Mesh stiffness and dynamic response analysis of modified gear system with thin web and weight reduction holes

Though the special gear foundation structure and tooth modification are effectively applied to weight optimization and vibration control, the lack of an effective mathematical model limits the investigation of their effects. The present work develops a general polygonal approximation method for weight reduction holes, which is introduced into an analytical-finite element (AFE) method along with the decomposition method to calculate the time-varying mesh stiffness (TVMS) of modified spur gear pairs with complex foundation (thin webs and weight reduction holes). The comparisons with the traditional finite element (FE) method show the superiority of the model in calculation accuracy and efficiency. Furthermore, the actual TVMS is introduced into the dynamics model of a high-speed gear-rotor-bearing system to analyze the dynamic responses, and the effectiveness of the model is verified by experiments. The results indicate that the thin web has a greater influence on the reduction of average amplitude in stiffness than holes. The thin web significantly controls the system vibration, while the tooth modification reduces the vibration fluctuation caused by holes at medium and high speeds. The analysis and experimental results provide an important reference for gear weight optimization and vibration reduction.