A study of optimum processing parameters and abnormal parameter identification of the twin-screw co-rotating extruder mixing process based on the distribution and dispersion properties for SiO 2 /low-density polyethylene nano-composites

Abstract

This study took nano-silica particles mixed in low-density polyethylene to implement the optimum processing parameters and make abnormal parameter identification for the twin-screw co-rotating extruder used in the manufacturing process. The mixing quality was divided into distribution and dispersion, where distribution was tested by an energy dispersive spectrometer and evaluated using the coefficient of variation. Dispersion was assessed by the surface effect and specific surface equations, as based on the spectrum of scanning electron microscopy. By using the Taguchi method in planning the experiment coupled with an analysis of variance, we conducted the single-quality characteristic analysis of the experimental results of the two quality characteristics, namely the distribution and dispersion. Then, by using the hierarchical architecture of analytic level process, we can obtain the optimized parameter factors and levels and the calculation of the total weighting of various parameter levels, as well as the ranking of the parameter levels. According to the confirmation experimental results, the signal-to-noise ratios of distribution and dispersion fell within 95% confidence intervals, indicating that the experiment can be represented and reliable. The optimum parameters combination is SiO₂ addition level 1%, screw speed 60 rpm, mixing time 5 min, temperature (upper) 150℃, temperature (middle), 175℃ and temperature (lower) 190℃. After that, by using the optimal parameters and operation processing parameters for support vector machine classification, the abnormality of the processing parameters can be identified for 100%. The good quality of the production can be guaranteed during the extrusion.

Keywords

low-density polyethylene spherical silica homogeneity Taguchi method analytic hierarchy process support vector machine extruder

The discovery of nanotechnology has led to the development of nanoparticles for various end uses, such us nano-composite fibers due to the high-tech applications of textiles. Therefore, studies on modifying the properties of polymeric fibers have increased lately.¹

Low-density polyethylene (LDPE) has branched-chain and straight-chain structures, and its molecular weight is usually 50,000 g/mol. It is considered to be an important thermoplastic polymer material, especially due to its low density, good fabricability and easy formability.^2,3 However, the production of high-stiffness and high-strength polyethylene fibers has long been one of the challenges faced by polymer scientists and engineers,^4–6 and the application of polyethylene fibers is often limited by relatively poor creep resistance as well as low shear modulus and strength. The main method adopted in today’s industry is to produce high-performance polyethylene fibers through a combination of melt spinning and drawing process parameters. However, Chantrasakul and Amornsakchai⁷ found that the introduction of a small amount of layered silicates into polyethylene materials could significantly improve the mechanical properties of polyethylene fibers in terms of the elastic modulus and breaking elongation properties. Zhang et al.⁸ studied the impact of the addition of silicon dioxide nanoparticles to polyethylene composite fibers and analyzed the material morphology, adhesion and mechanical properties. It was observed that compared with regular fiber, nano-silicon dioxide can promote lower crystal size and higher crystallinity, as well as significantly increase its mechanical properties and amplify interfacial adhesiveness to epoxy resin. Ju et al.⁹ presented the nano-silica/LDPE composites using a melt-mixing approach to improve the dielectric properties. Scanning electron microscopy (SEM) revealed that modified nano-silicas were dispersed more evenly in the matrix than the unmodified ones. The dispersion of nanoparticles in the polymer matrix is the key factor affecting the electric insulating properties of nano-composites. The traditional method of preparing polymer/silica composites was direct mixing of the silica into the polymer. The mixing could be done by melt blending. The main difficulty in the mixing process is the effective dispersion of the silica nanoparticles in the polymer matrix, because they usually tend to agglomerate.¹⁰

Nanoparticle silica is likely to aggregate for high surface activity and specific surface area and, thus, it is incompatible with polymers; however, the compatibility between the two materials can be increased by increasing the dispersion of nanoparticles in the composite.^11–16 Bula and Jesionowski¹⁷ melted and mixed different contents of silica and polyethylene for experimentation, and the results showed that the increase in Young's Modulus of the composite was related to the interface compatibility between plastics and nanoparticles and, thus, the interaction of plastics and silica reduced the size of the silica aggregate. Redhwi et al.¹⁸ designed the LDPE composite, which allows the interfaces of polymer and nano fillers to be increased by reducing the mean particle size of the filler and increasing the specific surface area. Thus, different nanoparticles had good dispersion, and the maximum enhancement efficiency was obtained using a nano material with the minimum surface area. They indicated that the composite properties cannot be predicted only by the specific surface area of particles, meaning the distribution of fillers in the polymer matrix is also a major factor. Hu et al.¹⁹ explained using SEM that the impact strength decreased at the aggregation site of the composite of silica particles and amorphous materials. Based on the above, silica needs to have good dispersion, leading to low nanoparticle agglomeration and contributing to increasing the mechanical properties of plastics. The points of these researches are viewing the impact of uniformity of nanoparticles on crystal size and crystallinity, so as to effectively improve the physical properties of fiber.

