1 Extrusion and Injection Molding - Analysis ver. 1 ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20112 Overview • Extrusion and Injection molding – Flow in screw – Flow in cavity or die • Injection molding – Clamp force – Cooling time – Ejection force ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20113 Extrusion schematic ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20114 Injection molding schematic ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20115 Schematic hopper heaters barrel screw nozzle clamp mold cavity pellets motor / drive throat ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20116 Flow in screw - Extrusion and Injection molding • Understood through simple fluid analysis • Unroll barrel from screw – rectangular trough and lid w/cosq H vx vz v=pDN q w is like normal pitch w/cosq is like axial pitch ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20117 Flow analysis • Barrel slides across channel at the helix angle • vz = pumping • vx = stirring w/cosq H vx vz v=pDN q w is like normal pitch w/cosq is like axial pitch ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20118 Flow rate • vz shows viscous traction work against exit pressure flow rate = f(exit pressure, vbarrel, m, d, w, l) ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20119 Flow analysis • Simplify by using Newtonian fluid • Separate into drag and pressure flows • Add solutions (superposition) ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201110 Drag flow in rectangular channel (QD) • Simple viscous flow between parallel plates, end effects negligible vo y H Hyvv0wHvAvQD210ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201111 Pressure flow in rectangular channel • Assumptions – no slip at walls – melt is incompressible – steady, laminar flow – end and side wall effects are negligible p p + dp dz y z 2y t t hopper exit ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201112 Pressure flow in rectangular channel Equilibrium p p + dp dz y z 2y t t hopper exit   022  dzydppptME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201113 Pressure flow in rectangular channel   022  dzydppptdzdpytdydvγτ mmNewtonian fluid ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201114 Pressure flow in rectangular channel • Eliminating t • Integrating and noting @ y = +/- H/2, v = 0 dyydzdpdv m128122yHdzdpvmME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201115 Total pressure flow (Qp) dzdpwHdyvwQHHp22312mME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201116 Total flow (Q) • dp/dz set by – back pressure on reciprocating screw (injection molding) – die resistance (extrusion) dzdpHHvwQQQzpDm1223f(screw speed) f(pressure drop) ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201117 Nomenclature • dz = helical length = axial length/sinq • vz = helix velocity = vbarrel*cosq ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201118 Flow rate flow rate output pressure w 2w ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201119 Schematics Injection molding Extrusion ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201120 Flow in round die or runner dr dz r z t + dt t p p + dp       dzrddrrdprdrr tttpp2][22Equilibrium Same assumptions as above ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201121 Flow in round die or runner Neglecting HOT  dzdrdrdpdrr ttpp22      dzrddrrdprdrr tttpp2][22   drrrddrrdrdrdzdptttME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201122 Flow in round die or runner  drCrrd t drrrdLpdzdptC  drCrrdtME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201123 Flow in round die or runner rLprC22t22rCr tME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201124 Flow in round die or runner • At center, t = 0 • At edge of tube (R), t = max LRp2maxtdrdumtNewtonian fluid ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201125 Flow in round die or runner mLrpdrdu2finally  224RrLpu mME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201126 Flow in round die or runner LpRdrurQRp0482mpp 224RrLpu mME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201127 Flow in rectangular die or runner • as above LpwHQpm123ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201128 Extrusion • Pressure generated by screw rotation – flow rate through screw = flow rate through die Q(extruder) = Q(die) – pressure rise in screw = pressure drop in die dp(extruder) = p(die) ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201129 Extrusion - Ex. 1-1 • Extrude a polymer through a die with dimensions diameter 5 mm, length 40 mm at rate 10 cm/s • Screw is fixed, barrel rotates • More data on next page • Calculate barrel RPM ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201130 • polymer density (r = 980 kg/m3 • polymer viscosity (m) = 103 N-s/m2 • barrel diameter (D) = 28 mm • channel width (w) = 21 mm • channel height (H) = 4 mm • helix angle (q) = 15 degrees • length of screw (L) = 1.25 m Extrusion - Ex. 1-2 ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 201131 Extrusion - Ex. 1-3 • First, calculate flow rate  smAvQpr oduct/1096.14005.01.0362pdzdpHHvwQzscrewm1223LpRQd iemp84pdp ME 6222: Manufacturing Processes and Systems Prof. J.S.