zbMATH — the first resource for mathematics

Design, generation and stress analysis of face-gear drive with helical pinion. (English) Zbl 1131.74323
Summary: Two versions of face-gear drive geometry with a helical pinion are considered. One version is based on a screw involute helicoid. The second version is a new geometry developed as envelopes of two mismatched parabolic racks of the pinion and the shaper. A face-gear drive with a spur pinion is considered as a particular case of the developed theory. A new method of grinding or cutting of face-gears by a worm of special shape has been developed. The following problems are considered: (i) generation of a grinding worm with surfaces free of singularities and (ii) generation of face-gear by a shaper with surfaces free of undercutting and pointing. Tooth contact analysis and stress analysis are applied combined with investigation of tooth bearing contact on both sides. The following advantages have been achieved for the geometry proposed: (a) existence of a longitudinal bearing contact, (b) avoidance of edge contact, and (c) reduction of contact stresses. A phenomenon of asymmetry of tooth bearing contact for the driving and coast sides has been discovered. A computerized design, generation and stress analysis for the new types of face-gear drives have been developed.

74K99 Thin bodies, structures
70E55 Dynamics of multibody systems
Full Text: DOI
[1] Argyris, J.; Fuentes, A.; Litvin, F.L., Computerized integrated approach for design and stress analysis of spiral bevel gears, Comput. methods appl. mech. engrg., 191, 1057-1095, (2002) · Zbl 0999.74084
[2] Bär, G., Curvatures of the enveloped helicoid, Mech. machine theory, 32, 1, 111-120, (1997) · Zbl 1052.53500
[3] Hibbit, Karlsson & Sirensen, Inc., ABAQUS/Standard 6.1 User’s Manual, 1800 Main Street, Pantucket, RI 20860-4847, 1998
[4] Korn, G.A.; Korn, T.M., Mathematics handbook for scientist and engineers, (1968), McGraw-Hill, Inc. · Zbl 0535.00032
[5] Fuentes, A.; Litvin, F.L.; Mullins, B.R.; Woods, R.; Handschuh, R.F., Design and stress analysis of low-noise adjusted bearing contact spiral bevel gears, J. mech. design, 124, September, (2002)
[6] F.L. Litvin, Theory of gearing, NASA RP-1212 (AVSCOM 88-C-C035), Washington, DC, 1989
[7] Litvin, F.L., Gear geometry and applied theory, (1994), Prentice Hall, Inc. Englewood Cliffs, New Jersey
[8] F.L. Litvin, Development of gear technology and theory of gearing, NASA Reference Publication 1406, ARL-TR-1500 1998
[9] F.L. Litvin, Y.-J. Chen, G.F. Heath, V.J. Sheth, N. Chen, Apparatus and method for precision grinding face gears, USA Patent 6,146,253, 2000
[10] Litvin, F.L.; Demenego, A.; Vecchiato, D., Formation by branches of envelope to parametric families of surfaces and curves, Comput. methods appl. mech. engrg., 190, 4587-4608, (2001) · Zbl 0995.70003
[11] Litvin, F.L.; Egelja, A.M.; De Donno, M., Computerized determination of singularities and envelopes to family of contact lines on gear tooth surface, Comput. methods appl. mech. engrg., 158, 1-2, 23-34, (1998) · Zbl 0963.70503
[12] Litvin, F.L.; Fuentes, A.; Gonzalez-Perez, I.; Carnevali, L.; Sep, T.M., New version of Novikov-wildhaber helical gears: computerized design, simulation of meshing and stress analysis, Comput. methods appl. mech. engrg., 191, 5707-5740, (2002) · Zbl 1083.74569
[13] Litvin, F.L.; Fuentes, A.; Zanzi, C.; Matteo, P.; Handschuh, F.R., Face gear drive with spur involute pinion: geometry, generation by a worm, stress analysis, Comput. methods appl. mech. engrg., 191, 2785-2813, (2001) · Zbl 1131.74325
[14] Litvin, F.L.; Fuentes, A.; Zanzi, C.; Matteo, P.; Handschuh, F.R., Design, generation and stress analysis of two versions of geometry of face-gear drives, Mech. machine theory, 37, 1179-1211, (2002) · Zbl 1062.70571
[15] Litvin, F.L.; Seol, I.H., Computerized determination of gear tooth surface as envelope to two parameter family of surfaces, Comput. methods appl. mech. engrg., 138, 213-225, (1996) · Zbl 0887.70002
[16] F.L. Litvin, J.-C. Wang, Y.-J.D. Chen, R.B. Bossler, G.F. Heath, D.J. Lewicki, Face-gear drives: design, analysis and testing for helicopter transmission applications, AGMA paper 92FTM2, 1992
[17] Litvin, F.L.; Zhang, Y.; Wang, J.-C.; Bossler, R.B.; Chen, Y.-J.D., Design and geometry of face-gear drives, ASME J. mech. design, 114, 642-647, (1992)
[18] M. Meyer, Gli Ingranaggi Frontali per Applicazioni di Grande Serie, Organi di Trasmissione, Numero 5 (Prima Parte), pp. 90-98, Numero 6 (Seconda Parte), 2003, pp. 58-61
[19] G.I. Sheveleva, Mathematical simulation of spiral bevel gear production and meshing processes with contact and bending stresses, in: Proc. IX World Congr. IFToMM, vol. 1, 1995, pp. 509-513, 1995
[20] Stadtfeld, H.J., Handbook of bevel and hypoid gears: calculation, manufacturing, and optimization, (1993), Rochester Institute of Technology Rochester, New York
[21] Zalgaller, V.A., Theory of envelopes (in Russian), (1975), Publishing House Nauka · Zbl 0334.52004
[22] V.A. Zalgaller, F.L. Litvin, Sufficient condition of existence of envelope to contact lines and edge of regression on the surface of the envelope to the parametric family of surfaces represented in parametric form, in: Proceedings of Universities: Mathematics (in Russian), Vol. 178, No. 3, pp. 20-23, 1977 · Zbl 0355.53001
[23] Zienkiewicz, O.C.; Taylor, R.L., The finite element method, (2000), John Wiley & Sons · Zbl 0991.74002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.