Complete Balancing of the Six-Bar Mechanism Using Fully Cartesian Coordinates and Multiobjective Differential Evolution Optimization

María T. Orvañanos-Guerrero, Mario Acevedo, Claudia N. Sánchez, Daniel U. Campos-Delgado, Amir Aminzadeh Ghavifekr, Paolo Visconti and Ramiro Velázquez
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María T. Orvañanos-Guerrero: Facultad de Ingeniería, Universidad Panamericana, Aguascalientes 20290, Mexico
Mario Acevedo: Facultad de Ingeniería, Universidad Panamericana, Zapopan 45010, Mexico
Claudia N. Sánchez: Facultad de Ingeniería, Universidad Panamericana, Aguascalientes 20290, Mexico
Daniel U. Campos-Delgado: Facultad de Ciencias, Instituto de Investigación en Comunicación Óptica, Universidad Autónoma de San Luis Potosí, San Luis Potosí 78295, Mexico
Amir Aminzadeh Ghavifekr: Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 5166616471, Iran
Paolo Visconti: Facultad de Ingeniería, Universidad Panamericana, Aguascalientes 20290, Mexico
Ramiro Velázquez: Facultad de Ingeniería, Universidad Panamericana, Aguascalientes 20290, Mexico

Mathematics, 2022, vol. 10, issue 11, 1-24

Abstract: The high-speed operation of unbalanced machines may cause vibrations that lead to noise, wear, and fatigue that will eventually limit their efficiency and operating life. To restrain such vibrations, a complete balancing must be performed. This paper presents the complete balancing optimization of a six-bar mechanism with the use of counterweights. A novel method based on fully Cartesian coordinates (FCC) is proposed to represent such a balanced mechanism. A multiobjective optimization problem was solved using the Differential Evolution (DE) algorithm to minimize the shaking force (ShF) and the shaking moment (ShM) and thus balance the system. The Pareto front is used to determine the best solutions according to three optimization criteria: only the ShF, only the ShM, and both the ShF and ShM. The dimensions of the counterweights are further fine-tuned with an analysis of their partial derivatives, volumes, and area–thickness relations. Numerical results show that the ShF and ShM can be reduced by 76.82% and 77.21%, respectively, when importance is given to either of them and by 45.69% and 46.81%, respectively, when equal importance is given to both. A comparison of these results with others previously reported in the literature shows that the use of FCC in conjunction with DE is a suitable methodology for the complete balancing of mechanisms.

Keywords: six-bar mechanism; dynamic balancing; fully Cartesian coordinates; multiobjective optimization; differential evolution; Pareto front (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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