Analysis of vibration and frequency transmission of high speed EMU with flexible model

When the operation speed of the high-speed train increases and the weight of the carbody becomes lighter,not only does the sensitivity of the wheel/rail contact get higher,but also the vibration frequency range of the vehicle system gets enlarged and more frequencies are transmitted from the wheelset to the carbody.It is important to investigate the vibration characteristics and the dynamic frequency transmission from the wheel/rail interface to the carbody of the high-speed electric multi-uint（EMU）.An elastic highspeed vehicle dynamics model is established in which the carbody,bogieframes,and wheelsets are all dealt with as flexible body.A rigid high-speed vehicle dynamics model is set up to compare with the simulation results of the elastic model.In the rigid vehicle model,the carbody,bogieframes and wheelsets are treated as rigid component while the suspension and structure parameters are the same as used in the elastic model.The dynamic characteristic of the elastic high speed vehicle is investigated in time and frequency domains and the di ff erence of the acceleration,frequency distribution and transmission of the two types of models are presented.The results show that the spectrum power density of the vehicle decreases from the wheelset to the carbody and the acceleration transmission ratio is approximately from 1%to 10%for each suspension system.The frequency of the wheelset rotation is evident in the vibration of the flexible model and is transmitted from the wheelset to the bogieframe and to thecarbody.The results of the flexible model are more reasonable than that of the rigid model.A field test data of the high speed train are presented to verify the simulation results.It shows that the simulation results are coincident with the field test data.

Research on two-dimensional fluid vibration axial transmission path model of axial piston pump

High speed and high pressure can enhance the vibration of axial piston pump. A fluid vibration transmission law of axial piston pump is studied in this paper. According to harmonic response analysis results, a transmission path analysis is used to establish a two-dimensional fluid vibration transmission path model in the vertical plane, which has characteristics of multi excitation sources, multi-path and multi-receptors. Model parameters are obtained by experimental and numerical analysis. Matlab is used to solve the model, and acceleration vibration response of three shells is got. To reduce the effect of mechanical vibration, the surface acceleration of pump is tested under low speed condition. Results show that the model can accurately reveal transmission law of fluid vibration and the accuracy is more than 90%. The research lays a foundation for exploring vibration transmission law and vibration control.

A novel method for vibration signal transmission and attenuation analysis in complex planetary gearboxes

Planetary gearboxes play a crucial role in altering rotary speed and transmitting power in large machines like wind turbines and sophisticated vehicles. There are many nonlinear interfaces, such as splines, bearings, and gear pairs, in planetary gearboxes, and the resulting vibration signal transmission and attenuation mechanisms are still unknown. In this study, a novel method for quantitatively analyzing the transmission and attenuation of vibration signals is proposed. A multibody dynamic model of the planetary gearbox considering nonlinear gear meshing is presented and experimentally validated. To avoid the interference of foundation vibration on the transmission of the fault signal, the fault impact factor(FIF) is used to describe the intensity of the failure, which aligns well with the experimental signals. Based on the FIF, the vibration signal attenuation of nonlinear interfaces such as splines, bearings, and gear meshing interfaces is quantitatively evaluated. To clarify the transfer paths of fault vibration signals inside the gearbox, the transfer path area method(TPAM) based on FIF is proposed. According to the simulated results,the primary transfer paths of fault vibration signals within the gearbox have been identified, which is of great help in understanding the transmission and attenuation of vibration signals in planetary gearboxes.

Influence of equipment excitation on flexible carbody vibration of EMU

To study the vibration transmission character istics of a flexible carbody and its suspended equipment, a vertical mathematical model of highspeed electric multiple unit was established with equipment excitation considered. And the dynamic unbalance and impact turbulence excita tion from equipment were taken into account in a single stage and twostage vibration isolation system, respectively. Results show that the excitation transferred to carbody increases with suspension stiffness but decreases with the equipment mass increasing; the vibration transmission can be reduced by increasing the equipment mass or reduce the suspension stiffness. To avoid vibration resonance, the dynamic unbalance frequency of equipment should be out of the possible range of the carbody flexible modes, and a small stiffness should be applied to reduce the impact tur bulence. A small stiffness, however, would result in a large movement of the equipment which is limited by the static deflection requirement, while a great stiffness will transfer high frequency vibration. Therefore, a preferred stiffness should make the suspension frequency of equipment a bit greater than the first bending mode of carbody. Additionally, a 3D rigidflexible coupled dynamics model was built to verify the mathematical analysis, and they show good agreements. Results show that a twostage isolation could reduce the excitation transmission and make the vibration of carbody and equipment acceptable.

