Numerical Characteristic of Gear System Attractor in Phase Space based on G-P Algorithm of Correlation Dimension - He Lin; Matthias Rätsch; Sanmin Wang; Guangshen Xu (Jixie chuandong)
In order to depict the numerical characteristic of the attractor structure in phase space for gear system effectively, a nonlinear dynamical spur gear transmission model including backlash and general transmission error is established, the calculation formula of equispaced gear system correlation dimension is deduced based on G-P algorithm. The numerical characteristics are explored quantitatively for both of periodic attractor and chaotic attractor by employing largest Lyapunov exponent as well as correlation dimension, the evolution and migration process of chaotic attractors is analyzed by means of Poincaré section. The evolution of chaotic attractor under the excitation of damping ratio and general transmission error is described by correlation dimension. The results show that the more complex of attractor structure generates the larger correlation dimension values, and causing strong vibration to the system, correlation dimension of chaotic attractor is between integer 1 and 2 with fractal characteristic.