A novel analytical model of the tooth pair meshing duration of orthogonal face gears

In this paper, a novel analytical model is proposed for calculating the tooth pair meshing duration of orthogonal face gears. Initially, the tooth surface equation, transition surface equation, and tooth width constraints are derived. Subsequently, the contact path of orthogonal face gears is determined based on the condition that the spatial position and normal vector of the contact point of the two tooth surfaces coincide respectively. Furthermore, an analytical model of the tooth pair meshing duration of the orthogonal face gears is established in accordance with the principle of gear meshing. Finally, the tooth pair meshing durations of orthogonal face gears in two cases (contact ratio 1 < ε ≤ 2 and 2 < ε ≤ 3) are discussed. The results show that when 1 < ε ≤ 2, at most two pairs of teeth and at least one pair of teeth are engaged in meshing simultaneously. The middle tooth pair contacts from the meshing-in point, passing through the double-single-double pairs of teeth meshing in sequence. When 2 < ε ≤ 3, at most three pairs of teeth and at least two pairs of teeth participate in meshing at the same time. The middle tooth pair contacts from the meshing-in point, successively transitioning through three-double-three-double-three pairs of teeth meshing. Single-tooth-pair meshing duration is absent.