Basically, using an extruder, the thermoplastic and nanoparticles are compounded by melting–compounding before spinning. Then, the filaments were spun using melt spinning. Therefore, it is of great significance to study the impact of nano-silicon dioxide/polyethylene on uniformity under the process parameters of the twin-screw extruder mixing process.¹⁴ Sasimowski et al.²⁰ used LDPE to test screw mixing, where the flow rate and viscosity, as resulted from the screw shape, had different torque values. Elemans et al.²¹ proposed the effect of mixing temperature on torque. Isac and George²² studied the relationship between viscosity and torque during the melt mixing of material. Kumar et al.²³ indicated that different factors would induce changes in torque. Crawford et al.²⁴ indicated that a higher temperature results in lower viscosity of material, and the torque changes slightly when the material flows. Yousfi et al.²⁵ indicated that the shear force increased with the screw speed, and the viscosity decreased as the temperature rose. Based on the above, the processing parameters during mixing can affect the torque, viscosity and shear force in the extruder. This study used the three data to validate the exceptions of the processing parameters of an extruder. Wang et al.²⁶ indicated that the maximum torque increases with the material content, and a steady state is reached after long-term mixing. Vercruysse et al.²⁷ and Dhenge et al.²⁸ found that, when different parameters are used for a mixing experiment, the steady state of the torque, viscosity and shear force values is reached after a period of time. Therefore, this study used these values as eigenvalues for the extruder mixing process.

In this study, the uniformity was divided into distribution and dispersion. The coefficient of the variation is used to discuss distribution. The specific surface area and surface effect are used to discuss dispersion. This experiment was designed based on the Taguchi method, and different processing parameters were used for multiple mixing to obtain single-quality optimum processing parameters. The experimental reproducibility was validated by confidence interval testing. Finally, the multi-quality optimum processing parameters were obtained by the analytic level process (AHP). The optimization experimental results show the feasibility of the dispersion and distribution defined in this study. The latter part of this study demonstrates that the multi-quality optimum processing parameters in the mixing process could be reflected in the online torque, viscosity and shear force values. These parameters can be used as the features of the processing factors, and the support vector machine (SVM) is applied to identify the abnormal parameters. The results can contribute to the evaluation of product quality in the actual process, and the processing parameter exceptions can be found by online data analysis during mixing. The defective mixed products can be directly removed from regular operation.

Materials

LDPE

The LDPE for this experiment was USI Corporation PAXOTHENE@NA 112-27. It is for use in blown film extrusion and injection molding. This resin is supplied in pellet form and contains a slip agent to improve machinability. The specifications of the LDPE are shown in Table 1.

Table 1.

The specifications of low-density polyethylene

Model no. Properties	NA 112-27
Density (g/cm³)	0.919
Hardness (Shore D)	52
Melt index (g/10 min)	3.0
Melt point (℃)	108
Vicat softening point (℃)	100
Low temperature brittleness (℃/F50)	<–76
Haze/gloss (60°)	7.0/100
Yield point tensile strength (film) (kg/cm²)	91/91
Break point tensile strength (film) (kg/cm²)	190/154
Ultimate elongation (film) (%)	340/550
Impact strength (Dart drop) g/F50	110

SiO₂

The spherical silicon dioxide for this experiment was the Fnami Co. model No. Sio-010-A1 product, which has high heat resistance, high moisture resistance, high dielectric coefficient, high loading, low swelling, low stress, low impurity and a low friction coefficient. The specifications of the spherical silicon dioxide are shown in Table 2. It could enhance the mechanical properties of LDPE.²⁹

Table 2.

The specifications of spherical silicon dioxide

Items	Data
Items	Standard value	Test value
Specific gravity (g/cm³)	2.25	2.25
D50 (µm)	1.0 ± 0.2	1.1
Specific surface area (m²/g)	15.0 ± 2	14.97
Spherical particles ratio (%)	90	95
Moisture (%)	<0.1	0.08

Experimental machine

The micro co-rotating twin-screw extruder has two co-rotating screws for mixing. The structure comprises a feed inlet, a three-stage heating part and a material outlet. The extruder has three characteristics:

small-quantity mixing, where the material mixed each time is less than 15 g;

cyclic mixing, where if the material outlet is not opened, the material returns to the top of the screw through the nearby channel, and is mixed again until the material outlet is opened and, thus, the mixing effect is better;

real-time online machine monitoring, where a computer screen directly displays the speed, viscosity and temperature of the material mixing machine.

The micro extruder used in this study was the Twinson International Limited model Xplore MC-15, as shown in Figure 1. The section is shown in Figure 1(b). The material was pressed by the extruder in the feed inlet, the material was molten and was mixed in the direction of the arrow in the screw. The material outlet was opened after the mixing time, and the mixed material was extruded from the material outlet by the screw. The extruder has six controlled parameters, which are the screw speed, three heating temperatures, SiO₂ addition level and mixing time. According to extruder processing,²⁹ the processing parameters are adjusted to SiO₂ addition levels of 1%, 2% and 3%; the screw speeds are 40, 50 and 60 rpm; the mixing times are 2, 3.5 and 5 min; the temperatures (upper) are 150℃, 155℃ and 160℃; the temperatures (middle) are 165℃, 170℃ and 175℃; the temperatures (lower) are 180℃, 185℃ and 190℃, as shown in Table 3.

Figure 1.

Co-rotating twin-screw extruder: (a) appearance; (b) structural diagram.

Table 3.

Control parameters

Factor	Description	Design value
1	SiO₂ addition	1	2	3	%
2	Screw speed	40	50	60	rpm
3	Heating time	2	3.5	5	min
4	Temperature (upper)	150	155	160	℃
5	Temperature (middle)	165	170	175	℃
6	Temperature (lower)	180	185	190	℃

In this study, the mixing qualities of the extruder will be divided into distribution and dispersion, which are represented by the numerical values for subsequent experiments. The distribution was tested by an energy dispersive spectrometer (EDS) and evaluated using the coefficient of variation. Dispersion was evaluated by the surface effect and specific surface equations, as based on the spectrum of SEM.

