4.2 Bucket motion studies
Figure 7 presents the results obtained from monitoring the
rotation rate of the bucket during a simulation. For clarity
Fig. 7 has been labelled in two zones (α, and β). The α zone is
where the bucket accelerates (start of the head pulley) and β is
the empty bucket exiting the head pulley. In the α zone, heavily
damped oscillations are observed over a total time period
of around 0.2 s. This duration is equivalent to 54 degrees of
pulley rotation. Peak bucket deceleration occurs at around
0.05 s after the tangency point; at around 14 degrees above
horizontal. Given that the belt is constrained at, and after,
the entry tangency point by the proximity of the pulley, we
expect the results presented to be largely reflected in experimental
evaluations.Video footage of laboratory bucket elevators
appears to support this numerical result, though current
footage lacks sufficient resolution for a definitive statement.
In the β zone the bucket decelerates back to the nominal
belt velocity however there is a much longer period of oscillation
(lower overall damping). This long period of oscillation
is ‘numerical’ due to the infinite stiffness of the trajectory
path used in the simulation and a low damping value
used for the numerical springs. The low damping used in
the DEM springs is unlikely to impact on the α section of the
graph due to the damping offered by the particles themselves.
In the β phase of Fig. 7 the oscillatory motion is unlikely to be
realised as the belt is effectively free to vibrate once past the
tangency point on the return leg. This capacity for the belt
itself to vibrate will absorb the predicted vibrations which
are largely due to the infinitely stiff nature of the constraining
path used in the simulation.
Laboratory observations on the return strand typically
showlowfrequency oscillations whichwe anticipate are fundamentally
the effect of the buckets deceleration phase on a
reasonably unconstrained belt.
Figure 8a, b illustrate the impact of the simulations ‘bucket
to belt’ spring constant on the motion of the bucket at entry
and exit to the head pulley. The ‘motion’ at time=1.8 s is the
buckets entry to the head pulley and at 2.5 s, the exit from the
pulley. In Fig. 8a the acceleration trace displays a complex
form for which we offer no explanation at this time. With
the higher spring constant (Fig. 8b) the decay in the oscillations
are much faster and the peak acceleration is much
higher (note the change in vertical scale). The motions occur
over a correspondingly shorter time frame. These very high
accelerations are not anticipated to be realised in physical
testing due to the mass and damping of the belt material, and
its additional freedom which was unable to be captured in
this current simulation.