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igeo.ig*- Figure 1.5 Tensile viscosity and shear rate viscosity of a polymer melt as a function of strain rate [21 ] 13.1 Apparent Shear Rate The apparent shear rate for a melt flowing through a capillary is defined as where Q is the volume flow rate per second and £ is the radius of the capillary. 1.3.2 Entrance Loss (1.19) Another rheological quantity of practical importance is the entrance losspc, representing the loss of energy of flow at the entrance to a round nozzle. This is empirically correlated by the relation [2] Table 1.1 Resin-Dependent Constants c and m in Equation 1.20 [2] Polymer ig*Mg/* Polypropylene (Novolen 1120 H) Polypropylene (Novolen 1120 L) Polypropylene (Novolen 1320 L) LDPE (Lupolen 1800 M) LDPE (Lupolen 1800 S) LDPE (Lupolen 1810 D) HDPE (Lupolen 6011 L) HDPE (Lupolen 6041 D) /V^o Polyisobutylene (Oppanol B 10) Polyisobutylene (Oppanol B 15) C 2.551 • 10" 5 1.463 • 10" 1 2.871 • 10~ 7 1.176- 10" 1 6.984 • 10° 5.688 • 10^ 3.940 • 10" 2 1.778 • 10° 6.401 • 10" 3 1.021 • 10" 7 m 2.116 1.976 2.469 1.434 1.072 1.905 1.399 1.187 1.575 2.614 (1.20)
where c and m are empirical constants and T is the shear stress. These constants can be determined from the well-known Bagley-curves as shown in Figure 1.7. The values of these constants are given in Table 1.1 for some thermoplastic materials. Shear stress and entrance loss are measured in Pa in the calculation of c and m. 1.3.3 True Shear Stress The flow curves of a particular LDPE measured with a capillary rheometer are given in Figure 1.6. The plot shows the apparent shear rate J^ as a function of the true shear stress T at the capillary wall with the melt temperature as a parameter. The entrance loss pc was obtained from the Bagley plot shown in Figure 1.7. Shear rate f S" 1 Figure 1.6 Flow curves of a LDPE [8] #=1mm ^= 0,6 mm Pressure p Shear stress T T-- 23O 0 C 19O 0 C 15O 0 C Capilary geometry L/R Figure 1.7 Bagley plots of a polystyrene with the capillary length L and radius R [3] bar Pa
Page 1 and 2: Natti S. Rao Gunter Schumacher D e
Page 3 and 4: Preface Today, designing of machine
Page 5 and 6: Figure 1.1 Deformation of a Hookean
Page 7: Figure 1.4 Shear flow The shear or
Page 11 and 12: Apparent viscosity 7\Q True viscosi
Page 13 and 14: Pa Shear stress T Figure 1.11 Deter
Page 15 and 16: Shift Factor for Crystalline Polyme
Page 17 and 18: The power law exponent is obtained
Page 19 and 20: 1.3.7.5 Klein's Viscosity Formula [
Page 21 and 22: where Mw = molecular weight JC —
Page 23 and 24: Steady state shear compliance J°t
Page 25 and 26: Ig 6\ Ig G" lga; Figure 1.22 Storag
Page 27 and 28: Characterization of the Transient S
Page 29 and 30: Time/ Figure 1.28 Tensile creep at
Page 31 and 32: 1.4.2.2 Nonlinear Viscoelastic Beha
Page 33 and 34: Figure 1.37 Maxwell fluid [1 ] The
Page 35 and 36: Die swel B1 Figure 1.40 Dependence
Page 37 and 38: 2 Thermodynamic Properties of Polym
Page 39 and 40: where u = internal energy T = tempe
Page 41 and 42: Enthalpy /7-/720 kWh kg Kl kg polyn
Page 43 and 44: Table 2.1 Approximate Values for th
Page 45 and 46: 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
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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
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X- Q Figure 5.24 Velocity and tempe
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(5.54) As seen from the equations a
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Figure 5.26 Three-zone screw [8] Th
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The profiles of stock temperature a
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where HF = feed depth H = metering
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Screw speed (rpm) Screw diameter D
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5.2.6 Mechanical Design of Extrusio
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Next Page Screw Vibration When the
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5.3.1 Pressure Drop in Runner As th
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Examples of calculating pressure dr
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Example with symbols and units The
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Flow length L mm Spiral height H Fi
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Solution The conversion factors for
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Figure 5.43 shows a sample plot of
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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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