Fundamentals of Die Casting Design

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1 Fundamentals of ie Casting esign Genick Bar Meir, Ph North Washtenaw Ave Chicago, IL barmeir at gmail dot com Copyright 2009, 2008, 2007, and 1999 by Genick Bar-Meir See the file copying.fdl or copyright.tex for copying conditions. Version (0.1.4 November 27, 2012)

2 We are like dwarfs sitting on the shoulders of giants from The Metalogicon by John in 1159

3 CONTENTS Nomenclature xv GNU Free ocumentation License xix 1. APPLICABILITY AN EFINITIONS xx 2. VERBATIM COPYING xxi 3. COPYING IN QUANTITY xxi 4. MOIFICATIONS xxii 5. COMBINING OCUMENTS xxiv 6. COLLECTIONS OF OCUMENTS xxiv 7. AGGREGATION WITH INEPENENT WORKS xxv 8. TRANSLATION xxv 9. TERMINATION xxv 10. FUTURE REVISIONS OF THIS LICENSE xxv AENUM: How to use this License for your documents xxvi CONTRIBUTORS LIST xxvii How to contribute to this book xxvii Credits xxvii Steven from artofproblemsolving.com xxvii Tousher Yang xxviii Steve Spurgeon xxviii Irene Tan xxviii Your name here xxviii Typo corrections and other minor contributions xxviii Prologue For The POTTO Project xxxi Preface xxxi Why Volunteer? xxxii iii

4 iv CONTENTS What Has been So Far xxxiii Prologue For This Book xxxvii Version 0.1 January 12, xxxvii pages 213 size 1.5M xxxvii Version October 9, xxxviii pages 178 size 3.2M xxxviii 1 Introduction The Importance of Reducing Production Costs esigned/undesigned Scrap/Cost Linking the Production Cost to the Product esign Historical Background Numerical Simulations Integral Models Summary Basic Fluid Mechanics Introduction What is fluid? Shear stress What is Fluid? What is Shear Stress? Thermodynamics and mechanics concepts Thermodynamics Basic efinitions Momentum Equation Compressible flow Speed of Sound Choked Flow imensional Analysis How The imensional Analysis Work Introduction The ie Casting Process Stages Filling the Shot Sleeve Plunger Slow Moving Part Runner system ie Cavity Intensification Period Special Topics Is the Flow in ie Casting Turbulent? issipation effect on the temperature rise Gravity effects Estimates of the time scales in die casting Utilizing semi dimensional analysis for characteristic time

5 CONTENTS v The ratios of various time scales Similarity applied to ie cavity Governing equations esign of Experiments Summary of dimensionless numbers Summary Questions Fundamentals of Pipe Flow Introduction Universality of the loss coefficients A simple flow in a straight conduit Examples of the calculations Typical Components in the Runner andvent Systems bend Y connection Expansion/Contraction Putting it all to Together Series Connection Parallel Connection Flow in Open Channels Introduction Typical diagrams Hydraulic Jump Runner esign Introduction Backward esign Connecting runner segments Resistance pq 2 iagram Calculations Introduction The common pq 2 diagram The validity of the common diagram Is the Common Model Valid? Are the Trends Reasonable? Variations of the Gate area, A The reformed pq 2 diagram The reform model Examining the solution Poor design effects Transient effects esign Process

6 vi CONTENTS 7.6 The Intensification Consideration Summary Questions Critical Slow Plunger Velocity Introduction The common models Garber s model Brevick s Model Brevick s circular model Miller s square model The validity of the common models Garber s model Brevick s models Miller s model EKK s model (numerical model) The Reformed Model The reformed model esign process Summary Questions Venting System esign Introduction The common models Early (etc.) model Miller s model General iscussion The Analysis Results and iscussion Summary Questions ensity change effects Clamping Force Calculations Analysis of ie Casting Economy Introduction The common model, Miller s approach The validity of Miller s price model The combined Cost of the Controlled Components ie Casting Machine Capital Costs Operational Cost of the ie Casting Machine Runner Cost (Scrap Cost)

