Materials Science Forum Submitte: 2017-08-13 ISSN: 1662-9752, Vol. 925, pp 473-480 Revise: 2017-12-09 oi:10.4028/www.scientific.net/msf.925.473 Accepte: 2018-01-12 2018 Trans Tech Publications, Switzerlan Online: 2018-06-20 Three-Dimensional Moeling of Green San an Squeeze Moling Simulation Yuuka Ito 1,a an Yasuhiro Maea 2,b* 1 Grauate Stuent, Dept. of Mechanical Engineering, Daio University, 10-3 Takiharu-cho, Minami-ku, Nagoya 457-8530, Japan 2 Professor, Dept. of Mechanical Engineering, Daio University, 10-3 Takiharu-cho, Minami-ku, Nagoya 457-8530, Japan a mm1601@stumail.aio-it.ac.jp, b y-maea@aio-it.ac.jp Keywors: Green San, Squeeze Moling, San Particle Size Distribution, Simulation, Discrete Element Metho Abstract. The green san mol with goo mol properties are useful to obtain the soun cast iron castings. For example, the green san mol with high ensity an uniform for compacting characteristics woul be require. Moling simulation is inispensable to make a goo san mol. In recent years, the package software was release from software venors of founry CAE, an the eman for moling simulation is increasing. Funamental algorithms of the green san particulate moel an the three-imensional Discrete Element Metho (DEM) were propose. They take into consieration of the particle size istribution an the cohesion of green san particles. In this stuy, the squeeze moling simulation is carrie out an we execute the re-evelopment of this metho uner the current computer environment. They are trie to simulate the ynamic behavior uring moling an to preict the mol properties after squeeze moling. The characteristics of green san with cohesion are reflecte in the particle moel calle Har-Core/Soft-Shell. The compacting behavior of squeeze moling is trace numerically, an the visualization by a three-imensional moel an comparison of ynamics moling are carrie out. From the simulation with several kins of particle istribution, it becomes clear the relationship between the voi fraction an the squeeze pressure uring moling. The effect of particle size istribution on san compacting behavior is also clarifie. Furthermore, the three-imensional isplay of green san with particle size istribution is very effective in the post-processing. Introuction In the fiel of casting, the computers are also use mainly for the casting CAE (Computer Aie Engineering) incluing the analysis of various casting phenomena, the preiction of casting efects, to obtain the optimum operating conitions an so on. Package software for the casting CAE almost consists of the mol filling, the heat transfer an soliification an the resiual stress an strain of prouct. On the other han, the green san mol with goo mol properties are useful to obtain the soun cast iron castings. The moling simulation is inispensable to make a goo san mol an the eman for moling simulation is increasing. Funamental algorithms of the green san particulate moel an the three-imensional Discrete Element Metho (DEM) were propose [1-5]. They take into consieration of the particle size istribution an the cohesion of green san particles. Furthermore, there are interesting reports using the Discrete Element Metho. E. Hava et. al. [6] simulate the flow ynamics of green san in the DISAMATIC mouling process. Y. Nakata an M. Yamanoi [7] analyse the mixe states of granular systems with shannon entropy. The simulation using the DEM is expecte to be a powerful tool for the moling process. In this research, the three imensional iscrete element metho consiering the particle size istribution of san particles an the cohesion of green san is re-evelope uner the current computer environment. When compare with about 15 years ago of [1], CPU performance evolve ramatically an parallel computing became possible. It is possible to use the enough capacity This is an open access article uner the CC-BY 4.0 license (https://creativecommons.org/licenses/by/4.0/)
474 Science an Processing of Cast Iron XI memory for large number of elements. Further, the ynamics behavior uring squeeze moling is analyze using the present moel. Discrete Element Metho In the present mathematical moel, the green san particles are assume to be viscoelastic elements. The motion of each element is obtaine by integrating the equations of motion step-by-step: 1 r = ( f + f ) + g (1) m e c where r is the position vector, m e the element mass, f c the summation of the contact force, g the gravity acceleration, an ot enotes a time erivative. For squeeze moling, the rag force f is zero because the air is not use. After a time step t, the velocity an position of an element can be given as v = v + r (2) 0 t r = r0 + v t (3) where v is the velocity vector an subscript 0 enotes the value before the first step. Contact Force The