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order to determine which one has a major effect on the deformation, numerical analysis under various conditions has been conducted and both effects were compared quantitatively.
The averaged deformation amounts along width and height are defined as W and H (Eqs. (13) and (14)) for battery cover, respectively, and similar procedure was also attempted for front cover. Figures 6(a) and 6(b) show numerical results with regard to the averaged deformation amounts along width, W, and height, H, for battery cover under the processing condition of cases 2 and 3 described in Table 1, respectively. The averaged deformation by total residual stress including thermal and flow-induced stress was shown. We also indicated the average deformation only by flow induced stress separately. If the effects of thermal- and flow induced residual stress were separated from each other, thermal residual stress affects total deformation greater than flow-induced stress as shown in Fig. 6(a).
As processing conditions was changed from case 2 to case 3, the averaged total deformation was increased at both sides but the relative portion of flow-induced residual stress still stays very small as shown in Fig. 6(b). Figure 6(c) shows the averaged deformation along width and height under the condition with increased gate number while other processing parameters remain same as case 2. Similarly the effect of flow-induced residual stress on total deformation was negligible compared with thermal-induced stress as shown in Figs. 6(a) and 6(b). In other words, if there is enough number of gates, the influence from flow-induced residual stress will be minimal.
Fig. 6 The averaged deformation corresponding to different processing conditions for battery cover (a) case 2, (b) case 3, and (c) case 2 with increased gate number
The averaged deformation for front cover also shows similar phenomena. Accordingly, we can conclude that thermal-induced residual stress has a relatively major effect on total deformation rather than flow-induced stress for current test geometry. Mobile device usually forms thin shell type geometry with relatively high curvature at the corner. To prevent miss-run during injection process, several number of gates are used in practice. With sufficient number of gates, flow induced residual stress could be considered negligible. It means that controlling processing parameters affecting thermal-induced residual stress can be the effective way to manage the deformation caused by injection molding process.
In this research, five possible variables related with thermal induced residual stress have been selected, which are mold temperature, Young’s modulus, Poisson’s ratio, thermal expansion coefficient of material, and cooling time before the injection molded part is ejected. DOE was introduced to assess the importance of each parameter to final deformation and find the critical factors. Especially, two-level factorial design was used in the current study. Maximum and minimum values of each variable have been selected considering materials and processing condition commonly used in injection molding process for mobile devices, as shown in Table 2.
3.2.2 Two-Level Factorial Design.
Table 3 represents the design matrix with total 25(¼32) runs based on two-level factorial design composed of five variables prescribed above. þ1 and 1 in the matrix symbolize the upper and lower limit of parameters shown in Table 2, respectively. Other processing conditions except for these parameters remained same as general values.
The relative magnitude of inpidual and interaction effects can be found by solving the following relation in case of five independent variables:
Here, y represents output variables required to be analyzed. Xi, having the value of þ1 or 1, and ci stand for each variable shown in Table 2 and its inpidual effect, respectively. The first term in the right hand side of Eq. (17) shows nominal constant and second term depicts inpidual effect and others represent interaction effect associated with each variables. With 32 runs, each coefficient c in Eq. (17) which exhibits relative importance can be found by matrix inversion.