| Gear transmission system is widely used in various machinery and equipment because of its compact structure, smooth transmission, high transmission efficiency, etc. With the continuous development of industrial technology, people have higher requirements for the dynamic performance of gear system. Intensive studies of the dynamical behavior of gear system under various nonlinear factors, and analysis generating mechanism and variation of the vibration of gear system, it will be provided theoretical basis for the design and manufacture of gear system with small vibration, low noise, high reliability and high transfer performance.This paper uses single-stage helical gears transmission system in the vehicle drive system as the research object. On the basis of vibration theory and consideration of multiple directions of the system movement, a 3-degrees-of-freedom shaft-torsion coupling dynamic model and a 5-degrees-of-freedom bending-torsion-shaft coupling dynamic model with considerations of the tooth surface friction of single-stage helical gears transmission are established. And numerical methods are used to solving them. The dynamical behavior of system with single-parameter and multi-parameter coupling is analyzed through calculating the local bifurcation diagram, phase diagram, Poincaré maps, the largest Lyapunov exponent, FFT spectrum, amplitude cloud and displacement-time image. etc. The main contents are as follows:The expression of a smooth continuous backlash function is obtained by the highly fitting of piecewise linear backlash function. Combined with characteristics helical gear transmission, the rationality of qualitatively that highly fitting of piecewise linear backlash function has been proved through analysis and comparison of the characteristics of chaotic bifurcation and vibration of adopt to different backlash function’s shaft-torsion coupling gear system.Consider the impact on the system of coincidence degree, dividing a single, double tooth meshing time. Based on the semi-empirical formula of Buckingham, the expression of the time-varying tooth surface friction coefficient caused by the change of meshing point is derived according to the principles of tribology combined with gear mesh principle to analyze the trend and prove its rationality.A bending-torsion-shaft coupling dynamic model with consideration of the tooth surface friction of single-stage helical gears transmission is established and solving movement differential equations by the numerical solution. In the analyzing process of the characteristic of chaotic bifurcation, boundary distortion phenomenon with the frequency of the system changes has been found existing in the system, combined with system’s cloud of the maximum amplitude and the amplitude-frequency characteristics superposition graphs can further discover vibration amplitude jump caused by boundary distortion and even stronger resonance response.Finally, system vibration unstable parameter region is obtained through selecting different torques, backlash, and calculating system’s amplitude cloud under the Ω~hk and Ω~ εh parameter plane. It has been found that the system exists the phenomenon of multiple jumps and strong resonance amplitude response when meshing frequency is coupled with torque and stiffness fluctuations. With the increase of torque, the system’s amplitude of the strong resonance also increases, while the vibration unstable parameter region of system is significantly reduced. In the meantime, it has been found that the position of system unstable vibration will be advanced as the torque increases. By computing the system’s displacement-time image, it is analyzed that the evolution process of the system will gradually become instable when the meshing time and frequency are changed. |
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