scholarly journals On the Synchronization of Two Eccentric Rotors with Common Rotational Axis: Theory and Experiment

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaozhe Chen ◽  
Xiangxi Kong ◽  
Xueliang Zhang ◽  
Lingxuan Li ◽  
Bangchun Wen
Keyword(s):  
Phase Difference ◽  
Structural Parameters ◽  
Steady Motion ◽  
Rotational Axis ◽  
Vibration System ◽  
Motion Feature ◽  
Small Parameters ◽  
Dimensionless Coupling ◽  
The Difference ◽  
Approach Zero

We study synchronization of two eccentric rotors (ERs) with common rotational axis in the vibration system of the far-resonant spatial motion. We deduce the dimensionless coupling equation of two ERs with applying the average method of small parameters. We convert the synchronization problem into the existence and stability of solving the zero solutions for the dimensionless coupling equations. By introducing the synchronization torque and the difference between the residual torques of two motors, we obtain the synchronization condition that two ERs achieve the synchronized motion. We derive the stability condition of the synchronized motion, which satisfies Routh-Hurwitz criterion. We discuss numerically the choosing motion feature of the vibration system, which indicates that the vibration system has two steady motion modes. The synchronization torque forces the phase difference to approachπwhen the structural parameters of the vibration system satisfy the condition of the spatial cone motion, and the synchronization torque drives the phase difference to approach zero when those satisfy the condition of the spatial circle motion. Finally, through the comparison and analysis of experimental data, the structural parameters of the vibration system satisfying the above two conditions can guarantee the synchronization stability for two ERs.

scholarly journals Analysis of harmonic vibration synchronization for a nonlinear vibrating system with hysteresis force

2019 ◽  
Vol 39 (4) ◽  
pp. 1087-1101
Author(s):  
Nan Zhang ◽  
Shiling Wu
Keyword(s):  
Nonlinear Vibration ◽  
Phase Difference ◽  
Nonlinear Dynamic ◽  
Dynamic Models ◽  
Harmonic Vibration ◽  
Vibration System ◽  
The Difference ◽  
Nonlinear Dynamic Models ◽  
The Stability ◽  
Nonlinear Vibration System

Harmonic vibration synchronization of the two excited motors is an important factor affecting the performance of the nonlinear vibration system driven by the two excited motors. From the point of view of the hysteresis force, the nonlinear dynamic models of the nonlinear vibration system driven by the two excited motors are presented for the analysis of the hysteresis force with the asymmetry. An approximate periodic solution for the nonlinear vibration system with the hysteresis force is investigated using the nonlinear models. The condition of harmonic vibration synchronization is theoretically analyzed using the rotor–rotation equations of the two excited motors in the nonlinear dynamic models and the stability condition of harmonic vibration synchronization also is theoretically analyzed using Jacobi matrix of the phase difference equation of two excited motors. Using Matlab/Simlink, harmonic vibration synchronization of the two excited motors and the stability of harmonic vibration synchronization for the nonlinear vibration system with the hysteresis force are analyzed through the selected parameters. Various synchronous processes of the nonlinear vibration system with the hysteresis force are obtained through the difference rates of the two excited motors (including the initial phase difference, the initial rotational speed difference, the difference of the motors parameters). It has been shown that the research results can provide theoretical basis for the design and research of the vibration system driven by the two-excited motors.

scholarly journals Synchronization of Two Asymmetric Exciters in a Vibrating System

2011 ◽  
Vol 18 (1-2) ◽  
pp. 63-72 ◽  
Author(s):  
Zhaohui Ren ◽  
Qinghua Zhao ◽  
Chunyu Zhao ◽  
Bangchun Wen
Keyword(s):  
Average Method ◽  
Structural Parameters ◽  
Positive Definite ◽  
Electromagnetic Torque ◽  
Coupling Matrix ◽  
Vibrating System ◽  
Frequency Capture ◽  
Small Parameters ◽  
The Difference ◽  
Dimensional Coupling

