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Multi-objective robust design optimization of a sewing mechanism under uncertainties

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Abstract

This work deals with the multi-objective robust design optimization of a needle-bar-and-thread-take-up-lever (NBTTL) mechanism used in sewing machines. A combined multi-objective imperialist competitive algorithm and Monte Carlo method are developed and used for the robust multi-objective optimization of the NBTTL mechanism. This robust optimization considers simultaneously the Needle Jerk, the transmission angle, the coupler tracking error and their standard deviations where the design parameters uncertainties are considered. The obtained results showed that the robust design reduces significantly the sensitivity of the NBTTL performances to the design parameters uncertainties compared to the deterministic one and to the commercialized Juki 8700 machine.

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Abbreviations

NJ:

Needle Jerk index

TE:

Tracking error of the coupler point

TA:

Transmission angle index

DP:

Design parameters

D(DP):

The search domain of DP

SR:

Robust solution

SD:

Deterministic solution

\({\upgamma }\) :

Deviation from original direction of colony

\(\hbox {Cost}_{\mathrm{imp}}\) :

Cost of an imperialist

\(\hbox {Cost}_{\mathrm{col}}\) :

Cost of a colony

\(\hbox {N}_{\mathrm{col}}\) :

Number of colonies

\(\hbox {C}_\mathrm{n} \) :

The normalized cost of the \(\hbox {n}{\mathrm{th}}\) imperialist

\(\hbox {P}_\mathrm{n} \) :

The normalized power of \(\hbox {n}{\mathrm{th}}\) imperialist

\(\hbox {q}_\mathrm{i} \) :

\(\hbox {i}{\mathrm{th}}\) NBTTL link measurement value

\(\bar{{\upsigma }}\) :

Standard deviation of \(\bar{\hbox {q}}\)

\(\bar{\hbox {q}}\) :

Mean value of a series \(\hbox {q}_\mathrm{i} \)

\(\upbeta \) :

Assimilation coefficient

\({\uptheta }\) :

Parameter of colonies’ deviation

N:

Number of empires

\({\upmu }\) :

Transmission angle of motion

\(\hbox {X}\) :

Direction parameter of colonies motion

\(\hbox {d}\) :

Distance between a colony and an imperialist

\(\hbox {f}_{\mathrm{j,n}} \) :

The value of the objective function j for the imperialist n

\(\hbox {f}_\mathrm{j}^{\min } \) :

The minimum values of objective function j in each iteration

\(\hbox {P}_{\mathrm{p}_\mathrm{n} } \) :

The possession probability of the \(\hbox {n}{\mathrm{th}}\) empire

\(\hbox {NTC}_\mathrm{n} \) :

The normalized total cost of the \(\hbox {n}{\mathrm{th}}\) empire

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Authors and Affiliations

  1. LGM, ENIM, University of Monastir, Monastir, Tunisia

    Bilel Najlawi, Mohamed Nejlaoui & Zouhaier Affi

  2. Department of Mechanical Engineering, American University of Sharjah, Sharjah, UAE

    Lotfi Romdhane

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  1. Bilel Najlawi
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  2. Mohamed Nejlaoui
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Correspondence to Bilel Najlawi.

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Najlawi, B., Nejlaoui, M., Affi, Z. et al. Multi-objective robust design optimization of a sewing mechanism under uncertainties. J Intell Manuf 30, 783–794 (2019). https://doi.org/10.1007/s10845-016-1284-0

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