Modification and nonlinear dynamics characteristics analysis of herringbone gears based on coupling of meshing force and stiffness

Gear modification is an important technology for the design and manufacturing of high-precision gear transmissions, which is an effective method to improve gear meshing performance, reduce vibration, and noise. This paper employs the coordinate transformation method to calculate the meshing angle of herringbone gear, which simplifies the calculation of the relative displacement of the meshing line. Also, considering the influence of dynamic meshing force at the meshing point of gear pairs on time-varying meshing stiffness, an improved nonlinear dynamic model was established, and a novel internal excitation real-time correction method was proposed to predict the system’s dynamic characteristics more accurately. Next, the effects of different modification methods, modification amounts, and damping ratios on the nonlinear dynamic characteristics of the herringbone gear pair were analyzed. The obtained results show that the average relative displacement of the meshing line increases with the increase of the amount of modification. Moreover, its standard deviation decreases with the increase of the modification in some rotating speed ranges. In some cases, it can even be reduced by more than 50%. When the damping ratio decreases gradually, the axial modification can shorten the chaos interval by 52.68%, but the periodic window will disappear after modification.