A study on control of heater power and heating time for thermoforming

Abstract

NOMENCLATUREC P =specific heat of ABS sheet, J/kg.K H=thickness of total sheets, m h=heat transfer coefficient, W/m 2 .K k=thermal conductivity of ABS, 0.174 W/m.K k eq =thermal conductance, W/m.K L=half of the total thickness, m N=total number of sheets q in =inputted heat flux, W/m 2 R c =contact resistance, m․ K/W T a =average temperature, K T c =center temperature, K T s =surface temperature, K T 0 =initial temperature, K T ∞ =environmental temperature, K t=time, s t h =heating time, s ρ=density of ABS sheet, 1050 kg m -3 α=thermal diffusivity of ABS, m 2 /s η n =eigen valueObtaining a uniform thickness of the final product using thermoforming is difficult, and the thickness distribution depends strongly on the distribution of the sheet temperature. In this paper, the time-dependent temperature distribution of the total sheets in the storing stage was studied because the temperature after the storing stage is the initial temperature of the heating process. An analytic solution for simulating the storing stage was derived. Using the solved analytic solution, the time-dependent temperature distribution of the total sheets was found out under the condition of assuming that the temperature-dependent specific heat of the ABS sheets was a certain constant value. Finally, the control method for a successful thermoforming using the heater power or heating time was researched in order to improve the quality of the final products. The results show that the satisfied temperature distribution can be obtained by adjusting the heater power or heating time. The method for analysis in this study will be used to improve the quality of the final products.

Multi-Objective Optimization of Plastics Thermoforming

“…Secondly, the sheet deformation during the shaping phase depends on the mechanical properties of the polymeric material used at the heating temperature. This temperature dependency makes it possible to obtain different sheet deformations in order to control the thickness distribution, that is, in the regions where more deformation is required, the temperature must be lower [11,18]. Figure 4 illustrates schematically the process of heating the plastic sheet.…”

“…Several parameters can be considered: (i) the number of heaters, for example, for sheets with higher thickness two heaters can be used, one each side; (ii) the distance between the heaters bank and the sheet; (iii) the dimensions of each Secondly, the sheet deformation during the shaping phase depends on the mechanical properties of the polymeric material used at the heating temperature. This temperature dependency makes it possible to obtain different sheet deformations in order to control the thickness distribution, that is, in the regions where more deformation is required, the temperature must be lower [11,18]. Figure 4 illustrates schematically the process of heating the plastic sheet.…”

“…where M is the number of points located in a line defining the center of the cup in direction x, t 0 is a reference thickness defined by the user and t i are the thicknesses of the M points. This is a bound constrained multi-objective optimization problem with the following decision variables and objectives limitations (dimensions in meters): 2.0 × 10 −3 ≤ x i ≤ 4.0 × 10 −3 Minimum thickness ≥ 1.0 × 10 −4 (11) where x i is the sheet thickness of the constant thickness along the x direction. The thickness along the x direction is then imposed using a spline variation based on the 10 control points (see Figure 3), or the thickness of the five control points determining the concentric thickness variation, from the center to the border of the circle represented in Figure 3C.…”

“…Li and co-authors [10,11] suggested a methodology to compute and optimize the sheet temperature by controlling the heater temperature. The steady-state optimum distribution of heater power is first ascertained by a numerical optimization to obtain a uniform sheet temperature.…”

Intervención tecnológica para la reconversión y automatización de una máquina termoformadora por vacío de una sola estación

“…Por otro lado Gauthier (2006) presenta un control iterativo que ajusta la temperatura final (setpoint), el cuan denomina TILC (Terminal Iterative Learning Control), que resulta bastante eficiente, sin importar la tasa de calentamiento. Sin embargo, Li et al (2010), coincide con Girard et al (2004), al consideran que es importante intervenir la potencia suministrada para el calentamiento (Heater Power), pues controla el tiempo de calentamiento, que garantiza la homogeneidad de la temperatura en el material. Por tanto, para el diseño del sistema de control, en el trabajo presente, es importante considerar el manejo adecuado de la velocidad de calentamiento y la temperatura de sostenimiento (setpoint).…”