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.

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.

Internal Resonance Analysis for Electromechanical Integrated Toroidal Drive

2010 ◽  
Vol 5 (4) ◽  
Author(s):  
Xiuhong Hao Lizhong Xu
Keyword(s):  
Free Vibration ◽  
Internal Resonance ◽  
Energy Exchange ◽  
Forced Response ◽  
Drive System ◽  
Design Stage ◽  
Internal Resonances ◽  
Resonance Analysis ◽  
Electromechanical Integrated ◽  
Electromechanical Coupled

In this paper, the electromechanical coupled nonlinear equations for the electromechanical integrated toroidal drive are proposed. Using the equations, the free vibration and forced response under internal resonance are investigated. The effects of the drive parameters on the resonance are investigated. Three different resonance types exist for the different drive parameters. They are the normal resonance, internal resonance, and jump vibration between the normal and internal resonances. Compared with the normal resonance without internal resonance, the internal resonance has a large amplitude and the energy exchange occurs between the vibrations of the different components. The resonance types of the drive system are dependent on the electromechanical parameters of the drive system. In the design stage, one can select properly the electromechanical parameters of the drive system to remove the internal resonance and the jump vibration.

LATERAL-FLEXURAL AND TORSIONAL VIBRATIONS OF FLEXIBLE RING FOR ELECTROMECHANICAL INTEGRATED ELECTROSTATIC HARMONIC ACTUATOR

2009 ◽  
Vol 09 (03) ◽  
pp. 391-409
Author(s):  
LIZHONG XU ◽  
YAOWU LI
Keyword(s):  
Natural Frequency ◽  
Dynamic Equation ◽  
Forced Response ◽  
Dynamic Responses ◽  
Torsional Vibrations ◽  
Vibration Modes ◽  
System Parameters ◽  
Electromechanical Integrated ◽  
Flexible Ring ◽  
Electromechanical Coupled

This paper presents an electromechanical coupled dynamic equation for the lateral-flexural and torsional vibrations of a flexible ring for an electromechanical integrated electrostatic harmonic actuator as well as the equation of the forced response of the electromechanical integrated electrostatic harmonic actuator to voltage excitation. By solving these equations, the natural frequency and vibration modes of the flexible ring for the actuator are investigated. Changes in the natural frequency with respect to the main system parameters are also examined and the dynamic responses of the actuator to voltage excitation obtained.

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.

Forced Response of Electromechanical Integrated Electrostatic Harmonic Drive to Voltage Excitation

2007 ◽  
Author(s):  
Lizhong Xu ◽  
Cuirong Zhu ◽  
Lei Qin ◽  
Yanling Zao
Keyword(s):  
Forced Response ◽  
Drive System ◽  
Harmonic Drive ◽  
Frequency Responses ◽  
Electromechanical Integrated ◽  
Generalized Force ◽  
Electric Field Force ◽  
Exciting Voltage ◽  
Generalized Coordinate ◽  
Electromechanical Coupled

In this paper, a micro electromechanical integrated electrostatic harmonic drive system is presented. The operating principle of the MEMS is introduced. The exciting electric field force under exciting voltage is given. Based on the electromechanical coupled dynamic equations of the drive system, by generalized force and generalized coordinate, the forced response of the drive system to voltage excitation are obtained. The forced frequency responses of the drive system to voltage excitation are investigated. Changes of the frequency response along with the system parameters are given as well.

