NONLINEAR DYNAMICS OF SPIRAL BEVEL GEAR FOR HELICOPTER TRANSMISSION IN THE PRESENCE OF AXIAL AND RADIAL MISALIGNMENTS

Spiral bevel gears (SBGs) play a significant role in mechanical transmissions systems when power is transferred from non-parallel shafts at high speed. SBGs are capable of bearing high levels of torque/power in a silent way, due to their high contact ratio. Nevertheless, their complex geometry necessitates understanding all geometric characteristics that determine the transmission efficiency and lifetime. In gear transmissions, vibration causes noise, malfunction, and imbalance in the stress distribution, thereby decreasing the lifetime of the gearbox. Due to manufacturing imperfections and flexibility of components, the system might experience misalignments that intensify or exert a destructive effect on the gear vibration. The main purpose of this study is to investigate the nonlinear dynamics of an SBG pair in the presence of two types of misalignments, namely, axial and radial. Investigating the mesh stiffness is significant to understand the dynamic behavior of gear systems; indeed, obtaining the mesh stiffness is needed to simulate the dynamic model of the geartrain. The loaded tooth contact analysis (LTCA) is employed to determine the static transmission error (STE) and mesh stiffness (MS) of a gear pair. To conduct LTCA, three main approaches could be utilized: finite element method (FEM), experimental, and analytical approaches. Based on the aforementioned methods, different software packages for LTCA have been produced and developed during the previous decade. One of the most powerful and reliable software regarding gear stress analysis is Transmission3D-Calyx, a FEM-based software, which is used in this study. Due to the backlash and MS fluctuation, the governing equations of motion are nonlinear and time-dependent. These equations are numerically solved through an implicit Runge–Kutta approach. To illustrate the dynamic scenario, results are analyzed by means of root mean square, phase portraits, Poincaré maps, and bifurcation diagrams.