Synchronization of Two Non-Identical Coupled Exciters in a Non-Resonant Vibrating System of Linear Motion. Part II: Numeric Analysis

Zhao, Chunyu; Zhu, Hongtao; Bai, Tianju; Wen, Bo

doi:10.1155/2009/826929

Cited by 36 publications

(47 citation statements)

References 7 publications

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“…When the parameters of this system meet the condition of achieving the synchronization, the numerical solution of ω m0 and α can be solved by (13), which are expressed as ω * m0 and α [14] 0 , respectively. When the vibration system operates synchronously, (12) is linearized at α = α 0 .…”

Section: Stability Condition Of Self-synchronization Motionmentioning

confidence: 99%

Self-synchronization theory of dual motor driven vibration system with two-stage vibration isolation frame

Liú

Jiang

et al. 2015

Appl. Math. Mech.-Engl. Ed.

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This paper studies self-synchronization and stability of a dual-motor driven vibration system with a two-stage vibration isolation frame. Oscillation amplitude of the material box large enough can be ensured on the vibration system in order to screen materials. Reduction of the dynamic load transmitted to the foundation can also be achieved for the vibration system. A Lagrange equation is used to set up the motion differential equations of the system, and a dimensionless coupled equation of the eccentric rotors is obtained using a method of modified average small parameter. According to the existence condition of zero solution in the dimensionless coupled equation of the eccentric rotors, the precondition for commencing self-synchronization motion is achieved. The stability condition of self-synchronization is obtained based on the Routh-Hurwitz criterion. The theoretical analysis is validated by simulations and experiments.

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Section: Stability Condition Of Self-synchronization Motionmentioning

confidence: 99%

Self-synchronization theory of dual motor driven vibration system with two-stage vibration isolation frame

Liú

Jiang

et al. 2015

Appl. Math. Mech.-Engl. Ed.

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“…Here, our attention is focused on the non-resonant vibrating system with small damping, i.e., the exciting frequency is much greater than the natural frequency of the vibrating system [3,4]. In this case, the effect of the coefficients of the angular velocities  i on the amplitude and phase angle of response of the vibrating system can also be neglected [10][11][12][13], i.e., the amplitudes and phase angles of the responses can be approximately expressed by that excited by the unbalanced rotors when their angular velocity is  m .…”

Section:     mentioning

confidence: 99%

“…The other analytical investigation of such a system without using the method of direct motion separation would have been most complicated and perhaps hardly possible at all [1]. Taking the disturbance parameters of the phase difference and average velocity of the two unbalanced rotors as the small parameters, the authors convert the problem of synchronizations of two unbalanced rotors into that of existence and stability of the zero solutions of the differential equations of the small parameters [10][11][12][13]. But when the number of the unbalanced rotors is more than two, investigation of the stability is difficult with the above methods.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of the four identical unbalanced rotors in a vibrating system of plane motion

Zhao

Wen

Zhang

2010

Sci. China Technol. Sci.

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A new mechanism is proposed to implement the synchronization of the four unbalanced rotors in a vibrating system, which consists of a main rigid frame (MRF) and two accessorial rigid frames (ARF). An analytical approach is developed to study the coupling dynamic characteristics of the four unbalanced rotors, which converts the problem of synchronization of the four unbalanced rotors into the existence and the stability of zero solutions for the non-dimensional differential equations of the angular velocity disturbance parameters (NDDEDP). The stability of zero solutions of the NDDEDP is decomposed into that of its generalized system and a system of the three first order differential equations for the disturbance parameters of the phase differences. The coupling dynamic characteristic of the four unbalanced rotors includes the inertia coupling, the stiffness coupling of angular velocity and the load torque coupling. The non-dimensional inertia coupling matrix is symmetric, the non-dimensional matrix of the stiffness coupling of angular velocity is antisymmetric and its diagonal elements are all negative. Hence, the general system of the NDDEDP automatically satisfies the generalized Lyapunov equations when the non-dimensional inertia coupling matrix is positive definite and its elements are all positive. Using Routh-Hurwitz criterion the condition of stability of differential equations for the disturbance parameters of the phase differences is obtained. The load torque coupling makes the vibrating system have the dynamic characteristic of selecting motions and self-synchronization of the four unbalanced rotors arises from the dynamic characteristic of selecting motion of the vibrating system. When the two coefficients of coupling cosine effect of phase angles are all greater than 0 and the three indexes of synchronization are all far greater than 1, the vibrating system can implement an elliptical motion of the main rigid frame required in engineering. Numeric results show that the structural parameters of the proposed mechanism can guarantee the non-dimensional inertia matrix to be always positive definite. Computer simulation is carried out to verify the results of the theoretical investigation. Nomenclature M; M i : (i=1, 2) mass matrix of the MRF, M= diag{ , }; m m mass matrix of the ARF i, 1 2 a a diag{ , } M m m   M M ij : (i = 1, 2; j = 1, 2) mass matrix of the unbalanced rotor ij, 0 0 diag{ , } ij m m  M J; J a : moment of inertia of the MRF about its mass center; moment of inertia of the ARFs about their spin axis J 0ij :(i=1, 2; j=1, 2) moment of inertia of the motor's rotor ij r ij :(i =1, 2; j=1, 2) eccentric radius of the unbalanced rotor ij, r ij = r 0 G: mass center of the MRF o i : (i=1, 2) center of the spin-axis of the ARF i 406

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“…Balthazar [16] has also given some short comments on self-synchronization of two non-ideal sources by means of numerical simulations. Many theories of synchronization of more than two exciters are studied by scholars, in which the main methods used are the method of direct motion separation [4][5][6][7][8][9][10] and the averaging method of small parameters [17][18][19][20]. In Refs.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Zhao

Wen

2013

Shock and Vibration

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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.

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Synchronization of Two Non-Identical Coupled Exciters in a Non-Resonant Vibrating System of Linear Motion. Part II: Numeric Analysis

Cited by 36 publications

References 7 publications

Self-synchronization theory of dual motor driven vibration system with two-stage vibration isolation frame

Self-synchronization theory of dual motor driven vibration system with two-stage vibration isolation frame

Synchronization of the four identical unbalanced rotors in a vibrating system of plane motion

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

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