Since the use of Discrete Element Modelling has become standard in the Bulk Materials Handling industry, it has become possible to calculate realistic loading conditions. To take advantage of this, the problem of skip response during filling is revisited. Recently WorleyParsons RSA was required to recommend skips of ever-increasing size to support the tonnage required by new mines. Skips of 50 tonnes payload are envisioned for future projects with correspondingly larger displacements during filling. This article describes the DEM of skip filling from a flask and the response of the skip to the loading.
Discrete Element Modelling
The DEM model is shown in Figure 1. The flask is first loaded by a conveyor belt resulting in a realistic distribution of material in the flask. Once the radial door opens, the material flows down the chute into the skip. The Centre of Gravity (CG) of the material moves from height 1 to 2.
Figure 1: DEM model showing the arrangement of the flask, chute and skip and a typical result
The mass flow rate during loading is shown Figure 2. The graph can be split into 3 regions labelled up (Δtu), steady-state (Δt) and down (Δtd). The total loading time is designated τ.
Figure 2: Mass flow rate for various cases
Skip Response
The response of the skip can be calculated using energy conservation. Assuming no losses, the potential energy of the payload before the skip door is opened must be equal to the potential energy after it has come to rest. It was found that this approach grossly overestimated the maximum displacement. Another approach is to approximate the response using a lumped parameter system as shown in Figure 3.
In Figure 3 the variables shown are:
m0 is the initial mass of the skip including the effective rope mass.
m(t) is the payload mass which varies as a function of time.
v is the absolute velocity at which the payload mass enters the system.
k is the stiffness of the rope at the loading station.
x is the vertical displacement of the skip.
The equation of motion must consider the change in mass of the skip rope system during loading. The change in momentum of the payload must also be considered as an external force.
Figure 3: Lumped parameter approximation of the skip rope system
The equation of motion is solved using the Runge-Kutta implementation in Matlab for 4 cases. The natural frequencies of the various cases were different and depended on the payload mass and the rope arrangement i.e. Koepe vs Blair Multi Rope. In order to compare the dynamic amplitude the normalised time response is shown in Figure 4.
Figure 4: Comparison of time response for the various cases
The Dynamic Load Factor (DLF) can be calculated in order to compare the response at various natural frequencies. Previously the DLF was often calculated by normalising the x-axis to the ramp up time (Δtu) and assuming the steady state loading to continue indefinitely (Biggs, Hamilton). In order to do this, various assumptions had to be made including that the mass of the system is constant while in reality it typically doubles during filling. These assumptions were effectively addressed by using the DEM calculated mass flow as an input. It was also found that normalising to the total loading time (τ) yields a more sensible graph (Figure 5).
Figure 5: DLF comparison
Conclusion
With the advent of DEM it is now possible to address the concerns that Hamilton expressed in his report by improving the accuracy of the loading imposed on the skip during loading. Importantly it is shown that the assumption of a system with a constant force and a finite rise time is unconservative. The recommended DLF of 1.5 in SANS 10208 part 3 is however affirmed by these results.