Synchronization of two coupled exciters in a vibrating system of spatial motion

The paper proposes an analytical approach to investigate the synchronization of the two coupled exciters in a vibrating system of spatial motion. Introducing the distur- bance parameters for average angular velocity of two excit- ers, we deduce the non-dimensional coupling equations of angular velocities of two exciters, in which the inertia cou- pling matrix is symmetric and the stiffness coupling matrix is antisymmetric in a non-resonant vibrating system. The analysis of the coupling dynamic characteristic shows that the coupled cosine effect of the phase angles will cause the torque acting on two motors to limit the increase of phase difference between two exciters as well as sustain its sym- metry of two exciters during the running process. It physi- cally explains the peculiarity of self-synchronization of two exciters. The cosine effect of phase angles of the vibrations excited by each exciter will decrease its moment of inertia. The residual moment of inertia of each exciter represents its relative moment of inertia. The stability condition of synchro- nization of two exciters is that the relative non-dimensional moments of inertia of two exciters are all greater than zero and four times their product is greater than the square of their coefficient of coupled cosine effect of phase angles, which is equivalent to that the inertia coupling matrix is positive definite and all its elements are positive. The numeric results show that the structure of the vibrating system can ensure the stability condition of synchronous operation.

Synchronisation and general dynamic symmetry of a vibrating system with two exciters rotating in opposite directions

We derive the non-dimensional coupling equation of two exciters, including inertia coupling, stiffness coupling and load coupling. The concept of general dynamic symmetry is proposed to physically explain the synehronisation of the two exciters, which stems from the load coupling that produces the torque of general dynamic symmetry to force the phase difference between the two exciters close to the angle of general dynamic symmetry. The condition of implementing synchronisation is that the torque of general dynamic symmetry is greater than the asymmetric torque of the two motors. A general Lyapunov function is constructed to derive the stability condition of synchronisation that the non-dimensional inertia coupling matrix is positive definite and all its elements are positive. Numeric results show that the structure of the vibrating system can guarantee the stability of synchronisation of the two exciters, and that the greater the distances between the installation positions of the two exciters and the mass centre of the vibrating system are, the stronger the ability of general dynamic symmetry is.

A virtual experiment showing single particle motion on a linearly vibrating screen-deck

A virtual sieving experimental simulation system was built using physical simulation principles.The effects of vibration frequency and amplitude,the inclination angle of the screen-deck and the vibration direction angle of screen on single particle kinematics were predicted.Properties such as the average velocity and the average throw height were studied.The results show that the amplitude and the angle of vibration have a great effect on particle average velocity and average height.The vibration frequency and the screen-deck inclination angle appear to have little influence on these responses.For materials that are difficult to screen the vibration frequency and amplitude,the screen-deck inclination angle and the vibration angle should be set to 14 Hz,6.6 mm,6° and 40°,respectively,to obtain optimal particle kinematics.A screening process can be simulated reliably by means of a virtual experiment and these results provide references for both screening theory research and sieving practice.

Synchronization of three homodromy coupled exciters in a non-resonant vibrating system of plane motion

In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced dimensionless coupling equation of three exciters, which converted the problem of synchronization into that of the existence and stability of zero solutions for the average differential equations of the small parameters. Based on the dimensionless coupling torques and characteristics of the cor- responding limited functions, the synchronization criterion for three exciters was derived as the absolute value of dimensionless residual torque difference between arbitrary two motors being less than the maximum of their dimensionless coupling torques. The stability criterion of its synchronous state lies in the double-condition that the inertia coupling matrix is positive definite and all its elements are positive as well. The synchronization determinants are the coefficients of synchronization ability, also called as the general dynamical symmetry coefficients. The double-equilibrium state of the vibrating system is manifested by numeric method, and the numeric and simulation results derived thereof indicate the indispensable and crucial role the structural parameters of the vibrating system play in the stability criterion of synchronous operation. Besides, by adjusting its structural parameters, the elliptical motion of the vibrating system successfully met the requirements in engineering applications.

Study of vibrating foundations considering soil-pile-structure interaction for practical applications

An investigation of soil-pile-structure interaction is carried out, based on a large reciprocating compressor installed on an elevated concrete foundation （table top structure）. A practical method is described for the dynamic analysis, and compared with a 3D finite element （FE） model. Two commercial software packages are used for dynamic analysis considering the soilpile-structure interaction （SPSI）. Stiffness and damping of the pile foundation are generated from a computer program, and then input into the FE model. To examine the SPSI thoroughly, three cases for the soil, piles and superstructure are considered and compared. In the first case, the interaction is fully taken into account, that is, both the superstructure and soil-pile system are flexible. In the second case, the superstructure is flexible but fixed to a rigid base, with no deformation in the base （no SSI）. In the third case, the dynamic soil-pile interaction is taken into account, but the table top structure is assumed to be rigid. From the comparison beteen the results of these three cases some conclusions are made, which could be helpful for engineering practice.

PI-type Iterative Learning Control for Nonlinear Electro-hydraulic Servo Vibrating System

For the electro-hydraulic servo vibrating system（ESVS） with the characteristics of non-linearity and repeating motion, a novel method, PI-type iterative learning control（ILC）, is proposed on the basis of traditional PID control. By using memory ability of computer, the method keeps last time＇s tracking error of the system and then applies the error information to the next time＇s control process. At the same time, a forgetting factor and a D-type learning law of feedforward fuzzy-inferring referenced displacement error under the optimal objective are employed to enhance the systemic robustness and tracking accuracy. The results of simulation and test reveal that the algorithm has a trait of high repeating precision, and could restrain the influence of nonlinear factors like leaking, external disturbance, aerated oil, etc. Compared with traditional PID control, it could better meet the requirement of nonlinear electro -hydraulic servo vibrating system.

Theoretical, Numerical and Experimental Study on Synchronization of Three Identical Exciters in a Vibrating System

The theory on synchronization of two exciters is more widely used in engineering, while that of more than two exciters is less considered. So it is of great significant to investigate synchronization of three exciters. Firstly by introducing the average method of modified small parameters, the dimensionless coupling equations(DCE) of three exciters are derived, which convert the problem of synchronization into that of existence and stability of zero solutions for the DCE and lead to the construction on criterions of synchronization and stability in the simplified form for three exciters. Then the synchronization criterion is discussed numerically, as well as the abilities of synchronization and stability, some results thereof indicate that the synchronization ability increases with the increase of the coupling moment among three exciters, but decreases with that of their phase differences. Finally, an experiment on synchronization with three exciters is carried out. Through the comparison and analysis of experimental data on phase differences among three exciters, responses of system, and phases of three exciters recorded by high-speed camera, the parameters of system satisfying the above two criterions can ensure the synchronous and stable operation of three exciters. As a result, the average method of modified small parameters can be used as a theoretical apparatus studying reasonably the synchronization mechanism of three exciters, it is also proved to be useful and feasible by numeric and experiment. The present research lays the foundation and guidance for the establishment of synchronization theory system with multi-exciter and engineering design.

Influence of Self-excited Vibrating Cavity Structure on Droplet Diameter Characteristics of Twin-fluid Nozzle

It is a great challenge to find effective atomizing technology for reducing industrial pollution; the twin-fluid atomizing nozzle has drawn great attention in this field recently. Current studies on twin-fluid nozzles mainly focus on droplet breakup and single droplet characteristics. Research relating to the influences of structural parameters on the droplet diameter characteristics in the flow field is scarcely available. In this paper, the influence of a self-excited vibrating cavity structure on droplet diameter characteristics was investigated. Twin-fluid atomizing tests were performed by a self-built open atomizing test bench, which was based on a phase Doppler particle analyzer(PDPA). The atomizing flow field of the twin-fluid nozzle with a self-excited vibrating cavity and its absence were tested and analyzed. Then the atomizing flow field of the twin-fluid nozzle with different self-excited vibrating cavity structures was investigated.The experimental results show that the structural parameters of the self-excited vibrating cavity had a great effect on the breakup of large droplets. The Sauter mean diameter(SMD) increased with the increase of orifice diameter or orifice depth. Moreover, a smaller orifice diameter or orifice depth was beneficial to enhancing the turbulence around the outlet of nozzle and decreasing the SMD. The atomizing performance was better when the orifice diameter was2.0 mm or the orifice depth was 1.5 mm. Furthermore, the SMD increased first and then decreased with the increase of the distance between the nozzle outlet and self-excited vibrating cavity, and the SMD of more than half the atomizing flow field was under 35 μm when the distance was 5.0 mm. In addition, with the increase of axial and radial distance from the nozzle outlet, the SMD and arithmetic mean diameter(AMD) tend to increase. The research results provide some design parameters for the twin-fluid nozzle, and the experimental results could serve as a beneficial supplement to the twin-fluid nozzle study.