Energy dispersive spectrometer

The energy dispersive spectrometer used was an Oxford model Inca energy 400; the distribution is measured by using the element content measured by the EDS.

SEM

A JEOL JSM-6390LV scanning electron microscopy with voltage 20 kV, height 12 mm, spot size 60 and magnified 1500 times was used for material surface structure analysis to evaluate the dispersion.

Research methods

This study took nano-silica particles mixed in LDPE to implement the optimum processing parameters and identify abnormal parameters for the twin-screw co-rotating extruder applied in the extrusion process. The mixing qualities of the extruder include dispersive mixing and distributive mixing.³⁰ Dispersive mixing refers to the break-up of the minor components of a mixture into smaller size particles, whereas distributive mixing leads to a homogeneous spatial distribution of the minor components into the polymer matrix.³¹

This study used the Taguchi method combined with the AHP to present optimization design of the twin-screw co-rotating extruder system for improving the two quality characteristics, namely distribution and dispersion. First, the Taguchi method was coupled with the analysis of variance (ANOVA) to obtain the best parameter combination on each single-quality characteristic of distribution and dispersion. In order to achieve the maximum mixing quality of the extruder system, the multi-quality analysis AHP was used to obtain the optimal control parameter combination according to the contribution degrees of quality weight. Then, the multi-quality optimum parameters were used as the factors and were identified by the SVM. Thus, the operation processing parameters are normal or not can be identified directly.

Distribution

The distribution defines the excellent nano-composite materials, and the particle contents in different positions of substrate should be about the same.^32,33 In the calculation of distribution, the content variance of SiO₂ in different positions of LDPE is calculated, where the larger the variation coefficient, the larger the tendency of dispersion of the group,^30,34,35 which is expressed as Equations (1)–(4)

CV = \frac{V}{\bar{x}} \times 100 %

(1)

V = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} (x - \bar{x})^{2}}

(2)

\bar{x} = \sum_{i = 1}^{N} x_{i}

(3)

where CV is the variation coefficient, V is the stand deviation,

\bar{x}

is the mean value and

Distribution = (1 - \frac{V}{\bar{x}}) \times 100 %

(4)

Dispersion

The dispersion defines the agglomeration degree of particles, where the purpose is to disperse the agglomerated particles into fine particles. When the particles are small, the specific surface area is large and the surface effect is high. In comparison to straight polymer, as the added nanoparticles have a very large specific surface area, the mechanical properties of nano-composite materials are significantly improved.^36,37 Therefore, the dispersion is discussed by using the definition of the image processing SEM spectrum, and the mean specific surface of particles in the range is calculated. The dispersion of particles is expressed in Equation (5)

Dispersion = circumference / area \times 100 %

(5)

where a larger value represents the larger specific surface area, stronger surface effect and better dispersion. The image is processed using MATLAB, and the circumference of the object is calculated directly by the program, divided by the area and represented by a percentage, and the units of circumference and area are calculated by pixels.

At present, documents regarding particle uniformity only discuss the agglomeration of particles, that is, the dispersion, while the subjective evaluation is given only by the SEM spectrum and, thus, there is no objective data for comparison.

Taguchi method

This study required that the qualities, dispersion and distribution are higher the better, so the larger-the-better signal-to-noise (S/N) ratios are used, expressed as Equation (6)

S / Nratio = - 10 log (\frac{\sum_{i = 1}^{N} \frac{1}{y_{i}^{2}}}{n})

(6)

where y_i is the measured value of quality and n is the number of measured groups.

This experiment used the screw speed, mixing time, temperature (upper), temperature (middle), temperature (lower) and additive SiO₂ to form six factors, including six groups of three-level processing parameters. Thus, the factor number and level value in this study use the last six sets of factors of L₁₈ (2¹× 3⁷) as the orthogonal array for this experiment.^38–40 The control factor levels are adjusted, as shown in Table 4.

Table 4.

Experimental parameters of the orthogonal array

Factor	SiO₂ (%)	Screw speed (rpm)	Heating time (min)	Temperature (upper) (℃)	Temperature (middle) (℃)	Temperature (lower) (℃)
Level 1	1	40	2	150	165	180
Level 2	2	50	3.5	155	170	185
Level 3	3	60	5	160	175	190

Analysis of variance

The experimental data derived from the orthogonal array were made into an experiment data sheet. The measured quality data were calculated by Equation (6) to obtain the larger-the-better S/N ratio. The S/N ratio factor response table was used to make an ANOVA table. The ANOVA table contains the experiment error, sum of square, degrees of freedom, average response value estimated variance and F distribution.

(1) Experimental error (S)

The experimental error is defined as in Equation (7)

S = \sqrt{\frac{\sum_{i = 1}^{r} (y_{i} - \bar{y})^{2}}{r - 1}}

(7)

where r is the times of measurement, y_i is the measured value of machine quality and

\bar{y}

is the mean value of measured quality values.

(2) Sum of squares (SS)

As various groups of data are measured independently, the degree of freedom (DOF) of the vector is n × r, the mean value of the measured total mechanical quality only contains one $\bar{y}$ value and the sum of squares is $n \times r \times {\bar{y}}^{2}$ , The sum of squares, ${SS}_{T},$ is expressed in Equation (8)

{SS}_{T} = (\sum_{i = 1}^{n} \sum_{j = 1}^{r} y_{ij}^{2}) - n \times r \times {\bar{y}}^{2}

(8)

where n is the number of experimental groups and r is the times of measurement.

