Dynamic Modeling and Nonlinear Analysis of a Spur Gear System Considering a Nonuniformly Distributed Meshing Force

In previous studies, the meshing force of a gear system is usually treated as being uniformly distributed for the convenience of analysis. In practical applications, however, it is nonuniformly distributed along the line of action due to machining errors, assembly errors, misalignment errors, etc. When a nonuniformly distributed meshing force is coupled with the shaft deformation, dynamic center distance, and time-varying meshing stiffness, the transmission performance of the gear system will be seriously degraded. Therefore, a nonuniformly distributed meshing force cannot be ignored when considering the gear systems used in complicated working conditions. In this study, the gear’s nonuniformly distributed meshing force is analyzed. Then, an 18 degrees-of-freedom bending-torsion-swing-coupled dynamic model of a pair of involute spur gears is put forward. Through this model, the coupling relationship between the nonuniformly distributed meshing force, shaft bending deformation, and dynamic center distance is accurately described. The influence of meshing frequency, stiffness excitation, damping, and error excitation on the nonlinear dynamic characteristics of the gear system was researched through bifurcation diagrams, phase diagrams, Poincaré maps, and time-domain diagrams. Various complicated nonlinear dynamic behaviors, such as quasiperiodic motion, bifurcation, chaotic motion, and chaotic banding, are revealed. Reasonable parameter ranges that guarantee the gear system is in a stable motion were extracted. By evading complicated nonlinear dynamic behavior, the transmission performance of a gear system was improved. This research will contribute to reducing the vibration and noise of gear systems.