Torque effect on vibration behavior of high-speed train gearbox under internal and external excitations

The high-speed train transmission system,experiencing both the internal excitation originating from gear meshing and the external excitation originating from the wheel-rail interaction,exhibits complex dynamic behavior in the actual service environment.This paper focuses on the gearbox in the high-speed train to carry out the bench test,in which various operat-ing conditions(torques and rotation speeds)were set up and the excitation condition covering both internal and external was created.Acceleration responses on multiple positions of the gearbox were acquired in the test and the vibration behavior of the gearbox was studied.Meanwhile,a stochastic excitation modal test was also carried out on the test bench under different torques,and the modal parameter of the gearbox was identified.Finally,the sweep frequency response of the gearbox under gear meshing excitation was analyzed through dynamic modeling.The results showed that the torque has an attenuating effect on the amplitude of gear meshing frequency on the gearbox,and the effect of external excitation on the gearbox vibration cannot be ignored,especially under the rated operating condition.It was also found that the torque affects the modal param-eter of the gearbox significantly.The torque has a great effect on both the gear meshing stiffness and the bearing stiffness in the transmission system,which is the inherent reason for the changed modal characteristics observed in the modal test and affects the vibration behavior of the gearbox consequently.

Internal Vibration and Synchronization of Four Coupled Self-Excited Elastic Beams

The vibration behavior and the synchronization between some internal points of four coupled self-excited beams are numerically studied. Coupling through the root of the beams is considered. The transverse displacements of the internal points and the beam tips are monitored, and the power spectra of the resulting time series are employed to determine the oscillation frequencies. The synchronization between beams is analyzed using phase portraits and correlation coefficients. Numerical results show multiple frequencies in the vibration pattern, and complex patterns of synchronization between pairs of beams.

Substrate-borne vibrational signals and stridulatory organs for sexual communication in leafminer, Liriomyza sativae (Diptera: Agromyzidae)

The vegetable leafminer(Liriomyza sativae[Burgess])is a highly polyphagous pest that threatens vegetables and horticultural plants.Although sexual communication is a key component of the animal behavioral repertoire,the mechanism underlying sexual communication in L.sativae remains to be elucidated.Here,we used laser vibrometry to characterize the vibrational signals emitted by L.sativae during pair formation.By emitting trains of vibrational pulses(male calling)the male initiated communication on the host plant.The female then became immobile and responded to the male calling by emiting replies(female replies),which in turn triggered male replies consisting of a rapid series of chirps and trills.If the female replied,a continuous exchange of male and female replies ensued,representing a duet.In playback trials,a playback signal caused responses from the opposite sex.Moreover,scanning electron microscopy revealed vibration-producing stridulatory organs in both male and female individuals.The files in males were more developed than those in females,and older male specimens had more signs of abrasion.The results provide new insight into the mating biology of L.sativae.

Simulation of nonlinear vibration responses of cab system subject to suspension damper complete failure for trucks

The strong vibration responses of the cab system can be restrained by the damper force and the friction of the suspensions for trucks.After the failures of dampers,especially in the case of the complete failure,the anti vibration effect of the friction is prominent.However,the nonlinear vibration response characteristics of the cab subject to the damper complete failure have not been revealed.In order to reveal the nonlinear vibration response characteristics,a dynamic model of the cab system was established and its vibration equations were given.The friction forces existing in the suspensions were determined by the bench test.The influences of the friction forces on the cab vibration under different amplitude harmonic inputs were investigated when the dampers completely fail.The cab vertical displacement changes with the excitation amplitude and the vibration represents various motion states,including the periodic motion,the quasi-periodic motion,and the chaotic motion.The simulation results show that when the dampers fail,the proper friction forces help to suppress the quasi-periodic motion and the chaotic motion of the cab and to reduce the amplitude of the periodic motion.The proper friction forces can make the cab movement far away from the chaos area.They also help to avoid the fatigue damage of the cab floor and suspension parts to improve the service life of the suspension parts and to reduce the maintenance cost of the cab suspensions.