Nonlinear identification and characterization of structural joints based on vibration transmissibility

In order to investigate the nonlinear characteristics of structural joint,the experimental setup with a jointed mass system is established for dynamic characterization analysis and vibration prediction,and a corresponding nonlinearity identification method is studied.First,the sine-sweep vibration test with different baseexcitation levels areapplied to the structural joint system to study the dominant modal of mass rigid motion.Then,based on t e harmonic balance method principle,t e measured vibration transmissibilities a e utilized for nonlinearity identification using different excitation levels.Experimental results show that nonlinear spring and damping force can be represented by a polynomial order approximation.The identified nonlinear stiffness and damping force can predict the system’s response,and they can reveal t e shifts of resonant frequency or damping due to discontinuity of contact mechanisms within a certain range.

Vibration transmissibility characteristics of smart spring vibration isolation system

The objective of this work was to study the vibration transmissibility characteristics of the undamped and damped smart spring systems. The frequency response characteristics of them were analyzed by using the equivalent linearization technique, and the possible types of the system motion were distinguished by using the starting and ending frequencies. The influences of system parameters on the vibration transmissibility characteristics were discussed. The following conclusions may be drawn from the analysis results. The undamped smart spring system may simultaneously have one starting frequency and one ending frequency or only have one starting frequency, and the damped system may simultaneously have two starting frequencies and one ending frequency. There is an optimal control parameter to make the peak value of the vibration transmissibility curve of the system be minimum. When the mass ratio is far away from the stiffness ratio, the vibration transmissibility is small. The effect of the damping ratio on the system vibration transmissibility is significant while the control parameter is less than its optimal value. But the influence of the relative damping ratio on the vibration transmissibility is small.

Flexural wave bandgap properties of phononic crystal beams with interval parameters

Uncertainties are unavoidable in practical engineering,and phononic crystals are no exception.In this paper,the uncertainties are treated as the interval parameters,and an interval phononic crystal beam model is established.A perturbation-based interval finite element method(P-IFEM)and an affine-based interval finite element method(A-IFEM)are proposed to study the dynamic response of this interval phononic crystal beam,based on which an interval vibration transmission analysis can be easily implemented and the safe bandgap can be defined.Finally,two numerical examples are investigated to demonstrate the effectiveness and accuracy of the P-IFEM and A-IFEM.Results show that the safe bandgap range may even decrease by 10%compared with the deterministic bandgap without considering the uncertainties.

Optimization Design and Performance Analysis of Vehicle Powertrain Mounting System

The design strategies for powertrain mounting systems play an important role in the reduction of vehicular vibration and noise. As stiffness and damping elements connecting the transmission system and vehicle body, the rubber mount exhibits better vibration isolation performance than the rigid connection. This paper presents a complete design process of the mounting system, including the vibration decoupling, vibration simulation analysis, topology optimization, and experimental verification. Based on the 6?degrees?of?freedom vibration coupling model of the powertrain mounting system, an optimization algorithm is used to extract the best design parameters of each mount, thus rendering the mounting system fully decoupled and the natural frequency well configured, and the optimal parameters are used to design the mounting system. Subsequently, vibration simulation analysis is applied to the mounting system, considering both transmission and road excitations. According to the results of finite element analysis, the topological structure of the metal frame of the front mount is optimized to improve the strength and dynamic characteristics of the mounting system. Finally, the vibration bench test is used to verify the availability of the optimization design with the analysis of acceleration response and vibration transmissibility of the mounting system. The results show that the vibration isolation performance of the mounting system can be improved effectively using the vibration optimal decoupling method, and the structural modification of the metal frame can well promote the dynamic characteristics of the mounting system.

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.

Reducing force transmissibility in multiple degrees of freedom structures through anti-symmetric nonlinear viscous damping

In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom （MDOF） structures, in which an isolator with nonlinear anti-symmetric viscous damping is assembled. The results reveal that the anti-symmetric nonlinear viscous damping can significantly reduce the force trans- missibility over all resonance regions for MDOF structures with little effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to solve the dilemma occurring in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant frequencies but increases the transmissibility over non-resonant frequency regions. This work is an extension of a previous study in which MDOF structures installed on the mount through an isolator with cubic nonlinear damping are considered. The theoretical analysis results are also verified by simulation studies.

Forced vibrational power flow input and transmission in a fluid-filled shell

The characteristics of vibrational power flow in an infinite elastic cylindrical shell filled with fluid are investigated. The simple harmonic motion of the shell and the pressure field in the contained fluid are described by the Fltigge shell equations and Helmholtz equation respectively. The vibrational equation of this system is obtained by using the coupling of shell and fluid. The dispersion curves are discussed for different circumferential orders. By using Fourier transform and its inverse transform, the input power into this coupled system excited by a simple harmonic linearly distributed driving force is studied. Along the shell, the transmission of the power flow carried by different shell internal forces and by the contained fluid are discussed

An experimental investigation on sound transmission loss and vibration reduction of a vessel in water

Experimental results of sound transmission loss in a range of frequency through bubbly curtains were obtained, where the air content was in a wide range by means of varying pressure differences and the diameters of the pores of bubble-produce apparatus . Vibration reduction of a vessel in water due to the bubbly curtain was found.

