Analysis of the tooth-root stress of external spur gears with high effective contact ratio

• A method to evaluate tooth-root stress in external spur gears is introduced. • The proposed method focuses on load-induced high contact ratio gears. • Validation is achieved through comparISOn with finite element models. • A new load-sharing coefficient, considering the load-sharing effect, is proposed. • The analytical formulation of the new coefficient is derived and presented. For spur gears with contact ratio close to 2, the extension of the contact interval resulting from loaded tooth deflections and local contact deformations may result in an effective contact ratio above 2. In these cases, the load is transmitted by at least two tooth-pairs, the maximum load and tooth-root stress decrease, and therefore the calculation methods of the gear rating Standards ISO and AGMA provide very conservative results. In this work, two models are applied to the calculation of the tooth-root stress of load-induced high contact ratio external gears: (i) an analytic model of load sharing, based on the minimum energy method, and (ii) a finite element model, which validates the results obtained from the previous model. Obtained values of the stress are compared with those provided by ISO and AGMA rating methods, which do not account for the stress reduction due to the higher contact ratio. A new modification coefficient is proposed to correct these conservative values, which allows the AGMA and ISO geometry factors to remain as no load-dependent factors and keep their actual calculation methods and significance.