# A mathematical model of a worm mechanism generated by a conical cutter

Research output: Contribution to journalArticle

4 Citations (Scopus)

### Abstract

In this article, an imaginary conical cutter was used to determine the geometric models of the worm-gear mechanism including a worm and a gear. Mathematical models of the worm and the gear were derived using an imaginary conical cutter and gear theory. Based on the geometric relations between the worm and conical cutter surfaces and between the gear and conical cutter surfaces, the worm and the gear were regarded as an envelope to the family of conical cutter surfaces when they rotated for one cycle. Using the developed mathematical model, the stress analysis of the proposed mechanism was examined. The results show that the von Mises stress and volume of the proposed worm and gear were smaller than those of the conventional worm-gear mechanism. Lastly, a numerical example was used to illustrate the geometric model of a gear and a worm with a gear ratio of 30:1.

Original language English 1707-1716 10 Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224 8 https://doi.org/10.1243/09544062JMES1953 Published - 2010 Jan 1

### Fingerprint

Gears
Mathematical models
Worm gears
Stress analysis

### All Science Journal Classification (ASJC) codes

• Mechanical Engineering

### Cite this

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title = "A mathematical model of a worm mechanism generated by a conical cutter",
abstract = "In this article, an imaginary conical cutter was used to determine the geometric models of the worm-gear mechanism including a worm and a gear. Mathematical models of the worm and the gear were derived using an imaginary conical cutter and gear theory. Based on the geometric relations between the worm and conical cutter surfaces and between the gear and conical cutter surfaces, the worm and the gear were regarded as an envelope to the family of conical cutter surfaces when they rotated for one cycle. Using the developed mathematical model, the stress analysis of the proposed mechanism was examined. The results show that the von Mises stress and volume of the proposed worm and gear were smaller than those of the conventional worm-gear mechanism. Lastly, a numerical example was used to illustrate the geometric model of a gear and a worm with a gear ratio of 30:1.",
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language = "English",
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In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 224, No. 8, 01.01.2010, p. 1707-1716.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A mathematical model of a worm mechanism generated by a conical cutter

AU - Yang, Hsueh-Cheng Yang

PY - 2010/1/1

Y1 - 2010/1/1

N2 - In this article, an imaginary conical cutter was used to determine the geometric models of the worm-gear mechanism including a worm and a gear. Mathematical models of the worm and the gear were derived using an imaginary conical cutter and gear theory. Based on the geometric relations between the worm and conical cutter surfaces and between the gear and conical cutter surfaces, the worm and the gear were regarded as an envelope to the family of conical cutter surfaces when they rotated for one cycle. Using the developed mathematical model, the stress analysis of the proposed mechanism was examined. The results show that the von Mises stress and volume of the proposed worm and gear were smaller than those of the conventional worm-gear mechanism. Lastly, a numerical example was used to illustrate the geometric model of a gear and a worm with a gear ratio of 30:1.

AB - In this article, an imaginary conical cutter was used to determine the geometric models of the worm-gear mechanism including a worm and a gear. Mathematical models of the worm and the gear were derived using an imaginary conical cutter and gear theory. Based on the geometric relations between the worm and conical cutter surfaces and between the gear and conical cutter surfaces, the worm and the gear were regarded as an envelope to the family of conical cutter surfaces when they rotated for one cycle. Using the developed mathematical model, the stress analysis of the proposed mechanism was examined. The results show that the von Mises stress and volume of the proposed worm and gear were smaller than those of the conventional worm-gear mechanism. Lastly, a numerical example was used to illustrate the geometric model of a gear and a worm with a gear ratio of 30:1.

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