We investigate synchronization of two asymmetric exciters in a vibrating system. Using the modified average method of small parameters, we deduce the non-dimensional coupling differential equations of the two exciters (NDDETE). By using the condition of existence for the zero solutions of the NDDETE, the condition of implementing synchronization is deduced: the torque of frequency capture is equal to or greater than the difference in the output electromagnetic torque between the two motors. Using the Routh-Hurwitz criterion, we deduce the condition of stability of synchronization that the inertia coupling matrix of the two exciters is positive definite. A numeric result shows that the structural parameters can meet the need of synchronization stability.

scholarly journals Theoretical and Experimental Study on Synchronization of the Two Homodromy Exciters in a Non-Resonant Vibrating System

2013 ◽  
Vol 20 (2) ◽  
pp. 327-340 ◽  
Author(s):  
Xue-Liang Zhang ◽  
Chun-Yu Zhao ◽  
Bang-Chun Wen
Keyword(s):  
Phase Difference ◽  
Structural Parameters ◽  
Circular Motion ◽  
Vibrating System ◽  
Frequency Capture ◽  
Rigid Frame ◽  
Small Parameters ◽  
Coupling Dynamic ◽  
The Stability ◽  
Elliptical Motion

In this paper we give some theoretical analyses and experimental results on synchronization of the two non-identical exciters. Using the average method of modified small parameters, the dimensionless coupling equation of the two exciters is deduced. The synchronization criterion for the two exciters is derived as the torque of frequency capture being equal to or greater than the absolute value of difference between the residual electromagnetic torques of the two motors. The stability criterion of synchronous state is verified to satisfy the Routh-Hurwitz criterion. The regions of implementing synchronization and that of stability of phase difference for the two exciters are manifested by numeric method. Synchronization of the two exciters stems from the coupling dynamic characteristic of the vibrating system having selecting motion, especially, under the condition that the parameters of system are complete symmetry, the torque of frequency capture stemming from the circular motion of the rigid frame drives the phase difference to approach PI and carry out the swing of the rigid frame; that from the swing of the rigid frame forces the phase difference to near zero and achieve the circular motion of the rigid frame. In the steady state, the motion of rigid frame will be one of three types: pure swing, pure circular motion, swing and circular motion coexistence. The numeric and experiment results derived thereof show that the two exciters can operate synchronously as long as the structural parameters of system satisfy the criterion of stability in the regions of frequency capture. In engineering, the distance between the centroid of the rigid frame and the rotational centre of exciter should be as far as possible. Only in this way, can the elliptical motion of system required in engineering be realized.

Periodically poled KTA crystal investigated using coherent X-ray beams

2000 ◽  
Vol 33 (4) ◽  
pp. 1149-1153 ◽  
Author(s):  
P. Pernot-Rejmánková ◽  
P. A. Thomas ◽  
P. Cloetens ◽  
F. Lorut ◽  
J. Baruchel ◽  
...  
Keyword(s):  
Phase Difference ◽  
Domain Walls ◽  
Structural Information ◽  
Periodically Poled ◽  
Synchrotron Source ◽  
X Ray ◽  
Diffracted Waves ◽  
Coherent Beams ◽  
Diffraction Imaging ◽  
The Difference

The distribution of inverted ferroelectric domains on the surface and within the bulk of a periodically poled KTA (KTiOAsO4) single crystal has been observed using a simple X-ray diffraction imaging setup which takes advantage of the highly coherent beams available at a third-generation synchrotron source, such as the ESRF. This technique allows one to reveal the phase difference between the waves that are Bragg diffracted from adjacent domainsviafree-space propagation (Fresnel diffraction). The phase difference of the diffracted waves is mainly produced by the difference in phases of the structure factors involved, and contains precise structural information about the nature of the domain walls.

scholarly journals Linear Structural Trends and Multi-Phase Intergrowths in Helvine-Group Minerals, (Zn,Fe,Mn)8[Be6Si6O24]S2

Minerals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 325
Author(s):  
Sytle Antao
Keyword(s):  
Cell Parameter ◽  
Structural Parameters ◽  
Unit Cell ◽  
Fluid Composition ◽  
Ternary Solid Solution ◽  
X Ray Diffraction ◽  
X Ray ◽  
The Difference ◽  
Multi Phase ◽  
And Diffusion

