نبذة مختصرة : The relevance of the discussed issue is caused by the need to provide serviceability and reliability of gearboxes for pipeline valve drives operating under cold conditions and to produce heavy crude oil from stripper wells using screw pumps and Henry Pumps. Bevel gears with a small shaft angle with double-concave-convex teeth have been studied to date. Gear cutting for such gears is extremely complicated and labor-intensive. The authors proposed and studied a straight bevel gear with a small shaft angle with a non-generated gear and a generated pinion. However, lack of longitudinal localization of the bearing contact does not allow providing the required torque and product reliability in the presence of transmission errors of the mating gears. The main aim of the study is to develop mathematical models of gear tooth surface generating with localized bearing contact and gears mesh of bevel gears with a small shaft angle with a non-generated gear and a generated pinion The methods used in the study: theory of mechanisms and machines, theory of gearing, methods of vector and matrix algebra, numerical techniques of the transcendental (nonlinear) equations. The results. The authors developed the bevel gears with a small shaft angle with a non-generated gear and a generated pinion for drives of oil and gas equipment. They proposed to manufacture longitudinally crowned gear tooth surfaces- and based on the theory of gearing the authors obtained the relationships describing the gear tooth surface. A program was developed to determine the position of the lines of action in meshing in a gear with the localized contact and curvature of gear tooth surface. This program is a base to calculate the load-carrying capacity and contact stresses of gears. The authors found out that gears are insensitive to position errors of the mating pinion and gear.
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