(3) DOFs

DOF_T denotes the DOFs of the total variation vector, DOF_A denotes the DOFs of the factor A effect vector, DOF_e denotes the DOFs of the error vector and the relationship is expressed as in Equation (9)

{DOF}_{T} = {DOF}_{A} + {DOF}_{B} + {DOF}_{C} + \dots + {DOF}_{e}

(9)

(4) Average response value estimated variance (Var)

The factor variation vector SS_i is divided by DOF_i, expressed as Equation (10)

{Var}_{i} = \frac{{SS}_{i}}{{DOF}_{i}}

(10)

(5) F distribution

The denominator of the F-value is the error variance Var_e estimated by the original sample number; the numerator is the variance Var_i of the original sample estimated by the sample mean, expressed as Equation (11)

F_{i} = \frac{{Var}_{i}}{{Var}_{e}}

(11)

Confidence intervals and confirmation experiment

The confidence intervals reflect the error. The confidence level is the probability of an uncertain measured value or calculated value occurring in an interval; this interval is called the confidence interval. The S/N ratio prediction value is expressed as Equation (12)

η_{predict} = \sum_{i = 1}^{n} η_{i} - (n - 1) \bar{η}

(12)

The confidence limits are the upper and lower bound value of the confidence interval, expressed as Equations (13) and (14)

{CL}_{predict} = η_{predict} \pm \frac{S}{\sqrt{m_{e}}} \times TINV (1 - α %, dof)

(13)

{CL}_{confirm} = η_{confirm} \pm \frac{S}{\sqrt{m_{r}}} \times TINV (1 - α %, dof)

(14)

where

η_{predict}

and η_{confirm}

are the mechanical quality S/N ratio prediction value and confirm experiment value, respectively, S is the standard deviation, m is the number of samples, TINV is the t-distribution function (TINV is an Excel built-in function), α is the confidence level and dof is the DOF for the calculating standard deviation.

When the experimental S/N ratio and predicted S/N ratio in the confirmation experiment are in the error range and close to each other, the reproducibility of this experiment is very high, the experimental model is reliable and CI is the α% permissible error difference between the prediction value and confirmation experiment value, or α% confidence interval, expressed as Equation (15)

CI = \pm \sqrt{\frac{S^{2}}{m_{e}} + \frac{S^{2}}{m_{r}}} \times TINV (1 - α %, dof)

(15)

where m_e is the number of equivalent samples, m_r is the number of measured samples, S is the standard deviation and α is the confidence level, where α for this experiment is 95%. Finally, the confidence interval is calculated and whether the difference between η_predict and η_confirm is in this interval is checked. If the value is in this interval, this experiment has reproducibility.

AHP

In this study, the two qualities characteristics are distribution and dispersion. However, the Taguchi method can only be used for the best solution of a single quality. Since this study wants to obtain the best solution of distribution and dispersion to achieve the maximum total quality of the extruder system, a multi-criteria analysis and decision-making technique, the AHP,^41,42 is chosen for analysis.

The hierarchical structure of this study comprises a multi-quality optimum parameter combination (ultimate objective), two product qualities (major factor layer) and six control factors (minor layer). The hierarchies are connected completely to form multiple hierarchies. The contributions of the six factors to the quality are obtained from the Taguchi method, and the single-quality optimization parameter group is obtained. In order to obtain multi-quality optimization parameter group, the importance matrix can be calculated by the importance of the two qualities to the research purpose, expressed as Equation (16)

A = [a_{ij}] = [\begin{matrix} 1 & a_{12} & \dots & a_{1 n} \\ \frac{1}{a_{12}} & 1 & \dots & a_{2 n} \\ : & : & : & : \\ \frac{1}{a_{1} n} & \frac{1}{a_{2} n} & \dots & 1 \end{matrix}]

(16)

The consistency of hierarchies is confirmed, and the weight value of the two qualities is obtained, expressed as Equation (17)

w_{i} = \frac{1}{n} \sum_{j = 1}^{n} \frac{a_{ij}}{\sum_{i = 1}^{n} a_{ij}}; i, j = 1, 2, \dots n

(17)

The weight value is multiplied by the contributions of the six factors to obtain the multi-quality optimum parameter group, expressed as Equation (18)

S_{ij} = w_{i} α_{ij}; i = 1, 2, \dots n; j = 1, 2, \dots r

(18)

SVM

The SVM^43,44 is a supervised learning method, giving training samples and tags. The SVM determines a model according to the training samples. The test samples can be classified during testing, and whether the tags of the test samples meet the model is analyzed. This method has a superior recognition rate for the two-classification problem. The SVM uses data samples to find out a boundary of a hyperplane and classification in a higher space. In the two-classification problem, the widest supporting hyperplane is found by the vector of the test sample, and the middle solid line of the supporting hyperplane is the optimum hyperplane, providing a reference for subsequent test sample classification. This study used MATLAB for the SVM classification. The radial basis function (RBF) is used as the kernel function of the SVM; the RBF kernel function maps the nonlinear data point into a high-dimensional space so as to find the optimum hyperplane in high-dimensional space for separation. Half of test and training samples are selected randomly.

Results and discussion

Uniformity test result

The experiment is performed according to the mixing processing parameters shown in Table 2 and the L₁₈ orthogonal array shown in Table 5.

