Abstract
Polyurethane is used for making mould in soft tooling (ST) process for producing wax/plastic components. These wax components are later used as pattern in investment casting process. Due to low thermal conductivity of polyurethane, cooling time in ST process is long. To reduce the cooling time, thermal conductive fillers are incorporated into polyurethane to make composite mould material. However, addition of fillers affects various properties of the ST process, such as stiffness of the mould box, rendering flow-ability of melt mould material, etc. In the present work, multi-objective optimization of various conflicting objectives (namely maximization of equivalent thermal conductivity, minimization of effective modulus of elasticity, and minimization of equivalent viscosity) of composite material are conducted using evolutionary algorithms (EAs) in order to design particle-reinforced polyurethane composites by finding the optimal values of design parameters. The design parameters include volume fraction of filler content, size and shape factor of filler particle, etc. The Pareto-optimal front is targeted by solving the corresponding multi-objective problem using the NSGA-II procedure. Then, suitable multi-criterion decision-making techniques are employed to select one or a small set of the optimal solution(s) of design parameter(s) based on the higher level information of the ST process for industrial applications. Finally, the experimental study with a typical real industrial application demonstrates that the obtained optimal design parameters significantly reduce the cooling time in soft tooling process keeping other processing advantages.
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Abbreviations
- L:
-
Low
- M:
-
Medium
- H:
-
High
- φ m :
-
Maximum packing fraction of disperse phase
- η r :
-
Relative viscosity of suspension
- η p :
-
Viscosity of melt polymer/matrix (Pa s)
- η c :
-
Equivalent viscosity of melt composite (Pa s)
- k c :
-
Equivalent thermal conductivity of composite (w/m k)
- k p :
-
Thermal conductivities of polymer/matrix (w/m k)
- k f :
-
Thermal conductivities of filler material (w/m k)
- V f :
-
Volumetric fraction of filler in the composite (%)
- E c :
-
Equivalent modulus of elasticity of composite (N/mm2)
- K c :
-
Equivalent bulk modulus of composite (N/mm2)
- G c :
-
Equivalent shear modulus of composite (N/mm2)
- G m :
-
Shear modulus of matrix/polymer (N/mm2)
- G f :
-
Shear modulus of filler material (N/mm2)
- G c :
-
Shear modulus of composite (N/mm2)
- K m :
-
Bulk modulus of matrix/polymer (N/mm2)
- K f :
-
Bulk modulus of filler material (N/mm2)
- P s :
-
Filler particle size (µm)
- S f :
-
Shape factor
- T :
-
Temperature (°C)
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Acknowledgments
The authors are thankful to DST (Department of Science and Technology), New Delhi, India, for supporting this research work under the BOYSCAST fellowship programme. Prof. K. Deb also acknowledges the Finland Distinguished Professor (FioDiPro) award by the Academy of Finland.
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Nandi, A.K., Datta, S. & Deb, K. Design of particle-reinforced polyurethane mould materials for soft tooling process using evolutionary multi-objective optimization algorithms. Soft Comput 16, 989–1008 (2012). https://doi.org/10.1007/s00500-011-0797-x
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DOI: https://doi.org/10.1007/s00500-011-0797-x