プラスチック成形加工学会第24回年次大会
プラスチック成形加工学会第 回年次大会

二軸スクリュ押出機の一般化HeleShaw流れ定式化に基づくFEM解析
FEM simulation based on
generalized Hele-Shaw flow formulation
for twin screw extruder
2013/5/22
株式会社HASL○谷藤 眞一郎
吉川 秀雄
株式会社プラスチック工学研究所
鬼防 崇
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

辰巳 昌典

□Background
Comparison of analysis method for twin screw extruder
MethodAccuracy

Computational
cost

Availability

Operability

3D◎

△○

△

1D△

◎△

◎

2.5D

○

○

○

○

◎：Excellent, ○：Good,△：Moderate

Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved□Modeling method

QLQR

F1:right to left flow

F1

F2:left to left flow

①F2

F3:right to right flow

F3Qex≒0 on the average estimationin the thickness direction

Qex③②Self wipe intermeshing co-rotating twin screw

Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

QL=QR

Generalized Hele-Shaw Formulation
Assumption:∂p=0∂ζ

Good

∂U ∂U
∂U>>
,∂ζ∂ξ ∂η
Variable: (u,v,w,p)

 ∂ 2u ∂ 2u ∂ 2u  ∂pη  2 + 2 + 2  = ,∂y∂z  ∂x ∂x ∂ 2 v ∂ 2 v ∂ 2 v  ∂p
η  2 + 2 + 2  = ,∂y∂z  ∂y ∂x ∂ 2 w ∂ 2 w ∂ 2 w  ∂p
η  2 + 2 + 2  = ,∂y∂z  ∂z ∂x ∂u ∂v ∂w  + + = 0∂∂∂xyz


Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

Doubtful, but…

Variable: (S, p)∂p+ Φx,∂x∂pv = −S+ Φy,∂y∂pw = −S ,∂z∂  ∂ ∂p∂p∂p   ∂  − S+Φ+−S+Φ+−S  = 0xy ∂x ∂x∂y∂y∂z∂z
u = −SAn efficient method for generating of the FEA model

3D model forvisualization

2.5D model
for analysis(Element number:16896,Node number:8544, Layer division number:10)

Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

UV unwound FEA model

Flow direction

Self wipe screw zone

Kneading screw zone

Self wipe screw zone

Left screw

Right screw

Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved:Channel region:Screw tip:Inter-meshing zone□Test example
Flow direction

0MPa0MPa

Self wipe

Kneading disk(Forward)

Kneading disk(Reverse)

Self wipe

Intermeshing co-rotating twin screw extruder
Screw rotational

100 rpm

Material

Newtonian (η=1000Pa・s)

Calculation cycle

48 (corresponding to the mesh division
number in the circumferential direction)

Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

List of the time consumption for a simulation
Operation

Time consumption

Pre-processing

Ignorable(<1 minute for numericparameter input)Analysis

CPU time : 40 sec ( for 48 cycles flowsimulation)

Post-processing

Turn around time : 10 sec(200 particles,1500 cycles calculation)(Particle trace simulation to estimate the streamline in a snap shot information)

Post-processing(Particle trace simulation to estimate the particle
path line in periodic flow fields)

Turn around time: 7 minutes(30 ~ 5430 particles,7500 cycles
calculation:60 rotations)(Computation environment: DELL Studio XPS 8100, 2.80GHz, 4.00GB)

Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

Flow directionAnimation 1: Pressure distribution & flow field in anintermeshing co-rotating twin screw extruder
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

UV mapping information

UV unwound model

3D modelUV unwound model

Channel thickness

Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

3D modelFlow vector

UV unwound model
Stream line in a snap
shot information

Translation of the numerical results into various models①③②① ② ③①①③③②②①

Experimental information
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

Stream line information mapped on the UV unwound model

Particle path trace simulation (3D visualized information)

Animation 2: Result of the particle trace simulation in an intermeshingco-rotating twin screw extruder (3D visualized information)
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights ReservedParticle path trace simulation (UV mapping information)

Animation 3: Result of the particle trace simulation in an intermeshing co-rotating
twin screw extruder (Mapping information on the UV expanded unwound model)
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights ReservedTime variation of the mixing pattern

0 rot. time:0 sec

Red particle

Blue particle

15 rot. time:9 sec

30 rot. time:18sec

Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

45 rot. time:27sec

60 rot. time:36sec

□Experimental verification
Pressure sensor

Layout of the testing machine
ReverseSelf wiping screw

Kneading disk Self wiping screw

FEA model
Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

Results of the thermal flow distribution

Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved

Experimental verification of the predicted pressure

Copyright© 2010 Hyper Advanced Simulation Laboratory Co., Ltd. All Rights Reserved□Conclusions

成果：・一般化Hele-Shaw流れの定式化及びメッシュ生成技術を併用することで二軸スクリュ押出機の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：
・パーティルトレース機能の改良（滞留時間分布、混合効率、動的溶融可塑化モデル）
・検証解析の継続
・異方向噛合型スクリュ、コニカルタイプ等への用途展開

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謝 辞

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