USING STOHASTIC OPTIMIZATION FOR MODELLING OF THE NEW COMPOSITE FROM RECYCLED GFP

Transcription

1 6th International DAAAM Baltic Conference INDUSTRIAL ENGINEERING April 2008, Tallinn, Estonia USING STOHASTIC OPTIMIZATION FOR MODELLING OF THE NEW COMPOSITE FROM RECYCLED GFP Kers, J. ; Goljandin, D. & Majak, J. Abstract: The main goal of the current study is to develop prospective methods for mechanical reprocessing of industrial composite plastic scrap. Composite plastic scrap consisted of acrylic plastic with glass fibre reinforcement in polyester resin matrix was used as industrial scrap. One of the subtasks of the current study is to mamize the density of the filler material. The relation between the density of the filler material and the fractions of the PMMA powder is modelled on the basis of the experimental data. The search for the mamum values of the filler material density is performed by use of stochastic optimization techniques. Hybrid genetic algorithm based numerical procedure is developed. Key words: composite plastic scrap, recycling, stochastic optimization 1. INTRODUCTION Recycling of composite plastic scrap has become an urgent issue. One of the ways of recycling plastic scrap is to produce powdered materials from technological scrap and end-of-life products. Thermosetting materials can also be part of the other category in the plastics recycling system. Thermosetting plastics are considered commonly to be non-recyclable because they cannot be re-melted and therefore, reformed into the original products. Many materials are recycled into products other than their original form and moreover, some are recycled without ever been melted, therefore the possibility of recycling the thermosetting plastics still ests [ 1, 2 ]. This type of recycling has been demonstrated by using several different types of thermosetting materials. In these applications, thermosetting plastics are ground into powders and then used as the fillers in other products. The mechanical properties of the products produced by using thermosetting fillers are only slightly less than those superior to the properties of virgin materials [ 1, 3 ]. Thermosets, such as GFP (the polyester resin matrix with the glass fibre reinforcement), are cross-linked and therefore cannot be re-melted, but can be ground to a fine powder, which is an effective filler in new compounds [ 4, 5 ]. In additional to mechanical direct contact recycling methods (ball-milling, attritor milling, hammer milling, etc.), plastics can be reprocessed by the collision method. Milling by collision means that the mechanisms of the particle size reduction of the ductile and brittle materials are different. The milling of brittle materials by collision results in a direct fracture. The theoretical studies on milling by the collision method, which were conducted at Tallinn University of Technology (TUT), were followed by the development of the appropriate devices, called disintegrators, and the different types of disintegrator milling, the DS-series systems [ 6, 7 ]. The reprocessing technology for the composite plastic scrap by using disintegrators in the separative and/or selective milling conditions was developed. The proposed technology provides the highest range of selectivity enabling to produce the acrylic plastic powder with a determined granularity and technological properties [ 8 ].

