Synthesis of an adaptive cylindrical gear with arched teeth with two contact zones spaced along the length of the tooth
https://doi.org/10.25206/1813-8225-2023-188-38-45
EDN: WVBWUR
Abstract
Cylindrical gears with arched teeth have the required performance in conditions of both non-rigid machine bodies and inevitable manufacturing and assembly errors. Error compensation is carried out by self-alignment of the wheels, the possibilities of which are limited in gears with one line of engagement. The article investigates an adaptive gear with arched teeth with two contact zones, which provides self-alignment of the wheels, regardless of the angle of misalignment of the teeth in engagement. The most promising in terms of implementation in the industry method of cutting arched teeth with a circular cutter head by the rolling method with a single division on CNC machines. Solved and illustrated by examples of the problem of calculating the parameters of the process of shaping the surfaces of arched teeth, which ensure the passage of two active lines in the meshing of the teeth through the given centers of the contact patches and the law of change of the transfer function required for the implementation of the approximate nature of the meshing.
About the Authors
V. N. Syzrantsev
Tyumen Industrial University
Russian Federation
Russian Federation
Vladimir N. Syzrantsev - Doctor of Technical Sciences, Professor, Head of Machines and Equipment for the Oil and Gas Industry Department, Industrial University of Tyumen (IUT).
Tyumen
AuthorID (SCOPUS) 6507778873
ResearcherID C-1075-2017
A. I. Starikov
Tyumen Industrial University
Russian Federation
Russian Federation
Aleksander I. Starikov - Senior Lecturer of Mechanical Engineering Technology Department, IUT.
Tyumen
AuthorID (RSCI) 176570
AuthorID (SCOPUS) 7006814382
References
1. Fuentes-Aznar A., Ruiz-Orzaez R., Gonzalez-Perez I. Comparison of spur, helical and curvilinear gear drives by means of stress and tooth contact analyses // Meccanica. 2017. Vol. 52. P. 1721-1738. DOI: 10.1007/s11012-016-0515-y. (In Engl.).
2. Syzrantsev V. N., Syzrantseva K. V. Tsilindricheskiye zubchatyye peredachi s arochnymi zub'yami: geometriya, prochnost', nadezhnost' [Spur gears with arched teeth: geometry, strength, reliability]. Tyumen, 2021. 170 p. ISBN 978-5-9961-2378-0. (In Russ.).
3. Syzrantsev V. N. Cylindrical Arc Gears: History, Achievements, and Problem // Mechanisms and Machine Science. 2021. Vol. 101. P. 131-151. DOI: 10.1007/978-3-030-73022-2_6. EDN: LGNAIU. (In Engl.).
4. Lagutin S. A. Predopredeleniye funktsii oshibok v peredachakh s dvoynoy modifikatsiyey zub'yev [Predetermination of the error function in gears with double tooth modification] // Prostranstvo zatsepleniy. Gearing Space. Izhevsk, 2001. P. 26-37. (In Russ.).
5. Arafa H. A. C-gears: Geometry and Machining, Part C // Journal of Mechanical Engineering Science. 2005. Vol. 219, no. 7. P. 709-726. DOI: 10.1243/095440605X31481. (In Engl.).
6. Bochkova D. E., Bobkov M. N., Zolotova S. A. Obrabotka krugovykh zub'yev pary tsilindricheskikh koles s lokalizovannoy zonoy kasaniya [Processing of circular teeth of a pair of cylindrical wheels with localized touch zone] // Izvestiya Tul'skogo gosudarstvennogo universiteta. Tekhnicheskiye nauki. Izvestiya Tula State University. Series Technical Sciences. 2020. No. 5. P. 344-349. EDN: PXFZWU. (In Russ.).
7. Syzrantsev V. N., Starikov A. I. Raschet geometro-kinematicheskikh kharakteristik zatsepleniya arochnykh zub'yev tsilindricheskoy peredachi pri pogreshnostyakh vzaimnogo raspolozheniya [Calculation of the geometric and kinematic characteristics of the engagement of the arched teeth of a cylindrical gear with errors in the relative position] // Vestnik YuUrGU. Seriya «Mashinostroyeniye». Bulletin of the South Ural State University. Ser. Mechanical Engineering Industry. 2023. Vol. 23, no. 1. P. 5-18. DOI: 10.14529/engin230101. (In Russ.).
8. Patent 2721579 Russian Federation, IPC F 16 H1/06. Adaptivnaya tsilindricheskaya peredacha s arochnymi zub'yami [Adaptive cylindrical gear with arched teeth] / Syzrantsev V. N., Syzrantseva K. V., Vibe V. P., Denisov Yu. G. No. 2019136799. (In Russ.).
9. Syzrantsev V., Syzrantseva K. The Arc Teeth Semi-rolled Cylindrical Gear Meshing Geometry // Acta Polytechnica Hungarica. 2022. Vol. 19, no. 2. P. 173-192. DOI: 10.12700/APH.19.2.2022.2.10. (In Engl.).
10. Parshin A. N. Izgotovleniye tsilindricheskikh koles s arochnymi zub'yami reztsovymi golovkami na stankakh s ChPU i opyt ikh vnedreniya [Arched toothed cylindrical gears manufacture on cnc lathes and experience of their inculcation] // Teoriya i praktika zubchatykh peredach. Theory and Practice of Gearings. Izhevsk, 2014. P. 151-159. (In Russ.).
