Improved analytical model for calculating mesh stiffness and transmission error of helical gears considering trochoidal root profile

•TVMS and TE are the main internal sources of vibration and noise in gear systems.•Improved analytical model (IAM) is developed to predict TVMS, LSTE, and PPTE.•IAM was more accurate and effective than TAM in calculating tooth stiffness.•IAM and FEA results were compared and IAM was successfully validated.