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Keywords: face worm gear, double-lead worm, computing the modifications, Newton's method, bisection method.

Summary

The paper consists of a brief description of a new type of face worm gear and specifies the advantages of it. The shaping process is also short described and illustrated.

The way of developing the equation of the tooth line and the main assumptions are provided. Some geometric models are presented, the complete derivation of the formula can be found in another author publication [1].

The paper describes the main issues connected with the tooth line formula developing, like for example: the limiting angle of the tool rotation, undercutting of the concave toothflank and the limiting radius of the face worm wheel. Some of these issues were also researched by others and their results can be found in [2,3,4,5,6].

The author presents the use of numerical methods (the bisection method and Newton's method) in computing the size of the tooth line modifications. Some exemplary graphs presenting particularly cases are given.

On the basis of the developed mathematical models a computer program was created and some results of it are also provided.

References

1: A. Gessner, "Theoretical Basis of Generation of Face Worm Gear Drive with Duplex Worm", 8th Biennial ASME Conference on Engineering Systems Design and Analysis, Proc. 2006 by ASME No. 1746 CD, ISBN: 0-7918-3779-3, Torino (Italy) 2006.
2: J. Favard, Course of Local Differential Geometry, Gauthier-Villars, Paris, 1957.
3: F.L. Litvin, Gear Geometry and Applied Theory, Prentice-Hall, Englewood Cliffs, NJ, 1994.
4: F.L. Litvin, Theory of Gearing, NASA Reference Publication 1212, 1988.
5: F.L. Litvin, A.M. Egelja, M. De Donno, "Computerized determination of singularities and envelopes to families of contact lines on gear tooth surfaces", Comput. Methods Appl. Mech. Engrg., 158, p. 23-34, 1998. doi:10.1016/S0045-7825(97)00219-3
6: F.L. Litvin, V.A. Zalgaller, "Sufficient condition of existence of envelope to contact lines and edge of regression on the surface of the envelope to the family of surfaces represented in parametric form", Proc. of Universities, Mathematics, No.3 (178), p. 20-23, 1977.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 85 PROCEEDINGS OF THE FIFTEENTH UK CONFERENCE OF THE ASSOCIATION OF COMPUTATIONAL MECHANICS IN ENGINEERING Edited by: B.H.V. Topping Paper 74 Numerical Methods for the Design of Face Worm Gears with Double-Lead Worm A. Gessner Institute of Mechanical Technology, Poznan University of Technology, Poland doi:10.4203/ccp.85.74 purchase the full-text of this paper Full Bibliographic Reference for this paper A. Gessner, "Numerical Methods for the Design of Face Worm Gears with Double-Lead Worm", in B.H.V. Topping, (Editor), "Proceedings of the Fifteenth UK Conference of the Association of Computational Mechanics in Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 74, 2007. doi:10.4203/ccp.85.74 Keywords: face worm gear, double-lead worm, computing the modifications, Newton's method, bisection method. Summary The paper consists of a brief description of a new type of face worm gear and specifies the advantages of it. The shaping process is also short described and illustrated. The way of developing the equation of the tooth line and the main assumptions are provided. Some geometric models are presented, the complete derivation of the formula can be found in another author publication [1]. The paper describes the main issues connected with the tooth line formula developing, like for example: the limiting angle of the tool rotation, undercutting of the concave toothflank and the limiting radius of the face worm wheel. Some of these issues were also researched by others and their results can be found in [2,3,4,5,6]. The author presents the use of numerical methods (the bisection method and Newton's method) in computing the size of the tooth line modifications. Some exemplary graphs presenting particularly cases are given. On the basis of the developed mathematical models a computer program was created and some results of it are also provided. References 1 A. Gessner, "Theoretical Basis of Generation of Face Worm Gear Drive with Duplex Worm", 8th Biennial ASME Conference on Engineering Systems Design and Analysis, Proc. 2006 by ASME No. 1746 CD, ISBN: 0-7918-3779-3, Torino (Italy) 2006. 2 J. Favard, Course of Local Differential Geometry, Gauthier-Villars, Paris, 1957. 3 F.L. Litvin, Gear Geometry and Applied Theory, Prentice-Hall, Englewood Cliffs, NJ, 1994. 4 F.L. Litvin, Theory of Gearing, NASA Reference Publication 1212, 1988. 5 F.L. Litvin, A.M. Egelja, M. De Donno, "Computerized determination of singularities and envelopes to families of contact lines on gear tooth surfaces", Comput. Methods Appl. Mech. Engrg., 158, p. 23-34, 1998. doi:10.1016/S0045-7825(97)00219-3 6 F.L. Litvin, V.A. Zalgaller, "Sufficient condition of existence of envelope to contact lines and edge of regression on the surface of the envelope to the family of surfaces represented in parametric form", Proc. of Universities, Mathematics, No.3 (178), p. 20-23, 1977. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £75 +P&P)
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