Pipe conveyor systems - an overview of its characteristics and current developments in research - Pijp-transportband systemen - een overzicht van eigenschappen en huidige ontwikkelingen in onderzoek

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Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

This report consists of 42 pages and 0 appendices. It may only be reproduced literally and as a whole. For commercial purposes only with written authorization of Delft University of Technology. Requests for consult are only taken into consideration under the condition that the applicant denies all legal rights on liabilities concerning the contents of the advice.

Specialization: Transport Engineering and Logistics Report number: 2017.TEL.8162

Title: Pipe conveyor systems - an

overview of its characteristics and current developments in research

Author: W.P.J. Vreeburg

Title (in Dutch) Pijp-transportband systemen - een overzicht van eigenschappen en huidige ontwikkelingen in onderzoek

Assignment: Literature assignment

Confidential: No

Supervisor: Dr. ir. Y. Pang

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Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl 2 Student: W.P.J. Vreeburg Assignment type: Literature assignment

Supervisor (TUD): dr. ir. Y. Pang (TU Delft) Creditpoints (EC): 10 Specialization: TEL

Report number: 2017.TEL.8162 Confidential: No

Subject: Overview of Characteristics and Current Developments in Research of Pipe Conveyor Systems

Belt conveyor systems find applications all over the world. In the past decade the development of conveyor technology has enabled the design and application of longer, faster and more efficient

conveyors with higher capacity and less environmental impact. Pipe conveyors are more and more used in various industrial production fields.

This assignment is to provide an overview of the current developments in research and the characteristics and applications of pipe conveyor systems based on worldwide literature sources. Both existing and the most recent under-construction projects will be surveyed. The survey of this literature assignment should cover the following:

 An overview of the working principles and components of pipe conveyor systems

 The application field of pipe conveyor systems (as compared to conventional conveying)

 The standards/norms and design considerations of pipe conveyor systems

 The current developments in research in pipe conveyor design

This report should be arranged in such a way that all data is structurally presented in graphs, tables, and lists with belonging descriptions and explanations in text.

The report should comply with the guidelines of the section. Details can be found on the website. The mentor,

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Abstract

This report made clear the potential pipe conveyor systems have to be a very powerful tool in bulk material handling. Pipe conveyor systems can provide significant improvements in many aspects over conventional conveyor systems, particularly in environmental protection and flexibility of route design. Due to the pipe conveyors enclosed shape, elimination of environmental contamination due to spillage and dust propagation can be accomplished. Its ability to negotiate tight corners and steep inclines can negate the need for expensive and messy transfer points and additional conveyors. Pipe conveyors are very compact in cross-sectional area, making the system also very suitable for application where space is limited, such as tunnels.

Standardization in the pipe conveyor system design is severely lacking, with only specialized companies offering design tools such as software applications. This can be disadvantageous for pipe conveyor system design, which requires the study of complex design considerations to ensure proper

functionality. For instance, transverse belt stiffness needs to be carefully selected to ensure a proper pipe shape of the belt. If the belt lacks transverse stiffness, the belt will collapse, causing alignment problems and possible damage and spillage. When the stiffness is too high, the belt will exert too much force on the idler rollers, causing extremely high power consumption of the system. Indentation rolling resistance is another design parameter that is attempted to be kept at a minimum to ensure low friction forces at the belt idler contact points.

A lot of research is performed in order to gain insight into these physical principles that govern the static and dynamic behavior of pipe conveyor systems. This is done with mathematical and numerical

modeling through FEM and DEM analyses, used in conjunction with newly developed experimental testing devices. This research and development will help in recovering its tarnished image as an

expensive and power hungry alternative to troughing conveyors. The range of the area of application for pipe conveyors is already very high, given it has the capability to negotiate tight corners and steep inclines, and will only increase with new developments that are announced as written in this report.

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Chapter 1 - Introduction

For more than a hundred years belt conveyors have been widely used for the transportation of bulk materials. Many advances in overland conveyor technology have improved its efficiency, investment and operational costs, making it a cheaper and more reliable alternative to conventional trucking for

instance in many cases. The overall design of conveyor belts however have mostly stayed the same.

1.1 Introduction to pipe conveyor systems

Pipe conveyor systems are an alternative design to conventional troughing conveyors, where the conveyor belt travels in a piped shape for most of its length. The design has been around since the 1980’s [2], but has remained far less implemented than conventional conveyors. Pipe conveyor systems can provide significant advantages in certain applications, such as a very secure protection of the bulk material due to its enclosed shape. It also has the ability to navigate much sharper turns and inclines, making it severely more cost-effective in applications where this is required. Without large scale implementation, the pipe conveyor system has no international industry standards for design.

1.2 Object of research and focus of report

In the past decade a lot of research has been performed on the design of pipe conveyor systems which could potentially drive an introduction of pipe conveyor standardization. Many research papers are published looking into improving the design to, for instance, increase the reliability, efficiency or sustainability of the system. The goal of this report is to provide a clear overview of the following aspects regarding pipe conveyor design:

 Characteristics  Application  Design

 Standards in design

 Recent development in research

The focus of the report lies on the design and recent developments in design and research on pipe conveyor systems. It explains the design considerations and the experimental setups, analytical and numerical tools used to research these design aspects. This research can ultimately improve the design of the system to become more efficient, cost-effective and environmentally friendly.

1.3 Report structure

The report in structured in a way to guide the reader through the process from understanding the pipe conveyor systems characteristics and working principles all the way to the recent research of detailed design aspects. This is done as follows:

Chapter 2

This first chapter gives a brief introduction on the working principle, components and operation of pipe conveyor systems. This chapter also provides an overview of the design historic development of the system in order to give the reader a sense of the considerations in the design process.

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Chapter 3

In this chapter the application field of pipe conveyors is summarized, as well as a thorough examination of the advantages and limitations of the system as compared to conventional conveyor design,

illustrated by several examples from the industry.

Chapter 4

In Chapter 4 the current tools and knowledge regarding design of pipe conveyors are described, which shows a lack of industry standards and provides argumentation for the importance of research on pipe conveyor system design.

Chapter 5

The research methodologies used to improve the pipe conveyor design are summarized in this chapter. Experimental, analytical and numerical methods are introduced to better understand the research that is performed on the system.

Chapter 6

Finally, an overview of the recent development in design of pipe conveyor systems is provided in Chapter 6, followed by the conclusions drawn from this report.

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Chapter 2 – Pipe conveyor system and operations

In this first chapter an introduction is given to the basics of how a pipe conveyor system works. Also the components of a pipe conveyor system are listed and explained. Furthermore, a separate subchapter is dedicated to the principle of belt alignment and finally the subject of monitoring and maintenance is handled.

