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<p>This paper proposes a novel double-enveloping toroidal worm pair using a rotational hyperboloid of two sheets as the generating surface, addressing limitations of traditional single-parameter, low-flexibility generating surfaces (planes, dual-cones, dual-tori). The hyperboloid has six adjustable parameters for flexible tooth profile optimization. The study explores the pair’s first and second-enveloping meshing mechanisms, derives the tooth surface and enveloping meshing equations of the worm and worm wheel, constructs a 3D model, and fabricates a prototype. Oil-clay tracing, angle measurement, and finite element simulation collectively confirm that the worm pair achieves central-region tooth contact and multi-tooth line contact, with over 90% of transmission errors remaining below 3%. Key parameter analysis shows rational selection optimizes tooth profiles, uniformizes contact stress, and enhances load capacity. This work provides a new theoretical method for hyperboloid double-enveloping toroidal worm pair design and enriches related gearing theory.</p>

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Construction method and contact analysis of a novel toroidal worm pair generated by hyperboloid of two sheets

  • 期刊论文

  • 发表日期：

    2026年1月6日

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  • Zeyi Jia,
  • Chengjie Rui,
  • Xiaoshuai Zhao,
  • Linping Lu,
  • Liliang Shen

摘要

This paper proposes a novel double-enveloping toroidal worm pair using a rotational hyperboloid of two sheets as the generating surface, addressing limitations of traditional single-parameter, low-flexibility generating surfaces (planes, dual-cones, dual-tori). The hyperboloid has six adjustable parameters for flexible tooth profile optimization. The study explores the pair’s first and second-enveloping meshing mechanisms, derives the tooth surface and enveloping meshing equations of the worm and worm wheel, constructs a 3D model, and fabricates a prototype. Oil-clay tracing, angle measurement, and finite element simulation collectively confirm that the worm pair achieves central-region tooth contact and multi-tooth line contact, with over 90% of transmission errors remaining below 3%. Key parameter analysis shows rational selection optimizes tooth profiles, uniformizes contact stress, and enhances load capacity. This work provides a new theoretical method for hyperboloid double-enveloping toroidal worm pair design and enriches related gearing theory.