Fundamentals of Die Casting DesignFundamentals of Die Casting Design
Genick Bar{Meir, Ph. D.
7449 North Washtenaw Ave
Chicago, IL 60645
email:barmeir at gmail dot com
Contents
GNU Free Documentation License . xi
1. APPLICABILITY AND DEFINITIONS xii
2. VERBATIM COPYING . xiii
3. COPYING IN QUANTITY . xiii
4. MODIFICATIONS . xiv
5. COMBINING DOCUMENTS . xvi
6. COLLECTIONS OF DOCUMENTS xvi
7. AGGREGATION WITH INDEPENDENT WORKS xvi
8. TRANSLATION xvii
9. TERMINATION xvii
10. FUTURE REVISIONS OF THIS LICENSE xvii
ADDENDUM: How to use this License for your documents . xviii
CONTRIBUTORS LIST xix
How to contribute to this book xix
Credits . xix
Steven from artofproblemsolving.com xix
Tousher Yang . xix
Steve Spurgeon xx
Irene Tan . xx
Your name here xx
Typo corrections and other “minor” contributions xx
Prologue For The POTTO Project xxiii
Preface xxiii
Why Volunteer? . xxiv
What Has been So Far . xxv
Prologue For This Book xxix
Version 0.1 January 12, 2009 xxix
pages 213 size 1.5M xxix
Version 0.0.3 October 9, 1999 . xxix
pages 178 size 3.2M xxix
iiiiv CONTENTS
1 Introduction 1
1.1 The Importance of Reducing Production Costs 2
1.2 Designed/Undesigned Scrap/Cost . 4
1.3 Linking the Production Cost to the Product Design . 4
1.4 Historical Background . 5
1.5 Numerical Simulations . 6
1.6 \Integral” Models . 9
1.7 Summary 11
2 Basic Fluid Mechanics 13
2.1 Introduction 13
2.2 What is fluid? Shear stress 14
2.2.1 What is Fluid? . 14
2.2.2 What is Shear Stress? . 14
2.3 Thermodynamics and mechanics concepts 16
2.3.1 Thermodynamics . 16
2.3.2 Basic Definitions . 16
2.3.3 Momentum Equation . 23
2.3.4 Compressible flow . 23
2.3.5 Speed of Sound 23
2.3.6 Choked Flow 25
3 Dimensional Analysis 33
3.0.1 How The Dimensional Analysis Work . 34
3.1 Introduction 35
3.2 The Die Casting Process Stages . 35
3.2.1 Filling the Shot Sleeve 36
3.2.2 Plunger Slow Moving Part 38
3.2.3 Runner system . 41
3.2.4 Die Cavity . 42
3.2.5 Intensification Period . 43
3.3 Special Topics . 43
3.3.1 Is the Flow in Die Casting Turbulent? 43
3.3.2 Dissipation effect on the temperature rise 47
3.3.3 Gravity effects . 47
3.4 Estimates of the time scales in die casting 48
3.4.1 Utilizing semi dimensional analysis for characteristic time 48
3.4.2 The ratios of various time scales . 56
3.5 Similarity applied to Die cavity 58
3.5.1 Governing equations 58
3.5.2 Design of Experiments 61
3.6 Summary of dimensionless numbers 61
3.7 Summary 63
3.8 Questions . 63CONTENTS v
4 Fundamentals of Pipe Flow 65
4.1 Introduction 65
4.2 Universality of the loss coefficients 65
4.3 A simple flow in a straight conduit 66
4.3.1 Examples of the calculations . 68
4.4 Typical Components in the Runner andVent Systems 68
4.4.1 bend 68
4.4.2 Y connection . 69
4.4.3 Expansion/Contraction 69
4.5 Putting it all to Together . 69
4.5.1 Series Connection . 69
4.5.2 Parallel Connection 70
5 Flow in Open Channels 71
5.1 Introduction 71
5.2 Typical diagrams 73
5.3 Hydraulic Jump 73
6 Runner Design 75
6.1 Introduction 75
6.1.1 Backward Design . 75
6.1.2 Connecting runner segments . 76
6.1.3 Resistance . 77
7 pQ2 Diagram Calculations 81
7.1 Introduction 81
7.2 The \common” pQ2 diagram 82
7.3 The validity of the \common” diagram 85
