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Ch13 math

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Ch13 math

1. 1. ©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />Extruder Screw<br />Figure 13.5 Details of an extruder screw inside the barrel.<br />
2. 2. Flight Angle A<br />The Flight Angle A can be determined from the following relationship.<br />tanA = pitch / πD (eq. 13.4)<br />A = tan-1(p / (πD))<br />©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />
3. 3. Volume Flow Rate<br />Drag flow results from friction between the viscous liquid and the two opposing surfaces moving relative to each other.<br />Qd = 0.5vdw (eq. 13.5)<br />v = velocity of the moving plate, in/sec (m/s)<br />v = πDN cos A (eq. 13.6)<br /> D = screw flight diameter, in. (mm)<br /> N = screw rotational speed, rev/sec<br />©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />
4. 4. Volume Flow Rate<br />Drag flow results from friction between the viscous liquid and the two opposing surfaces moving relative to each other.<br />Qd = 0.5vdw<br />d = distance separating the two plates, in. (m)<br />d = dc (eq. 13.7)<br /> dc = screw channel depth, in. (mm)<br />©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />
5. 5. Volume Flow Rate<br />Drag flow results from friction between the viscous liquid and the two opposing surfaces moving relative to each other.<br />Qd = 0.5vdw<br />w = the width of the plates perpendicular to velocity direction, in. (m)<br />w = wc = (πDtanA – wf)cosA (eq 13.8)<br />Reduces to wc = πDsinA (eq 13.9)<br />wc = screw channel width, in. (mm)<br /> A = flight angle<br />wf = flight land width, in. (mm)<br />©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />
6. 6. Volume Flow Rate<br />Drag flow results from friction between the viscous liquid and the two opposing surfaces moving relative to each other.<br />Qd = 0.5vdw<br />Qd = 0.5 π2D2NdcsinAcosA (eq 13.10)<br />©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />
7. 7. Volume Flow Rate<br />Back pressure flow in the barrel will reduce the material being moved by drag flow.<br />Qb = pπDdc3sin2A /12ηL (eq. 13.12)<br />p = head pressure in the barrel, lb/in2 (Mpa)<br />L = length of the barrel, in. (m)<br />η = viscosity of polymer melt, lb-sec/in2 (N-s/m2)<br />©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />
8. 8. Volume Flow Rate<br />Melt flow is the difference between drag flow and back pressure flow.<br />Qx = Qd – Qb<br />Qx = 0.5π2D2NdcsinAcosA - pπDdc3sin2A /12ηL<br />©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />
9. 9. Extruder and Die Characteristics<br />If back pressure is zero, then the flow would equal drag flow denoted as Qmax.<br />Qmax = 0.5π2D2NdcsinAcosA (eq. 13.14)<br />If back pressure was so great that there was no flow, then Qd = QbThe maximum head pressure would be pmax<br />pmax = 6πDNLηcotA / dc2 (eq. 13.15)<br />©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />
10. 10. Extruder and Die Characteristics<br />The actual operating parameters will lie somewhere between Qmaxandpmax.<br />Qx = Ksp (eq. 13.16)<br />Qx = flow rate, in.3/sec (m3/s)<br />p = head pressure, lb/in2 (MPa)<br />Ks = shape factor for the die, in.5/lb-sec (m5/Ns)<br /> for a circular die, Ks is:<br /> Ks = πDd4 / 128ηLd (eq. 13.17)<br />©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />
11. 11. Extruder and Die Characteristics<br />The actual operating parameters will lie somewhere between Qmaxandpmax.<br /> Ks = πDd4 / 128ηLd (eq. 13.17)<br />Dd=die opening diameter, in. (m)<br />η = melt viscosity, lb-sec/in2 (N-s/m2)<br />Ld = die opening length, in. (m)<br />©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />
12. 12. ©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />Shrinkage<br />Reduction in linear size during cooling from molding to room temperature <br />Polymers have high thermal expansion coefficients, so significant shrinkage occurs during solidification and cooling in mold <br />Typical shrinkage values: <br />PlasticShrinkage, mm/mm (in/in)<br />Nylon‑6,6 0.020<br />Polyethylene 0.025<br />Polystyrene 0.004<br />PVC 0.005<br />
13. 13. ©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e<br />Compensation for Shrinkage<br />Dimensions of mold cavity must be larger than specified part dimensions: <br />Dc=Dp + DpS + DpS2(eq. 13.19)<br /> where Dc = dimension of cavity, in. (mm)<br />Dp= molded part dimension, in. (mm) <br /> and S = shrinkage value<br />Third term on right hand side corrects for shrinkage in the shrinkage <br />