Mathematical model and algorithm for contact stress analysis of gears with multi-pair contact

•The problem of gear tooth contact pressure evaluation is considered.•A mathematical model for multi-pair contact analysis is developed.•A proposed algorithm can be used to study the multi-pair contact in any gears.•The number of teeth in contact is detected automatically.•An application of algorithm for spiral bevel gear is presented.

The problem of contact pressure evaluation in gears with predesigned parabolic function of transmission errors and with localized contact is considered. It is proposed that several tooth pairs are in contact simultaneously. We construct an algorithm to define the torque transmitted by each pair in contact. Number of pairs in simultaneous contact depends on applied load and phase of meshing. This number is not known in advance. The feature of the algorithm is an automatic detection of the tooth pair number that is in contact in any phase of meshing under load. The algorithm allows you to define forces and torques that are transmitted on each of the pairs of teeth being in contact. Moreover, it allows determining the contact pressure and tooth-to-tooth accuracy of transmission. The proposed algorithm is universal and can be used to study the multi-pair contact in any gears.An application of the algorithm for a spiral bevel gear has been demonstrated. It is shown that tooth overlap factor, dimensions of instant contact patch, tooth bearing contact and tooth-to-tooth accuracy of gears increase with growth of load.