The goal of experimental research

The aim of the experiments was to develop two empirical models describing the variability of torque observation and material temperature in extrusion head as a function of the variability of the studied factors: angle of mutual position of cooperating cam discs, distance between cam discs, speed rotational and extrusion rate.

Hartley’s experimental design was adopted. Experimental design was based on fractional factorial 2^4-1IV design (so called kernel design) augmented with center and star design sets. The operational range of individual factors along with their corresponding symbols is summarized below.

A - angle of the mutual position of cooperating cam disks: (-90, 90), deg;

B - distance between cam discs: (0.5, 4.5) mm;

n - rotational speed of screws: (420, 660) min^-1, W - extrusion output: (5, 6) kg/h;

139

Experimental systems of the test program are shown in Table 7. It should be noted that as a result of the experiment, both the kernel and star design sets were not replicated. Repetitions of result measurements were made only for the center design sets. On this basis, the random variavility of the observations was estimated. This approach is often an experimental practice and is accounted for a significant reduction in research costs.

On the basis of the adopted research program and results of measurement of the output variables, empirical models in the form of a polynomial of many variables were determined, taking into account the constant, linear, two-factor and quadratic interactions terms - equation 1.

𝑦 = 𝛽₀+ ∑^𝑛_𝑖=1𝛽_𝑖𝑥_𝑖+ ∑^𝑛_𝑖=1𝛽_𝑖𝑖𝑥_𝑖²+ ∑ ∑^𝑛_𝑖<𝑗=2𝛽_𝑖𝑗𝑥_𝑖𝑥_𝑗+ 𝜀 (1) In the quoted equation, y denotes the resulting variable, and x with the corresponding index (i) or (j) represents the studied factor. The symbols β followed by indices indicate the coefficients of the empirical model.

The symbol ε stands for model error subject to the normal distribution N (0, σ²).

140

Statistical analysis of empirical models makes it possible to assess which of the factors studied and their corresponding linear, curvature and interaction effects have a critical influence on the variability of the examined response surface.

The results of the statistical analysis are then used to select the setting values or to optimize the extrusion process.

Based on the measurements given, corresponding to the adopted research plan, the coefficients of the terms of the regression equations of the output variables were estimated: torque and temperature of the material.

Each of the regression models was subjected to standard procedures for verifying the correctness of their construction: statistical tests of regression coefficients, analysis of the residuals of models and model adequacy checking.

Fig. 3 and Fig. 4 show the results of the residual analysis of the torque and temperature of material models, correspondingly. Each diagram presents probability-probability plots of residuals. The assumptions of the structure of empirical models require that the probability distribution of differences between the approximate values of the model and the values of measurements (the so-called model residues) are subject to normal distribution. The points on both charts accumulate around the line that determines the ideal fit of the model's residuals to the value of the normal distribution variable. Both drawings do not represent a significant deviation from the assumptions of the construction of empirical models

Tables 8 and 9 list the results of the variation analysis. The individual rows of the tables contain a statistical assessment of the contribution of individual elements of the regression equation (1).

The model terms whose contribution to model variability is comparable to the model error, this is probability level p greater than the arbitrarily adopted level of significance 0.05, were considered statistically insignificant.

Figures 5 and 6 illustrate the comprehensive results of statistical analysis in the form of Pareto analysis of the standardized effects, comparing the contributions of individual terms to the overall variability of regression models.

Each of the analyzed empirical models was characterized by a high value of the determination coefficient.

Table 8. Torque model - table of variance (the probability value of α = 0.05 was assumed as the significance level of the test)

Model term SS df MS F p

A(L) 0.242 1 0.2420 0.568 0.45

A(Q) 6.157 1 6.1573 14.458 0.00

(2)b(L) 2.813 1 2.8125 6.604 0.01

b(Q) 6.420 1 6.4203 15.075 0.00

141

(3)n(L) 62.658 1 62.6580 147.126 0.00

n(Q) 1.135 1 1.1353 2.666 0.10

(4)W(L) 23.180 1 23.1801 54.429 0.00

W, kg/h(Q) 6.228 1 6.2285 14.625 0.00

1L vs.2L 15.688 1 15.6876 36.836 0.00

1L vs.3L 1.073 1 1.0726 2.518 0.11

1L vs.4L 0.300 1 0.3001 0.705 0.40

2L vs.3L 549.452 1 549.4516 1290.155 0.00

2L vs.4L 0.036 1 0.0361 0.085 0.77

3L vs.4L 0.078 1 0.0781 0.183 0.66

Error 78.788 185 0.4259

Total SS 1442.106 199

Table 9. Material temperature model - table of variance (the probability value of α = 0.05 was assumed as the significance level of the test)

