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Die constant Gtriangle: Pressure drop Ap from Equation 5.2: This result differs little from the one obtained by using the concept of substitute radius. Therefore this concept of SCHENKEL [5] is suitable for use in practice. 5.1.1.5 Temperature Rise and Residence Time The adiabatic temperature increase of the melt can be calculated from where AT = temperature rise (K) Ap = pressure difference (bar) pm = melt density (g/cm 3 ) cpm = specific heat of the melt kj/(kg <strong>•</strong> K) The residence time T of the melt in the die of length L can be expressed as u = average velocity of the melt Equation 5.19 for a tube can be written as R = tube radius ya = shear rate according to Equation 5.9 (5.17) (5.18) (5.19) (5.20)
The relation of a slit is H = height of slit ya = shear rate according to Equation 5.10 5.1.1.6 Adapting Die Design to Avoid Melt Fracture (5.21) Melt fracture can be defined as an instability of the melt flow leading to surface or volume distortions of the extrudate. Surface distortions [34] are usually created from instabilities near the die exit, while volume distortions [34] originate from the vortex formation at the die entrance. Melt fracture caused by these phenomena limits the production of articles manufactured by extrusion processes. The use of processing additives to increase the output has been dealt with in a number of publications given in [35]. However, processing aids are not desirable in applications such as pelletizing and blow molding. Therefore, the effect of die geometry on the onset of melt fracture was examined. The onset of melt fracture with increasing die pressure is shown for LDPE and HDPE in Figure 5.3 [38]. As can be seen, the distortions appear differently depending on the resin. The volume flow rate is plotted in Figure 5.4 [39] first as a function of wall shear stress and then as a function of pressure drop in the capillary for LDPE and HDPE. The sudden increase in slope is evident for LDPE only when the flow rate is plotted against pressure, whereas in the case of HDPE it is the opposite. In addition, for HDPE the occurrence of melt fracture depends on the ratio of length L to diameter D of the capillary. The effect of temperature on the onset of melt fracture is shown in Figure 5.5 [36]. With increasing temperature the onset of instability shifts to higher shear rates. This behavior is used in practice to increase the output. However, exceeding the optimum processing temperature can lead to a decrease in the quality of the product in many processing operations. From these considerations it can be seen that designing a die by taking the resin behavior into account is the easiest method to obtain quality products at high throughputs. Design procedure Using the formulas given in this book and in reference [33], the following design procedure has been developed to suit the die dimensions to the melt flow properties of the resin to be processed with the die. STEP 1: Calculation of the shear rate in the die channel STEP 2: Expressing the measured viscosity plots by a rheological model STEP 3: Calculation of the power law exponent STEP 4: Calculation of the shear viscosity at the shear rate in Step 1 STEP 5: Calculation of the wall shear stress STEP 6: Calculation of the factor of proportionality STEP 7: Calculation of die constant
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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
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
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: n = 3.043 RTh= 1.274 mm Shear rate
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 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
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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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