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 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.

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.

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.

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.

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.

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.

Electromechanical coupled non-linear vibration of the microplate

2010 ◽  
Vol 224 (6) ◽  
pp. 1383-1396 ◽  
Author(s):  
L Xu ◽  
L Sun
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Electrostatic Force ◽  
Forced Response ◽  
Linear Vibration ◽  
System Parameters ◽  
Exciting Frequency ◽  
Non Linear ◽  
Plate System ◽  
Electromechanical Coupled

In this article, the non-linear electromechanical coupled dynamic equation of the micro-plate subjected to an electrostatic force is presented. The non-linear free vibration of the electromechanical coupled micro-plate system and the non-linear forced response of the system to voltage excitation are investigated. Non-linear vibration frequencies of the micro-plate for every mode are calculated and compared with the linear natural frequencies. Changes in the non-linear frequencies with the system parameters are presented. The non-linear vibration displacements of the micro-plate at some typical cross-section are calculated for the first three modes. Effects of the system parameters on the displacements are analysed. The changes in the vibration amplitudes with respect to the exciting frequency under different modes and parameters are investigated. Moreover, the effects of the boundary conditions on the electromechanical coupled micro-plate system are also investigated.

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.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

Experimental and Numerical Assessment of Mistuning Effects on Vibratory Response of a Bladed Disk with Underplatform Dampers

2021 ◽  
Author(s):  
S. Mehrdad Pourkiaee ◽  
Teresa Berruti ◽  
Stefano Zucca ◽  
Geoffrey Neuville
Keyword(s):  
Model Identification ◽  
Forced Response ◽  
Response Level ◽  
Static Test ◽  
Bladed Disk ◽  
Experimental Campaign ◽  
Proposed Model ◽  
Numerical Assessment ◽  
Linearized Model ◽  
Forced Responses

Abstract This paper presents experimental and numerical investigation of mistuned forced responses of an integrally bladed disk with full set of underplatform dampers (UPDs). This research aims at providing: 1. An experimental benchmark for nonlinear dynamics of a mistuned bladed disks with UPDs. 2. A numerical model that can account for features of a mistuned forced response level. Accordingly, a detailed experimental campaign is conducted on a static test rig called Octopus. This rig is specifically designed to investigate the dynamics of a full-scale integrally bladed disk (blisk) with UPDs in a noncontact manner so that the dynamic response of the system is not modified. The effect of mistuning on experimental forced response levels is assessed and a linearized model is proposed to predict the modulation of frequency response functions (FRFs) due to the frequency splitting. In the development of the model, the mistuning pattern identified from the linear blisk without UPDs is used and it is assumed that adding the dampers does not change the structural mistuning of the blisk. In this study, the fundamental mistuning model identification (FMM ID) was employed to identify the mistuning pattern of the blisk. It is shown that the proposed model successfully predicts the modulation of linear mistuned FRFs. The linearized model is also able to predict the modulation of nonlinear mistuned FRFs in stick condition (when nonlinear friction damping is negligible) with a good accuracy validating this assumption that adding the dampers does not change the mistuning pattern.

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