A Theoretical Study of the Influence of Various Parameters on the Limit Torque of a Harmonic Drive

Specific work features of a harmonic drive are considered in this article. The mathematical model that takes into account spatial nature of deformation and interaction of the drive elements is presented. The resolving system of equations is obtained using the Bubnov–Galerkin’s method. The influence coefficients are determined by the methods of spatial theory of elasticity, while the limit torque is determined based on the generator slippage occurrence. The authors investigate the influence of various parameters on the limit torque of the harmonic drive with a cam wave generator and the flex spline shaped like a flexible bottom cup. The calculations have shown that radial deformation of the flex spline, depth of teeth engagement, main pressure angle of the basic contour and radial clearance in the flexible bearing have a significant influence on the limit torque, while preload in the gearing, length of the shell and shape of flex spline deformation have hardly any influence on this parameter.

References

[1] Shuvalov S.A. Osnovnye kriterii rabotosposobnosti volnovykh peredach [The main criteria for performance of the wave gear]. Vestnik mashinostroeniia [Russian Engineering Research]. 1976, no. 11, pp. 17–20.

[2] Shuvalov S.A., Poletuchii A.I. Predel’nyi krutiashchii moment, peredavaemyi volnovoi zubchatoi peredachei [The maximum torque transmitted wave gear]. Vestnik mashinostroeniia [Russian Engineering Research]. 1976, no. 11, pp. 16–19.

[3] Poletuchii A.I. Teoriia i konstruirovanie vysokoeffektivnykh volnovykh zubchatykh mekhanizmov [The theory and design of high-performance wave gear mechanisms]. Khar’kov, NAKU «KhAI» im. M. Zhukovskogo publ., 2005. 675 p.

[4] Poletuchii A.I., Stetsenko Ia.A. Optimizatsiia parametrov volnovoi zubchatoi peredachi po predel’nomu vrashchaiushchemu momentu [Optimization of the parameters for the wave gear torque limit]. Otkrytye informatsionnye i komp’iuternye integrirovannye tekhnologii: sb. nauch. trudov [Public information and computer integrated technologies: collection of scientific works]. 2007, no. 37, pp. 73–79.

[5] Ardelean F.A. 3D modeling of the harmonic drive using «CATIA». Annals of the Oradea University. Fascicle of Management and Technological Engineering, 2007, vol. 6 (16), pp. 882–885.

[6] Timofeev G.A. Razrabotka metodov rascheta i proektirovaniia volnovykh zubchatykh peredach dlia privodov slediashchikh system. Diss. dokt. tekhn. nauk [Development of methods of calculation and design of wave gear drives for servo systems. Dr. tech. sci. diss.]. Moscow, Bauman Press, 1997. 358 p.

[7] Liuminarskii I.E., Liuminarskii S.E. Matematicheskoe modelirovanie predel’nogo rezhima raboty volnovoi zubchatoi peredachi [Mathematical Modelling of the Limit Working Capacity of a Harmonic Drive]. Izvestiia vysshikh uchebnykh zavedenii. Mashinostroenie [Proceedings of Higher Educational Institutions. Маchine Building]. 2015, no. 12, pp. 17–26.

[8] Liuminarskii S.E., Liuminarskii I.E. Matematicheskaia model’ volnovoi zubchatoi peredachi s diskovym generatorom voln [Mathematical model of a harmonic drive with the disk wave generator]. Mashinostroenie i inzhenernoe obrazovanie [Mechanical Engineering and Engineering Education]. 2012, no. 2, pp. 45–52.

[9] Liuminarskii I.E. Raschet uprugikh sistem s odnostoronnimi sviaziami [Calculation of elastic systems with unilateral constraints]. Moscow, MGIU publ., 2006, pp. 38–99.

[10] Liuminarskii I.E., Liuminarskii S.E. Raschet sil vzaimodeistviia elementov volnovoi zubchatoi peredachi [The calculation of the forces of interaction of elements of the wave gear]. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie [Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering]. 2011, special is. Energeticheskoe i transportnoe mashinostroenie, pp. 230–240.

[11] Marchuk G.I. Metody vychislitel’noi matematiki [Methods of Computational Mathematics]. Moscow, Nauka, Gl. red. fiz.-mat. lit. publ., 1989, pp. 122–126.