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• 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]

Due to the symmetrical flank configuration, herringbone gears have no resulting axial forces and a smaller tooth width than helical gears. Because of existing manufacturing limitations, currently only double helical gears with wide center space or assembled herringbone gears are applied. In the present work, a novel machining method for herringbone gears by power skiving is presented. For this purpose, tool and technology are designed using a mathematical process model and tested subsequently. It is shown that the process can produce the required geometry with significant improvements on productivity and accuracy. Additionally, the unused center area can be eliminated. [ABSTRACT FROM AUTHOR]

• Crack initiation life model of herringbone gear is proposed by critical plane method. • Centring error and angular misalignment sharply reduce the crack initiation life. • Moderate tip relief can eliminate stress concentration and extend the gear life. • Angular adjustment balances the load in centring error gears, improving gear life. The effects of centring error and angular misalignment on crack initiation life in herringbone gears are investigated in this work. Herringbone gears with centring error or angular misalignment are modelled for contact analysis. A crack initiation life model of standard and error gears is proposed in accordance with tooth stress history and a critical plane method for nonproportional loading. Then, the effects of centring error and angular misalignment on crack initiation life in herringbone gears are investigated. Results show that centring error and angular misalignment sharply reduce crack initiation life, but a moderate tip relief can eliminate stress concentration and extend crack initiation life. Furthermore, angular adjustment balances the load distribution of the left and right teeth in herringbone gears with centring error, improving tooth crack initiation life. [ABSTRACT FROM AUTHOR]