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Temperature ratio &jb Temperature ratio 6fb Fourier number F0 Figure 3.9 Average temperature of an infinite slab (c), a long cylinder (b) and a sphere (a) during non-steady heating of cooling [2] Fourier number F^otZX 1 Figure 3.10 Axis temperature for multidimensional bodies [4] Q b c
The foregoing equations apply to cases, in which the thermal resistance between the body and the surroundings is negligibly small (OC0 -»), for example, in injection molding between the part and the coolant. This means that the Biot number should be very large, Bi —» oo. The Biot number for a plate is where aa = heat transfer coefficient of the fluid X = thermal conductivity of the plastic (3.42) As the heat transfer coefficient has a finite value in practice, the temperature ratio 0r based on the centre line temperature, is given in Figure 3.11 as a function of the Fourier number with the reciprocal of the Biot number as parameter [5]. Example 1 [6] Cooling of a part in an injection mold for the following conditions: Resin: LDPE Thickness of the plate: s =12.7 mm Temperature of the melt: Ta = 243.3 0 C Mold temperature: Tw = 21.1 0 C Demolding temperature: Tb = 76.7 0 C Thermal diffusivity: a =1.29 10~ 3 cm 2 /s The cooling time tk is to be calculated. Solution The temperature ratio 0Tb : Fourier number F0 from Figure 3.10 at 0Tb = 0.25 P0 = 0.65 cooling time tk:
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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 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: The equation for an infinite cylind
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 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
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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
Page 133 and 134:
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
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 and 160:
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
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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