Table 5.

L₁₈ orthogonal array

Factor Exp. no.	SiO₂ addition (%)	Screw speed (rpm)	Mixing time (min)	Temperature (upper) (℃)	Temperature (middle) (℃)	Temperature (lower) (℃)
1	1	40	2	150	165	180
2	1	50	3.5	155	170	185
3	1	60	5	160	175	190
4	2	40	2	155	170	190
5	2	50	3.5	160	175	180
6	2	60	5	150	165	185
7	3	40	3.5	150	175	185
8	3	50	5	155	165	190
9	3	60	2	160	170	180
10	1	40	5	160	170	185
11	1	50	2	150	175	190
12	1	60	3.5	155	165	180
13	2	40	3.5	160	165	190
14	2	50	5	150	170	180
15	2	60	2	155	175	185
16	3	40	5	155	175	180
17	3	50	2	160	165	185
18	3	60	3.5	150	170	190

The melting point of LDPE is 106℃, whereas the temperatures in the experiments on a twin-screw mixer in the references are 135℃, 145℃, 190℃, 195℃ and 215℃, so the mixing temperature range is set as 150℃ in this study, each level is increased by 5℃ to 190 C and smooth mixing is guaranteed.²⁹ According to Redhwi et al.,¹⁸ Isac and George²² and Jeziórska et al.,²⁹ the SiO₂ addition level is 1–5%; there are better mechanical properties when the addition level is 1%, so the levels are set as 1%, 2% and 3%. Such parameters as the screw speed and mixing time are designed according to the formula for smooth mixing in actual operation.

The mixing is performed five times for each experiment, and a section is analyzed; the sample section is circular and the diameter is about 3 mm, magnified 1500 times to test nine different positions of the section. The distribution and dispersion are calculated.

(1) Distribution

The nine positions of the section are tested by the EDS; the measuring area is 62 µm × 84 µm. For example, one group of measured silicon content is 2.35%, 2.17%, 3.12%, 2.29%, 2.97%, 2.35%, 2.22%, 2.10% and 2.07%; the values are substituted in Equation (4) and the calculated distribution is 85.37%.

(2) Dispersion

The nine positions of the section are analyzed by SEM, and the spectrum is extracted. The region size is 56 µm × 84 µm. The center point and edge of particles are selected by MATLAB to draw a circle automatically. The perimeter area ratio of the circled object is calculated by Equation (5), and the value is the distribution of the object. The average distribution of all objects in the same spectrum is the dispersion of this spectrum. Finally, the average dispersion of the nine spectra is the dispersion of this mixing material. Taking the dispersions of two mixings as examples, Figures 2(a)–(i) show that the average dispersion of the nine spectra is 17.71%, which is the dispersion of the mixing. Figures 3(a)–(i) show that the average dispersion of the nine spectra is 43.55%, which is the dispersion of this mixing. The two dispersion results are shown in Figure 3. The dispersion is better, the particles are smaller and there is no aggregation. According to Equation (5), the particle radius can determine the dispersion. For the limitation of silica particle size, the optimal dispersion is about 45% and the performance of dispersion is derived from pairwise comparison.

Figure 2.

Dispersion measurement (I): (a) dispersion 19.69%; (b) dispersion 15.80%; (c) dispersion 13.55%; (d) dispersion 17.97%; (e) dispersion 19.31%; (f) dispersion 19.53%; (g) dispersion 16.87%; (h) dispersion 16.93%; (i) dispersion 19.75%.

Figure 3.

Dispersion measurement (II): (a) dispersion 44.73%; (b) dispersion 43.77%; (c) dispersion 47.52%; (d) dispersion 44.80%; (e) dispersion 43.23%; (f) dispersion 41.59%; (g) dispersion 42.08%; (h) dispersion 41.87%; (i) dispersion 42.37%.

Single-quality optimal experimental results

The mixing experiment is performed according to the L₁₈ orthogonal array and processing parameter level to analyze the quality. The S/N ratio larger-the-better value is calculated by Equation (6), and the results are shown in Table 6. Afterward, the significant control factors in quality are determined. The factor level S/N ratio response table is made. The single-quality optimum parameter group can be derived from the larger-the-better S/N ratio response table, as shown in Table 7.

Table 6.

Signal-to-noise (S/N) ratio for larger-the-better analysis

	Distribution	Dispersion
No.	S/N	S/N
1	19.98	22.39
2	8.50	14.51
3	15.54	15.44
4	18.61	19.25
5	17.29	18.45
6	11.64	11.87
7	19.66	15.22
8	10.15	14.46
9	16.47	16.64
10	20.52	17.27
11	8.19	12.86
12	6.49	12.10
13	20.01	21.05
14	18.34	19.93
15	11.36	12.15
16	18.34	16.42
17	9.33	17.58
18	15.78	14.95

Table 7.

Optimal parameters for the single quality

	A	B	C	D	E	F
Distribution	3	3	2	1	3	3
Dispersion	1	2	3	1	2	3

The quality S/N ratio value in Table 6 is substituted in Equations (7)–(11) to calculate the ANOVA parameters. The distribution ANOVA shows that the significant factors are A, B and F. The dispersion ANOVA shows that the significant factors are A, C and E.

