Christian Hopmann, Walter Michaeli
Extrusion Dies for Plastics and Rubber
Design and Engineering Computations
Preface
6
Preface to the Third Edition
8
Preface to the Second Edition
10
Preface to the First Edition
12
Contents
14
1 Introduction
20
1.1 Reference of Chapter 1
26
2 Properties of Polymeric Melts
28
2.1 Rheological Behavior
28
2.1.1 Viscous Properties of Melts
29
2.1.1.1 Viscosity and Flow Functions
29
2.1.1.2 Mathematical Description of the Pseudoplastic Behavior of Melts
31
2.1.1.3 Influence of Temperature and Pressure on the Flow Behavior
38
2.1.2 Determination of Viscous Flow Behavior
45
2.1.3 Viscoelastic Properties of Melts
51
2.2 Thermodynamic Behavior
57
2.2.1 Density
58
2.2.2 Thermal Conductivity
60
2.2.3 Specific Heat Capacity
61
2.2.4 Thermal Diffusivity
62
2.2.5 Specific Enthalpy
62
2.3 References of Chapter 2
65
3 Fundamental Equations for Simple Flows
68
3.1 Flow through a Pipe
69
3.2 Flow through a Slit
75
3.3 Flow through an Annular Gap
79
3.4 Summary of Simple Equations for Dies
83
3.5 Phenomenon of Wall Slip
93
3.5.1 Model Considering the Wall Slip
93
3.5.2 Instability in the Flow Function - Melt Fracture
98
3.5 References of Chapter 3
101
4 Computation of Velocity and Temperature Distributions in Extrusion Dies
104
4.1.1 Continuity Equation
105
4.1.2 Momentum Equations
106
4.1.3 Energy Equation
107
4.2 Restrictive Assumptions and Boundary Conditions
111
4.3 Analytical Formulas for Solution of the Conservation Equations
113
4.4 Numerical Solution of Conservation Equations
119
4.4.1 Finite Difference Method
120
4.4.2 Finite Element Method
123
4.4.3 Comparison of FDM and FEM
128
4.4.4 Examples of Computations of Extrusion Dies
131
4.5 Consideration of the Viscoelastic Behavior of the Material
145
4.6 Computation of the Extrudate Swelling
149
4.7 Methods for Designing and Optimizing Extrusion Dies
155
4.7.1 Industrial Practice for the Design of Extrusion Dies
156
4.7.2 Optimization Parameters
159
4.7.2.1 Practical Optimization Objectives
159
4.7.2.2 Practical Boundary Conditions and Constraints When Designing Flow Channels
160
4.7.2.3 Independent Parameters during Die Optimization
161
4.7.2.4 Dependent Parameters during Die Optimization and Their Modeling
161
4.7.3 Optimization Methods
163
4.7.3.1 Gradient-Free Optimization Methods
165
4.7.3.2 Gradient-Based Optimization Methods
168
4.7.3.3 Stochastic Optimization Methods
169
4.7.3.4 Evolutionary Methods
169
4.7.3.5 Treatment of Boundary Conditions
171
4.7.4 Practical Applications of Optimization Strategies for the Design of Extrusion Dies
173
4.7.4.1 Optimization of a Convergent Channel Geometry
173
4.7.4.2 Optimization of Profile Dies
175
4.8 References of Chapter 4
181
5 Monoextrusion Dies for Thermoplastics
186
5.1 Dies with Circular Exit Cross Section
186
5.1.1 Designs and Applications
186
5.1.2 Design
194
5.2 Dies with Slit Exit Cross Section
199
5.2.1 Designs and Applications
199
5.2.2 Design
206
5.2.2.1 T-Manifold
209
5.2.2.2 Fishtail Manifold
209
5.2.2.3 Coathanger Manifold
211
5.2.2.4 Numerical Procedures
222
5.2.2.5 Considerations for Clam Shelling
224
5.2.2.6 Unconventional Manifolds
225
5.2.2.7 Operating Performance of Wide Slit Dies
228
5.3 Dies with Annular Exit Cross Section
231
5.3.1 Types
232
5.3.1.1 Center-Fed Mandrel Support Dies
232
5.3.1.2 Screen Pack Dies
236
5.3.1.3 Side-Fed Mandrel Dies
237
5.3.1.4 Spiral Mandrel Dies
238
5.3.2 Applications
241
5.3.2.1 Pipe Dies
241
5.3.2.2 Blown Film Dies
242
5.3.2.3 Dies for the Extrusion of Parisons for Blow Molding
244
5.3.2.4 Coating Dies
251
5.3.3 Design
254
5.3.3.1 Center-Fed Mandrel Dies and Screen Pack Dies
254
5.3.3.2 Side-Fed Mandrel Dies
258
5.3.3.3 Spiral Mandrel Dies
261
5.3.3.4 Coating Dies
265
5.4 Formulas for the Computation of the Pressure Loss in Flow Channel Geometries other than Pipe or Slit
