Structure design and simulation of MEMS vibrating ring gyroscope

MEMS gyroscope is a new inertial navigation sensor,which can measure the input angular rate of sensitive axis using Coriolis effect.Compared to the conventional gyroscope,it owns many unique advantages.A novel structure of vibrating ring gyroscope is proposed and the finite element model of the oscillator is established based on MEMS technology.Through the modal analysis,the natural frequency and mode shapes of the oscillator are obtained.By analyzing the effects of the structural parameters on the mode shapes and frequency of the harmonic oscillator,the optimal design parameters are got.The frequency difference between the operating mode and the other modes is greater than 1kHz after optimization,which can avoid the frequency coupling of the operating mode and other vibrating modes of the oscillator.The simulation results show that the performance parameters of the ring structure meet the design requirements and have obvious advantages.

Grain refinement of Al-5%Cu aluminum alloy under mechanical vibration using meltable vibrating probe

A mechanical vibration technique to refine solidified microstructure was reported. Vibration energy was directly introduced into a molten alloy by a vibrating horn, and the vibrating horn was melted during vibration. Effects of vibration acceleration and mass ratio on the microstructure of Al-5% Cu alloy were investigated. Results show that the present mechanical vibration could provide localized cooling by extracting heat from the interior of molten alloy, and the cooling rate is strongly dependent on vibration acceleration. It is difficult to refine the solidified microstructure when the treated alloy keeps full liquid state within the entire vibrating duration. Significantly refined microstructure was obtained by applying mechanical vibration during the initial stage of solidification. Moreover, mechanisms of grain refinement were discussed.

Improvement for design of beam structures in large vibrating screen considering bending and random vibration

Demand for large vibrating screen is huge in the mineral processing industry. As bending and random vibration are not considered in a traditional design method for beam structures of a large vibrating screen, fatigue damage occurs frequently to affect the screening performance. This work aims to conduct a systematic mechanics analysis of the beam structures and improve the design method. Total motion of a beam structure in screening process can be decomposed into the traditional followed rigid translation(FRT), bending vibration(BV) and axial linear-distributed random rigid translation(ALRRT) excited by the side-plates. When treated as a generalized single-degree-of-freedom(SDOF) elastic system analytically, the BV can be solved by the Rayleigh's method. Stochastic analysis for random process is conducted for the detailed ALRRT calculation. Expressions for the mechanics property, namely, the shearing force and bending-moment with respect to BV and ALRRT, are derived, respectively. Experimental and numerical investigations demonstrate that the largest BV exists at the beam center and can be nearly ignored in comparison with the FRT during a simplified engineering design. With the BV and FRT considered, the mechanics property accords well with the practical situation with the maximum error of 6.33%, which is less than that obtained by traditional method.

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.

Dynamic analysis and simulation of four-axis forced synchronizing banana vibrating screen of variable linear trajectory

A new concept of banana vibrating screen which has the same effect as traditional banana vibrating screen in a new way was put forward.The dynamic model of vibrating screen was established and its working principle was analyzed when the action line of the exciting force did not act through the centroid of screen box.Moreover,the dynamic differential equations of centroid and screen surface were obtained.The motions of centroid and screen surface were simulated with actual parameters of the design example in Matlab/Simulink.The results show that not only the amplitude has a significant decrease from 9.38 to 4.10 mm,but also the throwing index and vibrating direction angle have a significant decrease from 10.49 to 4.59,and from 58.10° to 33.29°,respectively,along the screen surface,which indicates that motion characteristics of vibrating screen are consistent with those of traditional banana vibrating screen only by means of a single angle of screen surface.What's more,such banana vibrating screen of variable linear trajectory with greater processing capacity could be obtained by adjusting the relative position of force center and the centroid of screen box properly.

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.

Comparison of microstructure and wear resistance of A356-SiC_p composites processed via compocasting and vibrating cooling slope

The influences of SiC content on the microstructure, porosity, hardness and wear resistance of A356？SiCp composites processed via two different methods of compocasting and vibrating cooling slope （VCS） were compared with each other. In the as-cast condition, the matrix of VCS and compocast processed composites exhibited globular and dendritric structures, respectively. While a more uniform distribution of SiC particulates in the matrix alloy as well as higher hardness values were obtained for the VCS processed samples, the composites produced via compocasting exhibited less porosity. The increased SiC content （up to 20% in volume fraction） resulted in a more uniform distribution of SiC particles within the matrix alloy and improved wear resistance for both the composite series. However, for the VCS processed composites, the increased SiC content, resulted in the decreased size and shape factor of globules as well as better tribological properties when compared with compocast composites. It was concluded that the improved properties of the VCS processed composites when compared with their compocast counterparts was a consequence of a more uniform distribution of SiC particulates in the matrix alloy as well as the globular microstructure generated during the VCS process.

Analysis of the Dynamic Response of a Shield Tunnel in Soft Soil Under a Metro-Train Vibrating Load

This paper concerns the impact of an operating metro train on the structure of a shield tunnel lining and its soft foundation. An elastoplastic 3D dynamic finite difference model was established by using the FLAC3D numerical soft- ware. By fully considering the joints, the A-B-K segments and the soft stratum, the dynamic response of the shield tunnel buried in thick, soft soil under the vibrating load induced by a metro train was numerically simulated. The simulation result, for which the joint was considered, was compared with the result when the joint was not considered. The results show that an operating metro train induces a significant dynamic response in the structure of the lining of the shield tunnel and its soft foundation. The severe dynamic response zones of the lining structure are largely distributed in the range of the lower half of the segment-ring and the nearer to the bottom of the segment-ring, the more severe the response. Of two horizontally symmetric, corresponding places on the segment lining, the one near the joint is more severe in its dynamic response than that of the one far from the joint; the nearer the zone of the foundation soil to the lower half of the seg- ment-ring, the more severe the dynamic response. The maximum shear strain of the foundation soil takes place near the joint between two normal segments at the bottom. The dynamic response influenced by joints is more severe than the response not influenced by joints, showing that the non-joint assumption is somewhat impractical.

