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 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.

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.

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.

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.

Comparative Studies of Surrogate Models for Response Analysis of Mistuned Bladed Disks

2020 ◽  
Vol 17 (10) ◽  
pp. 2050012 ◽  
Author(s):  
Shiyuan Deng ◽  
Jianyao Yao ◽  
Linlin Wang ◽  
Jianqiang Xin ◽  
Ning Hu
Keyword(s):  
Degrees Of Freedom ◽  
Surrogate Models ◽  
Forced Response ◽  
Statistical Characteristics ◽  
Kriging Interpolation ◽  
Response Analysis ◽  
Bladed Disks ◽  
Single Output ◽  
Random Mistuning ◽  
Forced Responses

The forced responses of bladed disks are highly sensitive to inevitable random mistuning. Considerable computational efforts are required for the sampling process to assess the statistical vibration properties of mistuned bladed disks. Therefore, efficient surrogate models are preferred to accelerate the process for probabilistic analysis. In this paper, four surrogate models are utilized to construct the relation between random mistuning and forced response amplitudes, which are polynomial chaos expansion (PCE), response surface method (RSM), artificial neural networks (ANN) and Kriging interpolation, respectively. A bladed disk with 2-degrees-of-freedom (2-DOF) each sector is used to validate the effectiveness of the surrogate models. The effects of number of training samples on the surrogate model accuracy are discussed. The responses results of one blade (single output) and maximum response of all blades (multi-output) indicate that PCE and Kriging interpolation could yield accurate and stable predictions of the statistical characteristics of the forced responses. PCE is recommended for the mistuned response predictions due to its accuracy and efficiency.

An Efficient Response Analysis Method for a Non-Linear/Parameter Changing System Using Sub-Structure Modes

1993 ◽  
Vol 207 (1) ◽  
pp. 41-52
Author(s):  
H K Kim ◽  
Y-S Park
Keyword(s):  
Equations Of Motion ◽  
Forced Response ◽  
Suggested Method ◽  
Response Analysis ◽  
Synthesis Methods ◽  
Lumped Mass ◽  
State Equations ◽  
Mass Model ◽  
Non Linear ◽  
Forced Responses

An efficient state-space method is presented to determine time domain forced responses of a structure using the Lagrange multiplier based sub-structure technique. Compared with the conventional mode synthesis methods, the suggested method can be particularly effective for the forced response analysis of a structure subjected to parameter changes with time, such as a missile launch system, and/or having localized non-linearities, because this method does not need to construct the governing equations of the combined whole structure. Both the loaded interface free-free modes and free interface modes can be employed as the modal bases of each sub-structure. The sub-structure equations of motion are derived using Lagrange multipliers and recurrence discrete-time state equations based upon the concept of the state transition matrix are formulated for transient response analysis. The suggested method is tested with two example structures, a simple lumped mass model with a non-linear joint and an abruptly parameter changing structure. The test results show that the suggested method is very accurate and efficient in calculating forced responses and in comparing it with the direct numerical integration method.

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.

scholarly journals How do conservative backbone curves perturb into forced responses? A Melnikov function analysis

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190494 ◽  
Author(s):  
Mattia Cenedese ◽  
George Haller
Keyword(s):  
Function Analysis ◽  
Melnikov Function ◽  
Forced Response ◽  
Numerical Continuation ◽  
Periodic Forcing ◽  
Near Resonance ◽  
Experimental Approaches ◽  
Backbone Curves ◽  
Forced Responses ◽  
Small Periodic

Weakly damped mechanical systems under small periodic forcing tend to exhibit periodic response in a close vicinity of certain periodic orbits of their conservative limit. Specifically, amplitude-frequency plots for the conservative limit have often been noted, both numerically and experimentally, to serve as backbone curves for the near resonance peaks of the forced response. In other cases, such a relationship between the unforced and forced response was not observed. Here, we provide a systematic mathematical analysis that predicts which members of conservative periodic orbit families will serve as backbone curves for the forced–damped response. We also obtain mathematical conditions under which approximate numerical and experimental approaches, such as energy balance and force appropriation, are justifiable. Finally, we derive analytic criteria for the birth of isolated response branches (isolas) whose identification is otherwise challenging from numerical continuation.

Influence of Structure Parameters on the Permanent Magnetic Planetary Gear Forced Vibration Frequency Response

2014 ◽  
Vol 635-637 ◽  
pp. 168-171
Author(s):  
Xue Jun Zhu ◽  
Li Zhong Xu
Keyword(s):  
Dynamic Performance ◽  
Low Frequency ◽  
Planetary Gear ◽  
System Structure ◽  
Structure Parameters ◽  
Magnetic Parameters ◽  
Low Frequency Vibration ◽  
Magnetization Intensity ◽  
Pair Number ◽  
Forced Responses

The time and frequency forced responses for the permanent magnetic planetary gear drive were computed and analyzed. The influence of magnetization intensity and pole pair number to frequency forced responses is discussed. Results show that the dynamic displacement when only considering output excitation is larger than that when only considering input excitation,and magnetic parameters have obvious effects on the low frequency vibration amplitude of elements. When magnetization intensity and pole pair number are too large or too small, they will seriously affect the dynamic performance of the system. So, selecting rational system structure parameters is very important, which can avoid system elements generating larger vibration.

scholarly journals Comparison of the SST-Forced Responses between Coupled and Uncoupled Climate Simulations

2014 ◽  
Vol 27 (2) ◽  
pp. 740-756 ◽  
Author(s):  
Hua Chen ◽  
Edwin K. Schneider
Keyword(s):  
A Priori ◽  
Atmospheric Model ◽  
Forced Response ◽  
Climate Simulations ◽  
Perfect Model ◽  
Time Lagged ◽  
Forced Responses ◽  
The Tropics ◽  
Indirect Tests ◽  
Linear Regressions

Abstract It is commonly assumed that a reasonable estimate of the SST-forced component of the observed atmospheric circulation is given by an atmospheric GCM (AGCM) forced with the observed SST. However, there are results that find different SST-forced responses from the observed, for example for the ENSO–monsoon relationship, and suggest that these differences are due to lack of coupling to the ocean rather than atmospheric model bias unrelated to coupling. Here, the coupling issue is isolated and examined through perfect model experiments. A coupled atmosphere–ocean GCM (CGCM) simulation and an AGCM simulation forced by the SST from the CGCM are compared to examine whether the SST-forced responses are the same. This question cannot be addressed directly, since the SST-forced response of the CGCM is a priori unknown. Therefore, two indirect tests are applied, based on the assumption that the noise decorrelation time scale is short compared to a month. The first test is to compare the time-lagged linear regressions of the atmospheric fields onto several SST indices (defined as the area-averaged SST anomalies in the tropics or extratropics), with SST leading the atmosphere by a month. The second test is to compare the time lagged linear covariances of several atmospheric indices (including two monsoon indices and a North Atlantic Oscillation index) and SST, with the SST leading the atmosphere by a month. Both tests find that the SST-forced responses are the same in the CGCM and SST-forced AGCM. These tests can be extended to compare the SST-forced responses between different AGCMs, CGCMs, and observations.

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