Stress optimization and study of the sensitivity to geometric variations of a spur gear tooth profile

David Guyonneau,Emmanuel Mermoz,Jean-Michel Sprauel,Jean-Marc Linares,Jean Mailhé

doi:10.1051/meca/2013046

Abstract

This paper presents an approach for obtaining an optimized geometry for the flank of a tooth by minimizing the equivalent contact stress. The stress calculation method is based on Hertz theory. As the majority of tooth profiles are involute, the geometric variation of the flank of the tooth is achieved variationally relative to the involute profile. The optimum profile is obtained by Monte Carlo simulation. During this optimization, a polynomial expression of the tooth geometry is used. The parameters influencing the simulation are the four characteristic contact points. The approach presented has been applied in a representative case. A study of the geometric sensitivity was conducted on the optimized tooth profile. Two different approaches were considered: by Monte Carlo simulation and analytical propagation. The robust and linear nature of the behavior of the tooth profile was demonstrated when it was subjected to geometric variations.

Highlights

NomenclatureA, B, C, D a, b, c, d C1 Cix, Ciy f (θ) FC I ncontact P1 Rpi Rbi Rti W xi yi zi (xi, yi, zi) Zi α εt μ θ ω1 σeq σ i 1 2 S ELatin Letters Contact characteristic points Tooth flank characteristic points Input torque Polynomial coefficients Polynomial function Contact load Primitive point Number of contacts Input power Primitive radius Basis radius Head radius Range X coordinate Y coordinate Z coordinate Cartesian reference system Tooth numberGreek letters Pressure angle Total contact ratio Friction coefficient Angular variable Input rotation speed Equivalent stress Standard deviationSubscripts Refers to element i Refers to the pinion Refers to the gear Refers to contact input (Start) Refers to contact output (End)Gearboxes (M.G.B.)
Two study paths are examined in this paper: presentation of a method for generating a tooth profile minimizing the equivalent contact stress during meshing and a study of the sensitivity of this tooth flank to geometric variations
The objective of our work is to propose a new gear tooth profile which minimizes the equivalent contact stress, and to study the robustness under stress of this new geometry according to manufacturing errors

Summary

Introduction

NomenclatureA, B, C, D a, b, c, d C1 Cix, Ciy f (θ) FC I ncontact P1 Rpi Rbi Rti W xi yi zi (xi, yi, zi) Zi α εt μ θ ω1 σeq σ i 1 2 S ELatin Letters Contact characteristic points Tooth flank characteristic points Input torque Polynomial coefficients Polynomial function Contact load Primitive point Number of contacts Input power Primitive radius Basis radius Head radius Range X coordinate Y coordinate Z coordinate Cartesian reference system Tooth numberGreek letters Pressure angle Total contact ratio Friction coefficient Angular variable Input rotation speed Equivalent stress Standard deviationSubscripts Refers to element i Refers to the pinion Refers to the gear Refers to contact input (Start) Refers to contact output (End)Gearboxes (M.G.B.). In the field of application to helicopter power gearboxes, specific work has been undertaken to extend the service life of gear assemblies and to ensure improved behavior under load. With respect to this problem, work is essentially focused on:. In this mechanical environment, the scientific literature proposes numerous studies; a representative sample will be presented in the bibliographical study Two study paths are examined in this paper: presentation of a method for generating a tooth profile minimizing the equivalent contact stress during meshing and a study of the sensitivity of this tooth flank to geometric variations.

Objectives

Methods

Results

Discussion

Conclusion