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5.2.3 Melting of Solids Physical models describing the melting of solids in extruder channels were developed by many workers, notably the work of TADMOR [6]. RAUWENDAAL summarizes the theories underlying these models in his book [8], Detailed computer programs for calculating melting profiles based on these models have been given by RAO in his books [3, 9]. The purpose of the following section is to illustrate the calculation of the main parameters of these models through numerical examples. The important steps for obtaining a melting profile are treated in another section for a quasi Newtonian fluid. 5.2.3.1 Thickness of Melt Film According to the Tadmor model [6] the maximum, thickness of the melt film (Figure 5.23) is given by Example with symbols and units Thermal conductivity of the melt Xm =0.174 W/(m K) Barrel temperature Th =150 0 C Melting point of the polymer Tm = 110 0 C Viscosity in the melt film rjf Pa <strong>•</strong> s Shear rate in the film fi s ~ l Velocity of the barrel surface Vb cm/s Velocity components Vbx, Vbz cm/s (Figure 5.24) Velocity of the solid bed V82 cm/s Output of the extruder G_ = 16.67 g/s Average film thickness S^ mm Temperature of the melt in the film Tf 0 C Average film temperature Ta 0 C Depth of the feed zone H1 =9 mm Width of the screw channel W = 51.46 mm Melt density pm = 0.7 g/cm 3 Density of the solid polymer ps = 0.92 g/cm 3 Specific heat of the solid polymer cps = 2.2 kj/(kg <strong>•</strong> K) Temperature of the solid polymer T5 = 20 0 C Heat of fusion of the polymer im =125.5 kj/kg Maximum film thickness
X- Q Figure 5.24 Velocity and temperature profiles in the melt and solid bed after TADMOR [6] a: solid melt interface, b: cylinder, c: solid bed Following conditions are given: b if c The resin is LDPE with the same constants of viscosity as in Example 1 of Section 4.1.1.4. The barrel diameter Db is 60 mm and the screw speed is 80 rpm. ^sy ^sy V Figure 5.23 Temperature profile in the melt film after TADMOR [6] a: solid bed, b: barrel surface, c: melt film, d: solid melt interface Y T Z ^bX h b C d y
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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
Page 67 and 68: At thermal equilibrium according to
Page 69 and 70: The rate of heat generation in a pl
Page 71 and 72: The mass of the fluid permeating th
Page 73 and 74: 4 Designing Plastics Parts The defo
Page 75 and 76: The parabolic failure criterion is
Page 77 and 78: Figure 4.3 Secant modulus [4] Stres
Page 79 and 80: where P = load (N) Lybyd = dimensio
Page 81 and 82: 5 Formulas for Designing Extrusion
Page 83 and 84: for values of the ratio n (R0 + R1)
Page 85 and 86: melt density pm = 0.7 g/cm 3 Soluti
Page 87 and 88: and finally the pressure drop Ap fr
Page 89 and 90: Pressure drop Ap from Equation 5.2
Page 91 and 92: Proportionality factor K from Equat
Page 93 and 94: n = 3.043 RTh= 1.274 mm Shear rate
Page 95 and 96: The relation of a slit is H = heigh
Page 97 and 98: Shear stress (N/m 2 ) Figure 5.5 Ef
Page 99 and 100: Figure 5.7 Surface distortion on a
Page 101 and 102: Residence time t (s) LDPE m = 40 kg
Page 103 and 104: Table 5.1 Dimensions of Square Scre
Page 105 and 106: Pressure drop in screen Mesh size F
Page 107 and 108: In practice, this efficiency is als
Page 109 and 110: 5.2.2 Melt Conveying Starting from
Page 111 and 112: md = 46.42 kg/h Equation 5.31 and E
Page 113 and 114: Solution Power Zc in the screw chan
Page 115 and 116: Indices: m: melt f: melt film b: ba
Page 117: Example with symbols and units a) S
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
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168 Index terms Links Index terms L
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viii Contents 1.4 Viscoelastic Beha
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x Contents 5.2 Extrusion Screws ...
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