Synchrotron high-resolution powder X-ray diffraction (HRPXRD) and Rietveld structure refinements were used to examine the crystal structure of single phases and intergrowths (either two or three phases) in 13 samples of the helvine-group minerals, (Zn,Fe,Mn)8[Be6Si6O24]S2. The helvine structure was refined in the cubic space group P4¯3n. For the intergrowths, simultaneous refinements were carried out for each phase. The structural parameters for each phase in an intergrowth are only slightly different from each other. Each phase in an intergrowth has well-defined unit-cell and structural parameters that are significantly different from the three endmembers and these do not represent exsolution or immiscibility gaps in the ternary solid-solution series. The reason for the intergrowths in the helvine-group minerals is not clear considering the similar radii, identical charge, and diffusion among the interstitial M cations (Zn2+, Fe2+, and Mn2+) that are characteristic of elongated tetrahedral coordination. The difference between the radii of Zn2+ and Mn2+ cations is 10%. Depending on the availability of the M cations, intergrowths may occur as the temperature, pressure, fugacity fS2, and fluid composition change on crystallization. The Be–Si atoms are fully ordered. The Be–O and Si–O distances are nearly constant. Several structural parameters (Be–O–Si bridging angle, M–O, M–S, average <M–O/S>[4] distances, and TO4 rotational angles) vary linearly with the a unit-cell parameter across the series because of the size of the M cation.

Synchronization Analysis of the Double Exciting Motors in Nonlinear Vibration System Based on Reaching Law

2011 ◽  
Vol 295-297 ◽  
pp. 2197-2200
Author(s):  
Xiao Hao Li ◽  
Jie Liu
Keyword(s):  
State Space ◽  
Nonlinear Vibration ◽  
Dynamic Model ◽  
Phase Difference ◽  
Sliding Mode ◽  
Design Feature ◽  
Vibration System ◽  
Reaching Law ◽  
Speed Difference ◽  
Nonlinear Vibration System

Based on the dynamic model of the nonlinear vibration system which driven by double exciting motors, the rotate speed difference and phase difference state space equations have been deduced. According to the design feature of the nonlinear vibration system and the vibration synchronization requirement of double exciting motors, the approach control synchronization strategy has been deduced with sliding mode reaching law. The practical examples and tests shows that the reaching law synchronization controller can effectively control the double exciting motors to realize the synchronization movement, and the synchronization controller has stronger robustness. The analysis result can provide the theoretical and test basis for the further exploitation of synchronization vibrating machine.

scholarly journals Mathematical and geometrical modeling of braided ropes bent over a sheave

2020 ◽  
Vol 15 ◽  
pp. 155892502093972
Author(s):  
Guifang He ◽  
Chunfu Sheng ◽  
Hongwei He ◽  
Rong Zhou ◽  
Ding Yuan ◽  
...  
Keyword(s):  
Mathematical Method ◽  
Phase Difference ◽  
Computational Simulation ◽  
The Other ◽  
Force Transmission ◽  
Helical Surface ◽  
Modeling Process ◽  
Mathematical Equations ◽  
The Difference ◽  
Final Equation

As soft elements for force transmission, braided fiber ropes play important roles in many fields where the fiber ropes are used bent over sheaves, while the relevant experiments are time-consuming and expensive. Computational simulation is a promising choice for evaluating the performance of fiber ropes when bent over a sheave. This article presents two methods that could be employed to build a model of braided rope bent over a sheave. One is the mathematical method which deduces the exact mathematical equations of braiding curves based on the Frenet–Serret frame. The spatial equations, considering the phase difference of strands in the same direction and the difference of strands’ projection in different directions, are discussed carefully. The final equation of braided strands is confirmed by modeling the braided rope in Maple® 17. The other method, which is inspired by the analysis of braiding movements, is based on the intersection of surfaces of braiding surface and helical surface which are introduced and defined based on the motion analysis of bobbins and take-up roller. The SolidWorks® 2018 is successfully employed to realize the modeling process.