2.1 Working principle

A pipe conveyor system is a type of conveyor belt system used to convey bulk solid material. As opposed to a conventional troughing conveyor belt, a pipe belt conveyor forms an enclosed circular shape for most of its length.

Figure 1: Conventional conveyor system setup compared with a pipe conveyor system, isometric and cross-sectional view (edited picture from [1])

After the material is loaded onto the belt through the loading chutes seen in Figure 1, several idler rollers, indicated in red, will guide the belt into a tubular shape throughout the length of the conveyor. The belt is unfolded in a similar fashion near the head pulley in order for the bulk material to be unloaded. On both the carrying and the return part the belt is folded like a pipe, which makes the pipe conveyor dust and spillage free. On the return side the overlap of the belt is on the bottom, but it is also possible to rotate the belt and fill it with material on the return side [14]. Material that manages to stick to the belt and fall off on the return side is caught within the belt until it unfolds. Spillage conveyors or screw conveyors can be installed underneath areas where the belt is unfolded and spillage occurs [2]. An effective and economical solution in the case of limited spillage is the installation of spillage plates [2].

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2.2 Components

In this subchapter the separate components of the pipe conveyor system are expanded on in order to gain insight into the components of the pipe conveyor system. The main components of a pipe conveyor system are:

 Rollers  Conveyor belt  Idler sets

 Head and tail pulley  Pulley drives  Take-up system

 Loading and unloading chutes

Apart from the first three components, most of these components are the same as in conventional conveyor systems. Information on these components is widely available, for instance in literature by Mr. G. Lodewijks [34].

Rollers

Throughout the length of the conveyor there are rollers installed that guide and support the belt in order to keep the belt in its desirable shape. Rollers are usually hollow cylindrical shells rotating around a steel axle with bearings on either end as shown in Figure 2 [13]. Also a seal cap is necessary to prevent dirt and dust from damaging the bearings. Rollers are fully

standardized in the industry and the dimensions come from international standards, which will be further explained in Chapter 4.

During the loading of the belt, the rollers need to be stronger to withstand the impact of the falling material. Usually a different type of idler is used known as impact rollers, which consists of several rubber donut-shaped discs along the roller axis. This again is an industry standard which stems from conventional conveyor systems.

After the belt is loaded, the belt goes gradually from a regular troughing shape to a piped shape. There are several idler frames with increasing troughing angle to start folding the belt. Once the belt needs to start its overlapping position, special finger shaped stub rollers can be used as seen in Figure 3[2].

Figure 2: An idler cut open to expose inner components (edited picture from [35])

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10 Belt

The belts used in a pipe conveyor system are very similar to those used in conventional troughing conveyors, consisting of a carcass and a cover layer on both sides. The carcass is the internal structure of the belt, which determines the tensile strength of the belt, and is made out of either steel cords

embedded in rubber or layers of reinforced fabric called ‘plies’ separated by cushioning layers [3]. Fabric reinforcements in the transverse direction are also present to get a specific transverse belt stiffness that is required for an application.

Again a lot of industry standards apply to belts and logically the greater the loads applied, the higher the tension needed in the belt, with steel cord belts being the stronger option. Above and below the carcass a protective, rubber cover is applied, which have different characteristics depending on the application of the conveyor system.

Figure 5: cross-section of steel cord conveyor belt for pipe conveyor systems[4]

One of the main differences with conveyor belts designed for the pipe conveyor system is that the side ends of the belt contains less reinforcement in order to lower the transverse stiffness on these side edges (see Figure 5). This is done to provide a smooth overlap when the belt is folded into a piped shape.

Pipe conveyor belts tend to have an overall higher transverse stiffness, since a regular belt would experience severe sagging at the top part of the piped shape after a while. In order to provide this transverse stiffness, special cross-rigid plies are implemented [2]. There is a difficult balance of how stiff the belt needs to be, since some flexibility for the transition from flat to pipe shape at the feed is also essential. This topic will be discussed further in the coming chapters.

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11 Idler sets

Once the belt is folded it is kept in a circular shape with a

supporting structure that holds six rollers in a hexagonal position, as can be seen in the cross-section in Figure 1. These rollers are mounted on a supporting frame placed alternatively on the front or the backside of the panel, as shown in Figure 6. The

construction of the panel which support the rollers is very simple and can be fabricated from rolled steel plates or pressed from sheet metal plates with jig drilled mounting holes generally in order to maintain roller mounting accuracy [2]. There are many different design options however for the supporting structure of a pipe conveyor system and nothing thus far has been standardized. Some design developments have been made which will be further discussed in subchapter 4.1.

2.3 Belt alignment

As with all belt conveyors, proper alignment of the belt is essential to prevent leaking of bulk material or damage to the belt and other components of the belt system. For a pipe conveyor system the overlap of the carrying side of the belt is at the top, as seen on the right in Figure 7 [3].

When the belt overlap starts to deviate from the proper alignment and starts to rotate towards the bottom, material can slip into the overlap causing spillage which is illustrated on the left in Figure 7. Usually after installation of a pipe conveyor system, the system is run past several alignment inspection checks under no-load conditions to see if belt training is required. Belt training is done similar to conventional belt system alignment, which is implementing training idlers at the source position of the misalignment. Training idlers are rollers placed at an angle (from a top view) from the direction of belt travel, causing the roller to push the belt to rotate. When the training idler is adjusted in a clockwise direction as seen from above, it will rotate the belt in an anti-clockwise direction (when viewed in the direction of belt travel), which is illustrated in Figure 9 [5].

Figure 6: Hexagonal idler setup with offset mounted on a frame[2]

Figure 7: Cross-section illustrating incorrect and correct belt alignment [3]

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12 The training idler arrangement is shown in Figure 8, which simply puts a regular idler onto a supporting bracket which can be bolted in different lateral positions. Training idlers are usually placed on the bottom idler, since it is the most supporting idler, giving it the biggest training adjustment effect. Adjustments in alignment are made in small increments, with a maximum of three or four adjacent idlers. The belt is then observed running for several minutes to allow the adjustment to take effect in order to prevent excessive adjustment of too many idlers. Finally tests are run with the belt partially loaded and eventually fully loaded to complete the training procedure.

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Chapter 3 – Pipe conveyor applications, characteristics and historic

design development

In this Chapter the application field of pipe conveyors is expanded on. This is done by comparing characteristics of pipe conveyor systems with those of conventional conveyor systems and seeing for which type of applications pipe conveyors can be beneficial.

