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t (1/s) Figure 5.6 Simulation results for a pelletizer die a) Pelletizer Dies The aim here is to design a die for a given throughput or to calculate the maximum throughput possible without melt fracture for a given die. These targets can be achieved by performing simulations on dies of different tube diameters, flow rates, and melt temperatures. Figure 5.6 shows the results of one such simulation. b) Blow Molding Dies Figure 5.7 shows a blow molding parison and the surface distortion that occurs at a specific shear rate depending on the resin. In order to obtain a smooth product surface, the die contour has been changed in such a way that the shear rate lies in an appropriate range (Figure 5.8). In addition, the redesigned die creates lower extrusion pressures, as can be seen from Figure 5.8 [36]. c) Blown Film Dies P (bar) Flow rate: 350 kg/h Temperature: 280 0 C g: Shear rate t Residence time LDPE 1414.7/S 0.0005654 s Die length (mm) Following the procedure outlined above and using the relationships for the different shapes of the die channels concerned, a blown film spider die was simulated (Figure 5.9). On the basis of these results it can be determined whether these values exceed the boundary conditions at which melt fracture occurs. By repeating the simulations, the die contour can be changed to such an extent that shear rate, shear stress, and pressure drop are within a range, in which melt fracture will not occur. Figure 5.10 and 5.11 show the shear rate and the residence time of the melt along the flow path [37]. The results of simulation of a spiral die are presented in Figure 5.12 as an example. As in the former case, the die gap and the geometry of the spiral channel can be optimized for the resin used on the basis of shear rate and pressure drop. 9 t
Figure 5.7 Surface distortion on a parison used in blow molding Flow length Old die Old die New die New die Pressure Figure 5.8 Die contour used for obtaining a smooth parison surface K
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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
Page 47 and 48: Figure 3.3 One-dimensional heat tra
Page 49 and 50: Figure 3.5 Heat flow in a multilaye
Page 51 and 52: The combination of convection and c
Page 53 and 54: The equation for an infinite cylind
Page 55 and 56: The foregoing equations apply to ca
Page 57 and 58: Figure 3.11 Midplane temperature fo
Page 59 and 60: Figure 3.12 Temperature distributio
Page 61 and 62: For drag flow the velocity gradient
Page 63 and 64: Lewis number: ratio of thermal diff
Page 65 and 66: 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: Shear stress (N/m 2 ) Figure 5.5 Ef
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 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
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Cooling time mm Distance between mo
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Table 5.2 Results of Optimization o
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Per cent unmelted Axial distance al
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A* [%] LDPE Axial length (screw dia
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A* [%] A* [%] LDPE LDPE Axial lengt
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Flow length (mm) Flow length (mm) F
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Flow length L (mm) Flow length L (m
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[26] VDI Warmeatlas, VDI Verlag, Du
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A Final Word The aim of this book i
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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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