7.3.1 Is the \Common” Model Valid? . 86
7.3.2 Are the Trends Reasonable? . 88
7.3.3 Variations of the Gate area, A3 89
7.4 The reformed pQ2 diagram . 89
7.4.1 The reform model . 90
7.4.2 Examining the solution 92
7.4.3 Poor design effects 105
7.4.4 Transient effects 105
7.5 Design Process . 106
7.6 The Intensification Consideration . 107
7.7 Summary 107
7.8 Questions . 107vi CONTENTS
8 Critical Slow Plunger Velocity 109
8.1 Introduction 109
8.2 The \common” models 110
8.2.1 Garber’s model 110
8.2.2 Brevick’s Model 112
8.2.3 Brevick’s circular model 113
8.2.4 Miller’s square model . 113
8.3 The validity of the \common” models 114
8.3.1 Garber’s model 114
8.3.2 Brevick’s models 114
8.3.3 Miller’s model . 115
8.3.4 EKK’s model (numerical model) . 115
8.4 The Reformed Model . 115
8.4.1 The reformed model 115
8.4.2 Design process . 118
8.5 Summary 118
8.6 Questions . 118
9 Venting System Design 119
9.1 Introduction 119
9.2 The \common” models 120
9.2.1 Early (etc.) model . 120
9.2.2 Miller’s model . 120
9.3 General Discussion . 121
9.4 The Analysis 123
9.5 Results and Discussion 125
9.6 Summary 128
9.7 Questions . 128
10 Density change effects 129
11 Clamping Force Calculations 133
12 Analysis of Die Casting Economy 135
12.1 Introduction 135
12.2 The \common” model, Miller’s approach . 136
12.3 The validity of Miller’s price model 136
12.4 The combined Cost of the Controlled Components . 137
12.5 Die Casting Machine Capital Costs 137
12.6 Operational Cost of the Die Casting Machine 138
12.7 Runner Cost (Scrap Cost) 139
12.8 Start{up and Mold Manufacturing Cost . 141
12.9 Personnel Cost 142
12.10Uncontrolled components 142
12.11Minimizing Cost of Single Operation . 144CONTENTS vii
12.12Introduction to Economics 147
12.12.1Marginal Profits 149
12.13Summary 151
12.14Question 151
A Fanno Flow 153
A.1 Introduction 153
A.2 Fanno Model 154
A.3 Non{Dimensionalization of the Equations 155
A.4 The Mechanics and Why the Flow is Choked? 158
A.5 The Working Equations 159
A.6 Examples of Fanno Flow . 162
A.7 Supersonic Branch . 168
A.8 Maximum Length for the Supersonic Flow 169
A.9 Working Conditions 169
A.9.1 Variations of The Tube Length ( 4DfL ) Effects 169
A.9.2 The Pressure Ratio, PP21 , effects 175
A.9.3 Entrance Mach number, M1, effects . 177
A.10 Practical Examples for Subsonic Flow 185
A.10.1 Subsonic Fanno Flow for Given 4fL
D and Pressure Ratio 185
A.10.2 Subsonic Fanno Flow for a Given M1 and Pressure Ratio 186
A.11 The Approximation of the Fanno Flow by Isothermal Flow . 189
A.12 More Examples of Fanno Flow 190
A.13 The Table for Fanno Flow 191
A.14 Appendix { Reynolds Number Effects 193
B What The Establishment’s Scientists Say 197
B.1 Summary of Referee positions . 198
B.2 Referee 1 (from hand written notes) . 199
B.3 Referee 2 200
B.4 Referee 3 203
C My Relationship with Die Casting Establishment 209 roduction
2.2 What is fluid? Shear streass
2.2.1 Thermodynamics and mechanics concepts
Thermodynamics
Control Volume, c.v
Energy Equation
2.2.4 Momentum Equaton
2.2.5 Compressible flow .
3 Dimensional Analysis
3.1 Introduction
3.2 The processes in die casting
3.2.1 Filling the shot sleeve
3.2.2 Shot sleeve
3.2.3 Runner system
3.2.4 Die cavity