Firstly, the single-quality optimum process parameters are used for the experiment, and then the S/N ratio prediction values of various qualities are calculated by Equation (12) using the factor response table and significant factors in the ANOVA table. The prediction value is compared with the experimental value by Equation (15) to check whether the difference is in the 95% confidence interval or not. The experimental results are shown in Table 8. According to the distribution ANOVA table, the significant factors influencing the distribution are (A) SiO₂ content, (B) screw speed and (F) temperature (lower); the standard deviation S = 1.57, dof_e = 11, Equations (12)–(15) calculated S/N ratio prediction value η = 39.09, the number of equivalent samples m_e = 2.57 and the 95% confidence interval is [–3.26, 3.26]. The distribution prediction value S/N ratio is 39.09 and the experimental value S/N ratio is 38.34; the difference is 0.75, and this error is in the 95% confidence interval. The experimental results show that the L₁₈ orthogonal array has good reproducibility, and then the multi-quality optimum parameters are analyzed.

Table 8.

The experimental results for single-quality optimum process parameters

Distribution optimal value (%)					Ex. S/N ratio	Predicted S/N ratio	Difference	95% confidence interval
75.40	87.09	73.69	84.03	92.53	38.34	39.09	0.75	±3.26
91.01	88.59	82.67	88.96	81.20
Dispersion optimal value (%)
47.49	46.27	47.15	47.16	45.47	33.40	33.32	0.08	±2.47
44.56	48.22	48.27	47.26	46.48

S/N: signal-to-noise.

The analysis table of the variance for each factor is shown in Tables 9 and 10, respectively.

Table 9.

Variance analysis for distribution

Factor	SS	DOF	Var	F	Confidence level
A	5.92	2	2.96	1.18	61.97%
B	7.42	2	3.71	1.48	68.71%
C	5.21	2	2.60	1.04	58.03%
D	3.78	2	1.89	0.75	48.23%
E	5.62	2	2.81	1.12	60.34%
F	6.73	2	3.36	1.34	65.81%
Error	12.55	5	2.51	S = 1.58
Total	47.23	17

SS: sum of squares; DOF: degree of freedom.

Table 10.

Variance analysis for dispersion

Factor	SS	DOF	Var	F	Confidence level
A	58.10	2	29.05	12.48	98.86%
B	0.28	2	0.14	0.06	5.76%
C	14.56	2	7.28	3.13	86.85%
D	2.19	2	1.09	0.47	34.97%
E	4.44	2	2.22	0.95	55.42%
F	1.56	2	0.78	0.33	26.95%
Error	11.64	5	2.33	S = 1.53
Total	92.76	17

SS: sum of squares; DOF: degree of freedom.

The more accurate factor contribution can be found through the variance analysis table. In the table, for the confidence level, where the screw speed has a significant effect on the distribution, the amount of SiO₂ added and the mixing time have a significant effect on the dispersion.

Multi-quality parameter optimization system

For a reasonable AHP of the single-quality optimum parameter group of distribution and dispersion, the weights and contributions of the multi-quality optimum parameter group are determined. The procedure is as follows.

Step 1: The hierarchical structure is built, and the multi-quality optimization parameter group is Layer 1; the distribution and dispersion quality characteristics are Layer 2; and the six control factors, SiO₂ addition level, screw speed, mixing time, temperature (upper), temperature (middle) and temperature (lower), are Layer 3.

Step 2: The relative importance levels of the quality terms of Layer 2 are evaluated by the AHP evaluation scale. The scales of distribution and dispersion quality characteristics are evaluated. The effects of the two qualities are compared. The distribution and dispersion are given equal importance in this study. In the view of distribution, if the distribution importance is 1, the dispersion importance is also 1. Similarly, in the view of dispersion, if the dispersion importance is 1, the distribution importance is also 1. The comparison results are shown in Table 11.

Table 11.

Important matrix of quality characteristic

	Distribution	Dispersion
Distribution	1	1
Dispersion	1	1

Step 3: After the consistency of hierarchies is confirmed, the weight of the local multi-quality optimum processing parameter combination is calculated by Equation (17). The quality importance weight is multiplied by the confidence level value of each factor of single quality in the Taguchi ANOVA table, that is, the level according to the single-quality optimal combination. The results are shown in Table 12. The calculation example is the screw speed (B3) of distribution and the distribution weight (W1) multiplied by the quality screw speed confidence level value 0.5 × 0.6871 = 0.34354. Finally, the level corresponding to the maximum weight of parameters is the local multi-quality optimum processing parameter level: the optimum parameter combination is SiO₂ addition level A1 is 1%; the screw speed B3 is 60 rpm; the mixing time C3 is 5 min, the temperature (upper) D1 is 150℃; the temperature (middle) E3 is 175℃; and the temperature (lower) F3 is 190℃.

Table 12.

The weights of the optimum parameter combination for multi-quality

	Distribution		Dispersion
SiO₂ addition	A3	0.30984	A1	0.49431
Screw speed	B3	0.34354	B2	0.02878
Heating time	C2	0.29014	C3	0.43426
Temperature (upper)	D1	0.24115	D1	0.17487
Temperature (middle)	E3	0.30170	E2	0.27710
Temperature (lower)	F3	0.32906	F3	0.13474

Finally, the local multi-quality optimum processing parameters and single-quality optimum processing parameters were used for the mixing experiment, and the measured 10 qualities were averaged, as shown in Table 13. The distribution of multi-quality optimum parameters is 83.01% and the dispersion is 44.36%. According to Table 13, the values are higher than the other tested values. For example, the result of multi-quality optimum processing parameters is 83.01%, higher than the distribution of 73.57% of the dispersion optimum parameters, but the multi-quality optimum parameters shall consider two qualities, and the dispersion and distribution are lower than the result of each single-quality optimum parameter.