7 CONTENTS vii 12.8 Start up and Mold Manufacturing Cost Personnel Cost Uncontrolled components Minimizing Cost of Single Operation Introduction to Economics Marginal Profits Summary Question A Fanno Flow 149 A.1 Introduction A.2 Fanno Model A.3 Non imensionalization of the Equations A.4 The Mechanics and Why the Flow is Choked? A.5 The Working Equations A.6 Examples of Fanno Flow A.7 Supersonic Branch A.8 Maximum Length for the Supersonic Flow A.9 Working Conditions A.9.1 Variations of The Tube Length ( 4fL ) Effects A.9.2 The Pressure Ratio, P2 P 1, effects A.9.3 Entrance Mach number, M 1, effects A.10 Practical Examples for Subsonic Flow A.10.1 Subsonic Fanno Flow for Given 4fL and Pressure Ratio A.10.2 Subsonic Fanno Flow for a Given M 1 and Pressure Ratio A.11 The Approximation of the Fanno Flow by Isothermal Flow A.12 More Examples of Fanno Flow A.13 The Table for Fanno Flow A.14 Appendix Reynolds Number Effects B What The Establishment s Scientists Say 191 B.1 Summary of Referee positions B.2 Referee 1 (from hand written notes) B.3 Referee B.4 Referee C My Relationship with ie Casting Establishment 203 Bibliography 219 Index 221 Subjects index Authors index

8 viii CONTENTS

9 LIST OF FIGURES 1.1 The profits as a function of the amount of the scrap Increase of profits as reduction of scrap reduction The velocity distribution in Couette flow The deformation of fluid due to shear stress as progression of time A very slow moving piston in a still gas Stationary sound wave and gas moves relative to the pulse Gas flow through a converging diverging nozzle The stagnation properties as a function of the Mach number, k= Various ratios as a function of Mach number for isothermal Nozzle Rod into the hole example Hydraulic jump in the shot sleeve Filling of the shot sleeve Heat transfer processes in the shot sleeve Solidification of the shot sleeve time estimates Entrance of liquid metal to the runner Flow in runner when during pressurizing process Typical flow pattern in die casting, jet entering into empty cavity Transition to turbulent flow in instantaneous flow after Wygnanski Flow pattern in the shot sleeve Two streams of fluids into a medium Schematic of heat transfer processes in the die The oscillating manometer for the example Mass Balance on the lest side of the manometer Rigid body brought into rest ix

10 x LIST OF FIGURES 4.1 The results for the flow in a pipe with orifice General simple conduit description General simple conduit description A sketch of the bend in die casting A parallel connection Equilibrium of Forces in an open channel Specific Energy and momentum Curves A geometry of runner connection y connection Schematic of typical die casting machine A typical trace on a cold chamber machine pq 2 diagram typical characteristics P as A3 to be relocated Presure of die casting machine P 1 as a function of P max K F as a function of gate area, A ie casting characteristics Various die casting machine performances Reduced pressure performances as a function of Ozer number Schematic of the plunger and piston balance forces Metal pressure at the plunger tip Hydralic piston schematic The gate velocity, U 3 as a function of the plunger area, A The reduced power as a function of the normalized flow rate A schematic of wave formation in stationary coordinates The two kinds in the sleeve A schematic of the wave with moving coordinates The Froude number as a function of the relative height The relative shrinkage porosity as a function of the casting thickness A simplified model for the venting system The pressure ratios for air and vacuum venting at end The control volume of the phase change Production cost as a function of the runner hydraulic diameter The reduced power as a function of the normalized flow rate Supply and emand A.1 Control volume of the gas flow in a constant cross section A.2 Various parameters in Fanno flow as a function of Mach number A.3 Schematic of Example (A.1)

