Analysis of forming error during thread and spline synchronous rolling process based on motion characteristic

  • Da-Wei ZhangEmail author
  • Sheng-Dun Zhao
  • Yong-Dong Bi


The thread meshing and the spline/gear meshing are intercoupling during thread and spline synchronous rolling (TSSR) process. The subtle difference between different meshing types will lead to profile error of workpiece. Exploring the influence of motion characteristic on the forming error during TSSR process is important for control of pitch error, design of profile compensation of rolling die, and improvement of rolling quality. Thus, in this paper, the accumulative pitch error for spline section of workpiece during TSSR process was defined and modeled according to the motion characteristic in the synchronous rolling process. A quantitative calculating program of the accumulative pitch error has been compiled by using MATLAB code based on the motion models during thread rolling process and spline rolling process. Then, the influences of calculation step, rotating parameter of rolling die at initial contact state, and initial values for numerical solution of motion models of thread section on the calculation accuracy were investigated. The influences of processing parameters and geometrical parameters on the accumulative pitch error were studied by means of orthogonal experiment design method.


Synchronous rolling Angular velocity difference Accumulative pitch error Round rolling die 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors would like to thank Mr. Bing-Kun Liu at School of Mechanical Engineering, Xi’an Jiaotong University, for the help in the three coordinate measurement.

Funding information

The authors would like to gratefully acknowledge the supports of the National Natural Science Foundation of China (Grant Nos. 51675415 and 51335009).


  1. 1.
    Zhang DW, Zhao SD (2014) New method for forming shaft having thread and spline by rolling with round dies. Int J Adv Manuf Technol 70:1455–1462CrossRefGoogle Scholar
  2. 2.
    Zhang DW (2018) Die structure and its trial manufacture for thread and spline synchronous rolling process. Int J Adv Manuf Technol 96:319–325CrossRefGoogle Scholar
  3. 3.
    Zhang DW, Zhao SD, Wu SB, Zhang Q, Fan SQ, Li JX (2015) Phase characteristic between dies before rolling for thread and spline synchronous rolling process. Int J Adv Manuf Technol 81((2015):513–528CrossRefGoogle Scholar
  4. 4.
    Zhang DW, Zhao SD (2015) Discussion of plastic forming for roller in PRSs. China Mech Eng 26(3):385–389 (in Chinese)Google Scholar
  5. 5.
    Zhang DW, Zhao SD (2016) Deformation characteristic of thread and spline synchronous rolling process. Int J Adv Manuf Technol 87:835–851CrossRefGoogle Scholar
  6. 6.
    Zhang DW, Li YT, Fu JH, Zheng QG (2009) Rolling force and rolling moment in spline cold rolling using slip-line field method. Chin J Mech Eng 22(5):688–695CrossRefGoogle Scholar
  7. 7.
    Zhang DW, Zhao SD, Li YT (2014) Rotatory condition at initial stage of external spline rolling. Math. Prob. Eng. 2014: article ID 363184. In: 12 pagesGoogle Scholar
  8. 8.
    Neugebauer R, Putz M, Hellfritzsch U (2007) Improved process design and quality for gear manufacturing with flat and round rolling. Ann CIRP 56(1):307–312CrossRefGoogle Scholar
  9. 9.
    Neugebauer R, Klug D, Hellfritzsch U (2007) Description of the interactions during gear rolling as a basis for a method for the prognosis of the attainable quality parameters. Prod Eng Res Devel 1(3):253–257CrossRefGoogle Scholar
  10. 10.
    Litvin FL (1989) Theory of Gearing. NASA Reference Publication 1212, Washington DCGoogle Scholar
  11. 11.
    Wu XT (2009) Principle of Gearing, second ed., Xi’an Jiaotong University Press, Xi’an. (in Chinese)Google Scholar
  12. 12.
    Peng Y, Song A, Shen Y, Lin X (2017) A novel arc-tooth-trace cycloid cylindrical gear. Mech Mach Theory 118:180–193CrossRefGoogle Scholar
  13. 13.
    Zhang DW, Zhao SD, Ou H (2016) Analysis of motion between rolling die and workpiece in thread rolling process with round dies. Mech Mach Theory 105:471–494CrossRefGoogle Scholar
  14. 14.
    Zhang DW, Zhao SD, Ou H (2016) Motion characteristic between die and workpiece in spline rolling process with round dies. Adv Mech Eng 8(7):1–12Google Scholar
  15. 15.
    Bo YX, Bo D (1992) Accumulative pitch error of k teeth in precision standard of gear. Tool Engineering 26(9):39–41 (in Chinese)Google Scholar
  16. 16.
    Compile Group for Handbook of Mathematics (1979) Handbook of mathematics. Higher Education Press, Beijing. (in Chinese)Google Scholar
  17. 17.
    Zhan ZP, Chang BY, Ming CX (1997) Involute spline standards application manual. Standards Press of China, Beijing (in Chinese) Google Scholar
  18. 18.
    He W, Xue WD, Tang B (2012) Experiment optimization design method and data analyzing. Chemical Industry Press, Beijing (in Chinese)Google Scholar
  19. 19.
    Taguchi G (1987) System of Experiment design, D. Clausing, translated, Kraus International Publications, New YorkGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringXi’an Jiaotong UniversityXi’anPeople’s Republic of China

Personalised recommendations