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.

A novel ring vibrating gyroscope based on side piezo-electrodes

Solid-state wave gyroscope is one kind of high-performance vibrating gyroscopes. The present work develops a new type of solid-state wave gyroscope—a ring vibrating gyroscope driven by piezo-electrodes located on the sidewall of the structure. It has advantages of large vibrating amplitude, high energy conversion efficiency and compact structure. The working principle of the piezoelectric ring vibrating gyroscope is based on the inertia effect of the standing wave in the axisymmetric resonator caused by Coriolis force. The finite element method(FEM) analysis has been implemented to characterize the ring type resonator. The prototypal gyroscope was manufactured and has been trimmed by mechanical way. The harmonic response of the ring vibrating gyroscope has been tested. The resonating frequency of the ring type resonator is 3715.6 Hz and the frequency split of the two working modes before trimming was about 5 Hz and was reduced to sub-0.01 Hz after trimming procedure. The Q-factor of the ring type resonator was 2504. Then, the turntable experiment was implemented. The measured scale factor k is 9.24 m V/[(°)·s] and the full scale range of the gyroscope is larger than ±300(°)/s.

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.

Microstructure and mechanical properties of Al-Mg_2Si composite fabricated in-situ by vibrating cooling slope

An innovative semisolid technique termed as vibrating cooling slope(VCS)has been applied to producing in-situ Al-25%Mg2Si(mass fraction)composite.The molten Al-16.5Mg-9.4%Si(mass fraction)alloy with 100°C superheat was poured on the surface of an inclined copper plate(set at 45°inclined angle)while it was vibrated at a frequency of 40 Hz and an amplitude of 400μm.After travelling the length of 40 cm on the slope,the resultant semisolid alloy was cast into a steel mold.For the purpose of comparison,reference composite samples were made by gravity casting(GC)and conventionally still cooling slope casting(CS)methods using the same alloy under identical conditions.The samples were hot extruded at 500°C.It was concluded that the size of Mg2Si particles was decreased by about 50%and 70%for the CS and VCS produced samples respectively when compared to that of the GC produced sample.Despite of their higher porosity contents,both the as-cast and hot-extruded VCS processed samples exhibited higher hardness,shear yield stress(SYS)and ultimate shear strength(USS)values as compared with their GC produced counterparts.These results were attributed to the refined and modified microstructure obtained via this newly developed technique.

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.

Dynamic simulation on rubber spring supporting equipment of vibrating screen

By ANSYS, dynamic simulation analysis of rubber spring supporting equipment used in vibrating screen was made. The modal frequency, mode, and harmonic displacement under working frequency were obtained. Variation of rubber spring supporting equipment＇s dynamic performance was discussed first, which is under the condition of existing spring stiffness difference and exciting force bias. Also, the quantitative calculation formulas were given. The results indicate that the performance of vibrating screen is closely related with rubber spring supporting equipment＇s dynamic performance. Differences of springs＇ stiffness coefficients reduce the modal frequency reduced, decrease the dynamic stiffness, and increase vibration displacement. Exciting force bias induces a larger lateral displacement. When rubber springs＇ stiffness coefficients exist, differences and lateral force accounts for 5% in total exciting force; rubber spring supporting equipment＇s side swing is larger than 1 mm, exceeding the side swing limit.

Vibrating Breakup of Jet for Uniform Metal Droplets

Uniform droplet formation from capillary stream breakup provides promising opportunities for many applications such as solder balls manufacturing, circuit board printing and rapid prototype manufacturing. In this study an apparatus capable of making monosize metal spheres by vibrating breakup has been developed. The droplets were electrically charged to avoid collision and merging with one another during flight. As a result, uniformly sized tin powders （180 μm in diameter） were obtained after cooling and solidification.

Simulation of the screening process on a circularly vibrating screen using 3D-DEM

A numerical study of the motion particulates follow along a circularly vibrating screen deck was done using the three dimensional Discrete Element Method (DEM). The motion of the particles was analyzed. The effects of vibration amplitude, throwing index, and screen deck inclination angle on the screening process are discussed. The results show that the average velocity of the particles increases along the lon- gitudinal direction of the deck. The screening efficiency is highest when the vibration amplitude, throw- ing index, and screen deck inclination angle are 3-3.5 mm, 2.7 and 15°, respectively. This work is helpful for developing a deep understanding of particle motion and for optimizing screen separator designs.

Static-deformation based fault diagnosis for damping spring of large vibrating screen

Based on the statics theory, a novel and feasible twice-suspended-mass method(TSMM) was proposed to deal with the seldom-studied issue of fault diagnosis for damping springs of large vibrating screen(LVS). With the static balance characteristic of the screen body/surface as well as the deformation compatibility relation of springs considered, static model of the screen surface under a certain load was established to calculate compression deformation of each spring. Accuracy of the model was validated by both an experiment based on the suspended mass method and the properties of the 3D deformation space in a numerical simulation. Furthermore, by adopting the Taylor formula and the control variate method, quantitative relationship between the change of damping spring deformation and the change of spring stiffness, defined as the deformation sensitive coefficient(DSC), was derived mathematically, from which principle of the TSMM for spring fault diagnosis is clarified. In the end, an experiment was carried out and results show that the TSMM is applicable for diagnosing the fault of single spring in a LVS.