Calculation of tooth pair stiffness by finite element analysis for the multibody simulation of flexible gear pairs with helical teeth and flank modifications

Optimizing the acoustic behavior – often referred to as Noise, Vibration, Harshness (NVH) – of drive train components, such as gearboxes, is paramount during the development process. NVH simulation models allow reducing the number of time-consuming and expensive iterations with physical prototypes during the development. These models therefore need to adequately depict the NVH behavior, which is defined by excitation, transfer behavior, and sound radiation. One main excitation source in drive train systems is meshing gear pairs because of the varying mesh stiffness. Although numerous approaches exist for calculating the stiffness of meshing gears, accurately incorporating the varying gear mesh stiffness into NVH system models remains challenging. This study investigates the possibility of modeling gear mesh excitations in system simulation by precalculating the meshing stiffness for individual contact pairs instead of a total gear mesh stiffness. The proposed method can account for variability in contact length due to changes in the gear stage state parameters (e.g., transmission ratio and center distance), which is common in system models with flexible shafts and bearings. With the presented approach, it is also possible to correctly distribute the meshing forces over the meshing tooth pairs, which improves the prediction of the excitation behavior. The method is demonstrated on an example gear pair, verified numerically, and compared to widely adopted methods from state-of-the-art tools and industry norms. The simulation results show good accuracy compared to traditional approaches with the added benefit of accounting for flexible system components by decoupling the positions of the contact pairs.