scholarly journals Free Vibration for an Electromagnetic Harmonic Movable Tooth Drive System

2015 ◽  
Vol 9 (1) ◽  
pp. 15-21 ◽  
Author(s):  
Yongli Liang ◽  
Lizhong Xu
Keyword(s):  
Natural Frequencies ◽  
Coupled System ◽  
Drive System ◽  
Vibration Modes ◽  
Electrical Parameters ◽  
Static Displacement ◽  
Coil Current ◽  
Coupled Dynamics ◽  
Flexible Ring ◽  
Electromechanical Coupled

The authors proposed an electromagnetic harmonic movable tooth drive system which is an electromechanical coupled system where the coupled dynamics controls its overall operating behavior. However, the coupled dynamics of such a system was not found in the literature. In this paper, an electromechanical coupled dynamics equation of the flexible ring subjected to electromagnetic force is presented. Using the equation, the natural frequencies and vibration modes of the flexible ring are investigated. The results show that the natural frequency of the drive system is affected by mechanical and electrical parameters among which, the coil current, the average static displacement of the flexible ring and the air gap have more obvious influence on the natural frequencies. The results are useful for the design and further study of the dynamics performance for the drive system.

scholarly journals Forced Response of an Electromagnetic Harmonic Movable Tooth Drive System to Current Excitation

2015 ◽  
Vol 9 (1) ◽  
pp. 65-70
Author(s):  
Yongli Liang ◽  
Lizhong Xu
Keyword(s):  
Forced Response ◽  
Drive System ◽  
Static Displacement ◽  
Coil Current ◽  
Ring Radius ◽  
Pair Number ◽  
Response Equation ◽  
Electric Parameters ◽  
Forced Responses ◽  
Flexible Ring

In this study, the authors proposed an electromagnetic harmonic movable tooth drive system. , The forced response equation of the drive system to exciting currents was developed. Using this equation, the forced responses of the drive system to exciting currents were investigated. The results show that the forced responses of the drive system to the exciting currents were affected by mechanical and electric parameters. To reduce the vibrating amplitudes, smaller coil current, flexible ring radius, and average static displacement of the flexible ring, increased thickness of the flexible ring, clearance between the flexible ring and coils, and coil pole pair number should be taken into account. The results can be used for designing the system and further study of the dynamics performance of the drive system.

scholarly journals Effects of molecule force on free vibration for a micro electromagnetic harmonic drive system

2021 ◽  
Vol 22 ◽  
pp. 12
Author(s):  
Dan Zhao ◽  
Lizhong Xu ◽  
Yuming Fu
Keyword(s):  
Free Vibration ◽  
Lower Order ◽  
Natural Frequencies ◽  
Van Der Waals ◽  
Drive System ◽  
Van Der Waals Force ◽  
Vibration Modes ◽  
Harmonic Drive ◽  
Force Dynamics ◽  
Flexible Ring

In this paper, a micro electromagnetic harmonic drive system is proposed. Considering Van der Waals force, dynamics equation of the flexible ring for the micro drive system is deduced and resolved. Using the equations, the effects of the molecule force on the natural frequencies and vibration modes of the drive system are investigated. Results show that considering molecule force, natural frequencies of the flexible ring are reduced and its vibration modes are changed. For lower order modes, smaller clearance between the flexible ring and stator, smaller thickness of the flexible ring and larger radius of the flexible ring, the effects of the molecule force on the natural frequencies and vibration modes are more obvious.

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.

A Discrete Lumped-Parameter Dynamic Model for a Planetary Gear Set with Flexible Ring Gear

2011 ◽  
Vol 86 ◽  
pp. 756-761 ◽  
Author(s):  
Jun Zhang ◽  
Yi Min Song ◽  
Jin You Xu
Keyword(s):  
Individual Component ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Vibration Modes ◽  
Ring Gear ◽  
Lumped Parameter ◽  
Planetary Gear System ◽  
Flexible Ring

A discrete lumped-parameter model for a general planetary gear set is proposed, which models the continuous flexible ring gear as discrete rigid ring gear segments connected with each other through virtual springs. The ring-planet mesh is analyzed to derive equations of motion of ring segments and planet. By assembling equations of motion of each individual component, the governing equations of planetary gear system are obtained. The solution for eigenvalue problem yields to natural frequencies and corresponding vibration modes. The simulations of example system reveal that the ring gear flexibility decreases system lower natural frequencies and the vibration modes can be classified into rotational, translational, planet and ring modes.

ELECTROMECHANICAL DYNAMICS FOR MICRO BEAMS

2006 ◽  
Vol 06 (02) ◽  
pp. 233-251 ◽  
Author(s):  
LIZHONG XU ◽  
XIAOLI JIA
Keyword(s):  
Balance Equation ◽  
Dynamic Equation ◽  
Natural Frequencies ◽  
Electrostatic Force ◽  
Critical Voltage ◽  
Vibration Modes ◽  
Linear Dynamic ◽  
Forced Responses ◽  
Electromechanical Dynamics ◽  
Electromechanical Coupled

In this paper, an electromechanical coupled dynamic equation of a micro beam under an electrostatic force as well as under an electromechanical coupled force is presented. The linearization of above dynamic equation is made, allowing the equation to be divided into a linear dynamic equation for dynamic displacement and a static balance equation for static displacement. Using the balance equation, the changes of the voltage along with displacement are studied. It is shown that there is a critical voltage at which the micro beam will buckle. From the linear dynamic equation, natural frequencies and vibration modes of the micro beam, and its forced responses to voltage excitation are derived. The results show that the natural frequencies and vibrating magnitudes of the micro beam are affected by mechanical and electric parameters. Smaller beam length and voltage as well as larger beam thickness and clearance should be selected in order to obtain smaller vibrating magnitudes. It is also shown that for higher vibration modes, more positions of the peak dynamic displacements occur.

