On the issue of optimizing the mass of a two-stage bevel spur gearbox

   The article is devoted to the optimization of a two-stage bevel spur gearbox to minimizing the mass of gears. The minimum weight and overall characteristics of the gearbox are its important competitive advantage. In designing multi-stage gearboxes, gear ratios should be selected in stages that ensure the mechanism has a minimum dimension. The optimal choice of gear ratios of the stages effect on the volume and the weight of the gears in each stage. A review of the available publications on this topic indicates a different intensity of analysis of the interrelationships of the operational and design parameters of the mechanism. The theoretical studies conducted by the authors showed that the results of dividing the gear ratio of the gearbox into stages are influenced primarily by the amounts of torque on the output shaft and of overall gear ratio, the type of heat treatment of the gears and a number of structural limitations. Objective function has been created taking into account the listed factors and represents minimized volume of gears. The search for the minimum objective function was carried out within the specified ranges of geometric and strength parameters of the parts and units of the gearbox, as well as its performance. The minimization results are presented as a function of the gear ratio of the spur stage and the overall gear ratio, the heat treatment of the gears and the torque on the output shaft. The results of calculation of the minimum allowable gear ratio of the spur stage depending on the gear ratio of the two-stage bevel spur gearbox are also given, in which there is no, in particular, cutting of the low-speed shaft and introduction of the milling cutter into the support neck of the bevel shaft; shows comparison with existing guidelines.

1. Ivanovskaya A.V., Zhukov V.A. Mathematical foundations of the development of a control system for marine lifting equipment. Research Bulletin by Russian Maritime Register of Shipping. 2024. № 75. Р. 66 — 74. — EDN: PSBVCR.

2. Starzhinsky V.E., Basinyuk V.L., Mardosevich E.I. Korrektirovka parametrov komponovki dvukhstupenchatogo tsilindricheskogo reduktora [Correcting configuration parameters of a two-stage cylindrical reduction gearbox]. Aktual'nye voprosy mashinovedeniya [Actual Problems of Machine Science]. 2017. Issue 6. P. 96 — 98.

3. Kudryavtsev V.N., Derzhavets Yu.A., Glukharev E.V. Konstruirovanie i raschyot zubchatyh reduktorov [Design and calculation of gearboxes]. Leningrad: Mashinostroenie, 1971. 328 s.

4. Chernavskii S.A., Snesarev G.A., Kozintsov B.S., Bokov K.N. et al. Proektirovanie mehanicheskih peredach [Design of mechanical gears : textbook. 5t^th ed.]. Moscow: Mashinostroenie, 1984. 560 p.

5. Dunaev P.F. Konstruirovanie uzlov i detalei mashin [Design of machine assemblies and components: textbook]. Moscow: Akademiya, 2003. 564 p.

6. Snesarev G.A. Optimizatsiya zubchatykh reduktorov [Optimisation of gearboxes]. Vestnik mashinostroeniya [Bulletin of Mechanical Engineering]. 1985. No. 10. P. 53 — 56.

7. Kurmaz L.V., Skoibeda A.T. Detali mashin. Proektirovanie [Machine components. Design : textbook]. Moscow: Vysshaya shkola, 2005. 309 p.

8. Ivanov K.Ya. Optimization of the basic parameters of a conical-cylindrical reducer. Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta im. akademika M.F. Reshetneva [Bulletin of the Siberian State Aerospace University named after M. F. Reshetnev]. 2009. No. 2 (23). P. 251 — 253. (In Russ.)

9. Meretukov M.A. K voprosu o raspredelenii obshchego peredatochnogo otnosheniya tsilindricheskogo reduktora mezhdu stupenyami [To the question of distribution of the general transfer ratio of the spur gearbox between stages]. Vestnik Adygeiskogo gosudarstvennogo universiteta. Seriya 4: Estestvenno-matematicheskie i tekhnicheskie nauki [Bulletin of Adygeya State University. Series 4: Natural-mathematical and technical sciences]. 2018. No. 2(221). P. 160 —163.

10. Schevchenko S.V., Mukhovaty A.A., Krol O.S. Osobennosti konstruirovaniya dvukhstupenchatogo konicheskogo reduktora [Features of two-stage conical reducer construction]. Avtomatizirovannoe proektirovanie v mashinostroenii [Automated design in mechanical engineering]. 2019. No. 7. P. 26 — 30.

11. Baryshnikov S.O., Afanasyev A.K., Ivanov A.N. Features of the distribution of ordinary gearboxes gear ratio with high tooth hardness for the drive of ship and crane mechanisms. Vestnik gosudarstvennogo universiteta morskogo i rechnogo flota im. admirala S.O. Makarova. 2021. Vol. 13, No. 5. P. 694 — 709. (In Russ.) DOI: 10.21821/2309-5180-2021-13-5-694-709.

12. Ershov R.S. Optimizaciya sposobov obrabotki zub'ev na val-shesterne [Optimization method for tooth modifications on pinions]. Obrazovanie. Nauka. Proizvodstvo: Materialy X Mezhdunarodnogo molodezhnogo foruma, Belgorod, 01 — 15 Oct. 2018 [Education. Science. Production: Proc. of X Intern. Youth Forum]. Belgorod: BGTU im. V.G. Shuhova, 2018. Р. 918 — 922.

13. Pechenev A.V. Mnogokriterial'naya optimizatsiya dvuhstupenchatogo konichesko-tsilindricheskogo reduktora [Multi-criteria optimisation of a two-stage bevel spur gearbox]. Issledovaniya i razrabotki v oblasti mashinostroeniya, energetiki i upravleniya : Materialy XIV Mezhdunarodnoi nauchno-tehnicheskoi konferentsii studentov, aspirantov i molodyh uchenyh [Research and Development in the Field of Mechanical Engineering, Power Engineering and Management : Proc. of XIV Intern. Scientific and Technical Conf. of Students, Postgraduate Students and Young Scientists]. Gomel, 24 — 25 Apr. 2014. Gomel: GGTU im. P.O. Suhogo. Р. 59 — 62.