11 LIST OF FIGURES xi A.4 The schematic of Example (A.2) A.5 The maximum length as a function of specific heat, k A.6 The effects of increase of 4fL on the Fanno line A.7 The development properties in of converging nozzle A.8 M in and ṁ as a function of the 4fL A.9 M 1 as a function M 2 for various 4fL A.10 M 1 as a function M A.11 The pressure distribution as a function of 4fL 4fL for a short A.12 The pressure distribution as a function of 4fL 4fL for a long A.13 The effects of pressure variations on Mach number profile A.14 Mach number as a function of 4fL 4fL when the total = A.15 Schematic of a long tube in supersonic branch A.16 The extra tube length as a function of the shock location A.17 The maximum entrance Mach number as a function of 4fL A.18 Unchoked flow showing the hypothetical full tube A.19 The results of the algorithm showing the conversion rate A.20 Solution to a missing diameter A.21 M 1 as a function of 4fL comparison with Isothermal Flow A.22 Moody diagram

12 xii LIST OF FIGURES

13 LIST OF TABLES 1 Books Under Potto Project xxxiii 1 continue xxxiv 2.1 Properties of Various Ideal Gases [300K] A.1 Fanno Flow Standard basic Table A.1 continue A.1 continue xiii

14 xiv LIST OF TABLES

15 NOMENCLATURE R Universal gas constant, see equation (2.36), page 18 l Units length., see equation (2.11), page 14 ρ ensity of the fluid, see equation (2.55), page 22 B bulk modulus, see equation (2.62), page 22 B f Body force, see equation (2.19), page 15 c Speed of sound, see equation (2.55), page 22 C p Specific pressure heat, see equation (2.33), page 17 C v Specific volume heat, see equation (2.32), page 17 E U Internal energy, see equation (2.13), page 15 E u Internal Energy per unit mass, see equation (2.16), page 15 E i System energy at state i, see equation (2.12), page 14 H Enthalpy, see equation (2.28), page 17 h Specific enthalpy, see equation (2.28), page 17 k the ratio of the specific heats, see equation (2.34), page 18 M Mach number, see equation (2.64), page 23 n The poletropic coefficient, see equation (2.60), page 22 P Pressure, see equation (2.57), page 22 xv

16 xvi LIST OF TABLES q Energy per unit mass, see equation (2.16), page 15 Q 12 The energy transferred to the system between state 1 and state 2, see equation (2.12), page 14 R Specific gas constant, see equation (2.37), page 18 S Entropy of the system, see equation (2.23), page 16 U velocity, see equation (2.14), page 15 w Work per unit mass, see equation (2.16), page 15 W 12 The work done by the system between state 1 and state 2, see equation (2.12), page 14

17 The Book Change Log Version Nov 27, 2012 (1.9M 269 pages) ˆ Additional discussion on the economics chapter on. Version Nov 8, 2012 (1.9M 265 pages) ˆ Improvements to some of the figures of dimensional analysis chapter (utilizing blender). ˆ Add an analysis of the minimum cost ordering supply. The minimum cost ordering refers to the analysis dealing with the minimum cost achieved by finding the optimum number of ordering. Version April 1, 2009 (1.9M 263 pages) ˆ Irene Tan provided many English corrections to the dimensional analysis chapter. Version Feb 8, 2009 (1.9M 261 pages) ˆ Add Steve Spurgeon (from ynacast England) corrections to pq 2 diagram. xvii

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18 Thank You for previewing this ebook You can read the full version of this ebook in different formats: HTML (Free /Available to everyone) PF / TXT (Available to V.I.P. members. Free Standard members can access up to 5 PF/TXT ebooks per month each month) Epub & Mobipocket (Exclusive to V.I.P. members) To download this full book, simply select the format you desire below

Fundamentals of Compressible Fluid Mechanics

Fundamentals of Compressible Fluid Mechanics Genick Bar Meir, Ph.. 7449 North Washtenaw Ave Chicago, IL 60645 email: barmeir@gmail.com Copyright 013, 01, 009, 008, 007, 006, 005, and 004 by Genick Bar-Meir