FREE TRANSVERSE VIBRATIONS OF A DOUBLE-WALLED CARBON NANOTUBE:GRADIENT AND INTERNAL INERTIA EFFECTS

This is a modest contribution on higher-order continuum theory for predicting size effects in small-scale objects. It relates to a preceding article of the journal by the same authors（AMSS, 2013, 26： 9-20） which considered the longitudinal dynamical analysis of a gradient elastic fiber but, in addition to an internal length, an internal time parameter is also introduced to model delay/acceleration effects associated with the underlying microstructure. In particular, the free transverse vibration of a double-walled carbon nanotube（DWNT） is studied by employing gradient elasticity with internal inertia. The inner and outer carbon nanotubes are modeled as two individual elastic beams interacting with each other through van der Waals（vdW） forces. General explicit expressions are derived for the natural frequencies and the associated inner-to-outer tube amplitude ratios for the case of simply supported DWNTs. The effects of internal length（or scale）and internal time（or inertia） on the vibration behavior are evaluated. The results indicate that the internal length and time parameters of the adopted strain gradient-internal inertia generalized elasticity model have little influence on the lower order coaxial and noncoaxial vibration modes,but a significant one on the higher order modes.

VIBRATION OPTIMIZATION OF A PASSIVE SUSPENSION SYSTEM VIA GENETIC ALGORITHM

In this paper,we have formulated mathematical models to optimize the bouncing transmissibility of the sprung mass of the half car system with passengers’seat suspensions considering different road conditions.The corresponding problem has been solved with the help of advanced real coded Genetic Algorithm(GA).The nonlinearity of suspension spring and damper,which are the most important characteristics of the suspension,has been taken into account in order to validate the model to real applications.The nonlinear cubic polynomial has been used to describe the spring characteristic and a quadratic polynomial has been used to describe the damper characteristic.The coefficients of each polynomial represent the design parameters of the suspension system and are to be determined.To find these parameters we have formulated a nonlinear optimization problem in which the bouncing transmissibility of the sprung mass at the center of mass has been minimized with respect to technological constraints and the constraints which satisfy the performance as per ISO 2631 standards.The advanced real coded GA has been used to solve this problem in time domain and the results obtained have been compared to those obtained using the existing design parameters.The objective function and the constraints have been evaluated by simulating the vehicle model over two roads with multiple bumps at uniform velocity.

Nonlinear vibration analysis of a rotor supported by magnetic bearings using homotopy perturbation method

In this paper,the effects of nonlinear forces due to the electromagnetic field of bearing and the unbalancing force on nonlinear vibration behavior of a rotor is investigated.The rotor is modeled as a rigid body that is supported by two magnetic bearings with eightpolar structures.The governing dynamics equations of the system that are coupled nonlinear second order ordinary differential equations(ODEs)are derived,and for solving these equations,the homotopy perturbation method(HPM)is used.By applying HPM,the possibility of presenting a harmonic semi-analytical solution,is provided.In fact,with equality the coefficient of auxiliary parameter(p),the system of coupled nonlinear second order and non-homogenous differential equations are obtained so that consists of unbalancing effects.By considering some initial condition for displacement and velocity in the horizontal and vertical directions,free vibration analysis is done and next,the forced vibration analysis under the effect of harmonic forces also is investigated.Likewise,various parameters on the vibration behavior of rotor are studied.Changes in amplitude and response phase per excitation frequency are investigated.Results show that by increasing excitation frequency,the motion amplitude is also increases and by passing the critical speed,it decreases.Also it shows that the magnetic bearing system performance is in stable maintenance of rotor.The parameters affecting on vibration behavior,has been studied and by comparison the results with the other references,which have a good precision up to 2nd order of embedding parameter,it implies the accuracy of this method in current research.

Phase behaviors of transfer functions in Vibrating systems

This paper investigates the applicabilitles of pole-zero model and wave propagation theory in estimating the phase characteristics of vibrating systems. The measured phase spectra are compared with the estlmated reverberant phase limit and wave propagation phase. The relations between transfer function phase and frequency, damping, and separation distance are described. The present results show that the pole-zero model provides a reasonable estimation of the reverberant phase limit in low frequency band below an identified transition frequency.The reverberant phase is linearly dependent on frequency in this band, but from the transition frequency and onwards the phase increases only with the square root of frequency. This behavior is characteristic for free propagating waves