This article presents a method for multidisciplinary design optimization of a one-stage gear train transmission for an industrial application. The formulation and implementation that enable the integrated design of the gearbox elements (gears, shafts, and bearings) are detailed. The analytical formulation problem is based on four disciplines: product reliability, customer preference, product cost, and structure. The proposed integrated design process takes into account constraints imposed by quality standards. The optimization of the gear train transmission is performed according to a multidisciplinary feasible architecture and uses a population-based evolutionary algorithm (non-dominated sorting genetic algorithm II) to generate Pareto-optimal fronts. Finally, a detailed case study is presented to illustrate the effectiveness of the proposed approach.
AlexandrovNMLewisRM (2002) Analytical and computational aspects of collaborative optimization for multidisciplinary design. AIAA Journal40(2): 301–309.
2.
AzizESChassapisC (2014) Comparative analysis of tooth-root strength using stress-strength interference (SSI) theory with FEM-based verification. International Journal of Interactive Design and Manufacturing8(3): 159–170.
3.
BloebaumCLHajelaPSobieszczanski-SobieskiJ (1992) Non hierarchic system decomposition in structural optimization. Engineering Optimization19(3): 171–186.
4.
BraunRD (1996) Collaborative optimization: An architecture for large-scale distributed design. PhD Thesis, Stanford University, Stanford, CA.
CramerEJDennisJEFrankPD, et al. (1994) Problem formulation for multidisciplinary optimization. SIAM Journal on Optimization4(4): 754–776.
8.
DebKPratapAAgarwalS, et al. (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation6(2): 182–197.
9.
DhaferGJérômeBPhilippeV, et al. (2013) Multi-objective optimization of gear tooth profile modifications. In: Fifth international conference design and modeling of mechanical systems, CMSM’2013, Djerba, Tunisia, 25–27 March, pp. 189–197. Berlin; Heidelberg: Springer.
FuchsHOStephensRI (1980) Metal fatigue in engineering. New York: John Wiley & Sons.
12.
GologluCZeyveliM (2009) A genetic approach to automate preliminary design of gear drives. Computers & Industrial Engineering57(3): 1043–1051.
13.
HaftkaRT (1985) Simultaneous analysis and design. AIAA Journal23(7): 1099–1103.
14.
HanHS (2014) Analysis of fatigue failure on the keyway of the reduction gear input shaft connecting a diesel engine caused by torsional vibration. Engineering Failure Analysis44: 285–298.
15.
HuangHZLiuZJMurthyDNP (2007) Optimal reliability, warranty and price for new products. IIE Transactions39(8): 819–827.
16.
HuangHZTianZGZuoMJ (2005) Multi-objective optimization of three-stage spur gear reduction units using interactive physical programming. Journal of Mechanical Science and Technology19(5): 1080–1086.
17.
ISO 6336-2:2006 (2006) Calculation of load capacity of spur and helical gears: part 2: calculation of surface durability (pitting).
18.
ISO 6336-3:2006 (2006) Calculation of load capacity of spur and helical gears: part 3: calculation of tooth bending strength.
19.
KanoNSerakuNTakahashiF, et al. (1984) Attractive quality and must-be quality. Journal of the Japanese Society for Quality Control14(2): 147–156.
20.
KimHMMichelenaNFPapalambrosPY, et al. (2003) Target cascading in optimal system design. Journal of Mechanical Design, Transactions of the ASME125(3): 474–480.
21.
KortaJAMundoD (2017) Multi-objective micro-geometry optimization of gear tooth supported by response surface methodology. Mechanism and Machine Theory109: 278–295.
22.
LiRChangTWangJ, et al. (2008a) Multi-objective optimization design of gear reducer based on adaptive genetic algorithm. In: 12th international conference on computer supported cooperative work in design, Xi’an, China, 16–18 April, pp. 229–233. New York: IEEE.
23.
LiXLiWLiuC (2008b) Geometric analysis of collaborative optimization. Structural and Multidisciplinary Optimization35(4): 301–313.
24.
