Abstract
Aiming at the problem of pitch error of helical gear pair in engineering practice, the influence of pitch error on vibration, bifurcation, and chaos characteristics of the helical gear pair system is mainly studied. Due to the periodic time-varying nature of pitch error, a method of simulating the pitch error as a sine function is proposed to calculate pitch error. A nonlinear dynamic model of bending-torsion-shaft coupling of the helical gear pair system is established considering the effect of pitch error. The influence of pitch error on the vibration, bifurcation, and chaos characteristics of the system is analyzed by the Runge–Kutta numerical integration method. The research results show that the introduction of pitch error has the most significant impact on the torsional vibration of the system. With the increase in pitch error, the system exhibits rich bifurcation and chaos characteristics in the torsional direction. Moreover, it is also found that the vibration response in the torsional orientation of the system increases or decreases to the same degree when the system is in a periodic motion state, and the pitch error varies by the same extent. Therefore, the impact of pitch error on the dynamic performance of the helical gear pair system should be considered in engineering practice.
Highlights
Helical gear pairs are widely used in various machines and mechanical equipment. ey are one of the most crucial motion and power transmission devices, whose mechanical properties have an important influence on the whole machine’s vibration, noise, and reliability
A bending-torsion-shaft coupling nonlinear dynamic model of the helical gear pair system is established considering the effect of pitch error. e pitch error is calculated by using the method of simulating the pitch error as a sine function. en, the motion equations of the system are solved by the Runge–Kutta numerical integration method
E major conclusions can be summarized as follows: (1) e introduction of pitch error has the greatest degree of effect on the vibration acceleration response of the helical gear pair system in the torsional direction, followed by the axial direction and the smallest in the tangential direction
Summary
Helical gear pairs are widely used in various machines and mechanical equipment. ey are one of the most crucial motion and power transmission devices, whose mechanical properties have an important influence on the whole machine’s vibration, noise, and reliability. Erefore, this paper comprehensively considers the pitch error, time-varying meshing stiffness, meshing damping, and tooth side clearance and establishes the bending-torsion-shaft coupling nonlinear dynamic model of the helical gear pair system. E structure of this paper is organized as follows: the nonlinear dynamic model and equations of motion of the system are established, where the pitch error, time-varying meshing stiffness, meshing damping, and tooth side clearance of the system are given. According to the relationship of the contact ratio, the formula for calculating the total contact line length l(t) in one meshing period of the helical gear pair is deduced as follows: Actual pitch
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