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Power and wall shear stress
→ For a graphical representation of the performance curve
Three models can be selected for power calculation in REX/PSI:
- Isothermal performance model
- Non-isothermal performance model (recommended model for melt extruders)
- Enthalpy model (recommended model for plasticising extruders)
All models are based on the results of the throughput, melting and temperature calculations. The enthalpy model also requires the pressure curve.
The accuracy of the power calculation therefore depends on the other curves. If experimental values are already known (e.g. flow rate), it is advisable to specify these for the power calculation.
For an accurate power calculation, the cylinder wall temperatures in particular must be specified in a practical manner.
The temperature control power is calculated in the same way for all models and is made up of the melt film and the melt vortex. The temperature gradient on the cylinder wall is determined for both areas and the required temperature control power is determined from this using an energy balance. The resulting outputs at each calculation point are summarised for the respective heating zones. The temperature control power calculation only takes into account the heat flow between the heating band and the melt, but not heat losses (of any kind) to the outside.
The following models calculate the drive power and the required torque of the extruder. Power losses (e.g. in the gearbox) are not taken into account.
The total power of the extruder is made up of the drive power and the heating heating zones.
Isothermal power model
When calculating the power, a distinction is made between the melting and melting-on areas. In the melting area, i.e. from the start of the first heating zone to the location of the melt vortex formation, the power can be determined via an average melt layer thickness assuming a pure drag current in the melt film. film can be determined. The power conversion in the pure solids area between the hopper and the first heating zone is neglected, as no pressure has yet built up there and the solids friction forces on the cylinder wall are negligibly small compared to the melt film friction forces.
The calculation for the other zones results in a summation of the wall shear stresses on the cylinder. Similar to the pressure throughput calculation, approximation equations based on numerical analyses are used here. A distinction is made here between the melting area, where high shear stresses occur in the melt film, and pure melt conveying.
Sources
- Obermann, Christian: Theoretische und experimentelle Untersuchungen zum Durchsatz- und Leistungsverhalten von Glattrohr-Plastifiziereinheiten. Dissertation, University of Paderborn, 2000
- Potente, H., Obermann, C.: Screw Drive Power of Single Screw Plasticating Units With Smooth Barrels. International Polymer Processing, Vol. 14, no. 1, 1999, pp. 21-27
Non-isothermal power model
The non-isothermal power model is an extension of the isothermal power model.
The model is based on an extensive test plan of non-isothermal FEM flow simulations. The simulation results were analysed and regressed in relation to the drive power and implemented in the theoretical model approach of the isothermal model.
The non-isothermal performance model is recommended for melt extruders.
Sources
- Bornemann, Markus: Erweiterung der modelltheoretischen Grundlagen zur Durchsatz- und Leistungsberechnung von Einschneckenplastifiziereinheiten. Dissertation, University of Paderborn, 2011
Enthalpy power model
The enthalpy model is a fundamentally different approach and only takes into account the conservation of energy (1st law of thermodynamics).
Accordingly, the following applies:
$P_{total} = P_{drive} + \dot{Q} = \dot{m}*\Delta h$
and therefore also:
$P_{drive} = \delta h_{temperature} * \dot{m}_{melt} + \delta p * \dot{V} - \dot{Q}$
The enthalpy model is recommended for plating extruders.