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