Advertisement

Analysis and modeling of error of spiral bevel gear grinder based on multi-body system theory

  • Shu-han Chen (陈书涵)
  • Hong-zhi Yan (严宏志)Email author
  • Xing-zu Ming (明兴祖)
Article

Abstract

Six-axis numerical control spiral bevel gear grinder was taken as the object, multi-body system theory and Denavit-Hartenberg homogeneous transformed matrix (HTM) were utilized to establish the grinder synthesis error model, and the validity of model was confirmed by the experiment. Additionally, in grinding wheel tool point coordinate system, the errors of six degrees of freedom were simulated when the grinding wheel revolving around C-axis, moving along X-axis and Y-axis. The influence of these six errors on teeth space, helix angle, pitch, teeth profile was discussed. The simulation results show that the angle error is in the range from −0.148 4 rad to −0.241 9 rad when grinding wheel moving along X, Y-axis; the translation error is in the range from 0.866 0 μm to 3.605 3 μm when grinding wheel moving along X-axis. These angle and translation errors have a great influence on the helix angle, pitch, teeth thickness and tooth socket.

Key words

six-axis grinder spiral bevel gear error model analysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    SHIH Y P, FONG Z H. Flank modification methodology for face-hobbing hypoid gears based on ease-off topography [J]. Journal of Mechanical Design, 2007, 129(12): 1294–1302.CrossRefGoogle Scholar
  2. [2]
    LIN C Y, TSAY C B, FONG Z H. Computer-aided manufacturing of spiral bevel and hypoid gears with minimum surface deviation [J]. Mech Mach Theory, 1998, 33(6): 785–803.CrossRefGoogle Scholar
  3. [3]
    LIN C Y, TSAY C B, FONG Z H. Computer-aided manufacturing of spiral bevel and hypoid gears by applying optimization techniques [J]. Journal of Materials Processing Technology, 2001, 114: 22–35.CrossRefGoogle Scholar
  4. [4]
    FAN Sheng-bo, WANG Tai-yong, WANG Wen-jin, WANG Wen-jin, LENG Yong-gang. Prediction of diameter errors compensation in bars turning [J]. Journal of Central South University of Technology, 2005, 12(S2): 264–268.CrossRefGoogle Scholar
  5. [5]
    LEI W T, SUNG M P. NURBS-based fast geometric error compensation for CNC machine tools [J]. Inter Mach Tools Manufact, 2008, 48: 1199–1213.Google Scholar
  6. [6]
    SRIVASTAVA A K, VELDHUIS S C, ELBESTAWIT M A. Modeling geometric and thermal errors in a five-axis CNC machine tool [J]. Inter J Mach Tools Manufact, 1995, 35(9): 1321–1337.CrossRefGoogle Scholar
  7. [7]
    LIN Y, SHEN Y. Modeling of five-axis machine tool metrology models using the matrix summation approach [J]. The International Journal of Advanced Manufacturing Technology, 2003, 21: 243–248.CrossRefGoogle Scholar
  8. [8]
    BOHEZ E L J. Compensating for systematic errors in 5-axis NC machining [J]. Computer-Aided Dsign, 2002, 34: 391–403.CrossRefGoogle Scholar
  9. [9]
    OKAFOR A C, ERTEKIN Y M. Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics [J]. Inter J Mach Tools Manufact, 2000, 40: 1199–1213.CrossRefGoogle Scholar
  10. [10]
    LEE J H, YANG S H. Measurement of geometric errors in a miniaturized machine tool using capacitance sensors [J]. Journal of Materials Processing Technology, 2005, 165: 1402–1409.CrossRefGoogle Scholar
  11. [11]
    YANG Hong, NI Jun. Dynamic neural network modeling for nonlinear, nonstationary machine tool thermally induced error [J]. Inter J Mach Tools Manufact 2005, 45: 455–465.CrossRefGoogle Scholar
  12. [12]
    YANG Hong, NI Jun. Adaptive model estimation of machine-tool thermal errors based on recursive dynamic modeling strategy [J]. Inter J Mach Tools Manufact, 2005, 45: 1–11.CrossRefGoogle Scholar
  13. [13]
    ZHAO Hai-tao, YANG Jian-guo, SHEN Jin-hua. Simulation of thermal behavior of a CNC machine tool spindle [J]. Inter J Mach Tools Manufact, 2007, 47: 1003–1010.CrossRefGoogle Scholar
  14. [14]
    FLORUSSEN G H J, DELBRESSINE F L M, VAN DE MOLENGRAFT M J G, SCHELLEKENS P H J. Assessing geometrical errors of multi-axis machines by three-dimensional length measurements [J]. Measurement, 2001, 30: 241–255.CrossRefGoogle Scholar
  15. [15]
    TONG Heng-chao, YANG Jian-guo, LIU Guo-liang, WANG Xiu-shan, LI Yong-xiang. The volumetric error modeling technique of the two-axis system in an NC lathe [J]. Journal of Shanghai Jiaotong University, 2006, 40(7): 1213–1217. (in Chinese)Google Scholar

Copyright information

© Central South University Press and Springer-Verlag GmbH 2008

Authors and Affiliations

  • Shu-han Chen (陈书涵)
    • 1
  • Hong-zhi Yan (严宏志)
    • 1
    Email author
  • Xing-zu Ming (明兴祖)
    • 1
    • 2
  1. 1.School of Mechanical and Electrical EngineeringCentral South UniversityChangshaChina
  2. 2.School of Mechanical EngineeringHunan University of TechnologyZhuzhouChina

Personalised recommendations