DOI: 10.18503/1995-2732-2023-21-1-55-64
Abstract
Problem Statement (Relevance). The use of cylindrical gears with arc teeth in locomotive drives, final reduction gears, and upper drives of drilling rigs makes it possible to increase manifold the service life of gears in comparison with spur and helical gears. There are currently proposed ten and a half methods of manufacturing arc teeth of cylindrical gears, differing in tools and shaping movements. A method of cutting arc teeth with cutter heads using the irregular division method on CNC machines is most advanced for industrial manufacturing of cylindrical gears with arc teeth. At the same time, studies on kinematic characteristics of gears, whose teeth are cut in this way, when working under conditions of errors, have shown that the position function has a sawtooth shape, and the teeth clash when meshing. To ensure approximate gearing, it is necessary to perform a profile modification of the tooth flank by using a cutter head with a more complex generating surface, rather than a right circular cone. Methods Applied. A mathematical model of the cutter head generating surface and formulae for calculating its geometric characteristics were developed by applying differential geometry and spatial gearing theory methods. Originality. The authors obtained dependence for coordinates of a radius vector and a unit normal vector, principal curvature of surface points, for the arc cutter head with the generating surface as the one-sheet hyperboloid. Result. The developed mathematical model of the cutter head generating surface contributes to modifying the gear arc teeth profile for both generating gear and gearing with rectilinear flank toothing options, when processing the concave side of the arc tooth. Practical Relevance. The use of circular cutter heads with a one-sheet hyperboloid generating surface ensures approximate gearing by modifying the arc tooth profile subject to errors in the gear and pinion relative position.
Keywords
cylindrical gears, cutter head, arc teeth, profile modification
For citation
Syzrantsev V.N., Starikov A.I. Cutter Head Geometry to Modify the Cylindrical Wheel Arc Teeth Profile. Vestnik Magnitogorskogo Gosudarstvennogo Tekhnicheskogo Universiteta im. G.I. Nosova [Vestnik of Nosov Magnitogorsk State Technical University]. 2023, vol. 21, no. 1, pp. 55-64. https://doi.org/10.18503/1995-2732-2023-21-1-55-64
1. Syzrantsev V.N., Syzrantseva K.V. Tsilindricheskie peredachi s arochnymi zubyami: geometriya, prochnost, nadezhnost: monografiya [Cylindrical gears with arch teeth: geometry, strength, reliability: monograph]. Tyumen: Tyumen Industrial University; 2021. 170 p. (In Russ.)
2. Syzrantsev V.N. Cylindrical arc gears: History, achievements, and problem. Mechanisms and Machine Science. 2021;101:131-151. DOI: 10.1007/978-3-030-73022-2_6
3. Arafa Hani A., Bedewy M. Manufacturability and viability of different C-Gear types: A comparative study. Proceedings of the ASME 2012 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2012. August 12-15, 2012, Chicago, IL, USA. DETC2012-71030.
4. Arafa H.A. C-gears: Geometry and machining, Part C. Journal of Mechanical Engineering Science. 2005;219(7):709-726.
5. Jiang Y. Contact ratio calculation of involute arc gear device. Academic Journal of Manufacturing Engineering. 2017;15(3):19-22.
6. Jiang Y.-Q., Hou L., Zhao Y. The equation of the contact line of the involute curvilinear-tooth cylindrical gear pump for the agricultural tractor. The Open Mechanical Engineering Journal. 2014;8:879-884.
7. Chang Q., Hou L. Parallel translating mechanism process-oriented mathematical model and 3D model for cylindrical gears with curvilinear shaped teeth. Jordan Journal of Mechanical and Industrial Engineering. 2016;10(3):171-177.
8. Jiang Y., Hou L., Sun Z., Xiao H. Meshing features of involute arc teeth cylindrical gears. Journal of Chemical and Pharmaceutical Research. 2014;6(7):2387-2393.
9. Ma Z., Deng C. CNC machining method of whole modified surface of cylindrical gears with arcuate tooth trace. Journal of Mechanical Engineering. 2012;48(5):165-171. DOI: 10.3901/jme.2012.05.165
10. Zhang Q., Hou L., Tang R., Wen G. Method of processing and an analysis of meshing and contact of circular arc tooth trace cylindrical gears. Transactions of FAMENA. 2016;40(4):11-24.
11. Song A., Wu W., Gao S. The ideal geometry parameters of arch cylindrical gear and its process method. Journal of Shanghai Jiaotong University. 2010;44(12):1735-1740.
12. Syzrantsev V.N., Syzrantseva K.V. Study of geometric characteristics of the arc teeth semirolled cylindrical gear meshing. FME Transactions. 2021;49(2):367-373.
13. Bochkova D.E., Bobkov M.N., Zolotova S.A. Machining circular teeth of a pair of cylindrical gears with a localized contact zone. Izvestiya Tulskogo gosudarstvennogo universiteta. Tekhnicheskie nauki [Proceedings of Tula State University. Engineering Sciences]. 2020;(5):344-349. (In Russ.)
14. Babichev D.T., Lagutin S.A., Barmina N.A. Russian School of the Theory and Geometry of Gearing. Part 2. Development of the classical theory of gearing and establishment of the theory of real gearing in 1976-2000. Mechanisms and Machine Science (Book Series). 2019;81:1-46.
15. Syzrantseva K.V., Syzrantsev V.N., Kolbasin D.S. Forming surfaces of a semirolled cylindrical gearing wheel and a gear arc teeth. Lecture Notes in Mechanical Engineering. 2021;134-141. DOI: 10.1007/978-3-030-54814-8_16
16. Wu Y., Hou Li, Ma D., Wei Y., Luo L. Milling machine error modelling and analysis in the machining of circular-arc-tooth-trace cylindrical gears. Transactions of FAMENA. 2021;44(4):13-29. DOI: 10.21278/ TOF.444009419