IFToMM WC 2019: Advances in Mechanism and Machine Science pp 1039-1048

# Optimization of the one stage cycloidal gearbox as a non-linear least squares problem

• Roman Król
• Marcin Wikło
• Krzysztof Olejarczyk
• Krzysztof Kołodziejczyk
• Albert Zieja
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

## Abstract

Cycloidal gearboxes are mechanisms which can work under higher loading conditions than other sprockets with comparable dimensions. Cycloidal gears can be smaller than other gears because in these complex mechanisms many lobes work at the same time. In this article, Levenberg-Marquardt algorithm for solving non-linear least squares problems is used for optimization of the one stage cycloidal gearbox. The results are compared with the Steepest Descent Method applied for the same theoretical model of the optimized gear. Application of gradient based optimization method for cycloidal gears is innovative. In other works, a genetical algorithm approach is used, but there are many simplifications in an objective function and constraints concerning the shape of the cycloidal gear. In this paper, the function for the accurate calculation of the cycloidal gear volume is presented. Optimization method was implemented in MATLAB software. In the presented method: the volume of the cycloidal gear, the contact stress in the internal sleeves, the contact stress at the lobes and the contact stress at the pits of the cycloidal gear are minimized with the box constraints implemented using the Penalty Function Method.

## Keywords

Cycloidal gearbox Levenberg-Marquardt algorithm Steepest Descent Method Optimization Penalty Function Method

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