Continuous preparation of strong and tough PVA nanocomposite fibers by mechanical stretching-assisted salting-out treatment

Polymer composite fibers with superior properties such as excellent combined strength and toughness and biocompatibility can be used in high-tech applications of braided protective devices and smart wearable,however the research of high-performance polymer composite fiber remains in the infant stage.Here we present a strategy to produce strong and tough anisotropic polymer nanocomposite fibers with orientedly aligned salt rods using mechanical stretching-assisted salting-out treatment.The prepared nanocomposite fibers have a tensile strength of up to 786±2.7 MPa and an elongation at break of 81%,and the anisotropic fibers exhibit good transmission of mechanical vibration in the longitudinal direction with high resolution.During the fabrication process,the salt builds up into oriented rods during the directional salting process,and the polymer is confined to the 150 nm domain between the rods after the solvent is completely evaporated,giving the nanocomposite fibers superior mechanical properties.The presented strategy can be applied to the continuous mass production of nanocomposite fibers and is also generalizable to other polymer nanocomposites,which could extend the applicability of nanocomposite fibers to conditions involving more demanding mechanical loading and mechanical vibration transmission.

Energy dissipation mechanism and experiment of particle dampers for gear transmission under centrifugal loads

As a passive means of vibration reduction, particle damping is mainly applied to the horizontal or vertical steady field. However, it is seldom applied to centrifugal fields. Under high speed and heavy loading, the vibration of tooth surfaces of gear transmissions becomes more severe shortening gear service life and augmenting noise. Under centrifugal loading, the particle system exhibits different characteristics, for example, particles are extruded at the end farthest from the center. We investigated gears with drilled via holes filled with damping particles. Using the discrete-element method, we developed an energy dissipation model for the particle system accounting for friction and inelastic collisions. Energy dissipation and damping characteristics of this system were analyzed. Experiments were also conducted with the gear system having different particle filling rates. The results show that this filling rate is an important parameter associated with particle damping in a centrifugal field. An unsuitable filling rate would significantly reduce damping effectiveness. With changes in rotation speed and load, the gear transmission system has different optimal filling rates. The results provide guidelines for the application of particle damping in centrifugal fields of gear transmissions.

Dynamic characteristics of dwarf Chinese hickory trees under impact excitations for mechanical fruit harvesting

Mechanical vibration is an effective fruit harvesting method.To evaluate the dynamic characteristics of dwarf Chinese hickory(Carya cathayensis Sarg.)trees and the influence of the tree structure on transmission and attenuation of dynamic response,a new method was proposed based on acceleration admittance measurement on dwarf Chinese hickory trees in orchard environment under impact excitation.The primary resonance frequencies of the tree can be determined based on the acceleration admittance measurement.The effect of the tree structure on the vibratory transmission was quantified using the attenuation ratio of the acceleration admittance.A 5-year-old dwarf Chinese hickory tree sample was tested.The responses at three resonance frequencies(5,9 and 12 Hz)were analyzed because they were identified as the most effective bands of excitation for the main part of the tree specimen.The results reveal that the variation of the dynamic response along the testing tree is greatly related to the Chinese hickory tree structure.The attenuation ratio of the acceleration admittance at the branch crotches indicates the leader top crotch may amplify the acceleration admittance no matter what the crotch angle and the branch diameter is.Unlike the crotches,the branch chain nodes generally have negative influence on the acceleration admittance along the branch chains which heavily depend on the branch chain configuration.The branch chains with a chain angle no less than 150°and a wood diameter ratio close to 1.0 could produce little influence on the vibration transmission.For those branches with chain angle less than 150°,the vibration was generally attenuated at their chain nodes at three resonance frequencies.To impose impact excitations on the tree,high mechanical harvesting efficiency could be achieved on those branch chains which are almost straight and uniform.

Time-varying stiffness analysis of double-row tapered roller bearing based on the mapping structure of bearing stiffness matrix

Time-varying stiffness is one of the most important dynamic characteristics of rolling element bearings.The method of analyzing the elements in the bearing stiffness matrix is usually adopted to investigate the characteristics of bearing stiffness.Linear mapping structure of the bearing stiffness matrix is helpful to understand the varying compliance excitation and its influence on vibration transmission.In this study,a method to analyze the mapping structure of bearing stiffness matrix is proposed based on the singular value decomposition of block matrices in the stiffness matrix.Not only does this method have the advantages of coordinate transformation independence and unit independence,but also the analysis procedure involved is geometrically intuitive.The time-varying stiffness matrix of double-row tapered bearing is calculated and analyzed using the proposed method under two representative load cases.The principal stiffnesses and principal axes defined in the method together indicate the dominant and insignificant stiffness properties with the corresponding directions,and the vibration transmission properties are also revealed.Besides,the coupling behaviors between different shaft motions are found during the analysis of mapping structure.The mechanism of the generation of varying compliance excitation is also revealed.