269
5.5 Dies with Irregular Outlet Geometry (Profile Dies)
274
5.5.1 Designs and Applications
274
5.5.2 Design
283
5.6 Dies for Foamed Semifinished Products
291
5.6.1 Dies for Foamed Films
293
5.6.2 Dies for Foamed Profiles
293
5.7 Special Dies
295
5.7.1 Dies for Coating of Profiles of Arbitrary Cross Section
295
5.7.2 Dies for the Production of Profiles with Reinforcing Inserts
296
5.7.3 Dies for the Production of Nets
297
5.7.4 Slit Die with Driven Screw for the Production of Slabs
298
5.8 References of Chapter 5
301
6 Coextrusion Dies for Thermoplastics
308
6.1 Designs
309
6.1.1 Externally Combining Coextrusion Dies
309
6.1.2 Adapter (Feedblock) Dies
310
6.1.3 Multimanifold Dies
313
6.1.4 Layer Multiplication Dies
313
6.2 Applications
315
6.2.1 Film and Sheet Dies
315
6.2.2 Blown Film Dies
317
6.2.3 Dies for the Extrusion of Parisons for Blow Molding
318
6.3 Computations of Flow and Design
319
6.3.1 Computation of Simple Multilayer Flow with Constant Viscosity
322
6.3.2 Computation of Coextrusion Flow by the Explicit Finite Difference Method
327
6.3.3 Computation of Velocity and Temperature Fields by the Finite Difference Method
330
6.3.4 Computation of Velocity Fields in Coextrusion Flows by FEM
333
6.4 Instabilities in Multilayer Flow
335
6.5 References of Chapter 6
342
7 Extrusion Dies for Elastomers
344
7.1 Design of Dies for the Extrusion of Elastomers
344
7.2 Fundamentals of Design of Extrusion Dies for Elastomers
346
7.2.1 Thermodynamic Material Data
346
7.2.2 Rheological Material Data
347
7.2.3 Computation of Viscous Pressure Losses
350
7.2.3.1 Formulas for Isothermal
350
7.2.3.2 Approaches to Nonisothermal Computations
353
7.2.4 Estimation of the Peak Temperatures
354
7.2.5 Consideration of the Elastic Behavior of the Material
355
7.3 Design of Distributor Dies for Elastomers
356
7.4 Design of Slotted Disks for Extrusion Dies for Elastomers
358
7.4.1 Computation of Pressure Losses
358
7.4.2 Extrudate Swelling (Die Swell)
361
7.4.3 Simplified Estimations for the Design of a Slotted Disk
365
7.5 References of Chapter 7
373
8 Heating of Extrusion Dies
376
8.1 Types and Applications
377
8.1.1 Heating of Extrusion Dies with Fluids
377
8.1.2 Electrically Heated Extrusion Dies
378
8.1.3 Temperature Control of Extrusion Dies
379
8.2 Thermal Design
381
8.2.1 Criteria and Degrees of Freedom for Thermal Design
381
8.2.2 Heat Balance of the Extrusion Die
383
8.2.3 Restrictive Assumptions in the Modeling
388
8.2.4 Simulation Methods for Thermal Design
388
8.3 References of Chapter 8
397
9 Mechanical Design of Extrusion Dies
400
9.1 Mechanical Design of a Breaker Plate
401
9.2 Mechanical Design of a Die with Axially Symmetrical Flow Channels
406
9.3 Mechanical Design of a Slit Die
416
9.4 General Design Rules
420
9.5 Materials for Extrusion Dies
421
9.6 References of Chapter 9
428
10 Handling, Cleaning, and Maintaining Extrusion Dies
430
10.1 References of Chapter 10
433
11 Calibration of Pipes and Profiles
434
11.1 Types and Applications
437
11.1.1 Friction Calibration
437
11.1.2 External Calibration with Compressed Air
438
11.1.3 External Calibration with Vacuum
439
11.1.4 Internal Calibration
443
11.1.5 Precision Extrusion Pullforming (the Technoform Process)
444
11.1.6 Special Process with Movable Calibrators
445
11.2 Thermal Design of Calibration Lines
445
11.2.1 Analytical Computational Model
447
11.2.2 Numerical Computational Model
451
11.2.3 Analogy Model
456
11.2.4 Thermal Boundary Conditions and Material Data
459
11.3 Effect of Cooling on the Quality of the Extrudate
460
11.4 Mechanical Design of Calibration Lines
461
11.5 Cooling Dies, Process for Production of Solid Bars
461
11.6 References of Chapter 11
465
Index
468
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