3.1 Application field introduction

The pipe conveyor system is used around the world in a wide range of applications. The original technology of the pipe conveyor system was patented by the company Japan Pipe Conveyor (JPC) in 1978, which led to the first successful application a year after [5]. After some national implementations, the first License Partner of JPC to be successful in marketing the system outside Japan was Bateman in South Africa. Soon other successful JPC Agents Internationally followed, listed below.

Table 1: JPC Agents Internationally [5]

JPC license partner

Koch Noyes Nova Dosco Simplicity Krupp Robins

Young Poony

Sistemas

Country/Area Germany France Italy United Kingdom

India USA Korea South America To date we find that any material that can be placed on the pipe conveyor can be conveyed. The typical materials handled are:

 Ores  Coal  Coke  Limestone  Crushed stone  Shale  Overburden

Some of the more difficult materials that are being handled on the pipe conveyor are copper concentrate, petroleum coke, clay, flue dust, ready mixed concrete, sludge, humidified fly ash, coal tailings, alumina and filter dust.

In order to show in what type of application field the pipe conveyor system is used, it is helpful to look at the capabilities the system has as compared to conventional conveyors. Therefore the next subchapter shows their differences and provides examples of applications where this can be beneficial.

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3.2 Application field through characteristics of pipe conveyor system vs.

conventional conveyors

Pipe conveyor systems have a lot of potential to be a more cost-effective alternative to conventional troughing conveyors. In this subchapter a clear overview is given of the benefits and drawbacks to pipe conveyor systems [9][10][11][12] as opposed to troughing conveyors, which is finally summarized in an overview table.

Environmental protection

The two main advantages of enclosed conveying are the environmental protection it provides and the protection of the bulk material itself. Environmental pollution is minimized as spillage along most of the belt length is eliminated and the material conveyed is protected from wind losses, other unwanted weather effects such as rain or snow, and theft. Spillage on the return side is also eliminated, with the belt folding back into its enclosed shape. Steep inclinations

The closely packed material in the piped shape allows for more material friction, which allows pipe conveyors to negotiate steeper inclines and declines than troughing conveyors, of up to 30 degrees. This is shown in Figure 10 [4], where also can be seen pipe conveyors are applicable for a maximum lump size of 125mm at 1 m/s, as opposed to 300mm for troughing conveyors. Although its maximum capacity is less than half than that of troughing conveyors, the pipe conveyor has a much higher capacity than other enclosed conveyor types. Sharp turns

A pipe conveyor system has idlers constraining the belt on all sides and is therefore capable of

negotiating horizontal turns of much sharper radii, contrary to troughing conveyors. This can be a huge advantage, because it eliminates the need for transfer points. A single pipe conveyor with multiple curves can replace multiple conventional belt conveyors connected through transfer points. Not only is there no need for chutes, extra foundations and dust suppression equipment, but also additional conveyors, each with auxiliary equipment, can be omitted. With the absence of transfer points there is no dust propagation, no product degradation and perhaps most significantly no associated maintenance.

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15 Space savings

The cross-sectional area of a conventional troughing conveyor is significantly bigger than a pipe conveyor with the same capacity. Conventional conveyors can have a width of up to 3 times the length of a similarly performing pipe conveyor’s diameter. Consequently the supporting structure of pipe conveyor systems can be significantly smaller than troughing conveyors, making them ideal in

applications where space is limited. A good example of this is the world record holder for longest pipe conveyor belt at 16.4km, designed to run partially through a tunnel running underneath the streets of Lima, Peru (see Figure 11) [13]. This solution saved the city from a conveyor running through the city streets somehow or even worse, adding more truck-congesting traffic to the city roads.

The versatility of pipe conveyor routing in both turns and inclines and its relatively small cross-sectional size can not only save space, but also avoid some of the property rights and land permitting issues, which are becoming more important in an already increasingly crowded world.

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16 Cost savings

As mentioned earlier the flexibility of the pipe conveyor system in regards to turns and inclinations can greatly reduce environmental impact with making transfer points obsolete. Along with the piped shape causing a lack of belt edge damage and buildup on idlers [14], maintenance costs for pipe conveyor systems can be kept at a minimum. The absence of transfer points (see Figure 12) also cuts construction costs of the system significantly.

Drawbacks

The pipe conveyor system has several drawbacks when compared to the conventional conveyor system, however these often become manageable or even negligible in light of the large improvements the systems provides mentioned before.

As mentioned before capacity and maximum lump size limitations narrow the application field of pipe conveyors compared to conventional conveyors [4]. In pipe conveyor systems over-sized particles can become a much bigger problem with the limited space within the closed pipe in combination with steep inclines and sharp turns.

Another issue linked to this limit of space is overloading of the pipe conveyor [2], causing the entire system to get stuck, which can potentially inflict major damage to the entire system. Therefore the loading of the conveyor must be ensured to not exceed certain filling rates, depending on the design [2]. For the belt to properly overlap, the belt of a pipe conveyor has to be specifically designed as explained in Chapter 2.2. Also the belt of a pipe conveyor has to be wider than conventional troughing conveyors

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17 capable of conveying the same amount of material in order to accomplish this proper overlap, all

resulting in higher costs for belting [4]. However, other conveyor system components standardized in the conveyor industry such as idlers, bearings, pulleys, and take-up weights can be implemented in pipe conveyor systems [3].

A pipe conveyor has more idlers in contact with the belt than a troughing conveyor; both on the top side and the bottom return side. Since a pipe belt has a relatively high cross sectional belt stiffness to

prevent it from collapsing, the pressure exerted on these idlers by the belt is also greater than with troughing conveyors, as stated in [12]. This additional contact pressure causes additional indentation rolling resistance [12]. This additional pressure coupled with the multitude of idlers in contact with the belt translates into a higher power consumption required to move a pipe conveyor system than its conventional counterpart [12].

Finally, the engineering of a pipe conveyor system is more complex in general than a conventional conveyor. If a pipe conveyor system is improperly engineered such as a belt unfit for the system, the problems that can arise are difficult and costly to resolve. Coupled with the lack of design standards, there are few practitioners with good understanding and experience to properly design these systems, which could also increase the capital and maintenance cost of potential proprietaries. This is prone to change however, once advancements in pipe conveyor systems are made and become widely available through design standards.

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18 Overview table

All the benefits and drawbacks mentioned can be found in Table 2 below, serving as a comprehensible overview. It clearly illustrates the potential for pipe conveyor systems given the many advantages over conventional conveying. It also stresses the importance of research and development of pipe conveyor systems technology and consequently the introduction of design standards, both discussed in the coming chapters.