Har-Core/Soft-Shell moel for the green san shown in Fig.1 is propose by Maea [1,2,3]. The Har-Core is moelle the basic san particle such as silica or artificial (ceramic) san, an the Soft-Shell is also the thin layer of bentonite or oolitics. The contact force is suggeste first by Cunall an Strack [8]. This moel expresses the contact forces by a spring, a ash-pot an a slier. The plural particles can be in contact with particle i at the same time. The total contact force acting on particle i is obtaine by taking the sum of the normal forces f an tangential forces f ctij with respect to j : cnij ( ) f = f + f. (4) ci cnij ctij j The calculation etails of contact forces cause by elements an element-wall collisions an friction are escribe in the literature [9]. Further, the particle size istribution is taken into consieration in the algorithm. For corresponence to a contact epth δ between elements i an j, the stiffness k ij is calculate by using the combine metho in the literature [1, 2]. element Har-core i Soft-shell K t δ δ b µ c η t K tb c η tb element j δ < δ b δ < δ b η nb i η n K nb c j δ δ b K n δ b Fig.1 Moeling of contact force for green san. δ
Materials Science Forum Vol. 925 475 Ientification of Particle Size Distribution In the DEM, it is appropriate to aapt one particle to one iscrete element. However, the moling 6 sans are compose of 110 10 particles/kg in the case of silica san. Therefore, it is ifficult to hanle all the particles iniviually in the green san moling. To treat the problem reasonably, the ientifie istinct element is use in the present simulation. Although the iscrete elements of uniform iameter are aopte in conventional results, the particle size istribution is an important factor for the san compacting. The particle size istribution is taken into consieration in the simulation. The istribution of mass percentage an the number of san particle per unit mass are use in the present stuy. The particle size istributions in this stuy are shown in Table 1. Figure 2 shows the istribution of mass percentage an the number of san particle per unit mass. In these figures, si is the iameter of particle on i steps of size istribution map. Conserving the mass of green san, the particle number is assigne by increasing the iameter of particle. Concretely, the practical istribution of the mass percentage an the number percentage with the imensionless iameter ivie by the characteristic iameter agree with simulation results as shown in the literature [1]. (Total mass) ms = me (Dimensionless number ratio) (Number ratio) (4) P = P nsi nei si sav ei = (5) eav where, P n enotes the number percentage, subscripts s an e enote the green san, an iscrete element respectively, an av enotes the characteristic iameter as average value. Using eqs.(4)-(6), the relationship between size an percentage of iscrete elements in the simulation region is shown in Fig.3. Table 1 The particle size istributions. (a) Silica san, ceramic san of mono-size M650 an M950 Sieve [mm] 0.363 0.256 0.181 0.128 0.091 0.064 GFN Silica 11.6 26 21.4 38.6 2.4 69 M650 14.1 83.2 2.6 68 M950 5.4 90.4 4 0.2 100 Sieve [mm] (b) Ceramic san of #650 an #950 (6) 0.425 0.3 0.212 0.15 0.106 0.075 GFN #650 2.9 40.3 43 12.2 66 #950 1.3 14.5 20.3 44.2 17.8 95 (a) mass percentage (b) number of particles Fig.2 Particle Size istribution of green san.
476 Science an Processing of Cast Iron XI (a) mass percentage (b)number of elements Fig.3 Size istribution of iscrete elements. Squeeze Moling In this stuy, the object is the same of the squeeze moling as shown in the literature [1]. The squeeze moling was carrie out to make test-piece φ 50 50h. A cylinrical flask φ 50 170h was use an the squeeze pressure was ajuste to 0.98MPa. The literature [1] showe the pressure on squeeze plate, the pressure on the sie wall, the ynamic compacting behavior of green san an the voi fraction (bulk ensity) for mol properties. The compactability of green san is ajuste as 40%. In the analysis, the case which moling was performe at a spee of 0.05m/s by the squeeze surface of φ 50 was calculate. Verification of Ientification Metho of Particle Size Distribution The verification of ientification metho of particle size istribution is carrie out in this section. For the squeeze process of test-piece using the ceramic san of #650, the literature [1] use the element number of 942. The total number of elements is change to 942, 2029, 3181 an the calculation conitions are shown in Table 2, 3, 4, respectively. Although the total number of elements has change using the ientification metho, the form of size istribution is the same as shown in Fig.4. Table 2 Element parameters of ceramic san #650 in the case of total number of elements is 942. Number of element [-] 4 146 439 353 Diameter of element [m] 1.01 10-2 7.16 10-3 5.07 10-3 3.58 10-3 Diameter of Har-core [m] 9.00 10-3 6.36 10-3 4.50 10-3 3.18 10-3 Thickness of Soft-shell [m] 5.67 10-4 4.00 10-4 2.83 10-4 2.00 10-4 Stiffness of Har-core [N/m] 361135 303590 255374 214656 Stiffness of Soft-shell [N/m] 72227 60718 51075 42931 Table 3 Element parameters of ceramic san #650 in the case of total number of elements is 2029. Number of element [-] 4 146 439 353 Diameter of element [m] 1.01 10-2 7.16 10-3 5.07 10-3 3.58 10-3 Diameter of Har-core [m] 9.00 10-3 6.36 10-3 4.50 10-3 3.18 10-3 Thickness of Soft-shell [m] 5.67 10-4 4.00 10-4 2.83 10-4 2.00 10-4 Stiffness of Har-core [N/m] 361135 303590 255374 214656 Stiffness of Soft-shell [N/m] 72227 60718 51075 42931
Materials Science Forum Vol. 925 477 Table 4 Element parameters of ceramic san #650 in the case of total number of elements is 3181. Number of element [-] 13 492 1483 1193 Diameter of element [m] 6.76 10-3 4.77 10-3 3.38 10-3 2.39 10-3 Diameter of Har-core [m] 6.00 10-3 4.24 10-3 3.00 10-3 2.12 10-3 Thickness of Soft-shell [m] 3.78 10-4 2.67 10-4 1.89 10-4 1.33 10-4 Stiffness of Har-core [N/m] 288982 242922 204341 171772 Stiffness of Soft-shell [N/m] 101144 85023 71519 60120 Figure 5 shows the compacting pressures on squeeze plate P sq changing with total number of elements. The voi fractions of each sans are aroun 0.6 before squeeze moling. In the present simulation, the calculate results are influence by initial placement of elements which are preset using ranom number. So, the average value of repetition five times is shown in Fig.5. Even if the total number of ientifie iscrete element is ifferent, the squeeze compacting behavior is almost the same tenency. This result shows that the propose ientification metho of san particle istribution is appropriate. Fig.4 Size istributions of elements changing with total number of elements. Fig.5 Compacting pressures on squeeze plate P sq changing with total number of elements. Silica San an Ceramic Sans Comparison of compacting behavior between silica san an ceramic sans is shown in Fig.6. The simulation is performe using silica san, ceramic san #650 an ceramic san #950, as shown in Fig.3. The calculation conitions are shown in Table 2, 5 an 6. The final voi fraction of silica san is lower than those of ceramic sans. The results are influence by the ensities of sans. These consieration accors with the result of literature [1]. However, it is ifficult to simulate the compacting behavior in accorance with san particle istribution ifference, as shown in [1]. They are two compacting mechanism in the green san moling. One is the rearrangement of the green san particles occurring in the early stage of compacting. The other is the eformation of cohesion layers. Especially, the ientification of parameters are not satisfie in the rearrangement mechanism. Table 5 Element parameters of silica san in the case of total number of elements is 1017. Number of element [-] 120 694 136 58 9 Diameter of element [m] 3.04 10-3 4.28 10-3 6.05 10-3 8.56 10-3 1.21 10-2 Diameter of Har-core [m] 2.73 10-3 3.84 10-3 5.43 10-3 7.68 10-3 1.09 10-2 Thickness of Soft-shell [m] 1.56 10-4 2.20 10-4 3.11 10-4 4.40 10-4 6.24 10-4 Stiffness of Har-core [N/m] 145145 172136 204691 243437 289883 Stiffness of Soft-shell [N/m] 16127 19126 22744 27049 32209
478 Science an Processing of Cast Iron XI Table 6 Element parameters of ceramic san #950 in the case of total number of elements is 3007. Number of element [-] 120 694 136 58 9 Diameter of element [m] 3.04 10-3 4.28 10-3 6.05 10-3 8.56 10-3 1.21 10-2 Diameter of Har-core [m] 2.73 10-3 3.84 10-3 5.43 10-3 7.68 10-3 1.09 10-2 Thickness of Soft-shell [m] 1.56 10-4 2.20 10-4 3.11 10-4 4.40 10-4 6.24 10-4 Stiffness of Har-core [N/m] 145145 172136 204691 243437 289883 Stiffness of Soft-shell [N/m] 16127 19126 22744 27049 32209 Fig.6 Relationship between voi fraction an pressure on the squeeze plate in the case of ceramic an silica san. Fig.7 Relationsip between voi fraction an pressure on the squeeze plate. Particle Size Distribution an Mono-Size The ceramic sans without the size istribution are prepare to investigate the influence of the particle size istribution on the compacting behavior. They are the M650 an M950 in Table 1(a). The ientifie iscrete elements are shown in Table 7 an 8. The relationship between the voi fraction an the squeeze pressure shows in Fig.7. It is ifficult to be rearrangement filling, because of there is not the particle size istribution an there are few particles which are smaller than the voi cavity. The san without particle size istribution shows linear compression behavior an the san with particle size istribution shows a small curve tenency