Nonlinear dynamic characteristics of modified variable hyperbolic circular arc tooth trace cylindrical gears

Nonlinear dynamic characteristics is one of the important performance indexes for the variable hyperbolic circular arc tooth trace (VH-CATT) cylindrical gear system. And accurate analysis of the nonlinear dynamic characteristics is of great significance to investigate service life of the VH-CATT cylindrical gear system. Therefore, the nonlinear dynamics study of the VH-CATT cylindrical gear is proposed. Firstly, the calculation methods or formulas of the time-varying stiffness, transmission error and meshing impact were given. Next, the mathematical model of the modified VH-CATT cylindrical gear was deduced based on the forming theory. Then, the controllable design model and tooth surface optimization design model were developed to calculate the best values of the modified parameters. Finally, a bending-torsion coupling dynamic model of the VH-CATT cylindrical gear pair was developed to investigate influence of the modification design on the nonlinear dynamic characteristics of the modified VH-CATT cylindrical gear, and the research conclusion was verified by the transmission experiments. Research shows that the tooth surface load reduces, the stiffness increases, the LTE and fluctuation range of the LTE decrease after modification. Modification makes the bifurcation diagram shift to the right and the complex motion of the unmodified VH-CATT cylindrical gear pair with the dimensionless frequency between 0.72 and 1.11 become a periodic motion. The vibration displacement of the modified VH-CATT cylindrical gear pair less than that of the unmodified VH-CATT cylindrical gear pair. The experiment also shows that the transmission error of the modified gear pair is less than that of the unmodified gear pair and the tooth surface modification design of the VH-CATT cylindrical gear improves the transmission efficiency. The tooth surface modification is beneficial to reduce the vibration and noise of the VH-CATT cylindrical gear pair. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear.