A model of the infrared cure of powder coatings based on surface absorptivities in-situ measurements

Abstract

The efficiency of radiative powder coatings curing depends both on the coating radiative properties and the spectral emissivities of the infrared emitters. This investigation is structured to develop a mathematical model using the radiative properties of the coating to describe precisely the coating temperature and deduce the degree of polymerization conversion during the cure. The reflectance measurements results obtained with a FTIR equipped with an integrating sphere are analyzed and implemented in a thermal model. These results show that reflectance values vary with the chemical composition, the pigment nature, and are influenced by the powder coatings cure. The thermal model, solved with the finite volume method, permits to compute the varying temperature within the thickness of the powder-coated metal sample and provides a good prediction of the temperature within the ''coating + substrate'' system. The experimental cure of powder coatings supporting this study was performed in a small test oven equipped with electrical infrared emitters.Heat capacity (J kg -1 K -1 ) e Thickness (m) E Activation energy (J mole -1 ) hConvective exchange coefficient DH 0 Total specific heat of the polymerization reaction (W m -2 K -1 ) kArrhenius parameter (J s) k 0Pre-exponentiel factor (J kg -1 ) m, nOrder of reaction (s -1 ) Q reaction Energy released by the exothermal polymerization reaction R Universal gas constant (W m -2 ) T Temperature (J mol -1 K -1 ) xConversion degree (K)Greek symbols a Absorption coefficient e Emissivity / Radiative flux (W m -2 ) k c Thermal conductivity (W m -1 K -1 ) k Wavelength (lm) q à Hemispherical reflectance q Density (kg m -3 ) sTransmission coefficient r Stefan-Boltzmann constant (W m -2 K -4 )Subscripts em Infrared emitter surf Surface

Experimental predictive control of the infrared cure of a powder coating: A non-linear distributed parameter model based approach

“…In (Salagnac et al, 2004), a PDE model of heat and cure of composite material parts in a small diameter autoclave was developed and validated experimentally. (Véchot et al, 2006) and (Bombard et al, 2008) developed the basis of the model used in this paper: it was a coupled heat transfer and cure PDE model of powder coating during infrared curing.…”

“…The substrate nature and its surface state can also influence the reflectance values; the effect can be more or less important, depending on the coating thickness and the pigment nature (Tongsuo et al, 2002). Although the efficiency of IR curing depends mostly on both the spectral emissions of the infrared source and on the coating radiative characteristics during the cure, we have not found any reference dealing with the measurement of the spectral reflectance during the cure cycle: Spectral reflectances are measured either before the cure (at the powder state) or after the cure (the cure state) (Bombard et al, 2008, Carr et al, 1999, Deans and Kögl, 2000. Reflectance values vary with the chemical composition, the pigment nature, and are influenced by the powder coatings cure.…”

“…The 1D thermal model used here was previously developed in (Bombard et al, 2008). It is based on the Fourier law of heat conduction and the Figure 2 shows the boundary conditions applied at the top surface of the powder (subscript p in the model) and at the bottom of the metallic substrate (subscript s in the model).…”

“…The thermo physical properties of the substrate are found in the literature. For the chemical conversion, the model is validated and more details about it may be found in (Bombard et al, 2006;Vechot et al, 2006).…”

“…It tackled both modeling and control aspects. The first complete model of the coating radiative properties and of the spectral emissivities of the infrared emitters may be found in (Véchot et al, 2006) and (Bombard et al, 2008). However, in this model used here, the reflectance and the emitter emissivity are not measured on-line during the curing, although they vary with the type of infrared flow emitted: any model based controller used for this process has therefore to be robust with respect to this modeling uncertainty.…”