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Pressure drop (bar) Pressure drop (bar) Channel depth H (mm) feed depth LDPE T = 200°C LLDPE T = 250°C T = 280 0 C metering depth Screw diameter (mm) Figure 5.31 Channel depth vs. screw diameter for LDPE [UD = 20) Die gap H (mm) Figure 5.32 Pressure drop vs. die gap for a flat die T = 300 0 C Die gap H (mm) Figure 533 Pressure drop vs. die gap for PET LDPE power law exponent n = 2.5 Flow rate = 36 kg/h PET Flow rate = 36 kg/h
5.2.6 Mechanical Design of Extrusion Screws 5.2.6.1 Torsion The maximum shear stress Tmax, which occurs at the circumference of the screw root as a result of the torque MT, is given by [8] where I? = root radius of the screw. The maximum feed depth Hmax can be computed from [8] where D = diameter Tzul = allowable shear stress of the screw metal Example [8] The maximum feed depth is to be calculated for the following conditions: D = 150 mm; Mx = 17810 Nm; Tzul = 100 MPa; Hmax is found from Equation 5.69: 5.2.6.2 Deflection Lateral Deflection (5.68) (5.69) The lateral deflection of the screw (Figure 5.34) caused by its own weight can be obtained from [8] (5.70)
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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
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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
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 and 118: 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: Screw speed (rpm) Screw diameter D
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 and 170: 168 Index terms Links Index terms L
Page 171 and 172: viii Contents 1.4 Viscoelastic Beha
Page 173 and 174: x Contents 5.2 Extrusion Screws ...
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