Modified involute helical gears: computerized design, simulation of meshing and stress analysis.

*(English)*Zbl 1054.70500Summary: The contents of the paper cover: (i) computerized design, (ii) methods for generation, (iii) simulation of meshing, and (iv) enhanced stress analysis of modified involute helical gears. The approaches proposed for modification of conventional involute helical gears are based on conjugation of double-crowned pinion with a conventional helical involute gear. Double-crowning of the pinion means deviation of cross-profile from an involute one and deviation in longitudinal direction from a helicoid surface. The pinion-gear tooth surfaces are in point contact, the bearing contact is localized and oriented longitudinally, edge contact is avoided, the influence of errors of alignment on the shift of bearing contact and vibration and noise are reduced substantially. The developed theory is illustrated with numerical examples that confirm the advantages of the gear drives of the modified geometry in comparison with conventional helical involute gears.

##### MSC:

70B15 | Kinematics of mechanisms and robots |

70-08 | Computational methods for problems pertaining to mechanics of particles and systems |

74M15 | Contact in solid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |

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\textit{F. L. Litvin} et al., Comput. Methods Appl. Mech. Eng. 192, No. 33--34, 3619--3655 (2003; Zbl 1054.70500)

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##### References:

[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] | Feng, P.-H.; Litvin, F.L.; Townsend, D.P.; Handschuh, R.F., Determination of principal curvatures and contact ellipses for profile crowned helical gears, ASME J. mech. des., 121, 1, 107-111, (1999) |

[3] | Hibbit, Karlsson & Sirensen, Inc., ABAQUS/Standard Userâ€™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] | F.L. Litvin, The investigation of the geometric properties of a variety of Novikov gearing, in: Proc. Leningrad Mechanical Institute, no. 24, 1962 (in Russian) |

[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] | Litvin, F.L.; Chen, N.X.; Lu, J.; Handschuh, R.F., Computerized design and generation of low-noise helical gears with modified surface topology, ASME J. mech. des., 117, 2, 254-261, (1995) |

[9] | F.L. Litvin et al., Helical and spur gear drive with double crowned pinion tooth surfaces and conjugated gear tooth surfaces, US Patent Office, patent no. 6,205,879, 2001 |

[10] | Litvin, F.L.; Fan, Q.; Vecchiato, D.; Demenego, A.; Handschuh, R.F.; Sep, T.M., Computerized generation and simulation of meshing of modified spur and helical gears manufactured by shaving, Comput. methods appl. mech. engrg., 190, 5037-5055, (2001) · Zbl 1005.70003 |

[11] | Litvin, F.L.; Lu, J.; Townsend, D.P.; Howkins, M., Computerized simulation of meshing of conventional helical involute gears and modification of geometry, Mechanism machine theory, 34, 1, 123-147, (1999) · Zbl 1049.70549 |

[12] | 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, 1-4, 213-225, (1996) · Zbl 0887.70002 |

[13] | Litvin, F.L.; Tsay, C.-B., Helical gears with circular arc teeth: simulation of conditions of meshing and bearing contact, ASME J. mechanisms, transm., automat. des., 107, 556-564, (1985) |

[14] | Stosic, N., On gearing of helical screw compressor rotors, Proc. imeche, J. mech. engrg. sci., 212, 587-594, (1998) |

[15] | Visual Numerics, Inc., IMSL Fortran 90 MP Library, v. 3.0, info@boulder.vni.com, 1998 |

[16] | Zalgaller, V.A., Theory of envelopes, (1975), Publishing House Nauka, (in Russian) |

[17] | Zienkiewicz, O.C.; Taylor, R.L., The finite element method, (2000), John Wiley & Sons · Zbl 0991.74002 |

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