Modeling of an aluminum melting process using constructive polynomial functions


Constantly increasing quality requirements and ever-stricter conditions pose difficult challenges for the foundry industry. They must produce the high-quality components demanded by the market at a reasonable cost. Modern technologies and innovative methods help to master this challenge. Until recently, production, from the design of the aluminum melting furnace to daily process, relied largely on traditional methods and experience. However, important data and information about the melting process—for example, the temperatures and the shape of the aluminum block in the furnace—can hardly be obtained with conventional experimental methods, as the temperatures exceed 700 °C. Therefore, this research project investigates the method of monitoring a melting process by means of optical sensors for the first time. The purpose of this paper is to predict the surface shape of the block during the melting process, as it is not possible to maintain a constant monitoring due to the heat and energy loss during measurement Behrens (Einsatz einer Lichtfeldkamera im Hochtemperaturbereich beim Schmelzvorgang von Aluminium, wt Werkstattstechnik online, 2016). To generate the necessary data, a 3D light-field camera is installed on top of an aluminum melting furnace in order to monitor the process. The basic idea is to find a general method for curve modeling from scattered range data on the aluminum surface in 3D space. By means of the (x, y, z) data from the 3D camera, the aluminum surface is modeled as a polynomial function with coefficient derived using various interpolation and approximation methods. This study presents an attempt to find the optimal polynomial function model that describes the aluminum surface during the melting process by interpolation or approximation methods. The best method for curve fitting will be extended and implemented for surface modeling. Based on this method, the melting process can be better controlled while the furnace operates continuously under stable conditions and the efficiency can therefore be increased. The proposed model can be modified for a wide variety of melting furnaces.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


  1. 1.

    Behrens B-A, Semrau H, Sauke S-O, Larki Harchegani H, Mohammadifard S (2016) Einsatz einer Lichtfeldkamera im Hochtemperaturbereich beim Schmelzvorgang von Aluminium, wt Werkstattstechnik online

  2. 2.

    Behrens B-A, Vucetic M, Peshekhodov I, Hübner S, Koparan I, Yilkiran D (2015) Schädigungsreduzierung beim Clinchen von Stahlblech (CR240BH) in Aluminiumdruckguss (AlSi10MnMg) mit öffnender Matrize, Fügetechnischen Gemeinschafts-Kolloquium

  3. 3.

    Neela V (2009) Three-dimensional heat transfer analysis of LENSTM process using finite element method. Int J Adv Manufac Technol 45: 935

    Article  Google Scholar 

  4. 4.

    Rakha H, Hellinga B, Van Aerde M, Perez W (1996) Systematic verification, validation and calibration of traffic simulation models. In: Transportation Research Board 75th Annual Meeting

  5. 5.

    van Ruijven L, Beek M, van Eijden T (1999) Fitting parametrized polynomials with scattered surface data. Academic Centre for Dentistry Amsterdam (ACTA), Amsterdam

    Google Scholar 

  6. 6.

    Uyanik G, Güler N (2013) A study on multiple linear regression analysis. In: Elsevier-4th International Conference on New Horizions in Education

  7. 7.

    Barrera D, Ibanez M, Roldan A, Roldan J, Yanez R (2017) Polynomial pattern finding in scattered data. J Comput App Math 318:107–116

    Article  Google Scholar 

  8. 8.

    Li T, Li S, Tan H (2017) Multi-focused microlens array optimization and light field imaging study based on Monte Carlo method. J Opt Exp 25:8274–8287

    Article  Google Scholar 

  9. 9.

    Rougier J (2016) Ensemble averaging and mean squared error. J Clim 29:8865–8870

    Article  Google Scholar 

Download references


Sponsored by the German Federal Ministry of Economics and Energy on the basis of a decision of the German Federal Parliament (Project name: Edusal II, sponsor number: 03ET1056B). The responsibility for the contents of this publication lies with the author.


Author information



Corresponding author

Correspondence to Sara Mohammadifard.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mohammadifard, S., Stonis, M., Langner, J. et al. Modeling of an aluminum melting process using constructive polynomial functions. Prod. Eng. Res. Devel. 12, 679–689 (2018).

Download citation


  • Melting process
  • Light-field camera
  • Polynomial function
  • Interpolation
  • Approximation
  • Aluminum surface model