scholarly journals Numerical Analysis on Chaotic Vibration of Drive System for a Movable Tooth Piezoelectric Motor

2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Chong Li ◽  
Jichun Xing ◽  
Jiwen Fang ◽  
Zhong Zhao
Keyword(s):  
Numerical Analysis ◽  
Drive System ◽  
Dynamic Equations ◽  
Piezoelectric Motor ◽  
Mesh Stiffness ◽  
System Parameters ◽  
Chaotic Vibrations ◽  
Chaotic Vibration ◽  
Nonlinear Dynamic Equations ◽  
Wave Generator

The nonlinear dynamic equations of the drive system for movable tooth piezoelectric motor are established. Using these equations, the chaotic vibrations of the system are investigated. The results show that chaotic vibrations occur in the movable tooth drive system under some parameters. The average mesh stiffness, theoretical radius, and wave generator offset significantly influence the nonlinear chaotic vibrations of the drive system of the movable tooth piezoelectric motor. The ranges for the system parameters that lead to a motor with bad dynamics are shown. The results can be used to predict the dynamic load and optimize power density of the proposed piezoelectric motor.

Nonlinear Dynamics Analysis of Gear System Considering Unbalance and Loosening Faults

2014 ◽  
Vol 875-877 ◽  
pp. 1976-1981 ◽  
Author(s):  
Li Cui ◽  
Da Fang Shi ◽  
Jian Rong Zheng ◽  
Xiao Guang Song
Keyword(s):  
Nonlinear Dynamic ◽  
Gear System ◽  
Dynamic Equations ◽  
Radial Clearance ◽  
Nonlinear Dynamic Model ◽  
Mesh Stiffness ◽  
Diverse Range ◽  
Runge Kutta Method ◽  
Nonlinear Dynamic Equations ◽  
Chaos Motion

Considering backlash, radial clearance of bearing and time-varying mesh stiffness, nonlinear dynamic model of gear bearing rotor system is established considering unbalance and loosening fault. Nonlinear dynamic equations are solved using Runge-Kutta method and Newton-Raphson method. Numerical simulations of the dynamic equations and the affection of the depth of crack and length of wear to the nonlinear dynamic behavior are studied. The results shows that tooth off, bilateral impact phenomenon are occurred, with increasing gear failure when unbalance occurs, and the gear system exhibits a diverse range of periodic, quasi-periodic and chaotic motion. When loosening fault occurs, the range of chaos motion is increased, and gear burnishing is also intensified.

scholarly journals Natural Frequencies and Vibrating Modes for a Magnetic Planetary Gear Drive

2012 ◽  
Vol 19 (6) ◽  
pp. 1385-1401 ◽  
Author(s):  
Lizhong Xu ◽  
Xuejun Zhu
Keyword(s):  
Natural Frequencies ◽  
Planetary Gear ◽  
Drive System ◽  
Dynamic Equations ◽  
The Sun ◽  
System Parameters ◽  
Meshing Stiffness ◽  
Torsion Mode ◽  
Gear Drive ◽  
Pair Number

In this paper, a dynamic model for a magnetic planetary gear drive is proposed. Based on the model, the dynamic equations for the magnetic planetary gear drive are given. From the magnetic meshing forces and torques between the elements for the drive system, the tangent and radial magnetic meshing stiffness is obtained. Using these equations, the natural frequencies and the modes of the magnetic planetary gear drive are investigated. The sensitivity of the natural frequencies to the system parameters is discussed. Results show that the pole pair number and the air gap have obvious effects on the natural frequencies. For the planetary gear number larger than two, the vibrations of the drive system include the torsion mode of the center elements, the translation mode of the center elements, and the planet modes. For the planetary gear number equal to two, the planet mode does not occur, the crown mode and the sun gear mode occur.

Nonlinear Free Vibration for Electromechanical Integrated Toroidal Drive

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Lizhong Xu ◽  
Fen Wang ◽  
Xiuhong Hao
Keyword(s):  
Operating Performance ◽  
Free Vibrations ◽  
Drive System ◽  
Vibration Frequencies ◽  
Mesh Stiffness ◽  
Nonlinear Free Vibration ◽  
System Parameters ◽  
Noise Radiation ◽  
Electromechanical Integrated ◽  
Electromechanical Coupled

Electromechanical integrated toroidal drive is an electromechanical coupled dynamics system. Here, the electromagnetic nonlinearity occurs which has important effects on the operating performance of the drive system. In this paper, the electromagnetic mesh stiffness is presented and nonlinear electromechanical coupled dynamic equations are deduced. Using the perturbation method, the nonlinear free vibrations of the drive system are investigated. Changes of the nonlinear vibration frequencies along with the system parameters are given. Results show that the electromagnetic nonlinearity has obvious effects on the vibration frequencies of the drive system. The results are useful in maximizing the power density of the drive system and reducing noise radiation.

Recognition of Neurons Impulses with the Use of Nonlinear Dynamic Equations

2001 ◽  
Vol 33 (5-8) ◽  
pp. 10
Author(s):  
Tatyana I. Aksenova ◽  
Igor V. Tetko ◽  
Olga K. Chibirova ◽  
Alexandro Villa
Keyword(s):  
Nonlinear Dynamic ◽  
Dynamic Equations ◽  
Nonlinear Dynamic Equations

scholarly journals Nonlinear Forced Response of Electromechanical Integrated Toroidal Drive to Coupled Excitation

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Lizhong Xu ◽  
Fen Wang
Keyword(s):  
Natural Frequencies ◽  
Forced Response ◽  
Drive System ◽  
Mesh Stiffness ◽  
Electric Excitation ◽  
Time Period ◽  
Electromechanical Integrated ◽  
Exciting Frequency ◽  
Mesh Parameter ◽  
Forced Responses

The electric excitation and the parameter excitation from mesh stiffness fluctuation are analyzed. The forced response equations of the drive system to the coupled excitations are presented. For the exciting frequencies far from and near natural frequencies, the forced responses of the drive system to the coupled excitations are investigated. Results show that the nonlinear forced responses of the drive system to the coupled excitations change periodically and unsteadily; the time period of the nonlinear forced responses depends on the frequencies of the electric excitation, the mesh parameter excitation, and the nonlinear natural frequencies of the drive system; in order to improve the dynamics performance of the drive system, the frequencies of the electric excitations should not be taken as integral multiple of the mesh parameter exciting frequency.

scholarly journals Application of the dynamic Lorentz model to modeling the motion of a rigid body

2021 ◽  
pp. 32-36
Author(s):  
Nikolay Makeyev ◽  
Keyword(s):  
Dynamical System ◽  
Qualitative Research ◽  
Rigid Body ◽  
Body Motion ◽  
Dynamic Equations ◽  
Lorentz Model ◽  
Dissipative Forces ◽  
System Parameters ◽  
Phase Trajectories ◽  
Inertia Forces

A qualitative research of the field of phase trajectories of the system of dynamic equations of an absolutely rigid body was carried out, moving around the selected pole under the influence of gyroscopic, dissipative forces and Coriolis inertia forces. The equations of body motion are reduced to a dynamical system generating a Lorentz attractor. Under parametric constraints imposed on the equations of a dynamical system, the structure of its phase trajectories is described depending on the values of the system parameters.

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