Research on the Relevant Meshing Theories and Meshing Performance of Elliptical Toroidal Worm Gears and Cylindrical Gears

doi:10.3901/JME.2025.03.325

Abstract

Abstract: The open-loop high-speed ratio and high-precision gear drive has important application value in the indexing system of high-end equipment and precision instruments, however, the involute enveloping toroidal worm (TI worm) gearing is influenced by the value of the helix angle, and there are issues of partial load and unable to participate in meshing with whole tooth flank in the transmission process, which cannot directly meet the indexing accuracy requirements of high-end equipment and precision instruments. To address these issues, firstly, a new form of elliptic toroidal worm (EI worm) gearing conjugated with the full tooth flank of involute gear is proposed, the spatial position relationship between the elliptic toroidal surface and the cylindrical surface of involute cylindrical gear is established, the generatrix equation of elliptic toroidal surface is derived, the relevant meshing theories of primary envelope elliptic toroidal worm is studied based on the principle of spatial conjugate mesh of gears. Secondly, by analyzing the influence of the meshing parameters on the instantaneous contact line, the distribution area of the instantaneous contact line on the gear tooth flank is optimized, the whole tooth flank of the cylindrical gear meshing with EI worm is realized. Finally, the influence of the meshing parameters on the induced normal curvature, lubrication angle and relative entrainment speed is analyzed. Under the ideal condition with the same parameters, by comparing the meshing area of gear and meshing performance of EI worm gearing and TI worm gearing, it is found that the meshing area of gear in EI worm gearing is 5.49 times larger than that of TI worm gearing, the induced normal curvature and lubrication angle are similar, and the relative entrainment speed is larger, so the EI worm gearing is of high fitting degree between conjugate tooth flank, high contact strength and good lubrication effect. The research results provided theoretical basis for high-performance worm gear gearing.

Key words: elliptical toroidal worm, cylindrical gear, distribution of tooth contact line, meshing performance, whole tooth flank meshing

CLC Number:

TH132

LING Siying, ZHANG Heng, YANG Zhenxiang, ZHANG Jiayang, LING Ming, WANG Fengtao. Research on the Relevant Meshing Theories and Meshing Performance of Elliptical Toroidal Worm Gears and Cylindrical Gears[J]. Journal of Mechanical Engineering, 2025, 61(3): 325-336.

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