Table 2: Advantages and disadvantages of pipe conveyor systems, as compared to conventional conveyor systems

Advantages Disadvantages

Environmental  Spillage eliminated along belt length

 material protected from environmental effects such as rain

 Spillage eliminated even on the return side

 No transfer points required, eliminating environmental contamination through dust propagation typical at transfer points

 Higher power consumption

Characteristics for type of application  Steeper inclinations possible

 Sharper turns possible

 Smaller cross-sectional size, ideal for tunnel application for instance  No particle degradation typical to

transfer points

 Material can be transported both ways  Highest capacity possible of all enclosed

type conveyor systems

 Limited capacity compared to conventional troughing conveyor  Limited lump size compared to

conventional troughing conveyor

Costs  No transfer points

o Construction costs savings o No additional conveyors required o No spillage due to dust

propagation at transfer points o Dust cleanup savings

o Maintenance costs savings  Lower maintenance costs due to piped

shape (lack of belt edge damage and buildup on idlers)

 Higher operation costs due to high power consumption

 Potentially costly construction due to high level of understanding and

experience required by design engineers  Higher risk of expensive maintenance if

improperly designed, due to lack of design standards and technological development maturity

 Special belt design, wider and differing stiffness along its width

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Chapter 4 – Pipe conveyor standards and design

With the potential of pipe conveyor systems clarified in the previous chapter, underlining the importance of its technological research and development, it is useful to examine the current design standards and methodologies. Therefor all current design standards and considerations are explained in this chapter.

First a brief summary of the historic design development is provided to give some insight in the design considerations that are struggled with in the design of pipe conveyor systems. Afterwards, the lack of availability of pipe conveyor specific standards is discussed and some examples of solution methods for this problem are expanded on. In subchapter 4.3 an overview of basic design considerations for pipe conveyors is given, including guidelines for system parameters provided by CEMA and other sources. This will provide a good indication of the general magnitude of system characteristics and general design complications that could be improved with the research outlined in Chapter 6.

4.1 Historic design development

As stated before the design of the pipe conveyor system has not changed significantly since its original development. The changes that were implemented however proved of great use for the overall functioning of the system.

One of these changes has been in the hexagonal layout of the idlers. The original design had all six idlers at the same side of the support frame panel. With this layout the idler edges were so close together the belt could get pinched in between them causing belt edge damage (see Figure 13) and there was

unwanted interference between idlers [4][5]. This was solved by placing three idlers on either side of the panel, as can be seen clearly in Figure 6.

Another aspect of the pipe conveyor that has undergone some changes since its inception is the panel design which holds the idlers. The panel has been modified from a steel plate to a beam construction in order to decrease its mass, which reduces waste in construction materials and reduces the load bearing pressures on the supporting structure underneath. A comparison of an old and a newer panel design is displayed in Figure 14, where both new designs are developed by Ckit [3].

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20 One of the biggest design improvements in pipe conveyor history so far has been made by Mr. L.K. Nordell of Conveyor Dynamics Inc. A big criticism of the pipe conveyor system has been the relatively high power consumption required for the system to run. In 1996 a paper was published by Mr. Nordell examining the rubber rolling resistance in belt conveyors [7]. Although the paper seemed to focus mostly on the effects of different types of polymers on conveyor performance, renewing test methodology and in turn updating the CEMA standard calculations [8] used for this topic, another finding in the report had a significant impact on pipe conveyor systems. Supported by field

measurements, he concluded that the power drawn by a conveyor is related to the idler diameter and the resulting indentation by the idler on the belt cover. When a larger diameter idler is used, it can significantly reduce friction and therefore power consumption. Historically small diameter idlers were used in pipe conveying due to lack of space with six idlers on one side of the panel and due to most early pipe conveyors being in a low capacity and length range, making idler loads small. This, coupled with the fact that pipe conveyor systems already have significantly more idlers in contact with the belt compared to troughing conveyors, made the impact of this change significant.

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4.2 Pipe conveyor standards and design considerations

With troughing conveyor systems dominating the market for the past decades, it has gained an extensive repertoire of standards. In Europe ISO standards are widely used, with country specific prefixes such as NEN or DIN for Dutch or German norms respectively, whereas in the United States CEMA standards are used. Pipe conveyor systems have no official standards today, with most

production companies having their own design calculation methods. With the majority of calculations being quite similar to troughing conveyor systems, companies that have developed design calculation software for conveyor systems have expanded their programs with pipe conveyor calculation packages. Examples of this are BELTSTAT conveyor belt design software developed by Conveyor Dynamics, Inc. (CDI) [15] or Belt Analyst and Dynamic Analyst software developed by Overland Conveyor Co., Inc. [16]. This type of software calculates characteristics of pipe conveyor systems such as power requirements and tension forces for component sizing; but it also runs

simulations for analyzing conveyor controls for transient conditions such as starting or stopping belt conveyors. It should be noted however that these software applications are merely an extremely useful tool in designing a pipe conveyor system and that a good pipe conveyor design still requires a truly dedicated and preferably experienced conveyor belt manufacturer who can properly use this tool to its advantage.

With a lot of pipe conveyor designers keeping their design calculations close to their chest, some information can be found on how for instance Beltstat found a method of incorporating the more complex transverse belt stiffness determination for pipe conveyors into their software. Also Mr. F.J. Loeffler from Loeffler Engineering Group released a paper suggesting some alterations in the CEMA standards to fit pipe conveyor applications [17]. These are discussed in the following paragraphs, along with some design considerations.

Transverse belt stiffness

Pipe conveyors are more belt sensitive in their design than conventional troughing conveyors due to the effects of transverse belt stiffness. When the belt possesses enough stiffness in lateral direction (called transverse belt stiffness), it exerts a contact force on all the six idlers of a panel, as shown on the left in Figure 16. Through experience, pipe conveyor design engineers have found that it is very important for the belt to always maintain good contact with all the rollers, including the top idlers. If the pipe belt collapses, resulting in loss of contact with the top rollers (Figure 16, right), it can lead to belt twisting and rolling and perhaps not properly opening or closing. This collapsing of the belt is not only due to gravity, since horizontal and vertical curves also exert forces that try to pull the belt away from the rollers. This effect can also occur at a later stage in the belts operation due to a decrease in transverse belt rigidity over time caused by repetitive belt flexing.

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22 The intuitive solution seems to be to increase the transverse belt stiffness, but this creates other

significant operational problems in terms of power requirements. When the belt is very stiff in the transverse direction, it will put a lot of pressure on all the six idlers in the hexagonal shape (Illustrated as the forces 𝐹1to 𝐹6in Figure 16). This mechanism of the belt ‘self-loading’ has a very significant effect on

the power required to move the belt due to the added friction between the belt and all those idlers in the pipe conveyor system. Engineers have found that the power demand on empty or loaded pipe conveyors can sometimes show little difference. The belt stiffness design is extensively discussed in Chapter 5 and Chapter 6.

