A spiral bevel gear system supported on thrust bearings considering the coupled bending-torsional nonlinear vibration is proposed and an eight degrees of freedom (8DOF) lumped parameter dynamic model of the spiral bevel gear system combined with time-varying stiffness, static transmission error, gear backlash, and bearing clearances is investigated. The spiral bevel gear system is analyzed with the equations of motion and the dynamic response is solved using the Runge-Kutta method. The effects of mesh frequency, mesh damping coefficient, load coefficient, and gear backlash are revealed, which describe the true mesh characteristics of the spiral bevel gear system. The bifurcation characteristics as jump discontinuities, periodic windows, and chaos are obtained by studying time histories, phase plane portraits, Poincaré maps, Fourier spectra, and global bifurcation diagrams of the gear system. The results presented in this study provide some useful information for engineers in designing and controlling such gear systems.
Zr) in geochemical samples by wavelength dispersive X-ray fluorescence spectrometer with a new sample preparation technique-high pressure pressed pellet and covered with a 3.6 μm polyester film is proposed. The pellet was pressed at 2,000 kN, which was particularly meaningful for the sample with high silicon content and ideal pellet was formed without binder. Coating with a polyester film prevented the variation of chlorine content after multiple analyses of the same pellet, which was caused by the vacuum and long-time irradiation.And 62 rock, soil and sediment reference materials were applied to create calibration curves. The accuracy of the method was evaluated with another eight certified reference materials that were not used in the regression curve. In most cases, the relative error between the certified value and the calculated value was <10% for major elements and <25% for trace elements, except for those approaching the limit of detection. The limit of detection obtained using this pellet preparation technology is suitable for geochemical analyses.
The variable axial transmission system composed of universal joint transmission shafts and a gear pair has been applied in many engineering fields. In the design of a drive system, the dynamics of the gear pair have been studied in detail. However few have paid attention to the effect on the system modal characteristics of the gear pair, arising from the universal joint transmission shafts. This work establishes a torsional vibration mathematical model of the transmission shaft, driving gear, and driven gear based on lumped masses and the main reducer system assembly of a CDV (car-based delivery vehicle) car. The model is solved by the state space method. The influence of the angle between transmission shafts and intermediate support stiffness on the vibration and noise of the main reducer is obtained and verified experimentally. A reference for the main reducer and transmission shaft design and the allied parameter matching are provided.
In the process of power transmission, vibration and noise are generated, which have a great effect on vehicle NVH performance. Automobile power transmission system is an important part of automobile, which mainly includes engine, clutch, gearbox, drive shaft, main reducer, half axle and driving wheel. The torque of engine transfers to driving wheel through clutch, gearbox, drive shaft and rear axle. During the operation of vehicles, it is found that dramatic vibration occurs when the engine rotation speed reaches a certain value.This phenomenon has been investigated experimentally. A torsional vibration test rig was developed to investigate the torsional vibration caused by engine excitation, including the torsional vibration responses of flywheel end of engine and gearbox input shaft (Yang et al., 2017). The torsional vibration signals of transmission system were collected and the results show that increasing the flywheel mass can effectively reduce the effect of engine excitation on the torsional vibration of transmission system. For the investigation of torsional vibration of drive shafts, a field test of torsional vibration of automobile drive shaft shows that the reasonable arrangement of universal joints can reduce the torsional vibration of drive shafts (Wu et al., 2013). The fluctuation of input torque induced by internal-combustion engines is an AbstractDuring the operation of vehicles, it is found that dramatic vibration occurs when the engine rotation speed reaches a certain value. In order to study this phenomenon, a theoretical model of automobile transmission system is developed in this paper. This model includes four sub-models of gearbox, drive shafts, main reducer and rear axle, which take into account the inhomogeneous transmission speed of universal joint of drive shafts as well as the effect of time-varying and nonlinear factors of main reducer gears. In this model, the transmission system is an elastic system characterized by mass, stiffness and damping. The torsional vibration responses of transmission system are simulated, and the natural frequencies of transmission system and corresponding mode shapes are calculated using this model. Simulation results indicate that the maximum amplitude of torsional vibration response appears at a certain speed. On the other hand, experimental investigation on the effect of rotation speed on torsional vibration is conducted to verify the theoretical model. Experimental results also show there is the maximum amplitude of torsional vibration response appearing at a certain speed. The results of FEA indicate that the excitation frequencies of drive shaft are quite close to the first order natural frequency of drive shaft, and the resonant vibration of drive shaft would induce the resonant vibration of transmission system, given that the first order natural frequency of drive shaft is quite close to the third order natural frequency of transmission system. In particular, it is discovered that deviations between the rotation speeds corresponding to the maximum...
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