Tribology and Lubricants

Korean Tribology Society (한국트라이볼로지학회)
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Transmission Error Analysis of ZI and ZA Profile Worm Gears

ZI 및 ZA형 웜기어의 치합전달오차 해석

  • Lee, Tae-Hoon (Graduate School, School of Mechanical Engineering, Pusan National University) ;
  • Suh, Junho (School of Mechanical Engineering, Pusan National University) ;
  • Park, Noh-Gill (School of Mechanical Engineering, Pusan National University)
  • 이태훈 (부산대학교 대학원 기계공학부) ;
  • 서준호 (부산대학교 기계공학부) ;
  • 박노길 (부산대학교 기계공학부)
  • Received : 2018.09.25
  • Accepted : 2018.11.29
  • Published : 2018.12.31
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Abstract

Automobiles and systems requiring high gear ratios and high power densities generally use worm gears. In particular, as worm gears have a small volume and self-locking function, home appliances such as refrigerators and washers consist of worm gears. We can classify worm gears into cylindrical worms and rectangular worms. According to the AGMA standard, there are four types of cylindrical worms, ZA, ZN, ZK and ZI, depending on the machining of the worm shaft. It is preferable to use a ZI-type worm shaft, which is a combination of a worm wheel having an involute helical tooth surface and a conjugate tooth surface. However, in many cases, industries mostly use ZK, ZN, and ZA worm shafts because of the ease of processing. This paper presents numerical approaches to produce ZI and ZA worm surfaces and worm wheel. For the analysis of the transmission error of a worm gear system, this study (1) generates surface profile functions of ZI profile worm gear and worm shaft based on the common rack theory, (2) adopts the Newton-Raphson method for the analysis of the gear surface contact condition, and (3) presents and compares the corresponding transmission errors of ZI and ZA worm gears.

Keywords

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Fig. 1. Global and local coordinate system.

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Fig. 1. Global and local coordinate system.

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Fig. 2. Common rack coordinate system.

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Fig. 2. Common rack coordinate system.

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Fig. 3. ZA worm - top & side view.

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Fig. 3. ZA worm - top & side view.

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Fig. 4. T.E. analysis algorithm.

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Fig. 4. T.E. analysis algorithm.

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Fig. 5. Gear transmission error (ZI vs ZA).

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Fig. 5. Gear transmission error (ZI vs ZA).

Table 1. Coordinate system and the corresponding unit vectors

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Table 1. Coordinate system and the corresponding unit vectors

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Table 2. Worm gear system configuration

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Table 2. Worm gear system configuration

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References

  1. AGMA, 6022-C93, "Design Manual for Cylindrical Wormgearing", pp. 5-8, 1993.
  2. Litvin, F. L., "Gear Geometry and Applied Theory, 2nd edition", Cambridge, 2004.
  3. Crosher, W. P., "Design and Application of the Worm gear", ASME Press, New York, pp. 38-61, 2002.
  4. Harris, S. L., "Dynamic loads on the teeth of spur gears", Proceedings of the Institution of Mechanical Engineers, Vol. 172, pp. 87-100, 1958. https://doi.org/10.1243/PIME_PROC_1958_172_017_02
  5. Litvin, F. L., Alfonso, Fuentes, "Gear Geometry and Applied Theory", Cambridge, 2004.
  6. Litvin, F. L., "Generalized concept of meshing and contact of involute crossed helical gears and its application", Computer Methods in Applied Mechanics and Engineering, Vol. 194, No. 34, pp. 3710-3745, 2005. https://doi.org/10.1016/j.cma.2004.09.009
  7. Kim, T. W., Hwang, J. Y., Cho, Y. J., "A study of spur gear tooth profile modification scheme for scuffing resistance improvement", J. Korean Soc. Tribol. Lubr. Eng., Vol. 18, No. 6, pp. 418-424, 2002.
  8. Tak, S. H., Hwang, G. S., Son, Y. S., Bae, H. J., Lyu, S. K., "A study on the transmission error of the gear on contact load", J. Korean Soc. Tribol. Lubr. Eng., Vol. 23, No. 3, pp. 117-122, 2007.
  9. Lee, S. C., "Tooth profile design of an oval gear according to the curvature of the pitch curve", J. Korean Soc. Tribol. Lubr. Eng., Vol. 28, No. 1, pp. 27-32, 2012. https://doi.org/10.9725/kstle.2012.28.1.027
  10. Cheon, G. J., "Optimal design of a gear pump for yarning", J. Korean Soc. Tribol. Lubr. Eng., Vol. 18, No. 4, pp. 279-284, 2002.
  11. Choi, J. H., Ahn S. C., Park S. S., "Tooth profile analysis for face gear with 1:2 gear ratio in handpiece with $160^{\circ}$ contra angle", J. Korean Soc. Tribol. Lubr. Eng., Vol. 30, No. 2, pp. 86-91, 2014. https://doi.org/10.9725/kstle.2014.30.2.86

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