Despite much research into this topic discussed in further chapters, an open source solution to incorporate this into current standards such as CEMA or ISO is not yet available. Beltstat for instance uses a customized conversion chart to account for this effect where only the belt transverse flexibility is needed from the belt manufacturer. This belt characteristic can be obtained through an internationally standardized test method known as ISO 703:2007 [31]. In this test method, a piece of belt of length 𝐵 is suspended from its side edges by two clamps, and the depth of its sag caused by its own weight

is measured as 𝐹, as seen in Figure 17. The ratio of 𝐹/𝐵 describes the troughability of the belt. The Beltstat software incorporated a ‘Transverse Stiffness Multiplier’ to account for pipe conveyor system designs to account for its special belt transverse stiffness effect, shown in Figure 18.

Figure 16: Contact forces between belt and idlers with sufficient transverse belt stiffness (left), and insufficient (right) transverse belt stiffness (edited picture from [26])

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23 Friction coefficient

With pipe conveyor designs having a significantly higher amount of idlers in contact with the belt than conventional conveyor systems, the idler friction coefficients in power and tension calculations have to be altered.

An example of an alteration in the determination of the effective tension in the American standard CEMA is provided by Mr. F.J. Loeffler of Loeffler Engineering Group[17], who proposes to alter a seal and grease churning friction factor, 𝐴𝑖. This affects the value of 𝐾𝑥, which is the frictional resistance of idler

rolls to rotation and sliding resistance between the belt and the idler rolls [8]. The change proposed deals mainly with adjusting the CEMA equations to accommodate the following characteristic changes:

 Increased amount of rollers

From three to six on carry side and from one or two to six on the return side  Increased idler and bearing diameters

An innovation proposed by Mr. Nordell [7] (see subchapter 4.1)  Return side idler spacing change

From double idler spacing return vs. carry side on conventional conveyors to the same idler spacing return vs. carry on pipe conveyors

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24 Indentation rolling resistance

When a conveyor belt is rolling over idlers, the belt slightly deforms due to the rubber’s viscoelastic properties. After this deformation of the rubber in the belt bottom cover (shown in Figure 19), the carcass of the belt does not have enough time to

completely recover to its initial state, causing an asymmetric stress distribution between the belt and the idlers. The hysteresis energy loss that occurs is significant, since the indentation rolling resistance can account for approximately 60% of the total rolling resistance [12]. Since this phenomenon is closely related to the material properties of the belt, lots of potential for improvement is to be gained from adjusting the belt, which is expanded on in subchapter 6.2.[18]

4.3 Pipe conveyor design characteristics

In this subchapter design characteristics in the design of a pipe conveyor system are provided in no particular order, along with tables with general guidelines for design parameter values.

Capacity

According to [19], the pipe conveyor industry has agreed only on the nominal diameter of the pipe, while other parameters that contribute to the allowable capacity are determined by the pipe conveyor designer, working together with the belt supplier. These parameters [19] include

 Amount of belt overlap

 For smallest range pipe diameters: 3 to 4 inches (roughly 9 cm)  For largest range pipe diameters: 10 to 12 inches (28 cm)  Flat belt width

 Usually hard metric values

 Most suppliers will build in 2 inch (50 mm) pipe diameter increments with the actual flat belt width in 6 inch (150 mm) increments

 Belt width should accommodate approximately 20% overlap with the belt edges, meaning 𝐵𝑒𝑙𝑡 𝑤𝑖𝑑𝑡ℎ = 1.2 ∙ 𝜋 ∙ 𝑝𝑖𝑝𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟

 Actual pipe diameter

 Diameter inscribed in the hexagonal arrangement of idlers

 Will vary between manufacturers/designers as they adjust the belt width and overlap  Belt thickness

 Will have a slight effect on capacity, which is based on actual inner diameter of the pipe, not its nominal diameter

A guide to pipe conveyor capacities is given by CEMA, shown in Table 3. The allowable capacity values in Table 3 are based on roughly 75% of the cross-sectional area of the actual pipe inner diameter. If the material is very lumpy, the conveyor navigates very tight curves or the feed control is very inconsistent,

Figure 19: Cross-section of belt rolling over an idler roll, causing the belt to deform [18]

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25 this value is decreased to 60% or lower. If the opposite is the case, this value can go to approximately 80-85%. [19]

Idler selection

Idler roll size selection depends on several factors, of which the most important ones are the maximum load on the rollers (in turn depended on several other factors such as belt and material weight and dynamic effects) and belt speed. Roller diameters are considerable in size compared to conventional conveyors, due to significant power consumption benefits as discovered by Mr. Nordell [7]. Idler roll diameters run from 63 mm for a pipe diameter of 200 mm up to 194 mm rollers for pipe diameters of 850 mm [19]. As can be seen in Table 3, the largest pipe capacity is 2296 mtph, which would require this 194 mm idler size. To give an indication on the difference in size, a conventional three idler set

arrangement with a capacity of 6000 mtph requires one smaller standardized size idler roll diameter of 159 mm [19].

Belt speed

To compensate for a relatively small allowable cross-sectional area, pipe conveyors are often designed to run at higher speeds than their conventional counterparts [19]. Over most of the pipe conveyor’s length this is not an issue due to its enclosed shape, but at the tail end loading zone and the head end discharge zone this high speed can affect the material [3]. This negative effect of these short open sections in the pipe conveyor system has to be taken into account in the choice of belt speed. Actual belt speeds of pipe conveyor systems run from roughly 2 m/s for small pipe diameters up to 5 m/s for a pipe diameter of 850 mm [14][16][19]. Speeds of 6 m/s or even higher are possible, but might not be practical [3].

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26 Lump size

In pipe conveyor design caution needs to be exercised when considering maximum allowable lump size. On a conventional conveyor large lumps can roll to the side of the belt or even off onto the ground, but in a pipe conveyor this kind of lump is trapped by the belt. This can cause severe damage to the belt, idler rolls and the structure. The lump size of the bulk material to be conveyed is therefore a much more important design characteristic than with troughing conveyors.

For pipe conveyors the general rule found in design literature such as [2][17][19] is to never exceed a lump size of 1/3 of the pipe diameter when conveying at the conventional 75% cross-sectional filling rate. While this is generally true, the maximum lump size depends heavily on the percentage of lumps [19]. When the material to be conveyed has a high percentage of lumps, the ratio of maximum lump size to pipe diameter should be closer to 1:4 [19].

