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The calculation method delivers the good angular
velocity of material ω G of the bulk material in the screw
conveyor. From this the determined coefficient of velocity
ζ* can be calculated through:
ζ
*
ωG
= 1−
2π
⋅ n
(16)
With the rotation speed n.
Creation of a Dimensioning and Sizing
method
In the following, the data of the coefficients of velocity
and power gathered up to now are analyzed with regard
to the influence of the examined parameters, and they
are processed for the generation of dimensioning and
sizing methods. As the presentation of the individual
measurements is often not sufficient to draw usable
conclusions on the influence of a parameter, a locally
weighted regression is used for descriptive assessment
of influences. Here the correlations between parameters
and command variables are estimated flexibly and free
from restrictions. Therefore it offers very accurate results,
which however have to be bought with a high complexity of
the model: Due to the completely free configuration of the
correlations it is often not possible any more to present the
connections found in compact formulas, which is desired
in the framework of this project. Nevertheless the graphic
presentation of the modeled correlation allows a glimpse
on the possible underlying effect.
Consecutively these effects create the basis for the
modeling of the regression analysis. This allows for a
presentation of the command variables coefficient of
velocity ζ and coefficient of power λ in a correlation formula,
in accordance to the examined influence parameter. Apart
from an adequate adjustment of the model to the existing
Table 4:
Calculated parameter level according to the Vollmann [1] method
Issue 04 | 2010
Parameter Unit Parameter levels
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data sets, the simplicity of the model is in the foreground,
i.e. the calculated model should be presentable in a simple
and complete form.
In conclusion the quality of the found formulas is
assessed. In order to do so, the values of the parameters
determined by the new formulas are faced with the
determined values and the standard error is calculated.
Through this the accuracy of the found formulas with
regard to the actual behaviour can be assessed.
Coefficient of velocity
Rotation speed n [1/s] 2 4 5 6 8 10 13
Inclination angle β [°] 30 40 50 60 70 80 90
Filling level φ [-] 0,2 0,3 0,4 0,5 0,6 0,7
Screw diameter D [m] 0,200 0,250 0,315 0,400 0,500 0,630 0,800
For the coefficient of velocity ζ* a regression model
should be found, subject to the parameter rotation
speed n, screw diameter D filling level φ and
inclination . As described above, in order to do so, a locally
weighted regression is calculated for the determined
coefficients of velocity. These are presented in picture
6, depending on the individual influencing factors. The
various influences on the coefficient of velocity can be
seen in the individual diagrams.
In the diagram above left the coefficient of velocity
ζ is plotted on the rotation speed n. An initially strong
positive linkage can be seen, which clearly lessens from
a rotation speed of approx n = 6 1/s. The course of the
curve corresponds to a logarithm- or power function. The
influence of the screw inclination β has been presented
above right. Here a reciprocal proportionality can be
identified. Alternatively the curve can also be interpreted
as a combination of two linear correlations with a cusp
between β = 40° and 50° inclination of the screw. The
influences of filling level φ and screw diameter D, pictured
below left and right, are evidently lowest. A slight linear
influence can be seen for the filling level, a slight nonlinear
influence for the screw diameter.
To begin with, this sufficiently identifies the types of
influence of the individual parameters on the determined
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