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Table 1.2 Effect of Pressure on Viscosity for Polystyrene, Equation 1.46 However, the relative measure of viscosity can be obtained from [9,15,16] where P bar 30 100 200 300 500 1000 3000 rjp = viscosity at pressure p and constant shear stress T0 T]0 = viscosity at constant shear stress T0 ap = pressure coefficient For styrene polymers rjp is calculated from [14] "> =thesp kL) where p - pressure in bar. (1.45) (L46) Thus the change of viscosity with pressure can be obtained from Equation 1.46. Table 1.2 shows the values of viscosity calculated according to Equation 1.46 for a polystyrene of average molecular weight. It can be seen that a pressure of 200 bar causes an increase of viscosity of 22% compared to the value at 1 bar. The pressure coefficient of LDPE is less than that of PS by a factor of 3-4 and the value of HDPE is again smaller by a factor of 2 compared to LDPE. This means that in the case of polyethylene an increase of pressure by 200 bar would enhance the viscosity only by 3 to 4%. Consequently, the effect of pressure on viscosity can be neglected in the case of extrusion processes which generally use low pressure. However, in injection molding with its high pressures, typically the dependence of viscosity on pressure has to be considered. 1.3.7.7 Dependence of Viscosity on Molecular Weight 1.03 TJ0 1.105 TJ0 1.221 TJ0 1.35 TJ0 1.65 TJ0 2.72 TJ0 20 TJ0 The relationship between viscosity and molecular weight can be described by [12] (1.47)
where Mw = molecular weight JC — resin dependent constant The approximate value of JC for LDPE is JC = 2.28 <strong>•</strong> 10" 4 and for polyamide 6 K'= 5.21 <strong>•</strong> 10" 14 according to the measurements of LAUN [21]. These values are based on zero viscosity. 1.3.7.8 Viscosity of Two Component Mixtures The viscosity of a mixture consisting of a component A and a component B can be obtained from [17] where 7] = viscosity C = weight per cent Indices: M: mixture Ay B: components 1.4 Viscoelastic Behavior of Polymers (1.48) Polymer machinery can be designed sufficiently accurately on the basis of the relationships for viscous shear flow alone. However, a complete analysis of melt flow should include both viscous and elastic effects, although the design of machines and dies is rather difficult when considering melt elasticity and therefore rarely used. WAGNER [18] and FISCHER [19] made attempts to dimension dies taking elastic effects into account. For a more complete picture of melt theology the following expressions for the viscoelastic quantities according to LAUN [20, 21] are presented. The calculation of the deformation of the bubble in film blowing is referred to as an example of the application of Maxwell's model.
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 and 8: Figure 1.4 Shear flow The shear or
Page 9 and 10: where c and m are empirical constan
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: 1.3.7.5 Klein's Viscosity Formula [
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
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
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4 Designing Plastics Parts The defo
Page 75 and 76:
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
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
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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
Page 125 and 126:
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
Page 137 and 138:
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
Page 161 and 162:
Flow length L (mm) Flow length L (m
Page 163 and 164:
[26] VDI Warmeatlas, VDI Verlag, Du
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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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