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Introduction

When we drop a pebble into the sand on a beach, the pebble does not bounce very much, but sticks in the hole it made. When we pluck the pebble out, some sand may flow back into the hole, but the indentation largely remains. This simple observation illustrates two unique properties of granular materials.

The first property is that the contact between the grains is 'dissipative'. The thousands of grain-to-grain contacts dissipate kinetic energy rapidly. While the material of each grain is relatively elastic, the relative motions between the grains dissipate the energy so that the overall behavior is inelastic. The fact that the sand does not flow back to fill the hole completely illustrates the common occurrence in nature of granular arrangements which are local minima but which are far from the global minimum energy state. The dent in the sand remains, although lower energy states are available, because thermal vibrations are insufficient to drive the particles to the lowest energy state.

These two properties make the behavior of granular systems unique. While they exhibit some of the properties associated with the gaseous, liquid and solid-states of matter, the granular-state cannot be characterized by any one of them alone. Discrete Element Methods (DEM) captures the contacts between individual particles in an explicit manner. In contrast to continuum methods that smear out the individual particles into a smooth plenum, the discrete element method captures the individual geometry and dynamics of each particle, including the dissipative effects of contact friction.

Discrete Element Modeling

DEM's are a family of numerical modeling techniques designed to solve problems in engineering and applied science that exhibit gross discontinuous behavior. It should be noted that problems dominated by discontinuum behavior can not be simulated with conventional continuum-based computer modeling methods such as finite element or finite difference procedures. There are a large number of examples like geo-engineering problems dominated by discontinuum behavior.  These include: stability of underground mine openings, stability of rock slopes, micro-mechanical behavior of particulate media, and the flow of bulk solids.

Figure 1:  Examples of DEM granular material analysis

In simple terms, DEM explicitly models the dynamic motion and mechanical interactions of each body or particle in the physical problem throughout a simulation or time, and provides a detailed description of the velocities, positions, and force acting on each body or particle at a discrete point in time during the analysis.

The fundamental unit of a discrete element scheme is the single body or grain. In contrast to the finite element approach, which often assembles a global, functional for the total system, the DEM views the individual grain or body as the fundamental unit. Interaction with neighboring grains is achieved by replacing the contact conditions between bodies by external forces. All communication between bodies occurs through a boundary forces and not through a global stiffness matrix.

Modeling Conveyor Transfer Points

A transfer point is the location on a conveyor where the material is loaded or unloaded. A typical transfer point is composed of metal chutes that guide the flow of material. In most real life applications, problematic material flow conditions occur because the design of transfer points often rely on rule-of-thumb techniques and years of experience. This approach often leads to arcane solutions that require field modification and costly maintenance.

Figure 2:  Typical conveyor system and and transfer points

The DEM has been shown as an excellent computational tool for simulating the material flow in transfer points (See Figure 2).

One engineering design tool which now leads the way in bulk material handling analysis of transfers and chutes is a program called Chute Analyst, a software application which integrates the DEM and Computer Aided Design (CAD).  The results from a DEM model provide a detailed evolution of the particles motion, interaction forces and stresses over the duration of the analysis. These features make the DEM a very powerful tool for analyzing bulk material-handling problems as it explicitly models bulk material flow and its effects on the transfer and chute structural elements.

One practical use of this new integrated DEM/CAD technology in the field of bulk material handling is in the analysis and design of belt-conveyor transfers.

Three dimensional visualizations of the modeling results provide an overall feel of the flow behavior in the chute. Wear profile, moment arm, and lateral force diagrams give the engineer with a definable means of improving transfer station design. Bulk material transfer modeling is used to optimize material flow, minimize belt/chute abrasion, reduce dust and material degradation.

Figure 3:  Typical transfer point, an everyday solution guided by past engineering practices.

In the transfer point, the material particles are DEM modeled with a system of spherical shaped bodies that are representative of the overall behavior of the material. The material bodies can interact with other material bodies, with steel transfer point surfaces, and with moving rubber conveyor belt surfaces. The contact/impact phenomena between the interacting bodies are modeled with a contact force law, which has components defined in the normal and shear directions. The normal contact force component is generated with linear elastic restoring component and a viscous damping term to simulate the energy loss in a normal collision. The linear elastic component is modeled with a spring whose coefficient is based upon the normal stiffness of the contact bodies and the normal viscous damper coefficient is defined in terms of an equivalent coefficient of restitution.

Transfer Point DEM Goals

An ideal transfer point would be designed to:

• Load the material on the center of the belt
• Load material at a uniform rate
• Load material in the direction of belt travel
• Load material at the same speed the belt is moving
• Load after the belt is fully troughed
• Load material with minimum impact

At the same time, the transfer point structure has to prevent:

• Plugging
• Chute and belt wear
• Creation of dust
• Spillage

An ideal transfer point chute are very difficult to achieve by rule-of-thumb engineering, as most chute geometries are unique and cannot be tested at full-scale or optimized in a laboratory or workshop. As such, most users live with unfortunate problems which lead to high maintenance costs and retrofits. This is where Chute Analyst, and computer simulation of bulk material flow has become an important technical advancement.

