• I.G. Brailov Omsk State Agrarian University, Omsk, Russia
  • M.O. Kirasirov LLC “TitaniumAuto”, Omsk, Russia
  • O.M. Kirasirov Omsk State Agrarian University, Omsk, Russia
  • R.K. Abdylmanova Omsk State Agrarian University, Omsk, Russia
  • R.F. Altynbekov M. Auezov South Kazakhstan University, Shymkent, Kazakhstan


Ключевые слова:

mathematical model, globoid worm, globoid wheel, screw parametric line, vector function


The parametric function of a vector screw line on a globoid worm is considered. The worm’s rotation angles and the worm wheel were selected as parameters. Based on the developed mathematical dependencies, a mathematical model of the screw line on the worm’s globoid surface was obtained. The worm in contact with the worm wheel is considered without regard to friction, the choice of parameters is not associated with the coordinate axes, but is tied to the technological parameter on the machine when processing the globoid worm. A single-thread worm is considered. The screw line’s pitch is regulated by the gear ratio of the worm gear. An algorithm for calculating points belonging to the screw line on the globoid worm is presented. Finding points belonging to the screw line on the globoid worm allows considering the necessary coordinates on all screw lines of the globoid worm when changing the radius and rotation angles. The work adopted an iterative method for calculating coordinates. The developed model is aimed at obtaining a mathematical model of the globoid worm’s screw lateral surface. The scientifically grounded method and algorithm for geometric calculation of gears with a reduced number of rolling elements located on the worm are presented. The developed methodology for calculating the geometric parameters of the end worm gear contributes to the introduction of energy-saving worm reduction gearboxes into production. The results of this work will contribute to a wider introduction of energy-saving gearboxes and multipliers in production, including agricultural mechanization and agricultural engineering.