Pipe opening and closing

The folding and unfolding of the belt at the head and tail ends of the pipe conveyor causes additional loads on the belt and idler rolls [2]. The longer the pipe conveyor, the less significant this impacts the power calculations [19]. This is however an effect that is not present in troughing conveyor power calculations and should be included for an accurate design. The transition distance from head end to piped shape or from piped shape to tail end is dependent on the pipe diameter. An indication of this transition distance is show in Table 6 [19].

Loading and overfilling

To ensure a proper folding of the belt around the material that is loaded onto it, loading the material in a central line is required to obtain proper alignment [2]. Arguably more important is to maintain a constant filling rate of the pipe conveyor belt. For these reasons a pipe conveyor belt will typically be loaded using a feeder and not directly loaded from a bin or hopper gate [2].

Deviations in the filling rate could cause overfilling, which could potentially have detrimental consequences. An overfill condition sensor should be installed at the loading area to shut down the conveyor in the event of excessive peaks [19].

Idler panel spacing and curve analysis

The allowable idler panel spacing for pipe conveyor systems depends on various characteristics, of which the most important are [19]:

 Pipe diameter  Belt construction  Local belt tension

 Pipe sag in between panels  Material and belt weight  Curve radius

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27 Table 4: Idler panel spacing guideline for pipe conveyors for pipe diameters and material bulk density

Pipe conveyor systems with larger pipe diameters force the designer to increase the belt’s longitudinal bending stiffness, allowing it to resist the forces causing belt sag in between panels and preventing the belt from unfolding. In turn this can allow for larger idler panel spacing. Heavier material in the pipe conveyor exerts a higher force on the pipe conveyor in horizontal direction, causing the overlap to slip and unfold the belt at the top. This is prevented by shortening the idler panel spacing. A preliminary guideline to idler panel spacing for pipe conveyor systems is provided by CEMA, shown in Table 4 [19].

Idler spacing is vastly different in curved sections of a pipe conveyor’s trajectory due to additional forces exerted on the belt and idler rolls mainly. With the addition of these forces, it is necessary to decrease the idler panel spacing, which is expressed as a percentage of the regular idler spacing depended on the type of curve and type of belt, as shown in Table 5 [17].

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28 This is again just an indication however, since factors like belt tension can influence the idler panel spacing in curves as well. Curves near the head end of the conveyor system will exert a greater force on the idler rolls than curves near the tail end for instance. Pipe conveyor drag is increased through every curved section of a pipe conveyor’s trajectory, also influencing the power calculations and therefore the design. The design of belt curves can be quite complex, but a rough indication of possibilities and limitations of curves in pipe conveyor systems is shown in Table 6 [2]. It shows a maximum curve radius for small to midsize pipe conveyors, dependent on the pipe diameter 𝐷, for different sizes of curves and different belt materials.

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29

Chapter 5 - Research methodology

It is clear that pipe conveyor systems are potentially superior to troughing conveyors for many applications. However, the amount of implementations is lacking due to its complexity of design, absence of sufficient research and development and a bad reputation, amongst other reasons. Proper research and development into pipe conveyor systems will cause an introduction of standardization and a wider implementation of the system in the industry, which in turn will make the bulk handling industry more environmentally friendly.

Before the recent development and research into pipe conveyor systems is expanded on, first a brief look into the research methodology that is used in this field is given. First a guide to most experimental testing that is performed in recent years to study static and dynamic behavior in pipe conveyors is given in subchapter 5.1. For the sake of clarity some of the research results are already discussed in this subchapter. In subchapter 5.2 the different mathematical models and accompanying numerical software that is used to verify the findings of experimental results are briefly summarized.

5.1 Test rigs

The experimental research on pipe conveyor systems focusses mainly on examining the contact forces between the belt and idler rollers, because this is an area where a lot of design improvements can be made. Examples of this are the optimization of the transverse belt stiffness or minimization of the indentation rolling resistance (see subchapter 4.2). To validate the mathematical models that describe the physics behind these theorems, which will be discussed in subchapter 5.2, it is vital to have properly calibrated testing devices.

Testing devices for pipe conveyor systems are not only for fundamental research, but also important to check the quality of the products on the market. With a lack of standardization in pipe conveyor systems, owners have to rely on the manufacturers to provide quality components, which could be of questionable quality. Sadly there are also no universal standards in place for testing devices and their configuration, which can lead to misinformation on performance and reliability parameters of pipe conveyor system components when results are compromised due to an improper test configuration or measurement errors. Below are several of the existing testing devices currently used and some of their advantages and disadvantages are shown, along with some of the yielded results[20][21][22].

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30 Six-point pipe belt stiffness testing device

Several belt manufacturers and universities have made a so-called six-point bel stiffness testing device [20][21][22][23] (see Figure 20) to test belts for their ability to keep and maintain their piped shape and to determine the contact force it makes with idler rolls. It consists of six plates equipped with force sensors, placed in a hexagonal shape. A short cutout of a piece of belt, a belt sample, is placed folded in between these plates. The plates are fitted with foil paper to eliminate unwanted friction forces and their position is adjustable to fit different pipe diameters.

The test rig can be used successfully, together with the troughability test (Figure 17), to identify a belt’s ability to form a stable pipe for conveyors with different transverse bending stiffness, pipe diameter and rate of overlap. It is a cheap and relatively simple testing device, but is very limited in its application. Although the ability to study effects of curved sections by applying lateral forces on the belt samples in the test rig has been tried, accurate

measurements or studying of belt buckling and twisting tendencies at spatial curves are lacking with this device. Also the impacts of bulk material inside the belt or dynamic effects are not an option to study using this test rig.

Static test rigs

In order to examine belt behavior on its longitudinal axis a larger test setup is required. This could allow for analysis of effects like longitudinal belt twisting at spatial curves or belt buckling under different belt tensions. Static test rigs will clamp a piece of belt of several meters in between multiple hexagonal idler roll panels, of which the middle panel is equipped with sensors to measure the contact forces. Most test rigs possess the ability to adjust the belt trajectory to measure contact forces in curves. Belt tension is varied by adjusting tension at one clamped edge using for instance a hydraulic press. To reduce belt edge friction at the belt overlap, which could influence the results, a Teflon foil can be used.

An overview of three static test rigs with their corresponding characteristics and goals of research are presented in Table 7.

Results of current static test rigs can deviate significantly, depending on its configuration. This signals a need for the development of a uniform standard regarding proper test rig configuration for pipe conveyors.

