Model of shell metal mould heating in the automotive industry

Jaroslav Mlýnek; Roman Knobloch

Applications of Mathematics (2018)

  • Volume: 63, Issue: 2, page 111-124
  • ISSN: 0862-7940

Abstract

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This article focuses on heat radiation intensity optimization on the surface of a shell metal mould. Such moulds are used in the automotive industry in the artificial leather production (the artificial leather is used, e.g., on car dashboards). The mould is heated by infrared heaters. After the required temperature is attained, the inner mould surface is sprinkled with special PVC powder. The powder melts and after cooling down it forms the artificial leather. A homogeneous temperature field of the mould is a necessary prerequisite for obtaining a uniform colour shade and material structure of the artificial leather. The article includes a description of a mathematical model that allows to calculate the heat radiation intensity on the outer mould surface for each fixed positioning of the infrared heaters. Next, we use this mathematical model to optimize the locations of the heaters to provide approximately the same heat radiation intensity on the whole outer mould surface during the heating process. The heat radiation intensity optimization is a complex task, because the cost function may have many local minima. Therefore, using gradient methods to solve this problem is not suitable. A differential evolution algorithm is applied during the optimization process. Asymptotic convergence of the algorithm is shown. The article contains a practical example including graphical outputs. The calculations were performed by means of Matlab code written by the authors.

How to cite

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Mlýnek, Jaroslav, and Knobloch, Roman. "Model of shell metal mould heating in the automotive industry." Applications of Mathematics 63.2 (2018): 111-124. <http://eudml.org/doc/294245>.

@article{Mlýnek2018,
abstract = {This article focuses on heat radiation intensity optimization on the surface of a shell metal mould. Such moulds are used in the automotive industry in the artificial leather production (the artificial leather is used, e.g., on car dashboards). The mould is heated by infrared heaters. After the required temperature is attained, the inner mould surface is sprinkled with special PVC powder. The powder melts and after cooling down it forms the artificial leather. A homogeneous temperature field of the mould is a necessary prerequisite for obtaining a uniform colour shade and material structure of the artificial leather. The article includes a description of a mathematical model that allows to calculate the heat radiation intensity on the outer mould surface for each fixed positioning of the infrared heaters. Next, we use this mathematical model to optimize the locations of the heaters to provide approximately the same heat radiation intensity on the whole outer mould surface during the heating process. The heat radiation intensity optimization is a complex task, because the cost function may have many local minima. Therefore, using gradient methods to solve this problem is not suitable. A differential evolution algorithm is applied during the optimization process. Asymptotic convergence of the algorithm is shown. The article contains a practical example including graphical outputs. The calculations were performed by means of Matlab code written by the authors.},
author = {Mlýnek, Jaroslav, Knobloch, Roman},
journal = {Applications of Mathematics},
keywords = {heat radiation; heat conduction; optimization; differential evolution algorithm; mathematical model; parallel programming},
language = {eng},
number = {2},
pages = {111-124},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Model of shell metal mould heating in the automotive industry},
url = {http://eudml.org/doc/294245},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Mlýnek, Jaroslav
AU - Knobloch, Roman
TI - Model of shell metal mould heating in the automotive industry
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 111
EP - 124
AB - This article focuses on heat radiation intensity optimization on the surface of a shell metal mould. Such moulds are used in the automotive industry in the artificial leather production (the artificial leather is used, e.g., on car dashboards). The mould is heated by infrared heaters. After the required temperature is attained, the inner mould surface is sprinkled with special PVC powder. The powder melts and after cooling down it forms the artificial leather. A homogeneous temperature field of the mould is a necessary prerequisite for obtaining a uniform colour shade and material structure of the artificial leather. The article includes a description of a mathematical model that allows to calculate the heat radiation intensity on the outer mould surface for each fixed positioning of the infrared heaters. Next, we use this mathematical model to optimize the locations of the heaters to provide approximately the same heat radiation intensity on the whole outer mould surface during the heating process. The heat radiation intensity optimization is a complex task, because the cost function may have many local minima. Therefore, using gradient methods to solve this problem is not suitable. A differential evolution algorithm is applied during the optimization process. Asymptotic convergence of the algorithm is shown. The article contains a practical example including graphical outputs. The calculations were performed by means of Matlab code written by the authors.
LA - eng
KW - heat radiation; heat conduction; optimization; differential evolution algorithm; mathematical model; parallel programming
UR - http://eudml.org/doc/294245
ER -

References

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