3.2.5 Intensification period and after
XIXCONTENTS
3.3 Special topics
3.3.1 Is the flow in die casting is turbulent?
Additional note on numerical simulation
3.3.2 Dissipation effect on the temperature rise
3.3.3 Gravity effects
3.4 Estimates of the time scales in die casting
3.4.1 Utilizing semi dimensional analysis for characteristic time
Miller’s approach
Present approach
3.4.2 The ratios of various time scales
3.5 Similarity applied to Die cavity
3.5.1 Governing equations
3.5.2 Design of Experiments
3.6 Summary of dimensionless numbers
3.7 Summary
3.8 Questions
4 Fundamentals of Pipe Flow
4.1 Introduction
4.2 Universality of the loss coefficients
4.3 A simple flow in a straight conduit
4.3.1 Examples of the calculations
4.4 Typical Components in the Runner andVent Systems
4.4.1 bend
4.4.2 Y connection
4.4.3 Expansion/Contraction
4.5 Putting it all to Together
4.5.1 Series Connection
4.5.2 Parallel Connection
5 Flow in Open Channels
5.1 Introduction . . . .
5.2 Typical diagrams . .
5.3 Hydraulic Jump . .
II DIE CASTING DESIGN 59
6 Runner Design
6.1 Introduction
6.1.1 Backward Design
6.1.2 Connecting runner seqments
6.1.3 Resistance
What have your membership dues
, 2000, by Dr. Bar-Meir done for you today? plagiarism?CONTENTS
7 pQ 2 Diagram Calculations
7.1 Introduction
7.2 The “common” pQ 2 diagram
7.3 The validity of the “common” diagram
7.3.1 Is the “common” model valid?
7.3.2 Are the trends reasonable?
Plunger area/diameter variation
Gate area variation
7.3.3 Variations of the Gate area, 7L3
7.4 The reformed pQ 2 diagram
7.4.1 The reform model
7.4.2 Examining the solution
The gate area effects
General conclusions from example 7.4.2 . . .
The die casting machine characteristic effects
Plunger area/diameter effects
Machine size effect
Precondition effect (wave formation)
7.4.3 Poor design effects
7.4.4 Transient effects
7.5 Design Process
7.6 The Intensification Consideration
7.7 Summary
7.8 Questions
8 Critical Slow Plunger Velocity
8.1 Introduction
8.2 The “common” models . .
Garber’s model
Brevick’s Model
The square shot sleeve . . . .
8.2.3 Brevick’s circular model . . . .
8.2.4 Miller’s square model
The validity of the “common” models
8.3.1 Garber’s model
8.3.2 Brevick’s models
square model
Improved Garber’s model . . .
8.3.3 Miller’s model
8.3.4 EKK’s model (numerical model)
The Reformed Model
8.4.1 The reformed model
8.4.2 Design process
Summary
Questions
What have your membership dues
XXI done for you today? plagiarise? , 2000, by Dr. Bar-MeirCONTENTS
9 Venting System Design 109
9.1 Introduction
9.2 The “common” models .
9.2.1 Early (etc.) model
9.2.2 Miller ’s model . .
9.3 General Discussion . . . .
9.4 The Analysis
9.5 Results and Discussion .
9.6 Summary
9.7 Questions
10 Clamping Force Calculations 119
III MORE INFO: Appendixes 121
A What The Establishment’s Scientists Say
A.l Summary of Referee positions
A.2 Referee 1 (from hand written notes) .
A.3 Referee 2
A.4 Referee 3
B My Relationship with Die Casting Establishment 135
C Density change effects 151
D Fanno Flow
D.l Introdcion
E Reference 159
What have your membership dues
, 2000, by Dr. Bar-Meir done for you today? plagiarism? XXII
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