FABRICATION AND TEST OF AN ELECTROMAGNETIC VIBRATING RING GYROSCOPE BASED ON SOI WAFER

Mode matching is the key to improve the performance of micro-machined vibrating ring gyroscopes.Mass and stiffness asymmetries can lend to normal modes badly mismatch for gyroscopes fabricated by single-crystal silicon.The mismatch of the normal nodes results in large normal mode frequency split and degraded sensitivity.To address this issue,a Silicon-On-Insulator(SOI) wafer is used to fabricate the sensor chips.Meanwhile,a compensate disk and the backside coated negative photo resist(AZ303) is employed to weaken the Lag and Footing effect during the Deep Reactive Ion Etching(DRIE) process.Test results reveal that frequency split between the normal modes is of less than 10 Hz before the following electronic tuning.Thus,the mode matching of the electromagnetic vibrating ring gyroscope is probable to be realized.

Enhanced Vibrating Particles System Algorithm for Parameters Estimation of Photovoltaic System

To evaluate the performance of a photovoltaic panel, several parameters must be extracted from the photovoltaic. These parameters are very important for the evaluation, monitoring and optimization of photovoltaic. Among the methods developed to extract photovoltaic parameters from current-voltage (I-V) characteristic curve, metaheuristic algorithms are the most used nowadays. A new metaheuristic algorithm namely enhanced vibrating particles system algorithm is presented here to extract the best values of parameters of a photovoltaic cell. Five recent algorithms (grey wolf optimization (GWO), moth-flame optimization algorithm (MFOA), multi-verse optimizer (MVO), whale optimization algorithm (WAO), salp swarm-inspired algorithm (SSA)) are also implemented on the same computer. Enhanced vibrating particles system is inspired by the free vibration of the single degree of freedom systems with viscous damping. To extract the photovoltaic parameters using enhanced vibrating particles system algorithm, the problem can be set as an optimization problem with the objective to minimize the difference between measured and estimated current. Four case studies have been implemented here. The results and comparison with other methods exhibit high accuracy and validity of the proposed enhanced vibrating particles system algorithm to extract parameters of a photovoltaic cell and module.

DYNAMIC BEHAVIOUR OF LIQUID DISPERSION IN A VIBRATING PLATE TANK

In this paper a new model of the drop breakage in a vibrating plate tank has been developed by a me-chanism based on the shearing stress in the neighborhood of the holes in the plates as a breakage force,andthe coalescence of drops may be dealt with by the process of gas molecule collision.Based on the theoreticalanalyses,simulation of drop breakage and coalescence which are random processes has been carried out byMonte-Carlo simulation technique.The parameters of breakage and coalescence rate have been obtained.

Synchronization and Stability of a Nonlinear Vibrating Mechanical System Characterized by Asymmetrical Piecewise Linearity

In previous studies about the synchronization of vibrators,the restoring forces of springs are mainly treated as linear directly,whereas the nonlinear features are rarely considered in vibrating systems.To make up this drawback,a dynamical model of a nonlinear vibrating mechanical system with double rigid frames(RFs),driven by two vibrators,is proposed to explore the synchronization and stability of the system.In this paper,the nonlinearity is reflected in nonlinear restoring forces of springs characterized by asymmetrical piecewise linear,where the nonlinear stiffness of springs is linearized equivalently using the asymptotic method.Based on the average method and Hamilton’s principle,the theory conditions to achieve synchronization and stability of two vibrators are deduced.After the theory analyses,some numerical qualitative analyses are given to reveal the coupling dynamical characteristics of the system and the relative motion properties between two RFs.Besides,some experiments are carried out to examine the validity of the theoretical results and the correctness of the numerical analyses results.Based on the comparisons of the theory,numeric and experiment,the ideal working regions of the system are suggested.Based on the present work,some new types of vibrating equipment,such as vibrating discharging centrifugal dehydrators/conveyers/screens,can be designed.

Effect of vibrating electrode on temperature profiles,fluid flow,and pool shape in ESR system based on a comprehensive coupled model

The vibrating electrode method was proposed in the electro-slag remelting(ESR) process in this paper,and the effect of vibrating electrode on the solidification structure of ingot was studied.A transient threedimensional(3D) coupled mathematical model was established to simulate the electromagnetic phenomenon,fluid flow as well as pool shape in the ESR process with the vibrating electrode.The finite element volume method is developed to solve the electromagnetic field using ANSYS mechanical APDL software.Moreover,the electromagnetic force and Joule heating are interpolated as the source term of the momentum and energy equations.The multi-physical fields have been investigated and compared between the traditional electrode and the vibrating electrode in the ESR process.The results show that the drop process of metal droplets with the traditional electrode is scattered randomly.However,the drop process of metal droplets with the vibrating electrode is periodic.The highest temperature of slag layer with the vibrating electrode is higher than that with the traditional electrode,which can increase the melting rate due to the enhanced heat transfer in the vicinity of the electrode tip.The results also show that when the amplitude and frequency of the vibrating electrode increase,the cycle of drop process of metal droplets decreases significantly.

