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U0026-2609201315465700

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()3-D Temperature Distribution and Longitudinal Residual Warpage Analysis of Steel Strip

in Continuous Annealing Line

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() Department of Mechanical Engineering

102

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102

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() Zong-Wei Kang

N18951275

117

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continuous annealing line (CAL) finite element method (FEM) energy balance method

(EBM) virtual layer method (VLM) warpage

19000046

60.4

Continuous Annealing LineCALEI

Finite Element Method

FEMEnergy Balance MethodEBMVirtual

Layers MethodVLM

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21/04/2015http://etds.lib.ncku.edu.tw/etdservice/view_metadata?etdun=U0026-26092013154657...

Electrical steel (ES) is mainly used for motors and transformers whose iron loss has a great

effect on the efficiency of electrical products and may be related to the residual warpage of

the strip, generally defined as a deviation from flatness on unloading. According to

statistics from the International Energy Agency (IEA), global electricity production was

about 19000 TWh, 46% of which is consumed by motors, leading to about 6,040

Megatonnes (Mt) of CO2 emissions. Therefore, improving the efficiency of motors is the

most effective way to save energy in industry.

The electrical steel produced by continuous annealing line (CAL) exhibit a significant

phenomenon of warpage during punching into the E- and I-type sheets. This geometric

defect is mainly attributed to the residual stress induced by the nonuniform temperature

and nonuniform plastic deformation along both the width and the thickness of strip when it

passes through the rolls in the line. It becomes more serious for the wider strip and may

degrade the quality of the products. In the thesis, the effects of various input parameters on

the warpage of strip were investigated and discussed. Three theoretical techniques,

including finite element method (FEM), energy balance method (EBM), and virtual layers

method (VLM), were adopted to evaluate the distributions of stress, temperature, and

plastic strain of the strip, respectively. The longitudinal residual warpage of strip can then

be calculated accordingly. It was found that the warpage of strip is sensitive to the

transverse temperature distributions and the yielding strength of strip as passing through

the rolls in CS, which is possibly to be controlled within an accepted range by applying a

suitable cooling scheme in this section.

I

ABSTRACT II

IV

CONTENTS V

LIST OF TABLES VIII

LIST OF FIGURES IX

NOMENCLATURES XII

Chapter 1 INTRODUCTION 1

1.1 Motivation 2

1.2 Literature Review 4

1.3 Objectives 6

1.4 Dissertation Organization 7

Chapter 2 CONTINUOUS ANNEALING LINE 9

2.1 Annealing treatment 10

2.2 Shapes of roll in CAL 13

2.3 Phase transformation 14

2.4 Electrical steel 18

2.5 Measurement of warpage 19

Chapter 3 MATHEMATICAL MODELS 21

3.1 Finite element method 21

3.1.1 Mechanical model of strip 22

3.1.2 Estimation of the emissivity 28

3.1.3 Thermal model of roll 30

3.1.4 Thermal model of strip 33

3.1.5 FEM Computational procedure 35

3.2 Energy balance method 36

3.2.1 Energy balances model 41

3.2.2 EBM Computational procedures 47

3.3 Virtual layers method 49

3.3.1 Virtual layers model 52

3.3.2 Residual stress of elements in straight status on unloading 56

3.3.3 Calculation of strip residual warpage 59

3.3.4 VLM Computational procedures 60

3.4 Computational procedures 61

Chapter 4 NUMERICAL RESULTS AND DISCUSSION 63

4.1 Mechanical model of strip 63

4.1.1 Contact pressure and thermal contact resistance 63

4.1.2 Tangential stress distribution of strip 65

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4.2 Temperature of roll surface 66

4.3 Equivalent heat convective coefficient 67

4.4 Thermal model of strip 68

4.4.1 History of strip temperature 68

4.4.2 Effect of phase transformation 70

4.4.3 Distribution of transverse temperature 71

4.5 VLM 73

4.5.1 Reliability test 74

4.5.2 Convergence test 74

4.5.3 Final residual warpage 76

4.5.4 History of warpage 76

4.5.5 Final accumulated plastic strain 78

4.5.6 Final residual stress 79

4.5.7 History of accumulated plastic strain 79

4.5.8 Effect of strip temperature at the outlet of CAL on warpage 80

4.5.9 Effect of cooling condition in CS on warpage 82

4.5.10 Effect of strip tension on warpage 82

4.5.11 Effect of crown and cooling effect in CS on final warpage 83

4.5.12 Effect of Youngs modulus and yielding strength of strip material on warpage 85

Chapter 5 CONCLUSIONS AND FUTURE STUDIES 87

5.1 Conclusions 87

5.2 Future studies 89

REFERENCES 90

APPENDIX 97

A. Simplified finite element models [39] 97

B. Influence of centrifugal force 100

C. Distribution of thermal contact resistances 101

D. Simplification of roll surface temperature [52] 103

D.1 2D model 105

D.2 Comparison with 3-D model 106

E. Emissivities 110

F. Enclosure of sections 111

G. Rolls specification 114

VITA 117

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