneous center excitation. Considering the tooth backlash, static transmission error and multifrequency parametric excitation, a nonlinear dynamic model of the NFG pair is presented. Based on the harmonic balance method and discrete Fourier transformation, a semi-analytic approach for the nonlinear dynamic model is given to analyze the dynamic behaviors of the NFG. Results demonstrate that, with increase in the eccentric ratio, input velocity and error amplitude, the NFG will undergo a non-rattle, unilateral rattle and bilateral rattle state in succession, and a jump phenomenon will appear in the dynamic responses when the rattle state of the gears is transformed from unilateral rattle to bilateral rattle.

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