Die Swell Ratio
Calculate the die swell ratio, B = D_extrudate ÷ D_die, from the extrudate diameter once it stabilizes D_extrudate and the die orifice diameter D_die. Die swell is one of extrusion's most characteristic and challenging phenomena: on leaving the die, the molten polymer EXPANDS, ending up larger than the orifice that shaped it (swells of 1.2-2× are common). The cause is the VISCOELASTIC nature of polymers: inside the die, the long molecular chains are compressed and oriented (stretched) by the flow; on exiting and losing confinement, they relax and elastically recoil, like a spring, swelling the material. Swell is greater the more elastic the polymer, the higher the shear rate and the shorter the die (less time to relax inside). It is critical in die design: to make a pipe or profile of the exact target size, the die must be designed SMALLER, anticipating the swell — and since it varies with temperature and speed, controlling swell is essential for dimensional accuracy. Enter the extrudate diameter and the die diameter.
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Inchamento do extrudado (die swell)
A razão de inchamento do extrudado (die swell) é B = D_extrudado ÷ D_matriz, a razão entre o diâmetro do material já estabilizado ao sair e o diâmetro do orifício da matriz. O inchamento é um dos fenômenos mais característicos e desafiadores da extrusão: ao sair da matriz, o polímero fundido expande, ficando com diâmetro maior que o do orifício que o moldou (inchamentos de 1,2 a 2 vezes são comuns). A causa é a natureza viscoelástica dos polímeros: dentro da matriz, as longas cadeias moleculares são comprimidas e orientadas (alongadas) pelo escoamento; ao saírem e perderem o confinamento, elas relaxam e se recontraem elasticamente, como uma mola, fazendo o material inchar. O inchamento é maior quanto mais elástico o polímero, mais alta a taxa de cisalhamento e mais curta a matriz (menos tempo para relaxar lá dentro). É crítico no projeto de matrizes: para produzir um tubo ou perfil com a dimensão exata desejada, a matriz precisa ser projetada menor, antecipando o inchamento — e como ele varia com a temperatura e a velocidade, controlá-lo é essencial para a precisão dimensional do produto. Informe o diâmetro do extrudado e o diâmetro da matriz.
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Estimate an extruder's head pressure, ΔP = (Q·μ) ÷ K, from the volumetric flow Q (m³/s), the melt viscosity μ (Pa·s) and the die conductance constant K (m³, summarizing the head+die flow-resistance geometry). Head pressure is the pressure the melt reaches at the screw end, before being forced through the die that gives the product its final shape. It results from the balance between the screw's pumping capacity (drag flow) and the die's resistance: more restrictive dies (smaller orifices, longer narrower channels) need higher pressure for the same flow. Extrusion pressures are very high — typically 100-400 bar (10-40 MPa) — and measuring and controlling them is essential: pressure indicates process state (blockages, viscosity changes from temperature, screw wear), governs flow and product uniformity, and has safety limits (excessive pressure can rupture the head or trigger burst disks). The screw-die balance, shown in the extruder's characteristic curve, is the heart of process control. Enter the flow, viscosity and die constant.
Extruder Drag Flow
Calculate the drag flow of a single-screw extruder, Q_d = ½·π²·D²·N·H·sin(φ)·cos(φ), from the barrel diameter D (m), screw speed N (rev/s), metering-zone channel depth H (m) and helix angle φ (degrees). Drag flow is an extruder's main pumping mechanism: the melt is dragged forward by the relative motion between the rotating screw and the fixed barrel, like a screw pushing a nut that cannot turn. This viscous drag is proportional to screw speed and channel geometry, and would be the maximum theoretical flow with no back-pressure. In practice the net flow is the drag flow MINUS the pressure flow (the backflow from die/head resistance). The balance between drag and pressure sets the extruder's operating point on its characteristic curve. Drag flow is the basis of extrusion screw design, the process that makes pipes, profiles, films, sheets, wire and the pellets of nearly all transformed plastic. Enter the diameter, speed, channel depth and helix angle.
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