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

scholarly journals Effects of Eccentricity on the Dynamic Behavior for Electromechanical Integrated Toroidal Drive

2013 ◽  
Vol 20 (2) ◽  
pp. 273-286 ◽  
Author(s):  
Lizhong Xu ◽  
Haifeng Li
Keyword(s):  
Dynamic Behavior ◽  
Natural Frequencies ◽  
Drive System ◽  
The Other ◽  
Dynamic Equations ◽  
Electromechanical Integrated ◽  
Drive Systems ◽  
Forced Responses ◽  
Design And Manufacture ◽  
Center Distance

In electromechanical integrated toroidal drive, eccentric center errors occur which has important influences on the dynamic behavior of the drive system. Here, the dynamic equations of the drive system with eccentric center are presented. Changes of the natural frequencies and vibrating modes along with eccentric center distance are analyzed. The forced responses of the drive system to eccentric center excitation are investigated. Results show that the eccentric center causes some natural frequencies to increase, and the other natural frequencies to drop. It also causes some vibrations to become weak, and the other vibrations to become strong. The eccentric center has more obvious effects on the dynamic behavior of the planets. The results are useful in design and manufacture of the drive systems.

Experiments on Quasiperiodic Wheel Shimmy

2009 ◽  
Vol 4 (3) ◽  
Author(s):  
Dénes Takács ◽  
Gábor Stépán
Keyword(s):  
Vehicle Dynamics ◽  
Vibration Frequencies ◽  
Lateral Vibration ◽  
Laboratory Measurements ◽  
Stability Boundaries ◽  
System Parameters ◽  
Quasiperiodic Oscillation ◽  
Delay Effects ◽  
Tire Models ◽  
Wheel Shimmy

The lateral vibration of towed wheels—so-called shimmy—is one of the most exciting phenomena of vehicle dynamics. We give a brief description of a simple rig of elastic tire that was constructed for laboratory measurements. A full report is given on the experimental investigation of this rig from the identification of system parameters to the validation of stability boundaries and vibration frequencies of shimmy motion. The experimental results confirm the validity of those tire models that include delay effects. A peculiar quasiperiodic oscillation detected during the experiments is explained by numerical simulations of the nonlinear time-delayed mathematical model.

The Three-Dimensional Dynamics for Toroidal Drive

2012 ◽  
Vol 562-564 ◽  
pp. 536-539
Author(s):  
Li Zhong Xu ◽  
Jin Liang Li ◽  
Ya Jun Li
Keyword(s):  
Natural Frequencies ◽  
Cone Angle ◽  
Three Dimensional ◽  
Drive System ◽  
Vibration Modes ◽  
Mesh Stiffness ◽  
Coupled Modes ◽  
Bearing Stiffness ◽  
Rigid Body Motions ◽  
Half Cone

In this paper, a model to simulate the dynamic behavior of the toroidal drive is developed. The three-dimensional dynamic model includes all six rigid body motions of the stator, worm, rotor and the planets. Using the model, the natural frequencies and vibration modes of the drive system are investigated. The vibration modes are classified into single modes and coupled modes. The single modes include planet mode, worm mode and stator mode. The vibration and frequency characteristics of different modes are obtained. The relation between modes and half cone angle of the planet tooth is discussed. The relation between vibrations and bearing stiffness is also discussed. When the bearing stiffness is about 10 times of the mesh stiffness, some vibration displacements of the drive system are quite small and can be neglected. Meanwhile, the dynamic equations for the drive system can be simplified.

Movement Mechanism Analysis of Electromechanical Worm Drive

2012 ◽  
Vol 490-495 ◽  
pp. 432-436
Author(s):  
Xue Mei Guan ◽  
Li Zhong Xu
Keyword(s):  
Mechanism Analysis ◽  
Harmonic Drive ◽  
Theoretic Analysis ◽  
Output Torque ◽  
Moment Distribution ◽  
Electromechanical Integrated ◽  
Movement Mechanism ◽  
System Output ◽  
Worm Drive ◽  
Electromechanical Coupled

In this study, an electromechanical integrated electromagnetism worm drive is proposed and its operating principle is introduced. The equations of electromechanical coupled force and the systematic output torque for the drive are given by means of electromagnetism harmonic drive and permanent magnet worm drive transmission principle . By using an example to analysis the system output moment distribution. This paper lays the theoretic foundation for deeper theoretic analysis on drive and manufacture technologies study.

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