MartinsJRRALambeAB (2013) Multidisciplinary design optimization: a survey of architectures. AIAA JOURNAL51(9): 2049–2075.
25.
MettasA (2000) Reliability allocation and optimization for complex systems. In: Annual reliability and maintainability symposium. 2000 proceedings international symposium on product quality and integrity, Los Angeles, CA, 24–27 January, pp. 216–221. New York: IEEE.
26.
MolchoGCristalAShpitalniM (2014) Part cost estimation at early design phase. CIRP Annals-manufacturing Technology63(1): 153–156.
27.
NaunheimerHBertscheBRyborzJ, et al. (2011) Automotive Transmissions: Fundamentals, Selection, Design and Application. 2nd edn.Berlin; Heidelberg: Springer.
28.
NiaziADaiJSBalabaniS, et al. (2006) Product cost estimation: technique classification and methodology review. Journal of Manufacturing Science and Engineering128(2): 563–575.
29.
ÖnerKBKiesmüllerGPvan HoutumGJ (2010) Optimization of component reliability in the design phase of capital goods. European Journal of Operational Research205(3): 615–624.
30.
PadulaSLAlexandrovNGreenLL (1996) MDO test suite at NASA Langley research center. In: Proceedings of the 6th AIAA/NASA/ISSMO symposium on multidisciplinary analysis and optimization, Bellevue, WA, 4–6 September, pp. 410–420. Reston, VA: AIAA.
31.
QiJZhangZJeonS, et al. (2016) Mining customer requirements from online reviews: a product improvement perspective. Information & Management63(8): 951–963.
32.
RadzevichSP (2012) Dudley’s Handbook of Practical Gear Design and Manufacture. 2nd ed.Boca Raton, FL: Taylor and Francis Group.
33.
ShehabEMAbdallaHS (2001) Manufacturing cost modelling for concurrent product development. Robotics and Computer Integrated Manufacturing17(4): 341–353.
34.
ShinandM-KParkG-J (2005) Multidisciplinary design optimization based on independent subspaces. International Journal for Numerical Methods in Engineering64(5): 599–617.
Sobieszczanski-SobieskiJ (1987) The case for aerodynamic sensitivity analysis. In: Sensitivity Analysis in Engineering, NASA Langley Research Center. Hampton, VA: NASA Conference Publication.
Sobieszczanski-SobieskiJAgteJSSanduskyJRR (2000) Bi-level integrated system synthesis. AIAA Journal38(1): 164–172.
39.
Sobieszczanski-SobieskiJMorrisAvan ToorenM (2015) Multidisciplinary Design Optimization Supported by Knowledge Based Engineering. Chichester: John Wiley & Sons.
40.
TavaresSMOde CastroPMST (2017) A comparison of methodologies for fatigue analysis of shafts: DIN 743 vs. approaches based on Soderberg criterion. Ciência and Tecnologia Dos Materiais29(1): e76–e81.
41.
ThompsonDFGuptaSShuklaA (2000) Tradeoff analysis in minimum volume design of multi-stage spur gear reduction units. Mechanism and Machine Theory35(5): 609–627.
42.
WangJHeGZhangJ, et al. (2017) Nonlinear dynamics analysis of the spur gear system for railway locomotive. Mechanical Systems and Signal Processing85: 41–55.
43.
WangXLiuXWangY, et al. (2016) Reliability analysis on the drive system of a gear-type oil pump with variable displacement. Advances in Mechanical Engineering8(3): 1–11.
44.
YaoXMoonSKBiG (2017) Multidisciplinary design optimization to identify additive manufacturing resources in customized product development. Journal of Computational Design and Engineering4(2): 131–142.
45.
ZhangGWangGLiL, et al. (2013) Global optimization of reliability design for large ball mill gear transmission based on the Kriging model and genetic algorithm. Mechanism and Machine Theory69: 321–336.
46.
ZhangYLiuQWenB (2003) Practical reliability-based design of gear pairs. Mechanism and Machine Theory38(12): 1363–1370.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