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 On the gyroscopic and centrifugal effects in the free vibration of rotating beams

2018 ◽  
Vol 25 (1) ◽  
pp. 219-227 ◽  
Author(s):  
Xiao-Dong Yang ◽  
Zhen Li ◽  
Wei Zhang ◽  
Tian-Zhi Yang ◽  
CW Lim
Keyword(s):  
Natural Frequencies ◽  
Coupled System ◽  
Free Vibrations ◽  
Constant Angular Velocity ◽  
The Other ◽  
Complex Eigenvalue ◽  
Vibration Modes ◽  
Rotating Beams ◽  
Numerical Examples ◽  
Elliptic Vibration

This paper addresses the gyroscopic and centrifugal effects on vibrations of rotating Bernoulli–Euler beams. The gyroscopically coupled system is established as a complex eigenvalue problem. It is concluded that there exist three types of velocity-dependent terms that contribute to the natural frequencies with different effects. In particular, the contribution of gyroscopic terms and static and dynamic centrifugal terms to the natural frequencies are discussed for free vibrations of rotating beams with constant angular velocity. On the other hand, the vibrations in different directions coupled through the gyroscopic terms are investigated. Some numerical examples for the elliptic vibration modes in the rotating plane are presented and the results reveal the actual vibration contour of the rotating beams.

Dynamic Displacements for Electromechanical Integrated Electrostatic Harmonic Drive

2008 ◽  
Vol 3 (3) ◽  
Author(s):  
Lizhong Xu ◽  
Lei Qin
Keyword(s):  
Natural Frequencies ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Frequency Equation ◽  
Drive System ◽  
Harmonic Drive ◽  
Electromechanical Integrated ◽  
Analysis Package ◽  
Design And Manufacture ◽  
Flexible Ring

The electromechanical integrated electrostatic harmonic drive is a new drive system invented by authors. The dynamic displacements of the flexible ring for the drive have important influence on operating performance of the drive system. In this paper, the three dimensional dynamic equations for the drive system are presented. The mode function equations and the frequency equation for the drive system are derived. The natural frequencies and dynamic displacements of the drive system are obtained. Using a finite element method analysis package, ANSYS, the natural frequencies and vibrating modes of the flexible ring for the drive system are simulated. The simulation results are compared to the analytical results above. The research is useful in design and manufacture of the drive system and can be used to design dynamic performance of the drive.

scholarly journals Vibration Analysis of a Two-Step Sine Movable Tooth Drive

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Lizhong Xu ◽  
Jinan Yang
Keyword(s):  
Natural Frequencies ◽  
Vibration Mode ◽  
Fem Analysis ◽  
Element Model ◽  
Drive System ◽  
Single Element ◽  
Total System ◽  
Vibration Modes ◽  
System Vibration ◽  
Analysis Package

In this study, a 3D model of a two-step sine movable tooth drive is developed in the UG software. The finite element model (FEM) analysis package, ANSYS, is used to calculate the natural frequencies and vibration modes of the drive system. The results show that the first twenty natural frequencies can be classified into five families, including the total system vibration mode, single-element vibration mode, two-element vibration mode, three-element vibration mode, and four-element vibration mode. The effects of the system parameters on the natural frequencies and the vibration modes are investigated. The track amplitude, the movable tooth radius, the radius of the movable tooth rotation, and the number of movable teeth affect the natural frequencies and vibration modes of the drive system.

Flexible wheel displacements for electromagnetic harmonic movable tooth drive system

2020 ◽  
pp. 1-17
Author(s):  
Yongli Liang ◽  
Lizhong Xu
Keyword(s):  
Electromagnetic Force ◽  
Radial Displacement ◽  
Magnetic Force ◽  
Air Gap ◽  
Drive System ◽  
Force Model ◽  
Coil Current ◽  
Concentrated Force ◽  
Pair Number ◽  
Flexible Ring

In this paper, the structure and operating principle of the electromagnetic harmonic movable tooth drive system is introduced. Equations of the magnetic density and the electromagnetic force are given. The force model on the flexible wheel under magnetic force is presented. The equivalent concentrated force applied to the flexible wheel is determined. Based on it, the displacement equations of the flexible wheel are deduced. Using these equations, the displacement distribution of the flexible wheel and its changes along with the main parameters are investigated. Relationship between coil current and the maximum radial displacement is determined. The limit current corresponding to the limit radial displacement is obtained and its changes along with the main parameters are analyzed. The results show that the displacements of flexible wheel increase with the radius of flexible wheel and the coil current, and decrease with the initial air gap and the thickness of flexible wheel. A limit current under which the flexible ring will be buckled occurs under electromagnetic force. The limit current corresponding to the limit displacement increases with the thickness of flexible wheel, the pole pair number and the air gap, and decreases with the radius of flexible wheel. The results can be used to design and analyze the drive system.

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