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Graetz number Gz Graetz number Gz Figure 5.60 Graetz number as a function of the product of Re, Pr, Br, and Eu The flow length as a function of injection pressure is shown in Figure 5.58 for LDPE as an example. The Graetz numbers calculated from the experimentally determined spiral lengths at different operating conditions and resins are plotted as functions of the product Re • Pr • Br • Eu as shown in Figure 5.60. As can be seen from this figure, the correlation of the Graetz number with this product is good and thus for any particular material the spiral length can be predicted from the relationship (5.101) Figure 5.61 shows the good agreement between measured and calculated spiral lengths for the experimentally investigated resins. Sample Calculation The example given below shows how the flow length of a given resin can be calculated from Equation 5.101: W= 10mm,H=2 mm,p= 1.06g/cm 3 ,cp = 2kj/kg• K,X = 1.5 W/K• m, TM = 270 0 C, Tw = 70 0 C and G = 211.5 kg/h. The melt viscosity rja is calculated from LDPE HDPE Graetz number Gz Re Pr Br Eu Re Pr Br Eu PP Re Pr Br Eu Graetz number Gz PS Re Pr Br Eu
Flow length L (mm) Flow length L (mm) Figure 5.61 Comparison between measured and calculated flow length ( calculated;D measured) The shear rate y is obtained from where Wmean = W + H • tana LDPE HDPE A0, A1, A2, A3, A4 are material constants, and aT the shift factor. For amorphous polymers the shift factor is obtained from with constants C1, C2 and melt and reference temperatures T and T0, respectively, in K. For semi-crystalline and crystalline polymers ar is calculated from with the constants bv b2 and melt temperature Tin K. Using the values of A0 = 4.7649, A1 = -0.4743, A2 = -0.2338, A3 = 0.081, A4 = -0.01063, C1 = 4.45, C2 = 146.3 and T0 = 190 0 C, the following output is obtained: Re = 0.05964, Pr = 76625.34, Br = 1.7419, and Eu = 10825.84. The Graetz number Gz for the product Re • Pr • Br • Eu follows from Figure 5.60: Gz = 217.63. Hence L = 420 mm. Flow length L (mm) Spiral height H (mm) Spiral height H (mm) PP Flow length L (mm) Spiral height H (mm) Spiral height H (mm) PS
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
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
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: Flow length (mm) Flow length (mm) F
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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