Table 13.

The experimental results from parameters (%)

Optimal value	Distribution	Dispersion
Optimal parameters for multi-quality	83.01	44.36
Optimal parameters for distribution	83.72	39.29
Optimal parameters for dispersion	73.57	46.83

According to previous references, the better the uniformity of silica particles in LDPE, the better the mechanical properties. There is no objective reference frame for discussing particle uniformity; this study proposes that the uniformity computing mode, the Taguchi method, the AHP and the extruder processing parameter conditions are used to find the local multi-quality optimum processing parameters. The distribution and dispersion quality results approach the single-quality optimal results. The uniformity computing mode can provide a reference for subsequent studies about uniformity evaluation.

Mixing data and abnormal parameter analysis

The normal and abnormal parameters are identified by online data in the mixing experiment. The normal parameters are the previously obtained multi-quality optimum parameter group. The first influential factors in the optimum parameter group are changed to an abnormal parameter group for mixing. The changes in the torque, viscosity and shear force of the optimum parameter group and abnormal parameter group during mixing are obtained from the online data. Finally, MATLAB executes the SVM to classify the abnormal parameter group and optimum parameter group. The test samples and training samples are selected randomly by the program.

Before the factor variation experiment, the factor that is the most influencing and likely to change due to machine problems should be determined. The confidence level values of factors of quality are obtained by the previous Taguchi ANOVA. As the SiO₂ addition level and mixing time are operated manually for the experiment, the two factors are fixed; the other influencing factors are the screw speed, temperature (lower), temperature (middle) and temperature (upper), so the three control factors with the greatest influence are changed, which are the screw speed, temperature (lower) and temperature (middle). The number of training and test samples is shown in Table 14.

Table 14.

Number of samples for support vector machine classification

	Number of experiments	Total number of samples	Number of training samples	Number of test numbers
Optimal parameters	80	80	40	40
Screw speed abnormal	80	80	40	40
Temperature (middle) abnormal	80	80	40	40
Temperature (lower) abnormal	80	80	40	40

The multi-quality optimum parameters are taken as standard, the speed is changed by ±10 rpm and the temperature is changed by ±10℃ so as to observe the changes in such online data as viscosity, torque and shear force of the extruder when the parameters are changed, so as to classify the mixing parameters of the quality result deviating from the multi-quality optimum parameters. The abnormal parameter group after the change is shown in Table 15.

Table 15.

Normal and abnormal values

Parameter	Group	SiO₂ addition (%)	Screw speed (rpm)	Heating time (min)	Temperature (upper) (℃)	Temperature (middle) (℃)	Temperature (lower) (℃)
Normal	1	1	60	5	150	175	190
Abnormal	2	1	50	5	150	175	190
	3	1	70	5	150	175	190
	4	1	60	5	150	165	190
	5	1	60	5	150	185	190
	6	1	60	5	150	175	180
	7	1	60	5	150	175	200

The eigenvalue is selected as the basis of SVM classification. The readable data in the micro extruder include the temperature, speed, current, torque, viscosity and shear force. As the temperature, speed and current will not change obviously after the machine is stable and set, the torque, viscosity and shear force are used as eigenvalues. The experimental eigenvalues are drawn pairwise, as shown in Figures 4–6. According to Figures 4–6, if the SVM executes classification by linear equation, it is difficult to identify normal and abnormal parameters by viscosity and shear force eigenvalues, and the viscosity eigenvalue is likely to identify normal and abnormal. Therefore, the three eigenvalues are used simultaneously for classification with the function RBF = 1 of the kernel function. The optimum parameters, the speed anomaly parameter, temperature (middle) anomaly parameter and temperature (lower) anomaly parameter, are mixed 20 times respectively. Half of the test and training samples are selected randomly by the program, and the final classification effect is good.

Figure 4.

Torque and viscosity eigenvalue distribution diagram.

Figure 5.

Shear force and torque eigenvalue distribution diagram.

Figure 6.

Shear force and viscosity eigenvalue distribution diagram.

This study used the MATLAB program to perform SVM classification. The RBF function of the kernel function was used, as the RBF value can adjust the accuracy of the kernel function; RBF = 1 is relatively precise. The abnormal parameters and optimum parameters of various factors were classified by the SVM with torque, viscosity and shear force eigenvalues. Firstly, pairwise eigenvalues were classified by the SVM 10 times; the results are shown in Table 16. The test and training samples were selected randomly by the program. Two eigenvalues of the results could not separate the optimum parameters from abnormal parameters completely, because the eigenvalues given to the SVM are insufficient. Finally, three eigenvalues were used for SVM classification, and the training samples and test samples were selected randomly by the program. According to the 10 identification results of SVM classification, the success rate of classification with three eigenvalues was 100%, proving that the SVM can classify abnormal and normal parameters completely when the torque, viscosity and shear force are used as eigenvalues for classification. The abnormal parameters can be identified by the three eigenvalues.

Table 16.