2 In current paper the technological properties of the milled acrylic plastic powders are under the study for modelling new powdered filler material with mamised density. The milled powder has been divided into six main fractions in order to prepare the mixtures of the filler material. The apparent and tap densities have been determined experimentally for each fraction of the powder and also for combined fractions. The obtained experimental data are used for modelling the relation between the density of the filler material and the fractions of the PMMA powder. For modelling new composite from recycled GFP the artificial neural networks (NN) and hybrid genetic algorithm (GA) are utilized. 2. EXPERIMENTAL STUDY The most common recycling methods for plastic scrap include mechanical granulators, hammer mills, energy recovery systems (the thermal reclamations of energy), the systems of chemical recycling and others. Material separation may be based on magnetic, electrostatic, density, visual, or other characteristics. A series of magnets may be used to remove ferrous metals from conveyors. While separation of ferrous and nonferrous metals is well-developed, the research into glass and plastics separation is urgently needed [ 9 ]. In addition to chemical, physical (melting) and mechanical direct contact (ball-milling, attritor milling, hammer milling, etc.), plastics can be reprocessed by the collision method. The fracture of particles in collision with the milling component of one of the rotating rotors is called disintegration [ 6 ]. To process different materials, the multifunctional DS-series disintegrators developed at TUT were used. These series include the laboratory disintegrator milling system DSL-175 with the productivity of some kg/h and the DSL-115 with the productivity of some hundreds kg/h. For the preliminary size reduction, the monorotor type experimental disintegrator DSA- 158 and semi-industrial DSA-2 are suitable [ 7 ]. For the characterization of the properties of plastic powders (granularity, morphology, and technological properties), the same methods and parameters commonly used for metallic powders are acceptable. The most common methods for determining the densities of metal powders are the ASTM B212 and ASTM B329 standards [ 10 ]. 2.1 Reprocessing of composite scrap The PMMA sheet is the most commonly used material in the manufacture of bathroom equipment. Industrial wastes of reinforced acrylic plastics form about 80% and the acrylic plastic scrap without technological additives account for appromately 20% of the total amount [ 8 ]. The composite plastic plates of PMMA+GFP were preliminarily cut into pieces with the dimensions of length 100 mm, width 100 mm and thickness 5 mm, were reprocessed by the mechanical method of milling by collision. The scheme of milling was the following: PMMA in the form of fine particles and coarse GF particles were separated by sieving. The particle size of the output in the DSA-158 disintegrator was appromately mm. The material preliminarily crushed was suitable for direct milling in the DSA- 2 disintegrator. To estimate grindability, the specific energy of treatment was used. The distribution of the particle size was described by the modified Rosin-Rammler distribution function. After the first two stages, a substantial size reduction takes place from 13 to 1 mm. The final milling in the DSL-115 disintegrator in the direct milling conditions at the double collision velocity reduced the size from 0.71 mm to 0.35 mm [ 8 ]. 2.2 Properties of acrylic plastic powder The study of the particle size and shape of the PMMA powder particles was

3 performed by the sieving analysis (SA) and image analysis (IA). The results of the particles size and shape characteristics were presented in our previous work [ 8 ]. The following technological properties of powders were determined according to standard ASTM B212: the apparent density (ρ a ) and the tap density (ρ t ) of the powder. The apparent density of the powders with the particle size less than 1.25 mm was determined by using the Scott volumeter (see Fig. 1) described in ASTM B329. is tapped or vibrated under specified conditions. The tap density is always higher than the free-flow apparent density. To determine the tap density, the standard mass (usually 50g) of powder is weighed ± 0.01 g. The powder is poured into a clean, dry graduated cylinder, taking care that a level surface of powder is obtained. The powder is settled in the cylinder by mechanical or hand tapping. The volume of a fully densified powder sample in the graduated cylinder is read and used in the following calculation of the tap density :, (1) where is the mass of powder in grams and is the volume of the tapped powder in cubic centimetres. The results should be reported as the nearest to 0.1 g/cm 3 [10]. 3. MODELLING OF THE NEW COMPOSITE Figure 1. The Scott volumeter The determination of the apparent density is made by pouring the powder into the funnel and allowing it to flow into 25 cm 3 density cup. The apparent density in grams per cubic centimetres is determined by weighing the powder in the cup in grams and dividing it by 25 cm 3 (cup volume). The tap density ρ t is defined as the density of the powder when the volume reception is tapped or vibrated under specified conditions. The tap density is always higher than the free-flow apparent density [ 10 ]. The tap density ρ t is defined as the density of the powder when the volume reception Based on the results of experimental study performed the relation between the density of the filler material and the fractions of the PMMA powder are modelled by use of two different numerical techniques: cubic B-splines and neural networks. The density of the filler material subjected to mamization. Best apparent and tap densities of the mixed filler materials correspond to different filler consistence. For that reason the minimization of the two different functions f ( x ) = f ( x ), (2) f ( apparent x ) = f ( x ), (3) tap is considered as two separate formulations of the problem. In (2)-(3) x is a parameter vector, f apparent ( x ) and f tap ( x ) stand for apparent and tap densities of the mixed filler material, respectively. Global optimization is performed by use of real-coded genetic algorithm and gradient method. Six fractions of the PMMA

