New method for calculating face gear tooth surface involving worm wheel installation errors

Abstract

The machining principle and realization method for the continuous generative grinding face gear by a worm wheel are introduced. Based on a five-axis linked CNC grinding machine, a new method is presented to deprive the equation of face gear error tooth surface by assuming the tool surface as the error surface, where actual tool installation position error is introduced into the equation of virtual shaper cutter. Surface equations and 3-D models for the face gear and the worm wheel involving four kinds of tool installation errors are established. When compared, the face gear tooth surface machined in VERICUT software for simulation based on this new method and the one obtained based on real process (grinding face gear by using a theoretical worm wheel with actual position errors) are found to be coincident, which proves the validity and feasibility of this new method. By using mesh planning for the rotating projection plane of the face gear work tooth surface, the deviation values of the tooth surface and the difference surface are acquired, and the influence of four kinds of errors on the face gear tooth surface is analyzed. Accordingly, this work provides a theoretical reference for assembly craft of worm wheel, improvement of face gear machining accuracy and modification of error tooth surface.

Keywords

face gear / grinding / worm wheel installation errors / VERICUT / error analysis

References

[1] DavidB D, RobertoA S. Gear parameters for specified deflections department of mechanical engineering [J]. Journal of Mechanical Design, 2001, 123: 416-421

[2] LitvinF L. Application of face gear drives in helicopter transmissions [J]. Transaction of the ASME, Journal of Mechanical Design, 1994, 116: 672-676

[3] HealthG F, FillerR R, TanJ. Development of face gear technology for industrial and aerospace power transmission [R]. NASA Contactor Report 211320, 2002

[4] FillerR R, HealthG F, SlaughterS C, LewickiD G. Torque splitting by a concentric face gear transmission [C]// The American Helicopter Society 58th Annual Forum. Montreal, Canada, 20021122

[5] LiZ-m-q, ZhuR-peng. Research on pointing of face gear by enveloping method [J]. China Mechanical Engineering, 2008, 19(9): 1029-1033

[6] StadtfeldH J. CONIFACE face gear cutting and grinding [J]. GEAR Solutions, 2010, 9: 38-47

[7] SuJ-z, FangZ-d, GuJ-gong. Tooth surface correction for spiral bevel gears [J]. Transactions of the Chinese Society of Agricultural Machinery, 2010, 41(3): 201-203

[8] ChenS-h, YanH-z, MingX-z, ZhongJ, XieY-dong. Establishment and analysis of error and difference surfaces in spiral bevel gear [J]. China Mechanical Engineering, 2008, 19(18): 2156-2161

[9] TangJ-y, LiY-y, ZhouC, LuY-feng. Relation between CNC bevel gear generator spatial errors and machine setting errors [J]. Chinese Journal of Mechanical Engineering, 2009, 45(4): 148-154

[10] ZhouC, TangJ-y, ZengT, LuY-feng. Relationship between grinding wheel and tooth surface error [J]. Chinese Journal of Mechanical Engineering, 2008, 44(2): 94-101

[11] WangX-c, WangJ, JiangH, LinR-f, FengW-jun. Tooth surface measurement and machine-settings correction of spiral bevel gear [J]. Journal of Mechanical Engineering, 2003, 39(8): 125-128

[12] LiJ-c, WangT-y, FanS-b, HeG-y, XingYuan. Error corrections of spiral bevel gear tooth surface based on digitized manufacturing [J]. Transactions of the Chinese Society of Agricultural Machinery, 2008, 39(5): 174-177

[13] LiX-z, ZhuR-p, LiZ-m-q, LiF-jia. Influence of setting error of tool on tooth profile and contact point of face gear drive [J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2014, 31(4): 370-376

[14] HeG-q, YanH-z, HeY, ShuT-l, RenX-li. Face-gear grinding simulation and tooth surface error snalysis [J]. Journal of Central South University: Science and Technology, 2014, 45(7): 2193-2200

[15] MingX-z, LiM-d, WangW, ZhaoLei. Analysis of the error sensitive direction and establishment of the equation of face gear tooth surface with error [J]. Journal of Mechanical Transmission, 2015, 39(5): 1-10

[16] GuoH, ZhaoN, HouS-wen. Machine error analysis and experimental study of grinding face gear based on disk wheel [J]. Journal of Northwestern Polytechnical University, 2013, 31(6): 915-920

[17] LitvinF LDevelopment of gear technology and theory of gearing [R], 1991, Cleveland, Ohio, USA, National Aeronautics and Space Administration

[18] LitvinF L, FuentesA, ZanziC, PontiggiaM, HandschuhR F. Face gear drive with spur involute pinion: Geometry, generation by a worm, stress analysis [J]. Computer Method in Applied Mechanics and Engineering, 2002, 191(2526): 2785-2813

[19] YangS-qunVERICUT NC machining simulation technology [M], 2010, Beijing, China, Tsinghua University Press

[20] GuoHuiResearch on method of hobbing face-gear and gearing performance [D], 2009, Xi’an, Northwestern Polytechnical University

[21] WangJ, WangX-c, JiangH, LiR-f, FengW-jun. Coordinate measurement of tooth surface of spiral gear [J]. Journal of Mechanical Engineering, 2003, 39(6): 151-154