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Contents Preface ......................................................................................... v 1. Formulas of Rheology .......................................................... 1 1.1 Ideal Solids .................................................................................... 1 1.1.1 Hooke's Law ................................................................ 3 1.2 Newtonian Fluids ........................................................................... 3 1.3 Formulas for Viscous Shear Flow of Polymer Melts .................... 4 1.3.1 Apparent Shear Rate ................................................... 5 1.3.2 Entrance Loss .............................................................. 5 1.3.3 True Shear Stress ........................................................ 6 1.3.4 Apparent Viscosity ....................................................... 7 1.3.5 True Shear Rate .......................................................... 7 1.3.6 True Viscosity .............................................................. 8 1.3.7 Empirical Formulas for Apparent Viscosity ................... 8 1.3.7.1 Hyperbolic Function of Prandtl and Eyring ......... 8 1.3.7.2 Power Law of Ostwald and de Waele ................ 9 1.3.7.3 Muenstedt's Polynomial ..................................... 11 1.3.7.4 Carreau's Viscosity Equation ............................. 14 1.3.7.5 Klein’s Viscosity Formula ................................... 16 1.3.7.6 Effect of Pressure on Viscosity .......................... 1.3.7.7 Dependence of Viscosity on Molecular 16 Weight ................................................................ 17 1.3.7.8 Viscosity of Two Component Mixtures ............... 18 This page has been reformatted by Knovel to provide easier navigation. vii
viii Contents 1.4 Viscoelastic Behavior of Polymers ................................................ 18 1.4.1 Shear ........................................................................... 19 1.4.1.1 Linear Viscoelastic Behavior .............................. 19 1.4.1.2 Nonlinear Viscoelastic Behavior ........................ 23 1.4.2 Uniaxial Tension .......................................................... 25 1.4.2.1 Linear Viscoelastic Behavior .............................. 25 1.4.2.2 Nonlinear Viscoelastic Behavior ........................ 28 1.4.3 Maxwell Model ............................................................. 1.4.4 Practical Formulas for Die Swell and Extensional 29 Flow ............................................................................. 31 2. Thermodynamic Properties of Polymers ............................ 35 2.1 Specific Volume ............................................................................. 35 2.2 Specific Heat ................................................................................. 36 2.3 Enthalpy ......................................................................................... 38 2.4 Thermal Conductivity .................................................................... 40 3. Formulas of Heat Transfer ................................................... 43 3.1 Steady State Conduction .............................................................. 43 3.1.1 Plane Wall .................................................................... 43 3.1.2 Cylinder ....................................................................... 44 3.1.3 Hollow Sphere ............................................................. 45 3.1.4 Sphere ......................................................................... 45 3.1.5 Heat Conduction in Composite Walls ........................... 46 3.1.6 Overall Heat Transfer through Composite Walls ............................................................................ 49 3.2 Transient State Conduction .......................................................... 50 3.2.1 Temperature Distribution in One-Dimensional Solids ........................................................................... 51 3.2.2 Thermal Contact Temperature ..................................... 57 This page has been reformatted by Knovel to provide easier navigation.
Page 1 and 2:
Natti S. Rao Gunter Schumacher D e
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Preface Today, designing of machine
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Figure 1.1 Deformation of a Hookean
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Figure 1.4 Shear flow The shear or
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where c and m are empirical constan
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Apparent viscosity 7\Q True viscosi
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Pa Shear stress T Figure 1.11 Deter
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Shift Factor for Crystalline Polyme
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The power law exponent is obtained
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1.3.7.5 Klein's Viscosity Formula [
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where Mw = molecular weight JC —
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Steady state shear compliance J°t
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Ig 6\ Ig G" lga; Figure 1.22 Storag
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Characterization of the Transient S
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Time/ Figure 1.28 Tensile creep at
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1.4.2.2 Nonlinear Viscoelastic Beha
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Figure 1.37 Maxwell fluid [1 ] The
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Die swel B1 Figure 1.40 Dependence
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2 Thermodynamic Properties of Polym
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where u = internal energy T = tempe
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Enthalpy /7-/720 kWh kg Kl kg polyn
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Table 2.1 Approximate Values for th
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Analogous to Ohm's law in electric
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Figure 3.3 One-dimensional heat tra
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Figure 3.5 Heat flow in a multilaye
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The combination of convection and c
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The equation for an infinite cylind
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The foregoing equations apply to ca
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Figure 3.11 Midplane temperature fo
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Figure 3.12 Temperature distributio
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For drag flow the velocity gradient
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Lewis number: ratio of thermal diff
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The Reynolds number ReL, based on t
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At thermal equilibrium according to
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The rate of heat generation in a pl
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The mass of the fluid permeating th
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4 Designing Plastics Parts The defo
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The parabolic failure criterion is
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Figure 4.3 Secant modulus [4] Stres
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where P = load (N) Lybyd = dimensio
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5 Formulas for Designing Extrusion
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for values of the ratio n (R0 + R1)
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melt density pm = 0.7 g/cm 3 Soluti
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and finally the pressure drop Ap fr
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Pressure drop Ap from Equation 5.2
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Proportionality factor K from Equat
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n = 3.043 RTh= 1.274 mm Shear rate
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The relation of a slit is H = heigh
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Shear stress (N/m 2 ) Figure 5.5 Ef
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Figure 5.7 Surface distortion on a
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Residence time t (s) LDPE m = 40 kg
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Table 5.1 Dimensions of Square Scre
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Pressure drop in screen Mesh size F
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In practice, this efficiency is als
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5.2.2 Melt Conveying Starting from
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md = 46.42 kg/h Equation 5.31 and E
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Solution Power Zc in the screw chan
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Indices: m: melt f: melt film b: ba
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Example with symbols and units a) S
Page 119 and 120: X- Q Figure 5.24 Velocity and tempe
Page 121 and 122: (5.54) As seen from the equations a
Page 123 and 124: Figure 5.26 Three-zone screw [8] Th
Page 125 and 126: The profiles of stock temperature a
Page 127 and 128: where HF = feed depth H = metering
Page 129 and 130: Screw speed (rpm) Screw diameter D
Page 131 and 132: 5.2.6 Mechanical Design of Extrusio
Page 133 and 134: Next Page Screw Vibration When the
Page 135 and 136: 5.3.1 Pressure Drop in Runner As th
Page 137 and 138: Examples of calculating pressure dr
Page 139 and 140: Example with symbols and units The
Page 141 and 142: Flow length L mm Spiral height H Fi
Page 143 and 144: Solution The conversion factors for
Page 145 and 146: Figure 5.43 shows a sample plot of
Page 147 and 148: With the values for the properties
Page 149 and 150: Cooling time mm Distance between mo
Page 151 and 152: Table 5.2 Results of Optimization o
Page 153 and 154: Per cent unmelted Axial distance al
Page 155 and 156: A* [%] LDPE Axial length (screw dia
Page 157 and 158: A* [%] A* [%] LDPE LDPE Axial lengt
Page 159 and 160: Flow length (mm) Flow length (mm) F
Page 161 and 162: Flow length L (mm) Flow length L (m
Page 163 and 164: [26] VDI Warmeatlas, VDI Verlag, Du
Page 165 and 166: A Final Word The aim of this book i
Page 167 and 168: 166 Index terms Links Index terms L
Page 169: 168 Index terms Links Index terms L
Page 173 and 174: x Contents 5.2 Extrusion Screws ...
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