affecte by rearrangement filling. It is necessary to check any parameters of DEM an to stuy the experiment. Table 7 Element parameters of ceramic san of mono-size M650 in the case of total number of elements is 961. Number of elements 51 836 74 Diameter of elements [m] 7.16 10-3 5.07 10-3 3.58 10-3 Diameter of har-core [m] 6.36 10-3 4.50 10-3 3.18 10-3 Thickness of Soft-shell [m] 4.00 10-4 2.83 10-4 2.00 10-4 Stiffness of Har-core [N/m] 297319 250099 210222 Stiffness of Soft-shell [N/m] 59464 50020 42044 Table 8 Element parameters of ceramic san of mono-size M950 in the case of total number of elements is 2998. Number of elements 54 2576 322 46 Diameter of elements [m] 5.07 10-3 3.58 10-3 2.53 10-3 1.79 10-3 Diameter of har-core [m] 4.50 10-3 3.18 10-3 2.25 10-3 1.59 10-3 Thickness of Soft-shell [m] 2.83 10-4 2.00 10-4 1.42 10-4 1.00 10-4 Stiffness of Har-core [N/m] 241785 203233 170951 143708 Stiffness of Soft-shell [N/m] 84625 71132 59833 50298
Materials Science Forum Vol. 925 479 Ceramic san #950 Ceramic san #650 Silica san Fig.8 Three-imensional visualization results of analysis results of Ceramics san #650, #950, an Silica san by ParaView. Three-Dimensional Visualization Using ParaView In this stuy, 3D graphic in the post-processing is investigate. ParaView [11] is software evelope by Kitware Inc. an istribute as open source. The initial conitions before operating squeeze press are create by the free falling of moling sans for both experiment an simulation. The compacting behaviors uring the squeeze moling obtaine by the simulation are shown in Fig.8. Figure 8 shows the outsie views of squeeze moling process for silica san, ceramic san #650 an ceramic san #950 obtaine by the simulations. The results are iscriminate by 5 colors epening on the initial position in orer to clarify the ynamic behavior. The free-fall behavior is calm. Then just after acting the squeeze press, 5 san layers are simply compacte without isturbance uring the squeeze moling. It is very useful for CAE engineer to isplay the visual images of the compacting behavior in the flask. Conclusion Time 0.0[s] 0.5[s] 1.0[s] 1.5[s] 2.0[s] Freefall Squeeze The compacting behavior of squeeze moling is trace numerically, an the visualization by a three-imensional moel an comparison of ynamics moling are carrie out. The characteristics of green san with cohesion are reflecte in the particle moel calle Har-Core/Soft-Shell. From the simulation with several kins of particle istribution, the following results are obtaine. The effectiveness of the ientification metho from a real particle size istribution to the iscrete element is investigate. The silica san an the ceramic san showe ifferent compression behavior. The results are influence by the ensities of sans. Three-imensional isplay of green san with particle size istribution is very effective. It is necessary to take the consieration of the compacting behavior by the rearrangement in the future.
480 Science an Processing of Cast Iron XI Acknowlegment This work was supporte by JSPS KAKENHI Grant-in-Ai for Scientific Research(C) 16K06816. References [1] Y. Maea, Y. Maruoka, H. Makino an H. Nomura: Squeeze Moling Simulation Using The Distinct Element Metho Consiering Green San Properties, J. Mater Process Tech, 135(2003), 172-178. [2] Y. Maea, Y. Maruoka, H. Makino an H. Nomura: San Compacting Simulation Using Distinct Element Metho Compacting Particle Size Distribution, J. JFS, 75(2002) 108-114. [3] Y. Maea, H. Makino an H. Nomura: Numerical Simulation of Green San Squeeze Moling Using Three-Dimensional Distinct Element Metho, J JFS, 75(2002), 102-107. [4] H. Makino, Y. Maea an H. Nomura: Computer Simulation of Various Methos for Green San Filling, AFS Transactions, 110(2002), 137-145. [5] H. Makino, Y. Maea an H. Nomura: Computer Simulation of Squeeze Moling Using the Distinct Element Metho, AFS Transactions, 109(2001), 43-49. [6] E. Hava, P. Larsen, J. H. Walther, J. Thorborg an J. H. Hattel: Flow Dynamics of green san in the DISAMATIC mouling process using Discrete element metho(dem), IOP Conf. Series: Materials Science an Engineering, 84(2015), 012023. [7] Y. Nakata an M. Yamanoi: Quantitative Evaluation of Mixe States of Granular Systems with Shannon Entropy, J. Soc. Power Technology, Japan, 54(2017), 296-304. [8] P. A. Cunall, O. D. L. Strack: Discrete numerical moel for granular assemblies, Geotechnique, 29-1 (1979) 47-65. [9] H. Makino, Y. Maea an H. Nomura: Force Analysis in Air-Flow Press Mouling using The Distinct Element Metho, Int. J. Cast Metal Res, 10(1997) 171-175. [10] R. D. Minlin an H. Deresiewicz: Elastic spheres in contact uner varying oblique forces, J. Appl. Mech. Trans. ASME, 20(1953), 327-344. [11] Information on https://www.paraview.org/