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References [I] PAHL, M., BALDHUHN, R., LINNEMANN, D.: Praktische Rheologie der Kunststoffschmelzen and Losungen, VDI Kunststofftechnik, Dusseldorf (1982) [2] MONSTEDT, H.: Kunststoffe 68, 92 (1978) [3] Kunststoff Physik im Gesprach, brochure, BASF, 1977 [4] EYRING, H.: I. Chem. Phys. 4, 283 (1963) [5] PRANDTL, L.: Phys. Blatter 5,161 (1949) [6] OSTWALD, W.: Kolloid Z. 36, 99 (1925) [7] DE WAALE, A.: /. Oil and Color Chem. Assoc. 6, 33 (1923) [8] RAO, N. S.: Berechnen von Extrudierwerkzeugen, VDI Verlag, Dusseldorf (1978) [9] RAUWENDAAL, C: Polymer Extrusion, Hanser Publishers, Munich (2001) [ 10] RAO, N. S.: Designing Machines and Dies for Polymer Processing with Computer Programs, Hanser Publishers, Munich (1981) [II] CARREAU, P. J.: Dissertation, Univ. Wisconsin, Madison (1968) [12] HERTLEIN, T., FRITZ, H. G.: Kunststoffe 78, 606 (1988) [13] MiCHAELi, W.: Extrusion Dies, Hanser Publishers, Munich (2003) [14] KLEIN, L, MARSHALL, D. L, FRIEHE, C. A.: /. Soc. Plastics Engrs. 21,1299 (1965) [15] AVENAS, P., AGASSANT, J. E, SERGENT, J.PH.: La Mise en Forme des Matieres Plastiques, Technique & Documentation (Lavoisier), Paris (1982) [16] MONSTEDT, H.: Berechnen von Extrudierwerkzeugen, VDI Verlag, Dusseldorf (1978) [ 17] CARLEY, J. E: Antec 84, S. 439 [18] WAGNER, M. H.: Dissertation, Univ. Stuttgart (1976) [19] FISCHER, E.: Dissertation, Univ. Stuttgart (1983) [20] LAUN, H. M.: Rheol. Acta 18,478 (1979) [21] LAUN, H. M.: Progr. Colloid & Polymer ScL 75, 111 (1987) [22] BRYDSON, J. A.: Flow Properties of Polymer Melts, Iliffe Books, London (1970) [23] BERNHARDT, E. C: Processing of Thermoplastic Materials, Reinhold, New York (1963) [24] COGSWELL, F. N.: Polymer Melt Rheology, John Wiley, New York (1981)
2 Thermodynamic Properties of Polymers In addition to the rheological data, thermodynamic properties of polymers are necessary for designing machines and dies. It is often the case that the local values of these data are required as functions of temperature and pressure. Besides physical relationships, this chapter presents regression equations developed from experimental data for calculating thermodynamic properties, as these polynomials are often used in the practice, for example, in data acquisition for data banks [I]. 2.1 Specific Volume According to the Spencer Gilmore equation, which is similar to the van der Waal equation for real gases, the relationship between pressure p, specific volume v, and temperature T of a polymer can be written as (2.1) In this equation, b is the specific individual volume of the macromolecule, p is the cohesion pressure, W is the molecular weight of the monomer, and R is the universal gas constant [2]. Example Following values are given for a LDPE: W = 28.1 g/Mol; b\ = 0.875 cm 3 /g; p =3240atm Calculate the specific volume v at T = 190 0 C andp = 1 bar. Solution Using Equation 2.1 and the conversion factors to obtain the volume v in cm 3 /g, we obtain The density p is the reciprocal value of the specific volume so that (2.2)
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: Die swel B1 Figure 1.40 Dependence
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
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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
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md = 46.42 kg/h Equation 5.31 and E
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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
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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
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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
Page 159 and 160:
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
Page 169 and 170:
168 Index terms Links Index terms L
Page 171 and 172:
viii Contents 1.4 Viscoelastic Beha
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x Contents 5.2 Extrusion Screws ...
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