Research nonlinear vibrations of a dual-rotor system with nonlinear restoring forces
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(2020) 42:461
TECHNICAL PAPER
Research nonlinear vibrations of a dual‑rotor system with nonlinear restoring forces Jun Liu1 · Chang Wang1 · Zhiwei Luo2 Received: 1 October 2019 / Accepted: 30 July 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract A dual-rotor system is a core component of an aero-engine, and it is very important to study the nonlinear vibrational characteristics for the aero-engine’s development. Based on analyzing structural characteristics of aero-engine’s rotors, a novel and more practical dual-rotor dynamic coupling model with nonlinear restoring forces of high-pressure and low-pressure rotors is first proposed. In the linear dynamic coupling model, the coupling critical speed, natural frequencies and vibration responses of the low-pressure rotor are analyzed systematically. In the nonlinear dynamic coupling model, the vibrational characteristics of the dual-rotor system with different nonlinear parameters are simulated numerically based on the nonlinear dynamic theory. The improved shooting method combined the harmonic balance method, and the genetic algorithm is proposed to calculate theoretical solutions of the nonlinear dynamic coupling model. The stability of theoretical solutions is investigated by the Floquet theory. The research results show that the dual-rotor system appears very complicated nonlinear vibrations such as nonlinear multitudinal solutions, double period motions, almost periodic motions and chaotic motions. The transition between nonlinear vibrations occurs suddenly. Keywords Dual-rotor system · Nonlinear restoring forces · Dynamic coupling model · Nonlinear vibrations · Chaotic motions List of symbols xi, yi Displacement in x and y directions ri Radial deflection of the rotor θx, θy Inclination of the lowpressure rotor in x and y directions Technical Editor: Thiago Ritto. * Jun Liu [email protected] Chang Wang [email protected] Zhiwei Luo [email protected]‑u.ac.jp 1
Tianjin Key Laboratory of the Design and Intelligent Control of the Advanced Mechanical System, National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin 300384, China
Department of Computational Science Graduate School of System Informatics, KOBE University, 657‑8501 Kobe, Japan
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θ, θ1 Inclination angle of the shaft at the position of the disk, Euler angle representing an inclination of the Z1-axis mi Mass of the dual rotor ei, τ Eccentricity of the dual rotor, skew angle of the low-pressure rotor I, Ip Moment of inertia of the low-pressure shaft, polar moment of inertia of the lowpressure disk c11, c12, c21, c22, c Damping coefficients of the dual rotor α, γ, δ, k Stiffness coefficients of the dual rotor βτ Inclination initial value of the low-pressure rotor
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Vol.:(0123456789)
461
Page 2 of 20
Journal of the Brazilian Society of Mechanical Sciences and Engineering
ωi, ωLj, ωH, ω Rotating speed of the dual rotor, major critical speed of the low-pressure rotor,
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