Research on CAD of Activatorof Vibrating Screen

Based on Autodesk Mechanical Desktop (MDT), three main. approaches of parametric part design including program-drive, table-drive and interactive-drive were studied. By using Visual Basic and ActivesX automation component programming, access database, parametric drawing and mechanism analysis were integrated. h probes into how to design mechanical products quickly and effectively by means of CAD.

Self-Synchronous Principle and Design of Vibrating Machines in Asymmetric System

Self-Synchronous principle of vibrating machines in asymmetric system is studied, and a design method is put forward. Based on Hamilton’s principle, a stable difference of phase angle is obtained,and this design method is proved correct.

THE RESPONSE OF TURBULENT FLOW TO THE DISTURBANCE OF A VIBRATING RIBBON

By use of the LDV, experimental investigation was carried out for a turbulent boundary layer which was disturbed with an electric-magnetic vibrating ribbon. It is found that, in the how, the response of the disturbance contains harmonic components besides the fundamental frequency of the ribbon vibration. The fundamental and harmonic disturbances can also enhance the energy of of the frequency components around them. In the experiments, the regular disturbance was introduced in the outer region of the boundary layer. Under the given flow conditions, they can significantly influence the downstream coherent structures in the wall region by suppressing the bursts and increasing their period. The effect on the burst period depends on the disturbing frequency.

A computational fluid dynamics investigation of a novel flooded-bed dust scrubber with vibrating mesh

This work proposes a vibrating mesh screen as an alternative to the static mesh screen currently used in conventional flooded-bed dust scrubbers for removing airborne coal mine dust in the continuous mining environment.Fundamental assessments suggest that a vibrating screen may improve the dust collection efficiency of scrubber systems and mitigate the clogging issues associated with the conventional design.To evaluate this hypothesis,computational fluid dynamics(CFD)simulations were carried out to assess the effects of vibration conditions(i.e.,frequency and amplitude)on the dust particle-mesh interaction and mesh wetting conditions,which are the two decisive factors in determining the dust collection efficiency.The results suggest that the vibrating mesh screen can enhance dust particle collision opportunities on the mesh and increase mesh wetted area as compared to the static mesh screen.The effects of mesh screen aperture,coal dust concentration,and spray nozzle flow rate on the performance of the vibrating mesh are also evaluated.Finally,a simplified three-phase flow simulation including airflow,dust particles,and water droplet spray is performed,and the results reflect a significant improvement of dust collection efficiency in the liquid-coated vibrating mesh screen.

Manipulating fluid with vibrating 3D-printed paddles for applications in micropump

This paper presents a novel working mechanism of a micropump using micropaddles(MPs)to actively manipulate fluid based on 3 D printing technology.The novel working principle is systematically discussed using analysis,computation and experiment methods.A theoretical model is established to research the working mechanism and crucial parameters for driving ability,such as MPs shape,size,vibration amplitude and frequency.Two different 3 D printing techniques that simplify the multi-step process into only one step are introduced to manufacture the prototype pump for investigating the principle experimentally.A testing system is designed to evaluate the flow rate of pumps with eight different vibrating paddles.A maximum flux of 127.9 mL/min is obtained at an applied voltage of 9 V.These experiments show that the active-type mechanical pump could not only freely control flow direction but also change flux by adopting different shapes or distribution ways.The advantage of the novel micropump is the application of the MP structure into the micropump system to actively manipulate fluid with flexibility and high driving ability at fairly low power.

VIBRATING VELOCITY RECONSTRUC-TION USING IBEM AND TIKHONOV REGULARIZATION

The inverse problem to determine the vibrating velocity from known exteriorfield measurement pressure, involves the solution of a discrete ill-posed problem. To facilitate thecomputation of a meaningful approximate solution possible, the indirect boundary element method(IBEM) code for investigating vibration velocity reconstruction and Tikhonov regularization methodby means of singular value decomposition (SVD) are used. The amount of regularization is determinedby a regularization parameter. Its optimal value is given by the L-curve approach. Numerical resultsindicate the reconstructed normal surface velocity is a good approximation to the real source.

The Anti-Vibrating-Impact Research of the Piezoelectric Resonator Force Sensor

Based on the analysis of one-dimension inertial accelerometer movement model,from which the resolution of the accelerometer inertial mass displacement equation was derived,the response of the sensor sensing element to vibration and impact of various frequencies was studied.The theoretical and experimental results show that a reasonable configuration among the sensing element inherent frequency,environmental exciting frequency and the damp factors of the sensor is the key to prevent the sensor from damage.The sensor has good anti-vibrating impact ability when the relative damp factor is 0.7,and the environmental interferential vibrating frequency is less than 0.35 times of the inherent frequency of the sensing element.