HANSER Hanser Publishers, Munich • Hanser Gardner Publications ...

More documents

Recommendations

Info

Shear rate f Figure 1.13 Power law exponent of a LDPE as a function of shear rate and temperature Example The viscosity for a LDPE is to be calculated with the following constants: A = 4.2541 Al = -0.4978 A2 = -0.0731 A3= 0.0133 A4- -0.0011 B = 5.13 -10" 6 Bl = 5640K at Y^ = 500 s" 1 and T = 200 0 C. Solution With Power law exponent n aT from Equation 1.34 7]a from Equation 1.36 Substituting the values of A0, A1, and so on yields PE-LD s- 1
The power law exponent is obtained from Equation 1.37 Using the values for A0, A v and so on n = 3.196 1.3.7.4 Carreau's Viscosity Equation [11] As shown in Figure 1.14 [12], the Carreau equation provides the best fit for the viscosity function, reproducing the asymptotic form of the plot at high and low shear rates correctly. The equation is expressed as (1.38) where A, B, C are resin-dependent constants. By introducing the shift factor aT into Equation 1.38, the temperature-invariant form of the Carreau equation can be given as (1.39) For a number of resins the shift factor can be calculated as a function of temperature from the following equation with good approximation [9,10] (1.40) where T1 ( 0 C) is the temperature at which the viscosity is given and T2 ( 0 C) the temperature at which the viscosity is calculated. The standard temperature TST is given by [9] TST=Tg +50 0 C (1.41) Viscosity 7? Vo=* Shear rate f /=1/B Slope: -C Figure 1.14 Determination of Carreau-parameters from a viscosity function [12]
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: Shift Factor for Crystalline Polyme
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
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
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 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 ...
show all

HANSER Hanser Publishers, Munich • Hanser Gardner Publications ...

Create successful ePaper yourself

Delete template?

Save as template?