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Research on a hybrid modeling method of a spiral bevel gear based on cutter simulation

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Abstract

Spiral bevel gears are essential components of mechanical devices; however, it is difficult to design, manufacture, and inspect them because their shapes are difficult to model on a computer. In this study, a method for modeling spiral bevel gears manufactured using a Gleason machine was investigated. The method to generate a gear tooth profile as point data and calculate transformation matrices between coordinate systems based on the machining process is explained in detail. The cutting volume is determined using multiple cross-sectional profiles created along the tool path, and the final gear shape is generated by subtracting the cutting volume from the workpiece. A spiral bevel gear modeling system is developed based on the proposed method, and its reliability is verified by measuring the actual gear and comparing it to the modeled shape. The verification results indicated that the modeled shape showed a 7.1 µm difference from the sample gear, implying that the proposed modeling method is reliable for modeling spiral bevel gears.

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Abbreviations

R f :

Radius of root circle

R o :

Radius of reference pitch circle

R :

Radius of operating pitch circle

Z :

Number of teeth

W :

Tooth face width

α o :

Pressure angle

x :

Shift factor of a tooth

m :

Module

r a :

Radius of cutter rounding

r f :

Radius of cutter fillet

h a :

Addendum of cutter

h f :

Dedendum of cutter

a, b :

Center of cutter rounding

P 1∼P 6 :

Refences points in generating 2D profile

Φ 1 :

Rack-cutter coordinate system in generating 2D profile

S 2 :

Gear coordinate system in generating 2D profile

S f :

Global coordinate system in generating 2D profile

Φ :

Rotation angle in generating 2D profile

r f :

Fillet curve in 2D profile

r i :

Involute curve in 2D profile

λ m :

Machine root angle

β :

Spiral angle

O g :

Origin of gear coordinate system

O c :

Origin of cradle coordinate system

O h :

Origin of head-cutter coordinate system

O b :

Origin of blade coordinate system

O p :

Origin of profile coordinate system

S g :

Gear coordinate system with origin at Og

S c :

Cradle coordinate system with origin at Oc

S h :

Head-cutter coordinate system with origin at Oh

S b :

Blade coordinate system with origin at Ob

S p :

Profile coordinate system with origin at Op

R b :

Radius of the blade

P b :

Midpoint of the blade

η :

Cutting angle

η s :

Cutting start angle

η e :

Cutting end angle

Y c :

Cradle angle

L c :

Length of cradle

L b :

Distance from origin of the cradle to midpoint of the blade

M bp :

Transformation matrix from the Sp coordinate system to the Sb coordinate system

M hb :

Transformation matrix from the Sb coordinate system to the Sh coordinate system

M ch :

Transformation matrix from the Sh coordinate system to the Sc coordinate system

M gc :

Transformation matrix from the Sc coordinate system to the Sg coordinate system

References

  1. K.-S. Lee, Development of a modeling system for involute spur gears considering backlash, profile modification, and crowning, Trans. Korean Soc. Mech. Eng. A, 45 (8) (2021) 645–655.

    Article  Google Scholar 

  2. F. L. Litvin and A. Fuentes, Gear Geometry and Applied Theory, 2nd Ed., Cambridge University Press, New York, USA (2004).

    Book  Google Scholar 

  3. V. Zeleny, I. Linkeova, J. Sykora and P. Skalnik, Mathematical approach to evaluate involute gear profile and helix deviations without using special gear software, Mechanism and Machine Theory, 135 (2019) 150–164.

    Article  Google Scholar 

  4. J. Brauer, Analytical geometry of straight conical involute gears, Mechanism and Machine Theory, 37 (1) (2002) 127–141.

    Article  MathSciNet  Google Scholar 

  5. G. Zhai, Z. Liaang and Z. Fu, A mathematical model for parametric tooth profile of spur gears, Mathematical Problems in Engineering, 2020 (2020) 1–12.

    Google Scholar 

  6. C. Salamoun and M. Suchy, Computation of helical or spur gear fillets, Mechanism and Machine Theory, 8 (1973) 305–322.