4 powder are considered in order to prepare the mixtures of the filler materials (size in mm 0.315; ; ; ; ). Two different fractions were mixed at a time with the ming ratio 50/50. By using only one fraction of the PMMA powder, the best apparent density 0.64 was measured for the fraction ( mm). The filler consisted of 50 mass % of coarse fractions ( mm) and 50 mass % of fine fractions ( mm) and had the best apparent density The filler material consisted of 50 mass % of coarse fractions ( mm) and 50 mass % of fine fractions ( mm) had the best tap density. 3.1 Cubic B-Spline model The surfaces constructed by the use of Bezier and B-splines do not normally contain the given points. Unlike a natural cubic spline and the least-square method, the Bezier and B-splines have the local control. Thus, modification of one control point affects the part of the surface near that control point only and the complety of the appromation and the computation cost are reduced significantly. The interpolating B-spline surface patch depends on 16 points [ 11 ]. The coordinates of any point determined from the experimental data can be given in the parametric form as and the matrix M b is given constant matrix j 1 j j + 1 j + 2, j 1, j, j + 1, j + 2 X =. (6) i, j x i + 1, j 1 + 1, j + 1, j , j + 2 j 1 j j + 1 j + 2 Similar bicubic equations (cubic in u and v) hold for y and z coordinates. In the case of problem posed above, the given surface points are located regularly with respect to x and y coordinates, since the values of the x and y coordinates are considered as the average values of the particle sizes of each fraction of the PMMA powder. Furthermore, the same values of the particle sizes are used in both x and y axes. Therefore, the expressions for x and y coordinates reduce from bicubic equation to cubic equations (no coupling). The equations for x i, j and y i, j can be solved with respect to variables u or v separately and the results can be used for evaluation z i, j ( u, v). The computation algorithm is implemented in MAPLE 10 (symbolic and numeric calculation) and Matlab 7.4 (numeric calculation, graphics) codes. The data exchange between the Maple and Matlab software packages is performed through text files. = x i( u,v ), yi = yi( u,v ), zi = zi( u,v ) (4) 3.2 Neural Networks model In the current study the neural networks are applied for the appromation of the where u,v are the independent variables density function (surface fitting). An that range over a given set of values (0 u approach suggested is based on the use of 1 and 0 v 1). Proceeding from the the MATLAB neural network toolbox. The matrix formulation for cubic B-splines model is constructed by applying the given in [ 12 ] the coordinates x i, j ( u,v ) can generalized regression of the neural be computed as network function newgrnn. The function [ 3 2 ] T [ 3 2 ] T, j(u,v ) = ( 1/ 36)u,u,u, 1MbXi, jmb v,v,v, 1 newgrnn creates a two-layer network. The first layer has radbas neurons and the (5) (4) X i, j where is the 4 x 4 matrix containing the x-coordinates of the 16 given points second layer has purelin neurons. In order to calculate the outputs for a concurrent set of input vectors, a network simulation function sim is employed. Using outputs generated by function sim the response

