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

More documents

Recommendations

Info

Previous Page Screw Vibration When the screw speed corresponds to the natural frequency of lateral vibration of the shaft, the resulting resonance leads to large amplitudes, which can cause screw deflection. The critical screw speed according to [8] is given by Substituting the values for steel, E = 210 <strong>•</strong> 10 9 Pa and p = 7850 kg/m 3 we get Numerical example For D = 150 mm and — = 30, NR is found from Equation 5.73 (5.72) (5.73) This result shows that at the normal range of screw speeds vibrations caused by resonance are unlikely. Uneven Distribution of Pressure Non-uniform pressure distribution around the circumference of the screw can lead to vertical and horizontal forces of such magnitude, that the screw deflects into the barrel. Even a pressure difference of 10 bar could create a horizontal force Fj1 in an extruder (diameter D = 150 mm within a section of length L = 150 mm) According to RAUWENDAAL [8], the non uniform pressure distribution is the most probable cause of screw deflection. 53 Injection Molding Other than extrusion, injection molding runs discontinuously and therefore the stages involved in this process are time-dependent [14]. The quantitative description of the important mold filling stage has been made possible by well known computer programs such as MOLDFLOW [15] and CADMOULD [16]. The purpose of this section is to present the basic formulas necessary for designing injection molding dies and screws on a rheological and thermal basis and illustrate the use of these formulas with examples.
5.3.1 Pressure Drop in Runner As the following example shows, the pressure drop along the runner of an injection mold can be calculated from the same relationships used for dimensioning extrusion dies. Example For the following conditions, the isothermal pressure drop Ap0 and the adiabatic pressure drop Ap are to be determined: For polystyrene with the following viscosity constants according to Equation 1.36, Section 1.3.7.3: A0 = 4.4475 A1 = -0.4983 A2 = -0.1743 A3 = 0.03594 A4 = -0.002196 C1 = 4.285 C2 =133.2 T0 = 190 0 C flow rate rh = 330.4 kg/h melt density pm = 1.12 g/cm 3 specific heat cpm= 1.6 kj/(kg <strong>•</strong> K) melt temperature T =230 0 C length of the runner L =101.6 mm radius of the runner R =5.08 mm Solution a) Isothermal flow Yz from Equation 1.19: (Q = volume flow rate cm /s) aT from Equation 1.35: n from Equation 1.37: 7]a from Equation 1.36:
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 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: Next Page Screw Vibration When the
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 ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?