    Article  Google Scholar 

  7. T.-W. Kim, J.-Y. Hwang and Y.-J. Cho, Development of spur gear design software using tooth profile modification, Journal of the Korean Society for Precision Engineering, 19 (10) (2002) 202–211.

    Google Scholar 

  8. J. Wang, L. Kong, B. Liu, X. Hu, X. Yu and W. Kong, The mathematical model of spiral bevel gears-a review. Strojniški vestnik-Journal of Mechanical Engineering, 60 (2) (2014) 93–105.

    Article  Google Scholar 

  9. Q. Fan, Computerized modeling and simulation of spiral bevel and hypoid gears manufactured by Gleason face hobbing process, Journal of Mechanical Design, 128 (6) (2006) 1315–1327.

    Article  Google Scholar 

  10. B. Sobolewski and A. Marciniec, Method of spiral bevel gear tooth contact analysis performed in CAD environment, Aircraft Engineering and Aerospace Technology, 85 (6) (2013) 467–474.

    Article  Google Scholar 

  11. J. Astoul, J. Geneix, E. Mermoz and M. Sartor, A simple and robust method for spiral bevel gear generation and tooth contact analysis, International Journal on Interactive Design and Manufacturing (IJIDeM), 7 (2013) 37–49.

    Article  Google Scholar 

  12. M. Wang and Y. Sun, Cutterhead approximation machining method of line contact spiral bevel gear pairs based on controlling topological deviations, The International Journal of Advanced Manufacturing Technology, 121 (3–4) (2022) 1623–1637.

    Article  Google Scholar 

  13. V. Simon, Design of face-hobbed spiral bevel gears with reduced maximum tooth contact pressure and transmission errors, Chinese Journal of Aeronautics, 26 (3) (2013) 777–790.

    Article  Google Scholar 

  14. G. Liu, K. Chang and Z. Liu, Reverse engineering of machinetool settings with modified roll for spiral bevel pinions, Chinese Journal of Mechanical Engineering, 26 (2013) 573–584.

    Article  Google Scholar 

  15. AGMA 201.02, Tooth Proportions for Coarse-Pitch Involute Spur Gears, 68th Ed., American Gear Manufacturers Association, USA (1974).

    Google Scholar 

  16. DIN867:1986, Basic Rack Tooth Profiles for Involute Teeth of Cylindrical Gears for General Engineering and Heavy Engineering, German Institute for Standardization, Germany (1986).

    Google Scholar 

  17. S. P. Radzevich, Dudley’s Handbook of Practical Gear Design and Manufacture, 3rd Ed., CRC Press, USA (2016).

    Book  Google Scholar 

  18. S. P. Radzevich, Gear Cutting Tools - Science and Engineering, 2nd Ed., CRC Press, USA (2017).

    Book  Google Scholar 

  19. S. P. Radzevich, Theory of Gearing: Kinematics, Geometry, and Synthesis, 2nd Ed., CRC Press, USA (2018).

    Book  Google Scholar 

  20. K. Lee, Principles of CAD/CAM/CAE Systems, Addison-Wesley, USA (1999).

    Google Scholar 

  21. Open CASCADE Technology, Available at https://www.opencascade.com/ (2022).

  22. Techno Enginering Technology Institute, Gear Design Handbook, Engineer Books, South Korea (2014).

    Google Scholar 

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Acknowledgments

This research was supported by the research fund of Hanbat National University in 2022.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Hanbat National University, Daejeon, Korea

    Kang-Soo Lee

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  1. Kang-Soo Lee
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Correspondence to Kang-Soo Lee.

Additional information

Kang-Soo Lee is a Professor at the Department of Mechanical Engineering at Hanbat National University, Daejeon, Korea. He received his B.S., M.S., and Ph.D. in mechanical design and production engineering from Seoul National University. His research interests include design of mechanical elements and CAD.

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Lee, KS. Research on a hybrid modeling method of a spiral bevel gear based on cutter simulation. J Mech Sci Technol 37, 6153–6162 (2023). https://doi.org/10.1007/s12206-023-2408-z

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  • DOI: https://doi.org/10.1007/s12206-023-2408-z

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