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Fuzzy set based cost model of additive manufacturing with specific example of selective laser sintering

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Abstract

A fuzzy set based cost model for additive manufacturing is proposed. The model is illustrated through an example of selective laser sintering (SLS), a commonly used additive manufacturing (AM) process. Initially, a deterministic cost model is developed. It is then converted to a fuzzy set based model by considering uncertainty in build time estimation and cost components. For the specific case of SLS, a build time estimation procedure is developed as a part of the cost model. A method to evaluate the reliability of the cost estimate in AM and its significance is also introduced. The cost model is illustrated through two examples of products manufactured by SLS.

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Abbreviations

a l :

Acceleration of the laser beam in mm/s2

a r :

Acceleration of the roller in mm/s2

c material :

Material cost in $/kg

c operator :

Operator cost in $/hr

c overhead :

Overhead cost in $/hr

c slicing :

Slicing cost in $/hr

d h :

Scan spacing of the laser beam in mm

d l :

Laser beam diameter in mm

d(μ):

Entropy associated with a membership grade

h :

High estimate of a fuzzy parameter

l :

Low estimate of a fuzzy parameter

l t :

Layer thickness in mm

l x :

Length of the product in x direction in mm

m :

Most likely estimate of a fuzzy parameter

m r :

Mass of the raw material in kg

s :

Distance covered in rapid velocity in mm

w y :

Width of the product in y direction in mm

C material :

Material cost in $

C operator :

Operator cost in $

C overhead :

Overhead cost in $

C slicing :

Slicing cost in $

C* :

Value of the total cost at which reliability is needed in $

C total :

Total cost of the product in $

C L(μ):

Left limits of the cost at membership grade μ in $

C R(μ):

Right limits of the cost at membership grade μ in $

h z :

Height of the product in mm

L r :

Distance travelled by the roller in mm

P I :

Possibility index

R e :

Reliability

T ap :

Time for adding powder in s

T b :

Time required to build the product in hr

T d :

Delay time between two layers in s

T eo :

Time for ending operation in s

T mp :

Time for machine preparation in s

T design :

Time required to convert the CAD model to proper STL format in hr

T post-processing :

Time required for post-processing operations in hr

T r,T r1,T r2 :

Time to travel at rapid speed in s

T scan :

Scan time in s

V max :

Maximum velocity attained by the roller in mm/s

V r :

Rapid velocity of the laser beam in mm/s

V s :

Scan velocity of the laser beam in mm/s

β :

Reliability index

μ :

Membership grade

ρ :

Ratio of the product volume to the volume of bounding box

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Acknowledgments

The authors wish to acknowledge the support provided by Ministry of Human Resource Development, India for supporting the research of the first author.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, India

    Faladrum Sharma & Uday Shanker Dixit

Authors
  1. Faladrum Sharma
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  2. Uday Shanker Dixit
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Corresponding author

Correspondence to Uday Shanker Dixit.

Additional information

Recommended by Associate Editor Yongho Jeon

Faladrum Sharma received his Master’s degree from National Institute of Technology (NIT) Silchar, India. Presently, he is a Doctoral Researcher in the Department of Mechanical Engineering at Indian Institute of Technology (IIT) Guwahati. India. He is working in the field of sustainability issues in 3D printing.

Uday Shanker Dixit is a Professor in the Department of Mechanical Engineering at IIT Guwahati. He has published more than 110 journal papers. He has authored six academic books and edited several books. He is the Associate Editor for the Journal of Institution of Engineers (India), Series C, and the Regional Editor (Asia) of the International Journal of Mechatronics and Manufacturing Systems.

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Sharma, F., Dixit, U.S. Fuzzy set based cost model of additive manufacturing with specific example of selective laser sintering. J Mech Sci Technol 33, 4439–4449 (2019). https://doi.org/10.1007/s12206-019-0840-x

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  • DOI: https://doi.org/10.1007/s12206-019-0840-x

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