Assessment of the Developed Partitioning Approach

Given that the heat area in the present application case is located at the bottom side of the tool, whereas the part is located at the top side of the tool, a distinction between two evaluation surfaces needs to be made: the area of dimensioning and the area of interest. The area of dimensioning is the inner heating area located at the bottom side of the tool where the heat flows were investigated to build the zonal allocations. In contrast, the area of interest is the contact area between the tool and the part, where temperature homogeneity is desired. Due to tool thickness and the resulting through-thickness conduction, the outcome is not necessarily similar. However, as the present application case features an aluminum plate with 4.8 mm thickness, this effect is very small. The impact increases with decreasing thermal tool conductivity as will be demonstrated in the following chapter. To evaluate the quality of the heat zone allocation made the mean temperature residualTr over the equidistant time-stepstbetween actual heat area temperature Tsim and set-point temperatureTSP is calculated for each elemente. The proposed dimensioning strategy was applied to the presented application case: First, a cure simulation was conducted with temperature boundary

con-ditions in the designated heating area according to the desired temperature cycle. The resulting RFL was used to calculate an areal surface heat flux and the clustering/merging algorithms presented were applied. Finally, the deter-mined heat zone allocation were incorporated in a second cure simulation with the appropriate representation of temperature-controlled heat zones defined by Equation 4-10. These cure analyses were compared with the cure simulation of the validation case and the quality of the heat zone dimensioning method was estimated by investigating the resulting temperature distribution apparent in the tool. A small change to the simulation model presented previously was made to prohibit that tool thickness conductivity generates a general offset in the derived temperature residual: The location of the control thermocouples were placed on the bottom side of the tool. Hence, perfect zonal allocation is able to reach a temperature residual of zero in the area of dimensioning.

In Figure 5-8, the mean temperature residua of the validation model and the models defined by the developed algorithms are compared for the tool-part contact surfaceTr,cs and the inner dimensioning areaTr,iha at the bottom side of the tool. The dashed white lines represent the location of the part and the areas of constant amount of plies with the 24-ply side located at low x-values.

Both mean temperature residua T_r,iha and T_r,cs in the validation set-up show the absence of transition zones leading to lower temperatures and, thus, higher temperature residua towards the border of the heating area (see Fig. 5-8 (a), (b)) . Hence, the temperatures at the edge of the laminate in x-direction are up to ∼ −4.8^◦C lower than set-point temperature due to their location close to unheated regions. The laminate edges in the y-direction are subjected to a mean temperature decrease of∼ −1.7^◦C compared to the set-point value.

Compared to the validation simulation, the zonal allocation determined by the LGM algorithm leads to a significant upgrade in temperature homogeneity in both considered areasTr,ihaandTr,cs. The mean temperature in the contact surface between tool and part deviates between −0.5^◦C and −1.7^◦C from the set-point value. Within the heating area on the bottom side of the tool, the biggest temper-ature deviations are located at the edges with a value of −5.6^◦C from set-point temperature.

The zonal allocation calculated with the DKC algorithm showed a further in-crease in temperature accuracy over the whole heating area (see Fig. 5-8 (e), (f)).

The mean temperature in the contact surface between tool and part deviates only between −0.5^◦C and −1^◦C from the set-point value, which fulfills typical temperature accuracy requirements currently applied in composite processing.

Within the inner heating area on the bottom side of the tool only regions close

Figure 5-8Residual mean temperature in the contact surfaceT_r,csand the inner heating areaT_r,iha in the validation model and the results of application of both developed algorithms.

to the four corners of the heating area deviate up to −4.8^◦C from the set-point temperature.

The in-plane temperature difference in the contact surface between the tool and the part is reflected in the in-plane degree of cure gradient, depicted in Figure 5-9.

A through-thickness degree of cure gradient cannot completely be avoided in the current manufacturing set-up as the heat source and the heat sink are located on opposite sides of the part. However, with a sound zonal allocation of the heating

patches, an in-plane degree of cure gradient can be prevented. In Figure 5-9 the in-plane degree of cure evolution and the resulting in-plane difference for the 24-ply zone is shown. The consulted nodes were chosen to represent the max-imal in-plane deviation apparent on the tool-part contact surface. The in-plane temperature deviation in the validation model resulted in a maximum degree of cure deviation of 7.9 %. On the contrary, improved temperature accuracy of the models with the numerical zone allocation showed a maximum deviation of 1.5 % in case of the LGM algorithm and 0.8 % in case of the DKC algorithm.

a)

Figure 5-9Maximal degree of cure differences in the 24-ply Zone 6 within the validation model in comparison with the results utilizing the numerical zone allocation: (a) Evolution of the degree of cureαand (b) maximal in-plane degree of cure∆αdeviation in the contact surface area.

Combining all three case studies above, two major findings can be stated: First, the presented thermal tool dimensioning strategy for composite processing is very well-suited to ensure temperature and degree of cure homogeneity in the tool-part interface. Negligible deviations from the set-point temperature are ob-served on the present application case if the zonal allocation, determined by the introduced method, is applied. Therefore, between the two proposed parti-tioning algorithms, the DKC technique proved to lead to temperatures closer to the set-point value and is recommended for further use based on the presented study. Second, transition zones in thermal tool dimensioning have a major im-pact on the resulting temperature field in the whole heating area and should be designed very carefully. In some applications, where the part does not have a significant thickness or material changes along its dimensions, the appropriate allocation of transition zones is more important than the allocation of the heating zones in the inner heating area.