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Screw Vibration
When the screw speed corresponds to the natural frequency of lateral vibration of the
shaft, the resulting resonance leads to large amplitudes, which can cause screw deflection.
The critical screw speed according to [8] is given by
Substituting the values for steel, E = 210 • 10 9 Pa and p = 7850 kg/m 3 we get
Numerical example
For D = 150 mm and — = 30, NR is found from Equation 5.73
(5.72)
(5.73)
This result shows that at the normal range of screw speeds vibrations caused by resonance
are unlikely.
Uneven Distribution of Pressure
Non-uniform pressure distribution around the circumference of the screw can lead to
vertical and horizontal forces of such magnitude, that the screw deflects into the barrel.
Even a pressure difference of 10 bar could create a horizontal force Fj1 in an extruder
(diameter D = 150 mm within a section of length L = 150 mm)
According to RAUWENDAAL [8], the non uniform pressure distribution is the most probable
cause of screw deflection.
53 Injection Molding
Other than extrusion, injection molding runs discontinuously and therefore the stages
involved in this process are time-dependent [14]. The quantitative description of the
important mold filling stage has been made possible by well known computer programs
such as MOLDFLOW [15] and CADMOULD [16]. The purpose of this section is to
present the basic formulas necessary for designing injection molding dies and screws on
a rheological and thermal basis and illustrate the use of these formulas with examples.