Overcoming Belt-Conveyor Transfer Point Problems

Most of the major problems with bulk material belt-conveyor transfer points can be attributed to problems with the original design, field retrofits and the low priority given during the design process. It is common for the transfer point to be the last part of a belt conveyor system designed almost as an afterthought. Although the transfer point is a vital part in the control of bulk material flow. Some of the major problems that mines/plants have with transfer points are:

Plugging:  Plugging can stop an entire operation

Figure 4, Spillage and Plugging

Spillage:  Corrosion, extra cost of maintenance and most importantly safety.  MSHA stats report that half of all the accidents that occur around belt conveyors in mines are attributable to cleanup and repairs required by spillage and buildup.

Belt Wear:  Poor chute design can reduce belt life by as much as 75% and belting is the largest single cost of the conveyor system.

Figure 5:  Belt and chute wear/impact damage.

Chute Wear:  As conveyor throughputs become larger, the down time to fix and repair a chute will not only be a direct maintenance cost but a lost of production, directly impacting the output of the facility.

Material Degradation:  Leads to dust generation, reduction in the quality of the material and in some extremes the cause of a fire or an explosion.

High Maintenance:  This is probably the most forgotten aspect of the chute. It is something that is a bad by product of a poor design that most operators live with and just tend to write it off on the bottom line.

The Solution:  Designing with DEM

How do we go about designing and creating an "accurate virtual world model" of a transfer point with DEM?  The typical process or steps that a designer and/or engineer performs to retrofit an old or design a new transfer points are:

1. Render accurate 3-D CAD representation of old transfer or new transfer
2. Identify chute geometry restrictions and manufacturing limitations
3. Identify project goals (i.e. dust emissions, flow restrictions, etc)
4. Identify material properties and develop representative particle description
5. Make design changes to chute geometry with CAD
6. Simulate performance using Chute Analyst
7. Evaluate simulation results (reiterate steps 5-6-7)
8. Detail Design
9. Manufacture
10. Installation

A good example of a transfer chute retrofit project is at Freeport/McMoRan's Grasberg Mine in Indonesia. This existing chute had been in place and operating for several years. This application seemed to be a very simple chute that could have been successfully designed using rule's-of-thumb. However, the resulting transfer chute had a very poor operational performance history with high maintenance expenses.

The original geometry and overall chute layout is shown in the photos below.

Figure 6, Head pulley and receiving chute, prior to retrofit

As it can be seen the original chute was made up of two sections, the upper and lower chute.  The upper chute had a rock box in it that was used to protect the sides and front of the chute from material wear and at the same time redirect the material flow down into the lower chute.

The lower chute had a slanted side and a rock box as to protect the sides of the chute, with vertical sections that would mate with the skirting of the chute to help to center load the receiving belt-conveyor. It looks like a very straightforward chute with the angle between the incoming and outgoing conveyor of 130 degrees.

Figure 7: DEM model original geometry with material flow show, blue color designates higher velocity particles, red slower

The major problems that were reported by the mine site were as follows:

• The material was not center-loaded on the receiving belt conveyor 
• The receiving conveyor belt was wearing out in 3 - 4 months
• Extreme build-up of material in the chute, leading to plugging

Using our nine-step process, chute geometry was developed that met our design criteria. Below is the brief example showing a test case and the final chute geometry.

Figure 8:  Test case, slanted, rock-box slide             Figure 9:  Final geometry wire-frame

Figure 10:  DEM of final geometry                             Figure 11:  Installed chute discharge

Computer Simulations Work !

With the increase in complexity of conveyor systems, the ability to accurately predict performance is becoming increasingly important. One method of quantifying performance is to construct a numerical model or DEM. This can be done quickly and economically and the influence of various parameters can be determined.

Perhaps the greatest benefit that can be derived form the use of these tools, is the feeling an experienced engineer can develop by visualizing performance prior to operation. From this, the design can be made to minimize and even eliminate the unwanted behavior. In other words, eliminate as much of maintenance and retrofit costs, while increasing the over all reliability and availability.

Contact our author:

Mr. Greg Dewicki
Overland Conveyor Company, Inc.
12832 W. Asbury Place
Lakewood, Colorado 80228
Telephone:  303.716.0569
Email:  dewicki@overlandconveyor.com
Web site:  http://www.overlandconveyor.com/

Editor's Note:  Free Trial - Overland Conveyor Company offers BELT ANALYST II as a free download. This is the fully functional program that you can try for 30-days. At any time, this temporary license can be upgraded to a full unlimited working program by purchasing a license.  Visit their web site for details.

Help others by posting your comments, suggestions and experiences with bulk solids feeding or any other materials handling concerns you may have on our On-Line Help Forum.  For past Ask Joe ! Articles, visit the Ask Joe! Archived Articles.

Guest articles for the Ask Joe! Column are always welcome, for more information please contact Joe Marinelli directly at his email address:  joe@solidshandlingtech.com.