In the process of forming grinding, the profile accuracy of the grinding wheel directly affects the machining precision of the gear. Aiming at meeting the requirement of accurate calculation of the grinding wheel profile, this paper propose a digital method based on the point-vector envelope to calculate the profile of the wheel and simulate the envelope surface. Firstly, the transverse profile of the gear is divided into a series of point-vectors and the geometrical features of the discrete points are completely described by the point-vector. The envelope of the surface is converted into the motion envelope of the point-vector along the helix. Secondly, the point-vector group formed by the envelope motion of the point-vector is projected onto the selected plane by coordinate transformation and rotation projection. A point-vector approximation algorithm is established to calculate the envelope point of the point-vector group on the calculation plane and the profile of the grinding wheel is formed by fitting all the envelope points. Thirdly, by using the space mapping of the point-vector in the enveloping process, the spatial contact line between the grinding wheel and the gear is determined. The contact lines at different grinding positions are calculated by the point-vector envelope method and the envelope surface of grinding wheel is simulated by all the contact lines, and the transverse profile of the envelope surface is extracted for error manifestation and prediction. Lastly, a kind of gear is taken as an example to complete the calculation of the grinding wheel profile and the simulation of the envelope surface. The accuracy of the point-vector envelope method is verified by the grinding experiment of standard gear, and the accuracy of the simulation results of the envelope surface is verified by the grinding experiment of lead modification gear.
HE Kun
,
LI Guolong
,
JIANG Lin
,
DONG Xin
,
LIU Pengxiang
. Calculation of Form Grinding Wheel Profile and Simulation of Envelope Surface Based on Digital Method[J]. Journal of Mechanical Engineering, 2018
, 54(1)
: 205
-213
.
DOI: 10.3901/JME.2018.01.205
[1] LITVIN F L,FUENTUS A. Gear geometry and applied theory[M]. 2nd ed. Cambridge University Press,2004.
[2] LITVIN F L. Development of gear technology and theory of gearing[R]. Washington,D.C.:NASA Reference Publication 1406,1997.
[3] FAYDOR L,LITVIN F L,IGNACIO G P,et al. Design, simulation of meshing,and contact stresses for an improved worm gear drive[J]. Mechanism and Machine Theory,2007,42:940-959.
[4] SU X,HOUSER D R. Alternative equation of meshing for worm-gear drives and its application to determining undercutting and reverse engineering[J]. ASME Journal of Mechanical Design,2000,122:207-212.
[5] YOU H Y,YE P J,WANG J S,et al. Design and application of CBN shape grinding wheel for gears[J]. International Journal of Machine Tools and Manufacture,2003,43:1269-1277.
[6] CHIANG C J,FONG Z H. Undercutting and interference for thread form grinding with a tilt angle[J]. Mechanism and Machine Theory,2009,44:2066-2078.
[7] CHIANG C J,FONG Z H. Design of form milling cutters with multiple inserts for screw rotors[J]. Mechanism and Machine Theory,2010,45:1613-1627.
[8] RADZEVICH S P. Design of shaving cutter for plunge shaving a topologically modified involute pinion[J]. Journal of Mechanical Design,2003,125(3):632-639.
[9] RADZEVICH S P. Computation of parameters of a form grinding wheel for grinding of shaving cutter for plunge shaving of topologically modified involute pinion[J]. Journal of Manufacturing Science and Engineering,2005, 127(4):819-828.
[10] RADZEVICH S P. On the accuracy of precision involute hobs:An analytical approach[J]. Journal of Manufacturing Processes,2007,9(2):121-136.
[11] ISHIBASHI A,YOSHINO H. Design and manufacture of gear cutting tools and gears with an arbitrary profile[J]. The Japan Society of Mechanical Engineers,1987,30:1159-1166.
[12] 周玉山,邵明. 粉末冶金齿轮模具成形磨齿砂轮的廓形计算方法[J]. 机械工程学报,2005,41(1):162-165. ZHOU Yushan, SHAO Ming. Form grinding technology for the mold of powder metallurgy gears[J]. ChineseJournal of Mechanical Engineering,2005,41(1):162-165.
[13] WU Y R,FONG Z H,ZHANG Z X. Simulation of a cylindrical form grinding process by the radial-ray shooting (RRS) method[J]. Mechanism and Machine Theory,2010,45(2):261-272.
[14] 李国龙,李先广,刘飞,等. 拓扑修形齿轮附加径向运动成形磨削中的砂轮廓形优化方法[J]. 机械工程学报,2011,47(11):155-162. LI Guolong,LI Xianguang,LIU Fei,et al. Method of profile optimization of a form grinding wheel for grinding with additional radial motion of topologically modified gear[J]. Journal of Mechanical Engineering,2011,47(11):155-162.
