Research Article A Multiobjective Optimization Analysis of Spur Gear Pair: The Profile Shift Factor Effect on Structure Design and Efficiency Samya Belarhzal , 1 Kaoutar Daoudi, 1 El Mostapha Boudi, 1 Aziz Bachir, 1 and Samira Elmoumen 2 1 Mechanical Department, Mohammadia School of Engineers, Mohammed V University, Rabat, Morocco 2 LIMSAD, Fsac, Hassan II University of Casablanca, Casablanca, Morocco Correspondence should be addressed to Samya Belarhzal; belarhzal.samya.1@gmail.com Received 20 September 2020; Revised 12 January 2021; Accepted 15 January 2021; Published 28 January 2021 Academic Editor: Jos´ eAnt´ onio Fonseca de Oliveira Correia Copyright © 2021 Samya Belarhzal et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Spurgearsareanindispensableelementofpowertransmission,mostofthetimeusedinsmallenvironmentswithsevereoperating conditions such as high temperature, vibrations, and humidity. For this reason, manufacturers and transmission designers are required to look for better gear designs and higher efficiency. In this paper, a multiobjective optimization was conducted, using genetic algorithms (GAs) for corrected spur gear pair with an objective to reduce the structure volume and transmission power lossandrevealtheinfluenceoftheprofileshiftfactorontheoptimalstructurefitness.eoptimizationvariablesincludedarethe pinion and wheel profile shift factors in addition to the module, face width, and the number of pinion teeth mostly used in standardgearoptimization.eprofileshiftfactorinfluencestheshapeofthegearteeth,thecontactratio,andtheloadsharing.It affects then the optimal results meaningfully. e gear pair volume, center distance, and efficiency presented the objective functionswhilecontactstress,bendingstress,facewithcoefficient,andtoothtipinterferencesservedasconstraints.Furthermore, a volume equation was developed, in which a bottom clearance formula is included for more accurate results. "Multiobjective optimization" is conducted at medium and high speeds, and the results show that the structure design is compact compared to standard gears with reasonable efficiency for medium contact ratio. 1. Introduction Gearsareusedintheindustrialfieldformotiontransmission fromoneshafttoanother.eycanworkinsmallsizeslike those mounted in watches or can be robust and heavy in powerful machines [1]. Gears can also operate under severe conditions, such as resisting pitting and bending stress, powerlosses,andotherenvironmentalissues[2].Nowadays, transmission designers look forward to obtain optimal structure designs in order to guarantee the system’s effi- ciency and safety and to satisfy economic requirements, as well as handling the effect of operating constraints. Researchers were first interested in reducing gear size and weight. Yokota et al. [3] were among the first to use genetic algorithms in weight/volume gear optimization. ey analyzed the efficiency of an improved program using nonlinear constraints and integer programming (NIP), re- ducing the structure’s volume by 33.6%. ompson et al. [4] then presented a global, multi- optimization design of two- and three-stage spur gears com- bining double objective functions. e approach shows the relationshipbetweenthepittingeffectandminimumstructure volume.Itwasprovedthattheapproachisvalidanditsfindings may help for future gear design development. In order to obtain a minimum volume, Gologlu and Zeyveli [5] proposed an automating initial model of gears using dynamic and static functions as penalty functions that improved the results of the GA approach. e optimum structure variables generated the number of teeth, module, and face width. For more accurate results in volume optimization, Wang et al. [6] traited on the volume structure of a transmission single-stage spur gear system. He analyzed the effect of bottom clearance and Hindawi Mathematical Problems in Engineering Volume 2021, Article ID 8873769, 10 pages https://doi.org/10.1155/2021/8873769