A Dual-Iterative Meshing Stiffness Model and Vibration Analysis for an Angular Misaligned Helical Gear Pair Considering Misalignment-Induced Contact Line Variation

Abstract Angular misalignment is a common error in gear transmission systems, significantly altering the contact and dynamic behaviors of the gear system. Conventionally, the time-varying mesh stiffness (TVMS) of helical gear pairs with angular misalignment is estimated under the assumption of a uniform load distribution along a fixed contact line. However, this simplification neglects the variations in contact line length and load distribution due to angular misalignment, thereby compromising the accuracy of TVMS predictions. To address this limitation, we propose a novel dual-iterative model for TVMS calculation in helical gears, accounting for the angular misalignment-induced contact line variation. This model combines traditional iterative calculations for gear slices with an additional iterative loop for the misalignment-induced contact line changes. Furthermore, it considers both axial and tangential meshing stiffnesses. The proposed dual-iterative TVMS model is verified by using the finite element (FE) method. Moreover, a six degree-of-freedom (DOF) dynamic model for misaligned helical gears is established to investigate the effects of misalignments on the vibration characteristics of the gear pair. An experimental setup utilizing a back-to-back helical gear test rig with adjustable angular misalignment is constructed to validate the proposed model. The experimental results exhibit a close alignment with the simulation predictions. It is concluded that the proposed model is suitable for estimating the TVMS and dynamic analysis of helical gear pairs with angular misalignment errors.