Support vector machine classification results of abnormal and normal parameters

Recognition no.	Eigenvalues
Recognition no.	Torque viscosity	Shear force torque	Shear force viscosity	Torque viscosity shear force
1	92.5%	97.5%	92.5%	100.0%
2	95.0%	95.0%	97.5%	100.0%
3	92.5%	97.5%	97.5%	100.0%
4	95.0%	87.5%	97.5%	100.0%
5	95.0%	95.0%	97.5%	100.0%
6	95.0%	97.5%	95.0%	100.0%
7	95.0%	95.0%	92.5%	100.0%
8	92.5%	95.0%	97.5%	100.0%
9	95.0%	97.5%	97.5%	100.0%
10	95.0%	97.5%	97.5%	100.0%

Conclusion

Nano-silica particles can enhance the properties of multiple materials, and good silica uniformity in the materials can enhance the dielectric properties or mechanical strength of materials. In this study, nano-silica is mixed in LDPE plastics by a micro extruder and we discuss the uniformity of nanoparticles in plastics using the Taguchi method, AHP and SVM classifier. Uniformity is divided into distribution and dispersion for SEM/EDS testing. The distribution is analyzed using the variation coefficient, the dispersion is analyzed by the specific surface theory and the local multi-quality optimum processing parameters are obtained by using the Taguchi method and the AHP. Finally, according to the experimental online mixing data: the torque, viscosity and shear force eigenvalues, as well as the abnormal parameters, are identified by the SVM classifier. Firstly, the uniformity of the particles in the plastics is analyzed, and then the local multi-quality optimum processing parameter group is determined by using the Taguchi method and the AHP, which is as follows: silica addition level 1%, screw speed 60 rpm; mixing time 5 min; temperature (upper) 150℃; temperature (middle) 175℃; and temperature (lower) 190℃. The measured uniformity quality of dispersion is 44.36% and distribution is 83.01%. The uniformity approaches that of the results of the single-quality optimum parameters, where dispersion is 46.83% and distribution is 83.72%; thus, the uniformity analysis method used in this study is proved effective. Finally, the mixing experiment is performed based on the three important factors of the multi-quality optimum processing parameters, while the torque, viscosity and shear force data during mixing are used as eigenvalues. The SVM classification result of the pairwise eigenvalues show that there will not be a good classification rate. Therefore, three eigenvalues are used as the basis of SVM classification. The recognition rate is 100% after 10 validations, while the exceptions of the processing parameters can be found by SVM classification with online data in order to remove defective products early and save the cost of measuring poor quality.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Ministry of Science and Technology of the Republic of China (Grant no. 106-2221-E-011-137-MY2).

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Factor Exp. no.	SiO₂ addition (%)	Screw speed (rpm)	Mixing time (min)	Temperature (upper) (℃)	Temperature (middle) (℃)	Temperature (lower) (℃)
1	1	40	2	150	165	180
2	1	50	3.5	155	170	185
3	1	60	5	160	175	190
4	2	40	2	155	170	190
5	2	50	3.5	160	175	180
6	2	60	5	150	165	185
7	3	40	3.5	150	175	185
8	3	50	5	155	165	190
9	3	60	2	160	170	180
10	1	40	5	160	170	185
11	1	50	2	150	175	190
12	1	60	3.5	155	165	180
13	2	40	3.5	160	165	190
14	2	50	5	150	170	180
15	2	60	2	155	175	185
16	3	40	5	155	175	180
17	3	50	2	160	165	185
18	3	60	3.5	150	170	190

Factor Exp. no.	SiO₂ addition (%)	Screw speed (rpm)	Mixing time (min)	Temperature (upper) (℃)	Temperature (middle) (℃)	Temperature (lower) (℃)
1	1	40	2	150	165	180
2	1	50	3.5	155	170	185
3	1	60	5	160	175	190
4	2	40	2	155	170	190
5	2	50	3.5	160	175	180
6	2	60	5	150	165	185
7	3	40	3.5	150	175	185
8	3	50	5	155	165	190
9	3	60	2	160	170	180
10	1	40	5	160	170	185
11	1	50	2	150	175	190
12	1	60	3.5	155	165	180
13	2	40	3.5	160	165	190
14	2	50	5	150	170	180
15	2	60	2	155	175	185
16	3	40	5	155	175	180
17	3	50	2	160	165	185
18	3	60	3.5	150	170	190

A study of optimum processing parameters and abnormal parameter identification of the twin-screw co-rotating extruder mixing process based on the distribution and dispersion properties for SiO 2 /low-density polyethylene nano-composites

Abstract

Keywords

Materials

LDPE

SiO2

Experimental machine

Energy dispersive spectrometer

SEM

Research methods

Distribution

Dispersion

Taguchi method

Analysis of variance

Confidence intervals and confirmation experiment

AHP

SVM

Results and discussion

Uniformity test result

Single-quality optimal experimental results

Multi-quality parameter optimization system

Mixing data and abnormal parameter analysis

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References

SiO₂

Factor Exp. no.	SiO₂ addition (%)	Screw speed (rpm)	Mixing time (min)	Temperature (upper) (℃)	Temperature (middle) (℃)	Temperature (lower) (℃)
1	1	40	2	150	165	180
2	1	50	3.5	155	170	185
3	1	60	5	160	175	190
4	2	40	2	155	170	190
5	2	50	3.5	160	175	180
6	2	60	5	150	165	185
7	3	40	3.5	150	175	185
8	3	50	5	155	165	190
9	3	60	2	160	170	180
10	1	40	5	160	170	185
11	1	50	2	150	175	190
12	1	60	3.5	155	165	180
13	2	40	3.5	160	165	190
14	2	50	5	150	170	180
15	2	60	2	155	175	185
16	3	40	5	155	175	180
17	3	50	2	160	165	185
18	3	60	3.5	150	170	190