Purpose. Development of a design procedure of tooth bending durability upon incomplete tooth contact by a finite element method and its application for research of a stress state of tumbling mill open gearing. Methodology. Calculation of the stress state is carried out with the finite element method. At the first stage the design model is formed. Further the construction and discretization of gearing geometrical model is done taking into account an axis misalignment angle. Displacements and stress in a tooth gearing upon incomplete tooth contact are calculated. Received distribution diagrams of displacements and stress are used for calculation of tooth bending stress. Findings. The article is devoted to the development of a design procedure of tooth bending durability taking into account gearing errors. The current state of the issue of tooth bending durability calculation upon incomplete tooth contact is investigated. The factors having a significant impact on a gearing error are defined. It is shown that the greatest impact on tooth gearing durability has an inclination angle of teeth in the plane of teeth contact. The estimation of the value of total inclination angle of teeth of tumbling mill МШРГУ 4500 x 6000 is given. The design model for calculating the tooth bending durability upon incomplete tooth contact with the finite element method is proved. Comparison of the results of calculation by the developed technique and by the engineering of ISO 6336 - 1:2006, 6336 - 3:2006 is made. It is shown that the existing engineering technique does not consider the features of large-sized tooth gearings stress state technique enough. The correction factors which allowing adapting an engineering technique for calculating tooth bending durability upon incomplete tooth contact are calculated. Originality. Significant influence of the central plate on tooth bending durability is established. It is established that upon incomplete tooth contact the load is distributed linearly along the theoretical line of the contact. Practical value. The algorithm of a design procedure of tooth bending durability upon incomplete tooth contact with the finite element method is developed. The quantitative estimation of tooth bending durability of tumbling mill МШРГУ 4500х6000 open gearing is received.

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