含齿面分形啮合刚度的齿轮传动系统动力学

为研究考虑齿面分形特性的时变啮合刚度对齿轮-轴承系统的影响,用分形理论描述齿轮轮廓,采用Weber-Banaschek公式计算和分析不同分形维数D对齿轮时变啮合刚度的影响,将不同分形维数D下的刚度代入计及滑动轴承非线性油膜力、综合传递误差及齿侧间隙等因素的齿轮-轴承系统中,分析不同分形维数D下的刚度对系统动力学特性的影响.采用Runge-Kutta法求解系统动力学微分方程,得到系统响应的相图、Poincaré截面图、时域图、分岔图以及三维频谱图等.结果表明:随着分形维数D的增大,时变啮合刚度波动降低,系统趋于更加稳定的周期运动;相比含随机扰动的刚度,齿轮-轴承系统对于考虑齿面分形特性的齿轮啮合刚度的变化更加敏感,更能表现因齿廓变化导致的系统响应的变化;随着阻尼比的增大,系统会趋于相对稳定的单周期运动.

Dynamics of gear transmission system with fractal meshing stiffness on tooth surface

The influence of time-varying meshing stiffness on the gear bearing considering the fractal characteristics of the tooth surface is studied. Firstly, the profile of gear is described by the fractal theory, and the Weber-Banaschek formula is used to calculate and analyze the influence of different fractal dimension D on the time-varying mesh stiffness, and the stiffness of different fractal dimension D is taken into the gear bearing system with the factors such as the nonlinear oil film force of the sliding bearing, the comprehensive transmission error and the backlash, etc. The influence of stiffness of different fractal dimension D on the dynamic characteristics of the system is analyzed. The dynamic differential equation is solved by Runge-Kutta method. The phase diagrams, the Poincaré diagrams, the time domain diagrams, the bifurcation diagrams and the three-dimensional spectrum diagrams of the response of the system are obtained. The results show that with the increase of fractal dimension D, the fluctuation of time-varying meshing stiffness decreases, and the system tends to more stable periodic motion; Compared with the stiffness of random disturbance, the gear bearing system is more sensitive to the change of gear meshing stiffness considering the fractal characteristics of the tooth surface, and it can better show the change of system response due to the change of tooth profile; With the increase of damping ratio, the system will tend to relatively stable single cycle motion.