NVH robust optimization of gear macro and microgeometries using an efficient tooth contact model. (November 2017)

• Record Type: Journal Article
• Authors: Garambois, Pierre; Perret-Liaudet, Joël; Rigaud, Emmanuel
• Is Part Of: Mechanism and machine theory. Volume 117(2017:Nov.)
• Page Start: 78
• Page End: 95
• Publication Date: 2017-11
• Subjects: Multi-objective optimization -- Mechanical design -- Monte-Carlo simulation -- Manufacturing errors -- Gear dynamics and whining noise -- Analytical tooth bending model; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2017.07.008
• Languages: English
• ISSNs: 0094-114X

Abstract

Highlights: A method for the multi-bjective robust optimization of both gear macro/microgeometries to minimize the meshing excitations. The method uses a genetic algorithm which allows testing of a high number of gears and the total design space. A new analytical tooth bending model coupling a thick plate theory and a Ritz-Galerkin method allows a very fast computation. Objectives are the transmission error and mesh stiffness fluctuations (with Monte-Carlo simulations for manufacturing errors). The method gives some gear compromises and a decision help tool for the designer who choose a gear according to its problem. Abstract: This paper presents a methodology for the multi-objective optimization of both gear macro and microgeometry parameters in order to minimize the Static Transmission Error (STE) and the mesh stiffness fluctuations generated by the meshing process. The optimization is performed using a genetic algorithm which allows testing of a high number of gears. As a fast evaluation of the gear excitation sources is required, a analytical tooth bending model is introduced. It computes the gear compliance with an analytical thick plate model evaluating the tooth strain energy and a Ritz–Galerkin approximation evaluating the tooth deflection. For each gear design analyzed, the robustness to manufacturing errors is evaluated by performing Monte Carlo simulations for a thousand random manufacturing errors samples. The Probability Density Functions describing the RMS values of the mesh stiffness and STE fluctuations of each gear are estimated, and their average values are the two objectives of each gear. Standard deviations and maximum values describing the dispersion of results are also evaluated. Finally, the methodology provides a range of gears and a decision help tool, illustrated with a reverse gear.