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Generating grinding profile between screw rotor and forming tool by digital graphic scanning (DGS) method

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Abstract

This work presents a digital graphic scanning (DGS) method, based on computer scanning graphics, to generate a grinding profile avoiding the difficulties appeared from the complex equations of the contact line. First the enveloping surface between the forming tool (rotor) profile and its corresponding cutting locus was developed, then based on Bresenham algorithm, the best possible pixels of the enveloping surface in the pixel matrix of screen were demonstrated using a specified color. Finally, the grinding profile data of the rotor (forming tool) were collected by scanning the pixel matrix of screen, capturing the coordinates of the indicated color of the best possible pixels. Comparing the analytical gearing envelope method and the DGS method, the feasibility of the DGS method was indicated. The DGS method was shown as a precise, rapid, efficient and stable computing tool to generate a grinding profile. In addition, such an approach can be applied in designing other similarly conjugated products such as gears, perpetual screws and milling cutters.

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Abbreviations

S r :

coordinate system of rotor

S g :

coordinate system of forming tool

z r :

rotation axis of rotor

z g :

rotation axis of forming tool

a :

center distance between zr and zg

ψ :

shaft angle between zr and zg

t :

parameter of arc length

e :

Revolving direction

p :

helix parameter

P z :

lead of rotor

φ :

rotation angle of the forming tool

u :

slope of linear

v :

intercept of linear in y direction

S :

enveloping surface

k :

slope of profile

x s , y s :

resolution of the screen

K 1, K 2 :

magnification

References

  1. Litvin, F. L., “Gear Geometry and Applied Theory,” PTR Prentice Hall, pp. 674–691, 1994.

    Google Scholar 

  2. Litvin, F. L. and Feng, P. H., “Computerized Design, Generation, and Simulation of Meshing of Rotors of Screw Compressor,” Mechanism and Machine Theory, vol. 32, no. 2, pp. 137–160, 1997.

    Article  Google Scholar 

  3. Xing, Z. W., “Screw Compressors: Theory, Design and Application,” China Machine Press, pp. 17–24, 2000. (In Chinese)

  4. Stosic, N., Smith, I., and Kovacevic, A., “Screw Compressors: Mathematical Modelling and Performance Calculation”, Springer Science & Business Media, pp. 45–48, 2005.

    Google Scholar 

  5. Stosic, N., Smith, I. K., Kovacevic, A., and Mujic, E., “Geometry of Screw Compressor Rotors and their Tools,” Journal of Zhejiang University SCIENCE A, vol. 12, no. 4, pp. 310–326, 2011.

    Article  Google Scholar 

  6. Stoši, N., “On Gearing of Helical Screw Compressor Rotors,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 212, no. 7, pp. 587–594, 1998.

    Google Scholar 

  7. Wei, J., Zhang, Q., Xu, Z., and Lyu, S., “Study on Precision Grinding of Screw Rotors using CBN Wheel,” Int. J. Precis. Eng. Manuf., vol. 11, no. 5, pp. 651–658, 2010.

    Article  Google Scholar 

  8. Wei, J., Sun, Q., Sun, X., and Sun, W., “A Study on Rotor Profiles Design for a Novel Twin-Screw Kneader,” Int. J. Precis. Eng. Manuf., vol. 14, no. 3, pp. 451–459, 2013.

    Article  MathSciNet  Google Scholar 

  9. Wu, B. H., Zhang, J., Yang, J., and Zhang, D., “Calculation Method for Edge Shape of Forming Wheel for Screw Rotors Machining,” Journal of Mechanical Engineering, vol. 48, no. 19, pp. 192–198, 2012. (In Chinese)

  10. Liang, X. C., Zhao, M., Yoshino, H., Li, Y. Y., and Zhou, Y. S., “Study on the Gear and Cutter Manufacture,” Chongqing University Press, pp. 107–119, 2001. (In Chinese)

    Google Scholar 

  11. Gofdfarb, V. I. and Lunin, S. V., and Trubachev, E. S., “Direct Digital Simulation for Gears Volume 1,” http:// wwwstepanlunincom/book1html (Accessed 23 NOV 2015)

  12. Di Puccio, F., Gabiccini, M., and Guiggiani, M., “Alternative Formulation of the Theory of Gearing,” Mechanism and Machine Theory, vol. 40, no. 5, pp. 613–637, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  13. Spitas, V., Costopoulos, T., and Spitas, C., “Fast Modeling of Conjugate Gear Tooth Profiles using Discrete Presentation by Involute Segments,” Mechanism and Machine Theory, vol. 42, no. 6, pp. 751–762, 2007.

    Article  MATH  Google Scholar 

  14. Wu, Y. R., Fong, Z. H., and Zhang, Z. X., “Simulation of a Cylindrical Form Grinding Process by the Radial-Ray Shooting (RRS) Method,” Mechanism and Machine Theory, vol. 45, no. 2, pp. 261–272, 2010.

    Article  MATH  Google Scholar 

  15. Bresenham, J. E., “Algorithm for Computer Control of a Digital Plotter,” IBM Systems Journal, vol. 4, no. 1, pp. 25–30, 1965.

    Article  Google Scholar 

  16. Kong, L. D., “Basics Tutorial of Computer Graphics,” Beijing: Tsinghua University Press, pp. 55–69, 2008. (In Chinese)

    Google Scholar 

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Authors and Affiliations

  1. Engineering School of Physics and Mechanical & Electrical Engineering, Xiamen University, Xiamen, 361-005, China

    Zhihuang Shen, Bin Yao, Weibin Teng, Wei Feng & Weifang Sun

Authors
  1. Zhihuang Shen
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  2. Bin Yao
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  3. Weibin Teng
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  4. Wei Feng
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  5. Weifang Sun
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Correspondence to Bin Yao.

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Shen, Z., Yao, B., Teng, W. et al. Generating grinding profile between screw rotor and forming tool by digital graphic scanning (DGS) method. Int. J. Precis. Eng. Manuf. 17, 35–41 (2016). https://doi.org/10.1007/s12541-016-0005-0

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  • DOI: https://doi.org/10.1007/s12541-016-0005-0

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