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31 Table 7: Overview of three static test rigs and their characteristics [21][32]

Picture

Assembly and/or testing by

Ckit Johannesburg, South Africa & TU Delft

TU of Košice, Slovak Republic [32] Phoenix conveyor Belt Systems and ITA at Leibniz University, Hannover

Layout Five metal frames with idler stations enclosing a 12m steel cord belt sample

Flat belt clamped on one end and three idler station with static rolls enclosing

Special modular and telescopic frames with five idler stations

Goal •Investigate belt deformation at curves •Deflection in between idler stations •Contact forces on the bottom idler roll at

various testing conditions

•Investigate contact forces at formation section of belt into piped shape

•Investigate belt deformation at curves •Deflection in between idler stations •Contact forces on the bottom idler roll at various testing conditions

Clamping method

Stripping edges of belt apart from the steel cords, which are clamped by a disk attached to a hydraulic jack at one end to apply tension (0 to 60 MPa)

Fabric belt clamped between plates with tightening bolts through the belt on either side

Hydraulic cylinders attached to replaceable mounting disks. Disks designed to fit specific steel cord belt, with precise pipe diameter and location and size of steel cords

Geometric adjustability

•Inclines with curve radii of up to 169m with shaft connection at bottom of frame and steel plates inserted at top connection of frame, lifting frames with hydraulic jack

•Overlap at top or bottom by rotating the clamp disks

•Belt tension adjustable

•Adjustable pipe diameter using screw rails on each of the six static rolls per idler station •Belt tension adjustable

•Belt tension adjustable, even in specific steel cords

•Idler spacing adjustable between 1 and 2m •Curve adjustability in vertical and horizontal planes with minimum radii of 50m

•Idler roll arrangement from one side to double side

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32 Results Proven to be a valid testing method to

investigate curve deformation and contact force determination when keeping drawbacks and limitations in mind. Validated using FEM

Some negative values in force which is not possible according to theory, caused by improper sensor calibration or

measurement procedure error

Provided similar results for three identical belt samples. Could potentially be used to test different belt types

Advantages

•Predict buckling and twisting tendency of belt specimen of the actual size at spatial curves •Testing possible with many variables such as

- Pipe diameter - Route curves - Belt types

- Belt tension, even of steel cords individually - Idler station pitch

- Idler roll arrangement

•Possibility to study the time effect and viscoelastic properties of the belt on its performance

General drawbacks of static test rigs

•Significant space requirements •Heavy and bulky test rig •Expensive

•Difficulties in eliminating effects of initial belt deformation

•Extensive time required to replace belt samples and adjust variables

•Belt sample needs to be of considerable length to eliminate impact of the fixed edges •No dynamic effects analysis possible

Drawbacks / limitations specific to test setup

•Measuring cells only in radial direction, impact of friction forces not considered or controlled

•Presence of relaxation effect in the belt, affecting the results

•Modelled inclination curve radii could be affected by vertical sag of heavy test rig frame

•No horizontal curves possible

•Lack of variables such as pipe diameter and pitch between stations

•Uneven tension in belt due to only partially clamping along belt width

•Produces inaccurate results

•Each belt sample requires manufacturing a specifically matching mounting disk

•Also used to test bulk material impact using piped shaped water tanks, which does not match reality. It does not reflect impact of the internal friction

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33 Figure 21: Dynamic test rig at the Institute for Materials-Handling Technology and Mining Machinery of

the University of Hannover in 1995 Dynamic test rigs and field tests

Dynamic test rigs are the closest possible replication of pipe conveyor dynamic behavior in industrial installations and therefore can be a valuable tool in optimizing pipe belt performance. Different dynamic test rigs have been made, since there are no standards for pipe conveyor testing methodology. From a simple setup of a clamped piped shape belt with a set of idler panels moving along the pipe length[33], to a whole pipe conveyor system tens of meters in length. An example of the latter is the dynamic test rig installed at the Institute for Materials-Handling Technology and Mining Machinery of the University of Hannover in 1995, shown in Figure 21. An idler station in the middle of the conveyor has multiple types of sensing equipment to measure radial and longitudinal forces of all six idler rolls and a steel cable arrangement that detects twisting torque in the belt. The test rig enables a variation in curve radius, conveyor speed, idler spacing, belt tension, a range of pipe diameters and the possibility to perform measurements on a belt loaded with bulk material.

Reported results from the dynamic test rig in Hannover were that the total vector sum of the radial contact forces are affected by the variation in belt speed, idler spacing and belt tension. The load distribution between the idler rolls did not change with the variation of these parameters however. Another possible way to study the dynamic behavior of pipe conveyor systems is to perform

measurements on working pipe conveyors on location. This is done by dismounting idler rolls from their panel and replacing them with units equipped with sensing devices. Each of these idler rolls has

calibrated force transducers installed in the brackets at both sides of the roll shaft. The sum of the forces from both transducers represents the total contact force on the corresponding roller. To properly position the idler rolls on the measuring idler panel, it is a possibility to use cords over the adjacent

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34 panel rollers for alignment. The belt speed can be measured by placing a rotary wheel encoder on the belt somewhere between two panels.

Results obtained from field measurements include a possible link between contact forces and exploitation time of the pipe belt. Particularly, the longer the belt is in use, the smaller the contact forces are that it generates. This can be explained by the belt rubber viscoelastic behavior and the Mullin effect, which is a type of stress softening in rubber. A long exploitation time of the belt leads to a decrease of the effective modulus of elasticity.

Results obtained by several dynamic test rigs examined by MSc. Maria E. Zamiralova at the TU Delft appeared to vary significantly. However, some similarities in the contact forces results were found. With the belt overlap at the top, the three most repeatable patterns are:

1. All the idler rolls are in contact with the belt, with the highest forces being in the bottom roller and the lower left and lower right roller

2. Contact loss of the belt at one of the top idler rolls, most frequently the top right roller (when the belt is folded left edge over right edge, see the belt in Figure 16 on the right for instance) 3. Contact loss at the top left and top right idler rolls, with a significantly large force at the top roll In case of the belt overlap located at the bottom, the bottom roller suffered a dramatic load increase with minor contact forces at the lateral rolls.[22][23]

Steep angle conveyor test rig

A research and development consortium founded by Contitech, Siemens, and Thyssenkrupp is

developing a high incline pipe conveyor with angles from 30 to even 45 degrees [24]. With the possibilty of the material rolling down through the pipe belt, special chevron ribbing patterns are applied on the carrying side of the belt to prevent this occurance. A test rig will be developed shown in Figure 22 to examine the bulk behavior under different design parameters.

