Abstract
A conventional worm wheel profile is obtained by establishing the meshing equation of the wheel and gear and determining the contact trace, which is difficult to use in calculating the non-standard profile gear. The second envelope method of point-vector (PV) is then proposed, which is actually a digital calculation method. The grinding wheel profile is formed by generating motion of the gear surface. The generating motion is divided into the first and second envelope motion. Using a PV approximation method, a gear profile is dispersed into a series of PVs to establish the PV envelope principle and the envelope approximation algorithm, determine the envelope point with the minimal orientation-distance to the wheel in the PV group, and obtain the wheel profile by fitting all the envelope points. In this paper, a detailed description of the wheel profile forward and gear profile backward calculation processes is provided using the second envelope method of PV. Experimental verification of the calculation results demonstrates that this method can be employed to calculate and machine any gear profile and achieve high accuracy.
Similar content being viewed by others
References
Litvin FL (1997) Development of gear technology and theory of gearing. NASA Reference Publication 1406
Litvin FL, Fuentes A (2004) Gear geometry and applied theory (Second Edition). Cambridge University Press
Su X, Houser DR (2000) Alternative equation of meshing for worm-gear drives and its application to determining undercutting and reverse engineering. ASME J Mech Des 122:207–212
Puccio FD, Gabiccini M, Guiggiani M (2005) Alternative formulation of the theory of gearing. Mech Mach Theory 40:613–637
Litvin FL, Ignacio GP (2007) Design, simulation of meshing, and contact stresses for an improved worm gear drive. Mech Mach Theory 42(8):940–959
You HY, Ye PJ, Wang JS (2003) Design and application of CBN shape grinding wheel for gears. Int J Mach Tools Manuf 43(9):1269–1277
Chiang CJ, Fong ZH (2009) Undercutting and interference for thread form grinding with a tilt angle. Mech Mach Theory 44:2066–2078
Chiang CJ, Fong ZH (2010) Design of form milling cutters with multiple inserts for screw rotors. Mech Mach Theory 45:1613–1627
Wei J, Zhang GH (2010) A precision grinding method for screw rotors using CBN grinding wheel. Int J Adv Manuf Technol 48:495–503
Radzevich SP (2007) Diagonal shaving of an involute pinion: optimization of the geometric and kinematic parameters for the pinion finishing operation. Int J Adv Manuf Technol 32:1170–1187
Radzevich SP, Krehe R (2011) Application priority mathematical model of operating parameters in advanced manufacturing technology. Int J Adv Manuf Technol 56:835–840
Radzevich SP, Krehe R (2012) Determination of the grinding wheel profile and its setup for use in finishing cylindrical gears with an evolvent profile. Int J Adv Manuf Technol 63:875–879
Ishibashi A, Yoshino H (1987) Design and manufacture of gear cutting tools and gears with an arbitrary profile. J Jpn Soc Precis Eng 30:1159–1166
Zhou YS, Shao M (2005) Form grinding technology for the mold of powder metallurgy gears. Chin J Mech Eng 41(1):162–165
Wu YR, Fong ZH, Zhang ZX (2010) Simulation of a cylindrical form grinding process by the radial-ray shooting (RRS) method. Mech Mach Theory 45(2):261–272
Sun YW, Wang J, Guo DM, Zhang Q (2008) Modeling and numerical simulation for the machining of helical surface profiles on cutting tool. Int J Adv Manuf Technol 36:525–534
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
He, K., Li, G. & Li, X. The second envelope method of point-vector and its application on worm wheel grinding modified gear. Int J Adv Manuf Technol 88, 3175–3184 (2017). https://doi.org/10.1007/s00170-016-9028-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-016-9028-z