Abstract:

The article presents numerical calculations of container loading with loose material, i.e. mineral aggregate. The work verified the effectiveness of the set parameters of transport by a belt conveyor and an iteration of the selection of sheet thickness and container profiles was performed. The strength analysis was performed using the finite element method, loading the structure with the pressure field generated in the analysis using the discrete element method. Rocky DEM and ANSYS Workbench Mechanical software were used for this purpose. The analysis was performed by engineering consultancy Caetica caetica.com as part of software tests in cooperation with company MESco sp.z o.o. mesco.com.pl – ANSYS Elite Channel Partner

Keywords: Finite Element Method FEM, Discrete Element Method DEM, bulk material, coupled analysis, Rocky DEM, ANSYS Workbench Mechanical

1.   Introduction

Construction works are often accompanied by the need to transport loose materials. These are for example gravel screening products or debris crushed in crushers which remained after the demolition of buildings. For the storage and transport of the aforementioned loose materials among others containers are used.

From the point of view of logistics on large construction sites, e.g. motorway construction sites, it is very important to properly design the process of loading and transporting containers in order to optimize the costs related to fuel and depreciation of construction machinery.  For this purpose the numerical analysis DEM (Discrete Element Method) coupled with the numerical analysis of the strength of the structure FEM (Finite Element Method) can be used. The aforementioned coupling uses the result of the DEM analysis, e.g. the distribution of forces or particle pressures, as a load in the FEM strength analysis. The leading software that can be used for this purpose is Rocky DEM and ANSYS Workbench Mechanical.

2.   Assumptions and the analysis goal  

The method of loading the aggregate was analyzed in terms of obtaining the answer whether the assumed loading time of 50 seconds with assumed particular mass flow is appropriate and whether the container is optimally filled. The goal was also to check how the loading proceeds for the assumed variants of the loading station, i.e. when the container vibrates in the plane of its floor and when it is stationary. The intention of the analysis was also to generate loads caused by the influence of loose material to the steel structure and to iterate the selection of sheet thickness for the assumed structure geometry, shown in Figure 1.

Fig. 1 Loading stand with a container

The loose material was mineral aggregate with polyhedron-shaped particles. The particles used were modeled in the Rocky DEM program. A single particle is shown in Figure 2 below.

Fig. 2 The shape of a mineral aggregate particle

Rocky DEM software allows to create particles of various shapes what allows to model many various issues.

3.   Results and discussion

For the assumed constant mass flow and the loading time of 50 seconds, the following container filling characteristics were obtained:

·         Stationary container

The curve below, shown in Figure 3, shows the characteristics of the change in the mass of the loaded aggregate while the container is still loading.

Fig. 3 The characteristics of the increase in aggregate mass in a stationary container during loading

During 50 seconds of the loading process, the stationary container held 13700 kg of aggregate. Figure 4 below shows the shape of the accumulation. Part of the aggregate leaked out of the container volume. Blocking of particles in the feeder was not observed during the analysis.

Fig. 4  50th second of  stationary container loading, absolute translational velocity

·         Container with a vibrating movement

The curve below shown in Figure 5 illustrates the change in the mass of the loaded aggregate during loading of the vibrating container in the plane of its floor.

During 50 seconds of the loading process, the vibrating container held 12,600 kg of aggregate.

Fig. 5 The characteristics of the increase in aggregate mass in a vibrating container during loading

Figure 6 below shows the shape of the formed accumulation, which is flatter and lower than in the case of loading a stationary container. Some of the aggregate also leaked out of the container volume. During the analysis with vibrating motion, blocking of particles in the feeder was also not observed.

Fig. 6 50th second of loading of vibrating container , absolute translational velocity

The reason for the addition of oscillating motion was the assumption that it will cause an increase in bulk density and to load more material. The assumed characteristics of the vibrating motion did not bring the desired results and reduced the loaded aggregate mass by over 1100 kg during 50 seconds of loading.

From the DEM analysis, the pressure distribution was obtained from the interaction of the loaded mass on the container steel sheets. For further analyzes, the pressure distribution derived from the case in which the container held more aggregate, i.e. 13700 kg, was used.

Rocky DEM can be configured as an ANSYS Workbench component in the Toolbox tree. Managing changes to the model is very effective and the transfer of pressure distribution from DEM analysis to static FEM analysis is easy. It is based on creating a connection between two programs. The connection operation diagram is shown in Figure 7 below.

Fig. 7 Transfer of pressure distribution from DEM to FEM in the ANSYS workbench window

Due to the coupling of the DEM + FEM software, the thicknesses of the sheets and profiles constituting the container frame were selected in a very short time based on the results of calculations of displacements and stresses in a linear static analysis.

For operational purposes, apart from the criterion of maximum allowable stress, an important aspect is also the level of maximum displacements. It was found that the maximum displacements in each direction should be smaller than the thickness of the sheets used. The obtained very small maximum displacements in relation to the sheet thickness and high stiffness of the structure allowed to avoid the need to perform nonlinear analysis [1].

After the optimization of the container sheets and profiles the maximum von Mises stress was obtained:   – Fig. 8

Fig. 8 Distribution of averaged von Mises stresses

The maximum vertical displacement of the floor plate was  – Fig. 9

Fig. 9 Vertical displacement –  Z axis

The maximum lateral displacement along the Y axis in the vertical walls of the container structure was   –  Fig. 10

Fig. 10 Lateral displacements – Y axis

The maximum longitudinal displacement along the X axis in the end plates of the container structure was   – Fig. 11.

Fig. 11 Longitudinal displacements - X axis

4.   Summary and conclusions

Thanks to the DEM analyzes, it was shown that with the assumed mass flow, the container is overfilled after a loading time of 50 seconds. Part of the aggregate falls out of the container both in the case of loading a stationary and vibrating container. Thanks to this, an important feedback was obtained about the need to verify the design assumptions in the construction of the loading station, i.e. in the selection of loading time, mass flow, the characteristics of motion of vibrating geometry, operation of the belt conveyor or positioning of the station. In turn, verification of the assumptions of the aggregate loading parameters will optimize the costs of the container design and aggregate transport.

References:
[1] Grzegorz Krzesiński, Tomasz Zagrajek, Piotr Marek, Paweł Borkowski, FINITE ELEMENT METHOD in mechanics of materials and structures, page. 216., OFICYNA WYDAWNICZA POLITECHNIKI WARSZAWSKIEJ, Warsaw 2015