5 surface is depicted. The obtained surface models corresponding to the apparent density of the PMMA powder materials is given in Fig 2, where the spread parameter value 1.0 is used as acceptable medium. As a result, the data are fitted a quite smoothly and closely. 3.3 Global optimization In order to determine the extreme values of the density of the filler material a hybrid genetic algorithm based numerical procedure is developed. Numerical solution of the optimization problem posed in divided into two subtasks: search for global extreme in global and local level. The global search is performed by use of MATLAB direct search and genetic algorithm toolbox function ga. In order to achieve higher accuracy the real coded algorithm is used. The local search is performed by use of gradient method, which needs calculation of derivatives of objective function with respect to design variables. The best individual of the population (solution) generated by GA is used as an initial value of the gradient method. In the cases where elite population (set of solutions obtained by fitness-based selection rule) contains individuals, which chromosomes differ substantially it is reasonable to perform local search for all these individuals. The number of local searches necessary depends on result of global search. As it can be expected, the extreme values of the density of the filler material increase with the decreasing values of the modelling parameter spread, and vice versa (see Table 1). Table 1. Dependence of the density of the filler material on parameter of the modelling spread (NN) Spread parameter Max of the app. density Max of the tap density The extreme values of the apparent and tap density of the filler material corresponding to cubic B-splines appromation are and 0.834, respectively. Density ρ a Fractions in mm Fractions in mm Figure 2. A surface model of the apparent density of the acrylic powder (neural networks).

6 4. CONCLUSION The multi-functional DS-series disintegrators developed at TUT has been used for processing of different materials. The technology of milling by the disintegrator devices is compared with the esting advanced technologies for the size reduction of the composite and compounded plastic scrap (by using horizontal shredders and granulators). The advantages of disintegrator milling can be outlined as: - simultaneous separation of the components of composite (impossible with shredders and granulators); - lower specific energy of treatment. To develop the new filler material from the milled PMMA powder, the following technological properties were examined: - the ratio of density of the filler material to the size of the fractions of the PMMA powder was determined. - the most densified filler consisted of 1:1 weight ratio of coarse fractions and fine fractions and thus, had the best apparent density Preceding from the results of size, shape and properties analysis of the milled powder particles the numerical algorithm for modelling of the density of the PMMA powder is developed. The response surface (RS) is modelled by use of NN and cubic B-splines, the search for optimal design is performed by use of hybrid GA. It appears that in the case of the optimization problem considered, the local search, performed by use of gradient method has not significant influence on objective function (i.e. the global search converges to point close to global extreme). Thus, the design improvement by use of local search can be omitted. However, the computation time used for local search is also marginal in comparison with the time needed for global search. The optimization algorithm proposed is developed for more general purpose and both search levels are included. 5. REFERENCES 1. Strong A. B. Plastics: materials and processing. Prentice Hall (2001). 2. Klempner, D., Frisch, K. C., Prentice, G. Advances in Plastics Recycling, CRC Press, (1999). 3. Burns, R. Polyester moulding compounds, Marcel Dekker (1982). 4. Rosato, D. Reinforced Plastics Handbook. Elsevier, (2005). 5. Tucker, N., Lindsay, K. Introduction to automotive composites, Rapra Technology (2002). 6. Tamm, B., Tymanok, A. Impact grinding and disintegrators, Proc. Estonian Acad. Sci. Engin., 2, 2, (1996). 7. Tümanok, A., Kulu, P. Treatment of different materials by disintegrator systems. Proc. Estonian Acad. Sci. Eng., 5, (1999). 8. Kers, J., Kulu, P., Goljandin, D., Mikli, V. Reprocessing technology of composite plastic scrap and properties of materials from recycled plastics Proc. Estonian Acad. Sci. Eng., 13/2, (2007). 9. Plastics and the environment, Edited by Andrady, A. L., Wiley (2003). 10. Powder Metal Technologies and Applications, ASM Handbook, Volume 7, Prautzsch, H., Boehm, W. and Paluszny, M. Bezier and B-Spline Techniques. Springer (2002). 12. Gerald, C. F., Wheatly, P. O. Applied Numerical Analysis, Fifth edition, California Polytechnic State University (1994). 6. ADDITIONAL DATA ABOUT AUTHORS Dr. Jaan Kers Department of Materials Engineering Tallinn University of Technology Ehitajate tee 5, Tallinn 19086, Estonia jaan.kers@ttu.ee