Nonlinear Dynamic Characteristics of Compound Planetary Gear Train Sets Based on Harmonic Balance Method

2011 ◽  
Vol 47 (01) ◽  
pp. 55 ◽  
Author(s):  
Shijing WU
Keyword(s):  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Planetary Gear ◽  
Balance Method ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Nonlinear Dynamic Characteristics

Harmonic Balance Method for Nonlinear Vibration of Compound Planetary Gear Sets

2015 ◽  
Author(s):  
Weilin Zhu ◽  
Shijing Wu ◽  
Xiaosun Wang
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Planetary Gear ◽  
Response Characteristic ◽  
Transmission Error ◽  
Balance Method ◽  
Time Varying ◽  
Algebraic Equations ◽  
Gear Backlash ◽  
Planetary Gear Sets

In this paper, a new nonlinear time-varying dynamic model for compound planetary gear sets, which incorporates the time-varying meshing stiffness, transmission errors and gear backlash, has been presented. The harmonic balance method (HBM), which is an analytical approach widely used for nonlinear oscillators, is employed to investigate the dynamic characteristics of the gear sets. The matrix form iteration algebraic equations has been established and solved by HBM and single rank inverse Broyden method to reveal the effect of transmission error and gear backlash on the frequency response characteristic of the system. Sub-harmonic resonant, super-harmonic resonant and jump phenomenon have been illustrated by several examples.

Effects of Temperature on the Time-Varying Mesh Stiffness, Vibration Response, and Support Force of a Multi-Stage Planetary Gear

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Hui Liu ◽  
Pengfei Yan ◽  
Pu Gao
Keyword(s):  
Temperature Change ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Thermal Deformation ◽  
Planetary Gear ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Vibration Displacement ◽  
Influence Of Temperature ◽  
Nonlinear Dynamic Characteristics

Abstract The thermal deformation of gears will affect the vibration of the planetary system; this research mainly studied the effect of thermal conditions on planetary systems nonlinear vibration under the thermal equilibrium state. To study the influence of gear temperature on the planetary gear system, a nonlinear dynamic model considering thermal deformation was established. The mathematical expression of the thermal time-varying mesh stiffness (TTVMS) varied with temperature, and the backlash caused by the temperature change was also computed. The influence of temperature on the TTVMS was investigated. The calculation results indicated that the methods used to determine the TTVMS and backlash of gear pairs were effective, and the trends of the change in the nonlinear dynamic characteristics with temperature were obtained. According to the fast Fourier transform (FFT) spectrums and root-mean-square (RMS) analysis, the influence of temperature change on the nonlinear dynamic characteristics of the system was analyzed. When the temperature was lower than 80 °C, the vibration displacement and the supporting shaft load remained unchanged or decreased. Once the temperature was higher than 80 °C, the vibration displacement and load of the system were strengthened.

scholarly journals Nonlinear dynamic characteristics of planetary gear transmission system considering squeeze oil film

2020 ◽  
pp. 146134842093566
Author(s):  
Jingyue Wang ◽  
Ning Liu ◽  
Haotian Wang ◽  
Lixin Guo
Keyword(s):  
Dynamic Characteristics ◽  
Chaotic Motion ◽  
Nonlinear Dynamic ◽  
Excitation Frequency ◽  
Planetary Gear ◽  
High Excitation ◽  
Gear Transmission System ◽  
Nonlinear Dynamic Characteristics ◽  
Period Motion ◽  
Lubricant Viscosity

Based on the planetary gear transmission system considering the coupling effects of friction and elastohydrodynamic lubrication, a torsional dynamic model considering friction, oil film, time-varying meshing stiffness, meshing damping, and gear backlash is established. The Runge–Kutta numerical method is used to solve the vibration equation of the system. The bifurcation diagram and largest Lyapunov exponent are used to analyze the dynamic characteristics of the system under different bifurcation parameters such as the excitation frequency, lubricant viscosity, sun–planet backlash, and planet–ring backlash. The numerical results demonstrate that with the increase of excitation frequency, the system exhibits rich nonlinear dynamic characteristics such as short-period motion, long-period motion, and chaotic motion. With the increase of lubricant viscosity, the chaotic motion of the system is suppressed at low excitation frequency and the periodic motion of the system increases at high excitation frequency. With the increase of sun–planet backlash, the chaotic motion of the system increases at low excitation frequency, and the bifurcation characteristics become complicated at high excitation frequency and enters chaotic motion in advance. With the increase of ring–planet backlash, the system delays into chaotic motion at low excitation frequency and bifurcates from single-period motion to multi-period motion in advance at high excitation frequency.

scholarly journals Nonlinear Dynamic Behaviour Analysis of a Clutch System with Uncertainties Using Polynomial Chaos and the Constrained Harmonic Balance Method

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
M.-H. Trinh ◽  
S. Berger ◽  
E. Aubry
Keyword(s):  
Limit Cycles ◽  
Nonlinear Dynamic ◽  
Harmonic Balance ◽  
Dynamic Behaviour ◽  
Polynomial Chaos ◽  
Equilibrium Points ◽  
Harmonic Balance Method ◽  
Unstable Equilibrium ◽  
Balance Method ◽  
Clutch System

The study of the nonlinear dynamic behaviour of friction systems in general and of clutch systems in particular remains an open problem. Noise and vibrations induced by friction in the sliding phase of a clutch are very sensitive to design parameters. The latter have significant dispersions. In the study of the system stability, the problem is not only to know if the parameter values lead to the appearance of unstable equilibrium points; the real challenge lies in estimating the vibration levels when such unstable equilibrium points occur. This estimation is analyzed using the limit cycles. This article aims to study the ability of robust approaches based on developments in nonintrusive generalized polynomial chaos and a constrained harmonic balance method to estimate the vibration levels through the limit cycles of a clutch system in the presence of uncertainty. The purpose is to provide a low-cost, high precision approach, compared to the classic Monte Carlo method.

scholarly journals Multi-level residue harmonic balance method for nonlinear vibration of the beam

2021 ◽  
pp. 146134842110384
Author(s):  
Abu SMZ Hasan ◽  
M S Rahman
Keyword(s):  
Dynamic System ◽  
Nonlinear Vibration ◽  
Nonlinear Dynamic ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Nonlinear Dynamic System ◽  
Balance Method ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Multi Level

This study presents the nonlinear vibration and chaotic response of a beam subjected to harmonic excitation. The multi-level residue harmonic balance method is applied to solve the geometrically cubic nonlinear vibration of the simply supported beam. The obtained results agree well with those of the numerical integration method. The amplitude frequency response curves are presented to illustrate the nonlinear dynamic system response both for a damping and without damping model. Also, the chaotic response is examined for a simply supported beam with a nonlinear dynamic system.

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