11. Syzrantsev V. N. Tsilindricheskiye peredachi s raznesennymi po dline arochnykh zub'yev zonami kontakta [Cylindrical gears with contact areas distributed along the arc teeth length] // Vestnik IzhGTU imeni M. T. Kalashnikova. Vestnik IzhGTU imeni M.T. Kalashnikova. 2021. Vol. 24, no. 2. P. 33-39. DOI: 10.22213/2413-1172-2021-2-33-39. EDN: AJKQPV. (In Russ.).
12. Arafa H. A., Bedewy M. Manufacturability and viability of different c-gear types: A comparative study // Proc. of the ASME Design Engineering Technical Conf. 2012. Vol. 5. P. 381. DOI: 10.1115/DETC2012-71030. (In Engl.).
13. Chang Q., Hou. L. Parallel translating mechanism process-oriented mathematical model and 3-D model for cylindrical gears with curvilinear shaped teeth // Jordan Journal Mechanical and Industrial Engineering. 2016. Vol. 10. P. 171 — 177. (In Engl.).
14. Zhang Q., Hou L., Tang R. [et al.]. Method of processing and an analysis of meshing and contact of circular arc tooth trace cylindrical gears // Transactions of FAMENA. 2016. Vol. 40, no. 4. P. 11-24. DOI: 10.21278/TOF.40402. (In Engl.).
15. Ma D., Ye Z., Yang H. Tooth surface reconstruction and tooth profile geometric analysis of circular arc tooth trace cylindrical gears // Transactions of FAMENA. 2019. Vol. 43, no. 1. P. 29-44. DOI: 10.21278/TOF.43103. (In Engl.).
16. Jiang Y. Contact ratio calculation of involute arc gear device Academic // Journal of Manufacturing Engineering. 2017. Vol. 15, no. 3. P. 19-22. (In Engl.).
17. Wu Y., Hou L., Lan L. [et al.]. Milling machine error modelling and analysis in the machining of circular-arc-tooth-trace cylindrical gears // Transactions of FAMENA. 2021. Vol. 44, no. 4. P. 13-29. DOI: 10.21278/TOF.444009419. (In Engl.).
18. Zhang X., Liang Z. Mathematical model and contact characteristics of curvilinear cylindrical gears with line contact // Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2021. Vol. 43, no. 4. DOI: 10.1007/s40430-021-02894-w. (In Engl.).
19. Zhang Q., Hou L., Tang R. [et al.]. Method of Processing and an Analysis of Meshing and Contact of Circular Arc Tooth Trace Cylindrical Gears // Trans Famena. 2016. Vol. 40, no. 4. P. 11-24. DOI: 10.21278/TOF.40402. (In Engl.).
20. Liu Y., Ma D. Surface modification and tooth contact analysis of variable hyperbolic circular-arc-tooth-trace cylindrical gears // Mechanical Sciences. 2011. Vol. 13. P. 909-920. DOI: 10.5194/ms-13-909-2022. (In Engl.).
21. Ma D., Liu Y., Ye Z. [et al.]. Meshing Contact Impact Properties of Circular Arc Tooth Trace Cylindrical Gear Based on Rotating Knife Dish Milling Process // Mathematical Problems in Engineering. 2021. Vol. 2021. DOI: 10.1155/2021/8819818. (In Engl.).
22. Guo R., Wei Y., Liu Y. [et al.]. Analytical solution to contact characteristics for a variable hyperbolic circular-arc-tooth-trace cylindrical gear // Mechanical Sciences. 2021. Vol. 12. P. 923-932. DOI: 10.5194/ms-12-923-2021. (In Engl.).
23. Wei Y., Guo R., Liu Y. [et al.]. Analytical Calculation of the Tooth Surface Contact Stress of Cylindrical Gear with Variable Hyperbolic Circular-Arc-Tooth-Trace // Symmetry. 2020. Vol. 12, no. 8. 1318. DOI: 10.3390/sym12081318. (In Engl.).
24. Yongqiao W., Shuhong Y., Qi Z. [et al.]. Numerical Analysis of Isothermal Elastohydrodynamic Lubrication of Cylindrical Gears with Variable Hyperbolic Circular Arc and Tooth Trace // Transactions of FAMENA. 2018. Vol. 42, no. 1. P. 61-72. DOI: 10.21278/TOF.42106. (In Engl.).
25. Lopato G. A., Kabatov N. F., Segal' M. G. Konicheskiye i gipoidnyye peredachi s krugovymi zub'yami [Bevel and hypoid gears with circular teeth]. 2nd ed. Moscow, 1977. 423 p. (In Russ.).
26. 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 // New Approaches to Gear Design and Production. 2020. Vol. 81. P. 1-46. DOI: 10.1007/978-3-030-34945-5_1. (In Engl.).
27. Volkov A. E., Medvedev V. I., Matveyenkov D. S. Algoritm optimizatsionnogo sinteza spiral'no-konicheskikh zubchatykh peredach [Algorithm of optimisation synthesis of spiral bevel gears] // Sovremennoye mashinostroyeniye. Nauka i obrazovaniye. Modern Mechanical Engineering. Science and Education. 2018. No. 7. P. 693-709. DOI: 10.1872/MMF-2018-59. (In Russ.).
Review
For citations:
Syzrantsev V.N., Starikov A.I. Synthesis of an adaptive cylindrical gear with arched teeth with two contact zones spaced along the length of the tooth. Omsk Scientific Bulletin. 2023;(4):38-45. (In Russ.) https://doi.org/10.25206/1813-8225-2023-188-38-45. EDN: WVBWUR
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