SIGMA Software Documentation

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Anonymous (anonymous@undisclosed.example.com) — 2026-09-04T12:29:27+00:00

Strangabkühlung - [Konvergenzkriterium]

paal (paal@undisclosed.example.com) — 2026-09-04T11:43:03+00:00

Strangabkühlung Ab der SIGMA-Version 11.1 gibt es erstmals die Möglichkeit, eine Wasserbad-Strangabkühlung zu modellieren. Hiermit kann die Temperaturverteilung innerhalb eines Polymerstrangs zu bestimmten Zeitpunkten ermittelt werden. Somit lassen sich Rückschlüsse auf die notwendigen Kühlzeiten bzw. Wasserbadlängen ziehen, sodass die Dimensionierung einer derartigen Kühlstrecke maßgeblich vereinfacht wird.$$\Delta x = \frac{L}{M} \tag{1}$$$$\Delta r = \frac{R}{N} \tag{2}$$$(T_{i,j})$$$\rho c_…

Faserbruchberechnung - [Lösung der Differentialgleichung]

paal (paal@undisclosed.example.com) — 2026-09-04T11:20:39+00:00

Faserbruchberechnung Grundlegende Betrachtungsweisen Für die folgenden Betrachtungen der Modellierung der Glasfaserabnahme während der Compoundierung wird zunächst die reale Geometrie in ein Kanalmodell übertragen, welches in der Ebene abgewickelt betrachtet wird. Das Kanalmodell wird kinematisch umgekehrt, so dass die Strömungsprozesse unter folgenden Annahmen beschrieben werden können:$$\frac{dl}{dt} = c \cdot l^{\infty} ; \text{mit } l = \frac{L - L_{\infty}}{L_0 - L_{\infty}} \tag{1}$$$L_…

Fiber Fracture Calculation - [Modeling]

paal (paal@undisclosed.example.com) — 2026-09-04T11:17:29+00:00

Fiber Fracture Calculation Basic Considerations For the following considerations of the modeling of the glass fiber reduction during compounding at first the real geometry is transferred into an unwind channel model. The channel model is kinematically reversed, so that the flow processes can be described under the following assumptions:$$\frac{dl}{dt} = c \cdot l^{\infty} ; \text{with } l = \frac{L - L_{\infty}}{L_0 - L_{\infty}} \tag{1}$$$L_0$$l$$L$$L_0$$L_{\infty}$$c$$α$$L_{\infty}$$\tau$$$\…

Scale-up - [Model Theory]

paal (paal@undisclosed.example.com) — 2026-09-04T09:04:13+00:00

Scale-up Model Theory For reasons of economy the development of new recipes in the area of polymer processing is usually carried out on laboratory machines. Only once an appropriate product quality has been attained the process transfer to the production machine is initiated. By reason of this two-tiered approach the transfer of processes and operating points in polymer processing assumes central importance. To minimize the risk of quality loss during the scale-up, the adoption of model laws a…

Mixing in Co-rotating Twin Screw Extruders - [References]

paal (paal@undisclosed.example.com) — 2026-09-04T09:01:30+00:00

Mixing in Co-rotating Twin Screw Extruders In order to obtain an overall description of the mixing effects within a co-rotating twin screw extruder one has to distinguish between three different mixing effects [Pot91], [For87], [Koc87], [Sch87], [Sch90], [Kes91], [PA90], [OC83], [Raa61], [Kre64], [Pah85], [BSL60], [Pot84], [PL85], [Lap85], [Pot88], [PA90]: * Longitudinal mixing, due to the residence time distribution,$$\sigma^2 = \int_{\Theta_1}^{\infty} (\Theta - 1)^2 f(\Theta)d\Theta \tag{…

Mischvorgänge im Gleichdrall-Doppelschneckenextruder - [Literatur]

paal (paal@undisclosed.example.com) — 2026-09-04T09:01:28+00:00

Mischvorgänge im Gleichdrall-Doppelschneckenextruder Um eine Gesamtbeschreibung der Mischwirkungen innerhalb eines Gleichdrall-Doppelschneckenextruders zu erhalten, muss man zwischen drei verschiedenen Mischwirkungen unterscheiden [Pot91], [For87], [Koc87], [Sch87], [Sch90], [Kes91], [PA90], [OC83], [Raa61], $$\sigma^2 = \int_{\Theta_1}^{\infty} (\Theta - 1)^2 f(\Theta)d\Theta\tag{1}$$$\sigma^2$$\Theta_1$$\Theta_1$$\Theta_1 = 1$$\Theta_1 = 0$$0,7 < \Theta_1 < 0,85$$0,5 < \Theta_1 < 0,75$$0,35 <…

Melt Conveying - [Flow in Simple Geometries]

paal (paal@undisclosed.example.com) — 2026-09-04T07:53:54+00:00

Melt Conveying The basis of the general mathematical description of flow is the equilibrium of mass, momentum and energy. A flow is described, if at any place and at any time the velocity vector and the values pressure and temperature in the flow domain are known. For the calculation of these values, the conservative equations and the constitutive equations are combined $$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \cdot v) = 0 \tag{1}$$$$\rho \frac{\delta v}{\delta t} = -\nabla p + …

Melting Calculation - [Temperature of the Solids at the Location of the First Melt]

paal (paal@undisclosed.example.com) — 2026-09-04T07:40:56+00:00

Melting Calculation Phenomenology The feed material is held in underneath the hopper opening by the screw-elements and is transported in the screws as a solid in the direction of the screw-tips. Through contact with the heated cylinder wall, the particles in the proximity of the cylinder wall begin to sinter and melt on until finally a continuous molten film over the solid tailback in the intermeshing area is formed. This process is supported in practice by reducing the pitch of the screw elem…

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deppe2 (deppe2@undisclosed.example.com) — 2026-08-15T09:56:21+00:00

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deppe2 (deppe2@undisclosed.example.com) — 2026-08-14T11:49:31+00:00

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