Human Response to Dynamic Rollover Conditions

2003 ◽  
Author(s):  
Jack Bish ◽  
Terence Honikman ◽  
Jason Sigel ◽  
Carl Nash ◽  
Donald Friedman
Keyword(s):  
Motor Vehicle ◽  
Rotation Axis ◽  
Test Subject ◽  
Rotational Axis ◽  
Human Response ◽  
Passenger Compartment ◽  
Hybrid Iii ◽  
Drop Tests ◽  
Vehicle Rollover ◽  
The Difference

To date, human responses in motor vehicle rollover accidents have been studied through the use of Hybrid III dummies in dolly vehicle rollover tests, quasi-static spit tests where the vehicle and occupant are rotated slowly about the rotation axis of the spit fixture, computer simulations and vehicle drop tests. To demonstrate human responses to dynamic rollover conditions more accurately we designed and built a fixture to accommodate a passenger compartment in a hoop structure that rotates as it translates. The rotational axis of the hoop structure is offset from the rotational axis of the passenger compartment to replicate vehicle center of gravity motion seen in dolly rollover tests. Testing showed the difference in restraint behavior depending upon whether the occupant was seated on the near (initially leading) or far side. It demonstrated that human and Hybrid III dummy neck response is very different. The human test subject received no injuries from diving into the roof of the passenger compartment even though this is the predicted injury mechanism reported in several technical papers.

Sensitivity Coefficients Utilized in Nonlinear Estimation With Small Parameters in a Heat Transfer Problem

1970 ◽  
Vol 92 (2) ◽  
pp. 215-221 ◽  
Author(s):  
J. V. Beck
Keyword(s):  
Model Building ◽  
Transfer Problem ◽  
Nonlinear Estimation ◽  
Transient Heat Conduction ◽  
Computer Time ◽  
Sensitivity Coefficients ◽  
Yield Information ◽  
Small Parameters ◽  
The Difference ◽  
Building Identification

The method of nonlinear estimation for determining parameters in differential equations is extended to treat more efficiently the problem of determining dominant and small parameters. Using the sensitivity coefficients, it is shown how to determine the dominant parameters first using nonlinear estimation and then using linear least squares to find the small parameters. This procedure can save a considerable amount of computer time. Even more important is the application to model-building (identification). The residuals for the difference of the temperatures calculated, assuming the small parameters are zero, and the measured temperatures are shown to yield information for discriminating between alternate mathematical models. A transient heat-conduction example is given to illustrate some of the concepts developed.

Three-Ring Gear Reducer Internal Tooth Plate Processing Method in the Research and Analysis

2014 ◽  
Vol 472 ◽  
pp. 312-315
Author(s):  
Hong Bin Yang ◽  
Qiang Wang
Keyword(s):  
Phase Difference ◽  
Processing Method ◽  
Motion Simulation ◽  
Ring Gear ◽  
Tooth Plate ◽  
Noise Impact ◽  
Cutting Out ◽  
Positioning Method ◽  
The Difference ◽  
Important Significance

Ref. [ based on the analysis of internal tooth plate in the process of locating method, on the basis of the author thinks that the positioning adjustment of internal tooth plate Angle is not easy to measure in actual processing, the positioning adjustment Angle is not easy to guarantee the positioning, a direct impact on the accuracy of phase difference between tooth plate. If the difference accuracy of inner teeth cannot guarantee, cause vibration and noise, impact of three-ring gear reducer will intensify, temperature increase, reduce the service life, even can't assembly. Through the analysis of the principle of three-ring gear reducer, the paper puts forward the inner tooth plate treatment positioning adjustment Angle is 120°, measurement is simple and convenient location, is advantageous to the guarantee of phase difference accuracy of inner teeth. Using UG NX7.0 platform, with a new positioning method to establish model of inner rack, and then using UG stretch command on the establishment of good internal tooth plate model of cutting out the tooth shape, and motion simulation. The results show that the new Angle of inner gear plate positioning adjustment feasible, and fast and convenient, has important significance to the development of three-ring gear reducer.

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