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Mathematical model and manufacture programming of loxodromic-type normal circular-arc spiral bevel gear

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Abstract

In this paper, loxodromic-type normal circulararc spiral bevel gear is proposed as a novel application of the circular-arc tooth profile at the gear transmission with intersecting axes. Based on the principle of molding-surface conjugation, the study develops a mathematical model for the tooth alignment curve and the computational flow at the design stage to enable the generation of the tooth surface. Machining of the tooth surface is then carried out to determine the interference-free tool path of the numerical control (NC). Moreover, a pair of loxodromic-type normal circular-arc spiral bevel gears is manufactured on computer numerical control (CNC) machine tools. The proposed theory and method are experimentally investigated, and the obtained results primarily reflect the superior performance of the proposed novel gear.

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References

  1. Wildhaber E. U.S. Patent, 1601750, 1926

  2. Novikov M L. USSR Patent, 109750, 1956

  3. Togashi S, Iyoi H. Improvement inW-N gears from the viewpoint of gear geometry-effects of mismatching or a difference in profile radii on the contact stresses. Mechanism and Machine Theory, 1973, 8(3): 351–363

    Article  Google Scholar 

  4. Lingaiah K, Ramachandra K. Photoelastic optimization of the profiles of Wildhaber-Novikov gears. Experimental Mechanics, 1976, 16(3): 116–120

    Article  Google Scholar 

  5. Dyson A, Evans H P, Snidle R W. Wildhaber-Novikov circular arc gears: Geometry and kinematics. In: Proceedings of the Royal Society of London A, 1986, 403: 313–340

    Article  Google Scholar 

  6. Ye G, Ye X Y. A new method for seeking the optimum gear tooth profiles-the theoretical basis of Wilhaber-Novikov gearing. Mechanism and Machine Theory, 2002, 37(10): 1087–1103

    Article  MATH  Google Scholar 

  7. Maiki M. On the theory of the contact of the helical gear on the tooth normal plane. Transactions of the Japan Society of Mechanical Engineers, 1995, 61(582): 492–494

    Article  Google Scholar 

  8. Tsay C B, Fong Z H, Tao S. Finite element stress analysis of Wildhaber-Novikov gears, In: Proceedings of 5th Conference on Mechanical Engineering, Taipei, 1988

  9. Colbourne J R. The contact stress in novikov gears. Mechanism and Machine Theory, 1989, 24(3): 223–229

    Article  Google Scholar 

  10. Tsay C B. Motion velocity of the contact ellipse over Wildhaber-Novikov gears. Journal of the Chinese Society of Mechanical Engineers, 1995, 16(2): 123–131

    MathSciNet  Google Scholar 

  11. Litvin F L, Tsay C B. Helical gears with circular arc teeth: simulation of conditions of meshing and bearing contact. Journal of Mechanisms Transmissions and Automation in Design, 1985, 107(4): 556–564

    Article  Google Scholar 

  12. Litvin F L, Fuentes A, Gonzalez-Perez I, Carnevali L, Sep T M. New version of Novikov-Wildhaber helical gears: computerized design, simulation of meshing and stress analysis. Computer Methods in Applied Mechanics and Engineering, 2002, 191(12): 5707–5740

    Article  MATH  Google Scholar 

  13. Kuo H M. A study on the bevel gear with circular-arc tooth profiles. Dissertation for the Master’s Degree. National Sun Yat-sen University, 2001

  14. Maiki M, Watanabe M. A study on WN spiral bevel gear manufactured by machining center, Journal of technological researches, 2005, 48(2): 91–97

    Google Scholar 

  15. Tsai Y C, Hsu WY. The study on the design of spiral bevel gear sets with circular-arc contact paths and tooth profiles. Mechanism and Machine Theory, 2008, 43(9): 1158–1174

    Article  MATH  Google Scholar 

  16. Yao L G, Gu B, Haung Sh J, Wei G, Dai J S. Mathematical modeling and simulation of the external and internal double circular-arc spiral bevel gears for the nutation drive. Journal of Mechanical Design, 2010, 132(2): 021008

    Article  Google Scholar 

  17. Monge G. Application de l’Analysis à la Géometrie. Histoire de l’Acad, Des Sciences de Paris, 1850

  18. Chen H J, Duan Z Y, Liu J, Wu H J. Research on basic principle of moulding-surface conjugation. Mechanism and Machine Theory, 2008, 43(7): 791–811

    Article  MATH  Google Scholar 

  19. Chen H J, Duan Z Y, Wu H J, Liu J. Study on the general principle of normal circular-arc gear transmission. Mechanism and Machine Theory, 2006, 41(12): 1424–1442

    Article  MATH  Google Scholar 

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Correspondence to Houjun Chen.

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Duan, Z., Chen, H., Ju, Z. et al. Mathematical model and manufacture programming of loxodromic-type normal circular-arc spiral bevel gear. Front. Mech. Eng. 7, 312–321 (2012). https://doi.org/10.1007/s11465-012-0308-5

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