This rig will enable analysis of the impact of dynamic effects caused by the belt running across the idler stations as well as the effects of different chevron ribbings, conveying materials and properties, granulations, and more. The time at which sliding starts from a relevant inclination for the coarse bulk material compared to fine-grained materials in commercially-available pipe belt conveyors is

considered valuable information for

future development. Figure 22: Model of Megapipe test rig to be build to test inclination angle effects [24]

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35

5.2 Numerical modeling

Mathematical models are necessary to understand the physical principles that are used in improving the design of pipe conveyor systems. A lot of mathematical theorems already exist for conventional

conveying and can be adjusted for pipe conveyor system calculations. Once a model is validated using experimental results, numerical models can be made in accordance with these mathematical models and be validated by them. Numerical models can therefore be extremely useful in preventing tedious and time consuming hand calculations. A brief introduction in the software required for this type of analysis is provided in this subchapter before these models are expanded on for pipe conveyor research in Chapter 6.

Finite element method (FEM)

Finite element method (FEM), also referred to as the finite element analysis (FEA), is a numerical

method for solving analytical problems with differential equations with a set of corresponding boundary and initial conditions. Commonly used software packages include ANSYS and Abaqus [25][26]. First a solid geometry model can be created defined by volumes, area, lines and keypoints or it can be

imported from other software such as CAD. These solid models are then meshed, which is the ‘filling’ of the model with nodes and elements, through which the calculations will be performed by the software. Finally after including every material property, the model can be loaded with different types of forces and the software runs these through every node and element and provides a usually colorful solution of the loads and stresses the model is subjugated to, seen in Figure 25.

Discrete element method (DEM)

The structure and components of a pipe conveyor system can be modeled and exposed to loads, but this does not accurately portray the bulk material load and behavior. This is where discrete element method becomes useful. DEM is a tool used to model individual particles, their contact with each other and with the environment, which in this case is bulk handling equipment. Where FEM considers the material as a continuum divided into a mesh to solve continuum equations, DEM is a particle based method that considers the particles as a modelling entity. In DEM software like EDEM, first particles are modeled and calibrated by adjusting all particle properties such as lump size and shape or friction forces. An example of the detail with which particles are simulated to provide accurate simulations is shown in Figure 23. Then they can be rendered in bulk and interact with a geometric model such as a pipe conveyor belt. DEM software like EDEM can be used in conjunction with FEM and is therefore extremely useful in studying bulk behavior and simulating real life scenarios for pipe conveyor configurations. An example of this coupled analysis is

shown in Figure 23 (right)[25], which will be discussed in Chapter 6.

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36

Chapter 6 – Recent development and research

In this report all the inner workings and components that make up a pipe conveyor system are made clear. Also the potential for the system being superior to conventional conveying methods is sufficiently argued. After providing an explanation of the design considerations and the lack of standardization, it is clear that current research and development can provide a solution to its lack in implementation. Several experimental testing devices and accompanying verification and analysis software is expanded on, some current topics of research papers that aim to improve pipe conveyor system design are discussed in this chapter.

With the importance of optimizing the transverse belt stiffness stressed in subchapter 4.2, first the recent development in establishing a universal model that determines this stiffness and that examines the troughability of a pipe conveyor belt is explained in subchapter 6.1. Next examples of research performed in the study of the contact forces between belt and idler rolls in a pipe conveyor system using coupled FEM and DEM analyses are given in subchapter 6.2. Subchapter 6.3 shows, by example, a study that constructs a mathematical model for the determination of indentation rolling resistance specific to pipe conveyors. These types of models are crucial in the development of design

improvements in pipe conveyor systems. Most of these improvements are in the optimization of the belt material characteristics, of which many are listed in subchapter 6.4.

6.1 Pipe troughability

In the bulk conveyor industry the only standardized method that reflects in some way belt bending stiffness in lateral direction is the troughability test ISO703 (Figure 17). For pipe conveyors no standard exist for this stiffness to ensure a well-sealed pipe shape. Besides the software tools like Beltstat mentioned in subchapter 4.2, other researchers are proposing new mathematical models to be used as a uniform validation technique for numerical models. Maria E. Zamiralova of the TU Delft published a paper, among others, that describes such a mathematical model, including verification through both FEM modeling and experimental tests using the six-point belt stiffness testing device. In order to study the ‘pipe-ability’ of a pipe conveyor belt, the contact forces (or lack thereof) are a good indicator to confirm a proper pipe shape.

Mathematical model for contact forces

Mathematical models that calculate the contact forces of pipe conveyors have been described in multiple studies, where many simplifications have been assumed in their analytical approach. Maria E. Zamiralova [26] formulated a 2D mathematical model that substitutes the contact forces with movable hinge supports with one reaction force, as shown in Figure 24. To imitate the load due to belt bending stiffness, a bending moment, 𝑀𝑏𝑠𝑡, is placed

at both belt edges, where also an axial force 𝑁′1is present. To

incorporate the stresses a belt is subjected to when bent into a piped shape from a flat stress-free state, a radial expansion load

𝑞_𝑠𝑡 is added. This stress that is evenly distributed along the belt Figure 24: Mathematical model of contact forces [26]

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37 cross-section geometry is not illustrated in Figure 24. Finally, 𝑞𝑏𝑤 as shown in Figure 24 is the weight of

the belt that is incorporated in the model. Bulk material weight is not incorporated in this analytical model. This model can be classified as statically indeterminate to the fourth degree and is solved using the Force Method.

Universal numerical model

Zamiralova [26] made two numerical models (Figure 25) using ANSYS and validated them with the mathematical model explained above. With given throughability data of a belt (using standard ISO 703), an effective modulus of elasticity can be quantified. The method used for this is restricted to small strains which will not exceed 5%, which is the case for pipe conveyor belts that get formed into a pipe shape under normal operational conditions. This means that the modulus of elasticity determined from the troughability test can be applied for quantifying the contact forces. With these contact forces quantified, the throughability of a pipe conveyor belt

can be determined, which is extremely useful in pipe belt design. Finally the impact of belt line mass is investigated together with the modulus of elasticity, from which the conclusion could be drawn that for a heavier belt, the bending rigidity needs to be higher in order to maintain pipe throughability.

6.2 Coupled FEM/DEM analysis

This subchapter gives two examples of coupled FEM/DEM analysis performed to study pipe conveyor systems.

Contact forces in loaded pipe conveyor Research financed by the Australian

Research Council and Longking Bulk Materials Science and Engineering Co. proposed a coupled FEM and DEM analysis of pipe conveyor systems to determine the load distribution of contact forces under different load conditions, i.e. zero gravity, empty pipe, and filling rate of 40% and 80%[25]. The belt is modeled in FEM as an orthotropic elastic shell, whereas the rollers are treated as rigid shells. The data for the numerical model used is taken from a paper by Zamiralova performing tests with the six-point

Figure 25: One of the FEM models created using ANSYS [26]

Figure 26: Coupled FEM/DEM simulation of a finite-length model pipe belt conveyor