Model term SS Df MS F p

A(L) 5.00 1 5.00 0.92 0.34

A(Q) 82.05 1 82.05 15.07 0.00

(2)b(L) 3.20 1 3.20 0.59 0.44

b(Q) 591.14 1 591.14 108.56 0.00

(3)n(L) 858.05 1 858.05 157.58 0.00

n(Q) 65.68 1 65.68 12.06 0.00

(4)W(L) 357.01 1 357.01 65.56 0.00

W, kg/h(Q) 82.05 1 82.05 15.07 0.00

1L vs.2L 39.01 1 39.01 7.16 0.01

1L vs.3L 28.06 1 28.06 5.15 0.02

1L vs.4L 19.01 1 19.01 3.49 0.06

2L vs.3L 97.66 1 97.66 17.93 0.00

2L vs.4L 10.51 1 10.51 1.93 0.17

3L vs.4L 9.11 1 9.11 1.67 0.20

Error 1007.38 185 5.45

Total SS 3513.88 199

142

Fig. 3. Normal probability plot of residuals of the empirical model of torque

Fig. 4. Normal probability plot of residuals of the empirical model of temperature material

143

Fig. 5. Pareto analysis of the standardized effects of the torque model

Fig. 6. Pareto analysis of the standardized effects of the material temperature model

144 8. The results of experimental research

The torque model is characterized by a very strong effect of interaction between the rotational speed and the distance between the cam disks. The effect of interaction between rotational speed and the distance between cam discs is also of great importance in explaining total variability (this effect is negative). Two other significant effects are the negative rotational speed effect and the positive extrusion rate effect.

Other effects of the model: the effect of curvature of rotational speed, the angle of mutual position of cooperating cam disks and the distance between cam discs, although they are statistically significant - they do not contribute much to the empirical model.

Figure 9 shows the strong effect of two-factor interactions between the rotational speed and the distance between the discs. The quoted comments are consistent with the results of the Pareto analysis of the standardized effects presented in Figure 5.

The temperature model of the material is characterized by a strong positive effect of rotational speed, a negative effect of curvature caused by a change in the distance between the cam disks and a negative effect of the extrusion efficiency.

In addition, the effect of the rotational speed influence on the temperature of the material depends on the level of variation in the distance between the disks, which is clearly shown in the 3D plot (Figure 7).

Fig. 7. Diagram of the cross section of the surface area of the temperature model response as a function of the rotational speed of the screw and the distance between

the cam disks

145

A similar strong interaction effect is observed for two variables: extrusion rate and rotational speed – see: Figure 8.

The remaining effects, according to the analysis of variance, have a negligible contribution to the variability of the temperature model (see Pareto analysis - Figure 6).

Fig. 8. Diagram of the cross-section of the surface of the temperature model response as a function of the extrusion efficiency and rotational speed of the screw

Fig. 9. Diagram of the cross-section of the surface of the torque model response as a function of the rotational speed of the screw and the distance between the cam disks

146

Fig. 10. Diagram of the cross-section of the response surface of the torque model as a function of the rotational speed of the screw and the extrusion rate

9. Conclusion

The lowest temperature value of the molten plastic in the extrusion head (210 °C) was obtained during the extrusion process realized at the screw speed of

480 min^-1, the extrusion rate 5.25 kg/h, the angle of mutual position of cooperating cam discs - 45º and the distance between the cam disks 3.5 mm.

References

[1] L. Nakonieczny, M. Zimowski „PP – właściwości i formowanie” PlastNews 11 2009, 32-34.

[2] A. Stasiek, D. Łubkowski, „Badania wpływu konstrukcji segmentów ślimaków wytłaczarek dwuślimakowych współbieżnych oraz parametrów technologicznych na proces wytłaczania polipropylenu modyfikowanego talkiem” Przetwórstwo Tworzyw 1/(133)/16 (styczeń – luty) 2010).

[3] A. Stasiek „Wpływ konstrukcji segmentów ślimaków wytłaczarek dwuślimakowych na charakterystykę procesu wytłaczania”, Przetwórstwo Tworzyw 5/(119)13 wrzesień – październik 2007.

[4] J. Stasiek, K. Bajer, A. Stasiek, M. Bogucki, „Wytłaczarki dwuślimakowe współbieżne do kompozytów polimerowych. Metoda doświadczalnego badania procesu”, Przemysł Chemiczny 91/2/(2012) 224-230.

[5] A. Stasiek, „Badania procesu współbieżnego dwuślimakowego wytłaczania modyfikowanego polipropylenu przy zmiennej geometrii ślimaków”,

147

Rozprawa doktorska, Wydział Inżynierii Mechanicznej, Uniwersytet Technologiczno-Przyrodniczy, Bydgoszcz 2015, obroniona 2016.

[6] A. Stasiek, D. Łubkowski, M. Bogucki, „Badania procesu wytłaczania polipropylenu modyfikowanego talkiem”, Przemysł Chemiczny 91/8(2012) 1625-1629.

[7] A. Stasiek, A. Raszkowska – Kaczor, K. Formela, Badania wpływu nieorganicznych napełniaczy proszkowych na właściwości polipropylenu”, Przemysł Chemiczny 93/6(2014) 888-892).

[8] Materiały informacyjne firmy Orlen.

[9] Materiał informacyjny firmy Mondo Minerals.

148

Volodymyr Krasinskyi¹, Oleh Suberlyak¹, Viktoria Zemke¹, Yurii Klym¹, Ivan Gajdos²

REVIEW ON THE PROCESSING AND PROPERTIES OF NANOCOMPOSITES BASED ON THE MIXTURES OF