Issue 44

G. G. Bordonaro et alii, Frattura ed Integrità Strutturale, 44 (2018) 1-15; DOI: 10.3221/IGF-ESIS.44.01 11 The coefficients of the mathematical model in equation (1) are computed by Multiple Linear Regression. The mathematical model for Y 1 (to be maximized) is: Y 1 = 24.8 - 0.1X 1 + 0.0X 2 + 11.3X 3 (***) + 3.1X 4 (***) + 0.2X 1 X 2 - 0.1X 1 X 3 - 0.2X 1 X 4 + (3) - 0.0X 2 X 3 - 0.1X 2 X 4 + 0.9X 3 X 4 (***) + 0.1X 1 2 - 0.2X 2 2 - 0.5X 3 2 - 0.3X 4 2 Figure 10 shows the plot of the coefficients. Two linear terms (b 3 and b 4 ) and one interaction (b 34 ) are statistically significant, with b 3 being by far the most important. Figure 10 : Plot of the coefficients of the mathematical model of the response Y 1 (to be maximized). The mathematical model for Y 2 (to be maximized) is: Y 2 = 166 - 63X 1 (***) + 3X 2 - 10X 3 - 10X 4 + 10X 1 X 2 + 10X 1 X 3 - 13 X 1 X 4 - 8X 2 X 3 - 11X 2 X 4 + (4) - 12X 3 X 4 + 12X 1 2 - 16X 2 2 - 4X 3 2 - 15X 4 2 Figure 11 shows the plot of the model coefficients. Only the linear term b 1 is significant. Temperature decrease causes an increase of the response Y 2 , effective stress in the contact region. Figure 11 : Plot of the coefficients of the mathematical model of the response Y 2 (to be maximized). The mathematical model for Y 3 (to be minimized) is: Y 3 = 163 - 59X 1 (***) + 3X 2 - 12X 3 + 20X 4 + 12X 1 X 2 + 12X 1 X 3 - 2X 1 X 4 - 11X 2 X 3 - 12X 2 X 4 + (5) - 14X 3 X 4 + 11X 1 2 - 22X 2 2 - 14X 3 2 - 3X 4 2 Figure 12 shows the plot of the model coefficients. Only the linear term b 1 is significant. Temperature decrease causes an increase of the response Y 3 , effective stress in the non-contact region.