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Representation of the normal to the generating (enveloped) helicoid surface in the form of a vector field of a fixed space is considered. Invariant properties of the helicoid are given. The application of the vector field of normals and simplifications obtained in solving the problems of predicting the tooth undercut at the stage of the gear scheme synthesis, calculation of geometric and kinematic parameters of meshing (direction of lines of conjugate contact, velocities of movement of contact points, radii of curvature of meshing surfaces), synthesis of machine-tool settings for tooth machining and localized contact are shown.

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Vector Field of Normals as an Effective Technique for Analysis and Synthesis of Worm-Type Gears

  • 会议论文

  • 发表日期：

    2026年

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  • Evgeniy S. Trubachev

摘要

Representation of the normal to the generating (enveloped) helicoid surface in the form of a vector field of a fixed space is considered. Invariant properties of the helicoid are given. The application of the vector field of normals and simplifications obtained in solving the problems of predicting the tooth undercut at the stage of the gear scheme synthesis, calculation of geometric and kinematic parameters of meshing (direction of lines of conjugate contact, velocities of movement of contact points, radii of curvature of meshing surfaces), synthesis of machine-tool settings for tooth machining and localized contact are shown.