Increasing the Overlap Factor in the Elastic Model of a Modified Gear

Coupled and approximate gears are considered in this article. Methods of localization of the contact patch and the elimination of edge impact are analyzed. Based on the solution of the Hertz problem, mathematical models of gearing in the MathCAD program are constructed, with the help of which the overlap ratio of the gearing is calculated taking into account contact deformations. Circular and parabolic modifications for cylindrical spur gears are proposed. The allowed values of the modification parameters are determined. Contact stresses are equal to the allowable stresses when calculating multi-cycle fatigue. The influence of contact deformation on the load capacity of non-conjugate gears is analyzed.

References

[1] Babichev D.T., Volkov A.E. History of the development of the gears theory. Vestnik nauchno-tekhnicheskogo razvitiya, 2015, no. 5, pp. 25–42 (in Russ.).

[2] Timofeyev B.P., Abramchuk M.V. Problems of new Russian standards compatibility with the ISO recommendations. Journal of Instrument Engineering, 2012, vol. 55, no. 6, pp. 33–38 (in Russ.).

[3] Podrigalo N.M. Estimation of exactitude influence of gear pair production on its reduction ratio. Vestnik Khar’kovskogo natsional’nogo avtomobil’no-dorozhnogo universiteta, 2013, no. 61–62, pp. 205–209 (in Russ.).

[4] Zabelin D.A. Influence of manufacturing errors and assembly of gear transmission on their kinematic accuracy. Vestnik Belorussko-Rossiyskogo universiteta, 2009, no. 2, pp. 78–87 (in Russ.).

[5] Antonyuk V.E., Basinyuk V.L., Serenkov P.S., Buzhan I.A. Zubchatyye peredachi. Normativno-metodicheskoye obespecheniye tochnosti zubchatykh peredach na etape proyektirovaniya [Gear. Regulatory and methodological support of gear accuracy at the design stage]. Minsk, Belorusskaya nauka publ., 2016. 251 p.

[6] Timofeyev B.P. Errors of higher kinematic pairs at their joint work. Teoreticheskiye i prikladnyye problemy tochnosti i kachestva mashin, priborov, sistem. Mat. mezhdunar. nauch. shkoly [Theoretical and applied problems of accuracy and quality of machines, devices, systems. Materials of the international scientific school]. 1996, no. 6, pp. 47–52 (in Russ.).

[7] Vinogradov A.B. Obespecheniye trebuyemogo urovnya kachestva mashin pri proyektirovanii i izgotovlenii. Dokt. Diss. [Ensuring the required level of quality of machines in the design and manufacture. Doct. Diss.]. Novosibirsk, 2005. 348 p.

[8] Iosilevich G.B., Lebedev P.A., Strelyayev V.S. Prikladnaya mekhanika [Applied mechanics]. Moscow, Mashinostroyeniye publ., 1985. 576 p.

[9] Nakhatakyan F.G. Mechanics of Contact Approach of Elastic Bodies in Hertz Problem. Journal of Machinery Manufacture and Reliability, 2010, vol. 39, no. 5, p. 444.

[10] Nakhatakyan F.G. The impact of skew on the load distribution in the gear teeth and between the satellites in the planetary gearing. Kand. Diss. [The impact of skew on the load distribution in the gear teeth and between the satellites in the planetary gearing. Cand. Diss.]. Moscow, 2008. 156 p.

[11] Nakhatakyan F.G. Napryazhenno-deformirovannoye sostoyaniye uprugikh elementov zubchatykh mekhanizmov i sooruzheniy pri ikh lineynom i kromochnom kontakte. Dokt. Diss. [Stress-strain state of elastic elements of gear mechanisms and structures at their linear and edge contact. Doct. Diss.]. Moscow, 2014. 213 p.

[12] Tretyakov E.M. Influence of the relative size of contact pads on the values of ultimate stresses and contact strength of solids. Journal of machinery manufacture and reliability, 2005, no. 6, pp. 51–61.

[13] Matlin M.M., Mozgunova A.I., Starikov A.A., Kulikova M.A. On the Problem of Calculating an Elastic Approachduring Initially Linear Contacts of Machine Elements. Journal of Machinery Manufacture and Reliability, 2009, vol. 38, no. 1, p. 35.

[14] Kravchuk A.S., Chigarev A.V. Mekhanika kontaktnogo vzaimodeystviya tel s krugovymi granitsami [Mechanics of contact interaction of bodies with circular boundaries]. Minsk, Tekhnoprint publ., 2000. 196 p.

[15] Dzhonson K. Mekhanika kontaktnogo vzaimodeystviya [Mechanics of contact interaction]. Moscow, Mir publ., 1989. 510 p.

[16] Hertz H. Miscellaneous papers. London, MacMillan, 1896. 384 p.

[17] Argatov I.I., Dmitriyev N.N. Osnovy teorii uprugogo diskretnogo kontakta [Fundamentals of the theory of elastic discrete contact]. Sankt-Petersburg, Politekhnika publ., 2003. 233 p.

[18] Sheveleva G.I. Teoriya formoobrazovaniya i kontakta dvizhushchikhsya tel [The theory of shaping and contact of moving bodies]. Moscow, 1999. 490 p.