塑料注射成型收缩值英文文献和中文翻译(7)

y ¼ b0 þ b1x1 þ b2x2 þ b11x2 þ b

x2 þ b

x1x2 þ e ðEq 6Þ

1 22 2 12

x3 ¼ x12; x4 ¼ x22; x5 ¼ x1x2; b3 ¼ b11; b4 ¼ b11; b5 ¼ b12

Y2 ¼ b0 þ b1x1 þ b2x2 þ b3x3 þ b4x4 þ b5x5 þ e (Eq 7)

The method of the least squares is typically used to estimate the regression coefﬁcients (b0, b1, b2) in the multiple linear regression models. Y1 is the response of the ﬁrst-order model and Y2 is the second-order model, respectively. The method of the least squares can be deﬁned by the following equations:

not, R2 (R-sq) is the correlation coefﬁcient, R2 (adj) is the ad- justed statistic, MSE is the mean square error, RMSE is the

root mean square error, and APE (%) is the average absolute percentage error.

4. Results and Discussion

The results obtained from the statistical and Moldﬂow analyses in this study have been investigated in two categories:

the ﬁrst is the statistical results consisting of multiple regression and ANOVA analysis, and the second is the simulation results involving Moldﬂow analysis during the plastic injection molding process.

4.1 Statistical Results

A multiple regression analysis using Minitab (Ref 20) have performed to determine the mathematical relationship between the process parameters and the shrinkage obtained from the values of the FE analyses based on the plastic injection molding. For this purpose, the ﬁrst-order and the second-order regression models have developed to ﬁnd the values of the shrinkage when compared to the values from the FE analyses taken from Moldﬂow. After that, the ANOVA analyses have conducted to check the adequacy of the developed regression models and to evaluate the effects of the process parameters on the shrinkage.

The ﬁrst-order regression model in terms of coded values of process parameters is given below:

Shrinkage ¼ 1:01 þ 0:00127Tmold þ 0:0375Tmelt

— 0:0003Pinj — 0:389Itime — 0:0133Ctime

ðEq 17Þ

Table 5 presents the results of the ﬁrst-order regression model for the shrinkage. In Table 5, R2, which is expressed in Eq 13, is the correlation coefﬁcient and is called R-sq. When R2 approaches the value of 1, the multiple regression models match very well with the experimental results. R2 is calcu- lated to be 0.959 (95.9%) by utilizing the ﬁrst-order regres- sion model given in Eq 17. The T value of the process parameters can be utilized to control whether the predictor

Shrinkage ¼ 1:14 þ 0:0375 Tmelt — 0:489 Itime

— 0:0133 Ctime þ 0:0251 Itime (Eq 18)

Table 7 demonstrates the results of the second-order regres- sion model for the shrinkage. In Table 7, R2 is calculated to be 0.958 (95.8%) using the second-order regression model, as given in Eq 18. In Table 7, Tmelt, Itime, Ctime, and I2 are sta- tistically the most signiﬁcant process parameters for the shrinkage. The other process parameters (Pinj and Tmold) and their interactions are not signiﬁcant because their P value is bigger than 0.05. Table 8 illustrates the results of the ANOVA analysis verifying that the process parameters for the shrink- age are statistically signiﬁcant. The F value of 124.45 in Table 8 indicates that the second-order regression model is signiﬁcant.

In the comparison of the results in Table 5 and 7, it can be seen that R2 (R-sq) values are almost the same, both for the ﬁrst-order and the second-order regression models. However, ﬁve process parameters, Tmold, Tmelt, Pinj, Itime, and Ctime, are used to develop the ﬁrst-order regression model, whereas three process parameters, including Tmelt, Itime, and Ctime, are employed to develop the second-order regression model. The comparison of the ANOVA results in Table 6 and 8 shows that the F value (124.45) of the second-order regression model is greater than the F value (98.72) of the ﬁrst-order regression model. This result indicates that the second-order regression model is more signiﬁcant than the ﬁrst-order regression model in terms of the statistical approach. 塑料注射成型收缩值英文文献和中文翻译(7):http://www.751com.cn/fanyi/lunwen_79121.html