Dynamic behavior analysis of spiral bevel gears of helicopter’s intermediate reducer with vibration error and lubrication

In the dynamic simulation of spiral bevel gears (SBGs), the modeling and contact analysis of the SBGs are extremely complicated; therefore, dynamic analysis of the SBGs generally simplifies the SBG model. The vibration in the meshing process will cause the meshing trajectory to deviate, resulting in changes in the meshing stiffness, oil film thickness, and load distribution between teeth. These changes cannot be realized using simplified models. To accurately calculate the dynamic behavior of the SBG pair of the intermediate reducer of a helicopter under the influence of vibration displacement, a load-tooth contact analysis(LTCA) of the SBG with error was performed based on the finite element method(FEM) and gear meshing principle. A calculation method for the meshing stiffness, considering the errors and elastohydrodynamic lubrication (EHL) factors, is proposed. To establish the coupling nonlinear dynamic model of the tail drive thin-walled shaft Timoshenko beam element and SBG lumped mass methods, applied the Newmark conjugate gradient method. Changes in parameters such as vibration displacement, meshing trajectory, tooth side clearance, oil film thickness, and meshing stiffness were obtained. The results show that the contact stiffness after considering the oil film stiffness is reduced by 17.7% compared to that without considering the effect of the oil film, and the oil film stiffness fluctuates more because the coupled model takes into account the vibration effect of the time-varying system, and the amplitude increases by 18.5% compared to the commercial software. The coupled kinetic model calculates the dynamic meshing force, normal relative displacement, single tooth meshing period and oil film thickness, and finds that the amplitude of the relevant parameters increases. The obtained time-varying lubrication parameters provide a theoretical basis for studying the evolution of the transmission system under the loss of lubrication.