Optimal Feeding System Design of Steel Casting by … · Casting by IPOPT based on Casting Simulation Technology Shen Xu, ... ion method Modulus constrain Volume ... Relation between

Optimal Feeding System Design of Steel Casting by IPOPT based on Casting

Simulation Technology

Shen Xu, Zhou Jianxin, Yin Yajun, Wang Tong, Ji Xiaoyuan

State Key Laboratory of Materials Processing and Die & Mould Technology

Huazhong University of Science and Technology(HUST)InteCAST Software Center

SOUTH AFRICAN METAL CASTING CONFERENCEGauteng, South Africa (14-17, March, 2017)

1



Outline

Results and Discussion

Opimization by IPOPT

Introduction

Summary

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3

About InteCAST Software Center

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4 Professors

12 Ph.Ds

38 Masters

16 Engineers

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Aeronautics and Astronautics

Automotive industryNational Major Equipment

Perspect Casting and Mold SystemSimulate Mold-filling and Solidification Processes

Forecast Casting Defects

Ship industry

5



Highlight of application history

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Multiphase flow simulation

1

2

,, 0

,

d x xx t x

d x x

, 0x t

0d Vd t t

N

31 2 nn nNx y z

Level Set Method

Distance Field Equation

Level Set EquationNormal vectors

Curvature of the interface

VOF Method

Volume function 0u v wF F FF

t x y z

1

2

Physical Phase A

Physical Phase B

7



Experiment of Benchmark

Simulation of Benchmark

Multi-phase flow simulation results of practical casting

Multiphase flow simulation

8



Soft Core

Hard Core

Stiffness settings in mold

Different hardness casting sand core

2

2

2

01 2

01 2

01 2

E TG u G

x x

E TG v G

y y

E TG w G

z z

Elastic-plastic conditions Complex boundary condition

Stress Simulation

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Application

Cracks

Thermal cracking

Crack Prediction

Stress Simulation

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Multi-grain (50) simulation in Personal Computer

Micro-structure Simulation

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3D Slice-A Slice-BTime：5.0e-6s，4.0e-5s，8.0e-5s

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Heat Treatment Simulation

Initial grain distribution Initial cold-rolled Structure

Recrystallization Simulation

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Heat Treatment Simulation

Z direction stress by annealing at 19.96h

Equivalent stress by annealing at 19.96hPractical crack defect

Application

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Smelting process simulation

“A, φ-A” method:ü Define a new magnetic vector A: ü Define a new electric scalar potential φ:ü → t

AE

Governing equations of electromagnetic field:

Governing equations of temperature field:

Governing equations

Definition of solving area

15

2 2 2 2

2 2 2

| |p

T T T T JCt x y z

1 1

( ) 0

1 1( ) ( )

m

m

o

in Vt

in Vt

in V

0

s

AA A

A

A A J

agnetic permeabilitylectrical conductivity

temperature,thermal conductivityspecific heat

me

, /

:

p

whe

K

re

T

JC kg K

B A

t

BE 0

t

AE



Smelting process simulation

Temperature distribution and liquid fraction

(a)20 min (b)25 min

(c) 30 min (d) 35 min

Mesh Figure (Red- Furnace Cover, Green- Coil, Light Blue-

Furnace Lining, Yellow- Melt, Blue-Air)

Simulation Results

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Optimization of casting process

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Optimization method

Modulus constrain

Volume constraint

Riser volume of A unit

Riser volume of B unit

GA

1.1 0.56 1.63607*107 3.26228*106

1.2 0.56 2.53502*107 3.26229*106

1.3 0.56 — 3.26228*106

1.1 1.06 1.6237*107 6.17505*106

1.1 1.56 1.62728*107 9.08837*106

FOA

1.1 0.56 3.6774*106 3.26229*106

1.2 0.56 3.6774*106 3.26228*106

1.3 0.56 3.6773*106 3.26228*106

1.1 1.06 6.9607*106 6.17503*106

1.1 1.56 1.0244*107 9.08778*106

IPOPT

1.1 0.56 4.79814*106 3.26228*106

1.2 0.56 5.8808*106 3.26228*106

1.3 0.56 7.05959*106 3.26228*106

1.1 1.06 6.96068*106 6.17503*106

1.1 1.56 1.0244*107 9.08778*106Relation between modulus

constraint and riser volume Relation between volume constraint

and riser volume

B B

BA

The wheel hub casting



Outline



Introduction

Summary

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IPOPT (Interior Point OPTimizer)

min ( )

s.t. ( )

nx RL U

L U

f x

g g x gx x x

The general nonlinear programming problems

The auxiliary barrier problem 1

min ( ) ( ) ln( )

s.t. ( ) 0

n

n

ix R i

x f x x

c x

The first-order optimality conditions

( ) ( ) 0( ) 0

0, 0

f x c x y zc xXZe ex z



Flow chart of the IPOPT algorithm

The Newton step

1 ( ) ( )( )( )( ) 0

k k k kk k k k kT

k kk

x x c x yW X Z I c xy c xc x

2 ( ) 2 ( )

1( ) ( )

mj j

k k k kj

W f x y c x

Where

The new iterate

1 ,

1 ,

,max1

xk k k l k

xk k k l k

zk k k k

x x x

y y y

z z z



Outline



Introduction

Summary

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Geometry of the adjusted ring

Basic optimal steps for castings

Modulus

Constraint

VolumeConstrai

nt

Riser Diameter (D/mm)

Riser Height (h/mm)

Riser Neck Diameter (d/mm)

Riser Neck

Height (h/mm)

Riser Volume (mm3)

1.1 0.56 337.054 501.128 254.384 27.4771 4.61099×107

1.2 0.56 337.073 501.071 254.443 27.4673 4.61099×107

1.3 0.56 337.113 500.969 254.51 27.4232 4.61099×107

1.1 1.06 417.207 622.596 313.92 27.98 8.72795×107

1.1 1.56 474.777 709.582 356.813 28.2527 1.28449×108

The results of the IPOPT algorithm optimization



Comparison and analysis

The simulation results for different optimization algorithms: (a) Genetic algorithm, (b) Fruit fly algorithm and (c) IPOPT algorithm.

Shrinkage distribution in the riser



Outline



Introduction

Summary

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In this study, three optimal solutions were applied on the casting process by the optimal the riser system: the genetic algorithm, the fruit fly algorithm, and the IPOPT algorithm. By studying the casting process of an adjusted ring, the following conclusions can be drawn:

(1) The riser volume remained constant as the modulus constraint increased, and increased as the volume constraint increased. The riser size was sensitive with the volume constraint.(2) The 3 algorithms optimized the riser. All three optimal algorithms adapted 10000 iterations, the modulus constraint was 1.1, and the volume constraint was 0.56. The numerical calculations showed that there were no shrinkage cavities in casting, and only some shrinkage porosities remained.(3) IPOPT obtained the best results with the lowest amount of shrinkage porosities in the casting, while the genetic algorithm and fruit fly algorithm showed similar optimization abilities. Furthermore, the IPOPT algorithm completed solidification faster than did the other 2 algorithms.

Summary



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Summary



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Summary



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Summary



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Optimal Feeding System Design of Steel Casting by … · Casting by IPOPT based on Casting Simulation Technology Shen Xu, ... ion method Modulus constrain Volume ... Relation between