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In herringbone gears transmission, the pinion generally adopts the axial floating installation through the axial movement to realize the balance of axial force at both ends, which is called the load-sharing phenomenon. Load-sharing is an important characteristic of herringbone gears transmission, the essence of load-sharing analysis is the calculation of axial displacement at low rotation speed. The axial displacement at low rotation speed periodically changes with the tooth meshing (tooth frequency) and shaft rotation (shaft frequency), which is one of the excitation of the system vibration at high speed. However, it is not considered in the current dynamic characteristics study of herringbone gears. Therefore, the axial displacement under low rotation speed is calculated and is treaded as a kind of error excitation to put in the dynamic model of herringbone gears in this paper. Further, the impact of load-sharing on dynamic characteristics of herringbone gears is studied and the results show that the displacement, velocity, and acceleration in direction of bending, torsion, and axial all have changed, the maximum variation is up to 81,651% while considering the axial displacement. Therefore, the impact of load-sharing should not be ignored in the dynamic characteristics analysis, especially for the accurate analysis of dynamic characteristics for herringbone gears. The study enriches the theory of dynamic characteristic analysis of herringbone gears. [ABSTRACT FROM AUTHOR]

• Developed a dynamic model for herringbone gears with multi-state meshing. • Proposed a dynamic stability rate (DSR) calculation method. • Identified multi-state meshing behavior and its correlation with DSR. 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. [ABSTRACT FROM AUTHOR]