Analysis of multi-state meshing and dynamic stability of herringbone gears considering friction based on nonlinear dynamics

During the operation of herringbone gears some phenomena such as gear disengagement and back-side meshing (BSM) can lead to dynamic instability. Precise description of the behavior of multi-state meshing (MSM) is essential for the optimization of structures and for evaluation of its performance. In this article a nonlinear dynamic model for a herringbone gear is introduced. This model includes MSM and takes backlash and friction into account. MSM behavior is identified, and a dynamic stability rate (DSR) is calculated using various Poincaré maps. In addition, a number of bifurcation diagrams and phase diagrams are examined as well as the correlation between MSM characteristics and DSR. The study reveals that as the meshing frequency increases, the system transitions from stable periodic motion to complex periodic and chaotic responses before stabilizing into periodic motion. Transmission errors significantly influence MSM characteristics, with smaller errors making the DSR more sensitive to bifurcations and phase trajectory changes. Increased damping improves stability by suppressing BSM and chaotic motion. Under varying loads, the system transitions through different dynamic states, with periodic jumps notably affecting DSR at higher loads. Additionally, backlash plays a critical role in MSM behavior, influencing the transitions between periodic and chaotic responses. These findings highlight the importance of optimizing damping, load, and backlash to enhance the motion stability and performance of herringbone gear systems.