プラスチック成形加工学会第23回年次大会

単軸スクリュ押出機の一般化HeleShaw流れ定式化に基づく一貫FEM解析
Integrated FEM simulation
based on generalized Hele-Shaw flow formulation
for single screw extruder
2012/6/12
株式会社HASL○谷藤 眞一郎
福澤 大輔
吉川 秀雄
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AGENDA□研究の背景□成形現象の定量化モデル□解析モデルの効率的作成法□テスト機を利用した検証解析□複雑形状のミキシングエレメントを有する単軸スクリュ押出機の一貫解析□まとめ
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□研究の背景
Table 1. Comparison of analysis method for single screw extruder
MethodAccuracy

Computationalcost

3D○×△×1D×○△○

2.5D△△○△

Availability

Operability○：Good, △：Moderate,×：BadCopyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved□成形現象の定量化モデル
ホッパー～ホッパー～固体輸送領域 ① 嵩密度自重による静圧分布定量化モデル(Walker model)
 4 BD* ( h − H )  ρ b gD 
 4 BD* (h − H )  
1 − exp P(h) = patom exp +* 4DBDD② ペレットとバレル/スクリュ間の動摩擦係数を利用した動圧分布定量化モデル(Darnell & Mol model)p ( z ) = p (0) exp( −λz )λ=A1 K s − B1,
A2 K s + B2

A1 = Wb f b sin φ + 2 Hf s sin θ b + Ws f s sin θ b ,Fig.1 Analysis model for hopperand solid feed zone.
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

B1 = Wb f b cos φ − 2 Hf s sin θ bDDcot θ − Ws f s sin θ b s cot θ sDbDb

溶融可塑化領域③ 静的評価モデル
静的評価モデル② Melt film

③ Melt poolyVbx
TlHδVsyTsT = Tm : melt temperatur eXew
① Solid bedx
Fig.2 Tadmor model ; melt film/solid bed interfaceδ = Φ X ,Φ =2κ l (Tb − Tm ) + ηV j2Vbx ρ l [C s (Tm − Ts ) + λ ]d(ρ sVsz ( H − δ ) X ) = − Vbx ρl Φ X2dz

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④ 動的評価モデル
Temperature on the spherical surface:
T(R)<Tm; melt temperature

Solid phase

Time sequence

Thermal equation and boundary conditionρ s C psT(R)=TmDT 1 ∂  2 ∂T = 2  λs r
Dt r ∂r ∂r ∂T∂T= 0 at r = 0, λs= h(Tl − T ( R, t )) at r = R∂r∂r
ρ s : Solid density
C ps : Solid thermal capacity
λs : Solid thermal conductivity
Tl : Liquid temperature surround the spherical modelMelting phase

Thermal equation and boundary conditionρ s C psDT 1 ∂  2 ∂T = 2
 λs r
Dt r ∂r ∂r ∂T= 0 at r = 0, T = Tm at r = R∂rKinetic equation for time evolution of spherical radiusλs∂TdR= h(Tl − Tm ) + ρH
∂rdtFig.3 Lagrangian spherical melting model.
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H: heat of fusion

溶融体輸送領域⑤ Generalized Hele-Shaw formulation
BarrelChannel

Leakage flow(Considered )h<<W(Neglected)

FlighthScrew

W
Pressure gradient flow &Drag flow (Considered)h<<W(Neglected)

Fig.4 Circulation flow in a cross section of the screw channel.
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved□解析モデルの効率的作成法

Numerical input of screw
dimensions for the automeshing of the FEA model.

Fig.5 An efficient method for generating of the FEA model
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② UV mapping① Generation of the base model③ Modification of the UV mapping information④ Generation of the2.5D wound model

Fig.6 FEA model generated from UV unwound mapping information.
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved□テスト機を利用した検証解析
Fig.7 FEA model for experimental verification.

Table 2. Computational conditions

解析押出機

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Material

LDPE

Frictionparameter

Pellet/Barrel:0.35
Pellet/Screw:0.25

Screw rotational
speed

20,60,100,140rpm

Temperature
condition

Barrel:180℃
Inlet:30℃

Pressurecondition

Inlet:0MPa,Outlet:0Mpa

140rpm：output;29.2kg/h

100rpm：output;21.0kg/h

60rpm：output;12.6kg/h

20rpm：output;4.1kg/h

Fig.8 Predicted solid bed distributions
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Fig.9 Experimental verification of predicted pressure distributions
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved□複雑形状のミキシングエレメントを有する
単軸スクリュ押出機の一貫解析
Hopper (Height:200mm,Diameter:120mm)

Pineapple Mixing
Shear Spiral : Maddock
Element(45mm)
Mixing Element(80mm)
Egan Mixing
Element(60mm)

Solid Feed Zone
(L/D:5,225mm)

Melting Zone:
Barrier (Double) Flight(L/D:10,450mm)

Melting Zone:
Triple Flight(L/D:10,450mm)

Melt Conveying Zone:
Single Flight(L/D:5,225mm)

Die(Annular;L/D:1,45mm,Circular； L/D:3,135mm,Diameter:15mm)

Fig.10 FEA model for a practical screw extruder withcomplicate mixing elements.

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Table 2. Computational conditions
Material

HDPE (Power law fit)
Heat of Fusion: 201189 J/kg
Melt temperature:130℃

Frictionparameter

Pellet/Barrel:0.35
Pellet/Screw:0.25

Screw rotational
speed100rpm

Temperature
condition

Barrel:170~200℃
Inlet:30℃

Pressurecondition

Inlet:0MPa,Outlet:0Mpa

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Numerical results:

Fig.11 Predicted pressure distribution( Min:0MPa,Max:30MPa)

Fig.12 Predicted Temperature distribution( Min:30℃℃,Max:230℃℃)
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Fig.13 Predicted residence time distribution( Min:0sec,Max:50sec)

Fig.14 Predicted solid bed distribution(Red:solid bed,Blue:melt pool)
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights ReservedAnimation 1: Lagrangian spherical melting model simulation(Initial particle’s diameter:5mm)
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights ReservedAnimation 2: Lagrangian spherical melting model simulation(Initial particle’s diameter:2mm)
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved□まとめ成果：・スクリュ押出機内成形現象の古典的定量化モデルと一般化HeleShaw流れの定式化、動的溶融可塑化モデル、及びメッシュ生成技術を併用することで効率的な解析法を構築した。
・実験検証解析を通じて解析結果の妥当性を検討した。

今後の課題：
・固体輸送領域、溶融可塑化領域の定量化モデルの精度向上
・検証解析の継続
・二軸スクリュ押出機に対する用途展開

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