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Hereby ζ is the coefficient of velocity, as mentioned
above, that lies in the interval of 0 ≤ ζ ≤ 1. The set limits of
the parameter can vividly be described: On one hand there
is no conveyance for ζ = 0. As demonstrated in picture 2,
this case can also occur in screw driving speeds higher
than n = 0 1/s, if it falls below the minimum driving speed
needed for conveyance. On the other hand the maximum
axial velocity of material of the horizontal conveyance
is achieved for ζ = 1. With the last two equations the
achievable volume flow in inclined screw conveyors can
be summarized as
I V ax
Issue 04 | 2010
2 2 ( D − d ) ⋅π
⋅ S ⋅ ζ
1
= A⋅
v = ϕ ⋅ ⋅
n ⋅
4
Hereby the coefficient of velocity ζ is the last unknown
value and is determined as the result of empirical tests,
depending on the described influencing factors.
Calculation of Driving Power
In an inclined screw conveyor the required driving
power also results from a range of different loss portions.
Apart from the lifting power to overcome the difference in
height, there are mainly friction powers between the bulk
material and the geometry, as well as power losses inside
the bulk material. From these only the lifting power P Hub can
easily be determined analytically. This is calculated from
the volume flow to be conveyed I V , the bulk density ρ and
the conveying height H according to formula:
PHub V
= I ⋅ ρ ⋅ g ⋅ H
(7)
For further power losses through friction, among others,
the following are to be mentioned [1]:
• Friction power between good and inner wall of the tube
(6)
• Friction power between good and screw spiral
• Friction power between good and screw shaft
• Power loss in the intermediate bearings
• Gap losses
• Dissipated power in shear planes
• Power losses from acceleration of goods
These loss portions cannot be calculated easily, although
some analytical approaches exist to describe them [1], [6],
[7], [8]. These approaches apply a fictitious total friction
power – based on the semi-empirical approach of Fottner
[9] – which describes all friction parts with the help of
empirically determined parameters. Also in the approach
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for the friction power the principal approach of DIN 15262
[5], which was also applied by Gabler [7] and Vollmann [1]
is used. Here the friction power is calculated similar to
the principle of the Coloumb friction, as the product of a
fictitious conveying factor with the normal force F N on the
conveying tube and the absolute velocity of material v G .
According to Rong [6] the normal force on the conveying
tube is proportional to the conveyed volume flow I V . The
acceleration a of the mass is dependant on the type
of conveyance - translational and rotational portions-
and is initially disregarded. With the bulk density ρ, the
conveyance length L and the axial velocity of the good v ax
the normal force F N results as:
F
IV
⋅ ρ
= ⋅ L ⋅ a (8)
v
N
a x
According to Vollmann [1], the absolute velocity of goods
can be presented with inclusion of the velocity parameter
ζ with the screw diameter D, the rotation speed n and the
screw pitch S:
v G
= D ⋅π
⋅ n ⋅
⎡
−1
( 1−
ζ ) ⋅ cos ⎢arctan⎜
⋅ ⎟⎥
⎝1
− ζ D ⋅π
⎠⎦
⎣
⎛
ζ
S
⎞⎤
(9)
In order to have a simple and practical dimensioning
method for the determination of the power losses through
friction, the portions depending on the coefficient of
velocity ζ as well as the unknown fictitious conveyance
factor are combined to the coefficient of power λ. The
acceleration a of the mass in the screw conveyor is also
included as portion of the gravitational acceleration g.
This is required, as the type of conveyance is not known.
However this is of decisive importance for the type of
acceleration that influences the bulk material. In case of a
purely translational conveyance, the bulk material is only
subjected to gravitational acceleration. In case a rotational
portion is included, the bulk material is also influenced by
centripetal acceleration, and in case of a vertical screw
conveyor, this type of acceleration is exclusively present.
Therefore the following correlation results for the fictitious
total friction power:
D
= λ ⋅ ⋅ I ⋅ ρ ⋅ g ⋅ L
S
(10)
PReib V
As such the components of the required power for
conveyance in an inclined screw conveyor are known and
can be summarized as follows:
⎛ D ⎞
= PReib
+ PHub
= I ⋅ ρ ⋅ g ⋅⎜
λ ⋅ ⋅ L + H ⎟ (11)
⎝ S ⎠
P V
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