Bucketwheel stacker/reclaimers: an analysis of stacking/reclaiming methods

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Delft University of Technology

FACULTY MECHANICAL, MARITIME AND MATERIALS ENGINEERING

Department Marine and Transport Technology 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 35 pages and 8 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: 2012.TEL.7724

Title:

Bucketwheel stacker/reclaimers:

an analysis of stacking/reclaiming

methods.

Author:

K. C. van Horssen

Title (in Dutch) bucketwheel in- en afslag machines: een analyse van de storten afgraafmethoden.

Assignment: literature assignment

Confidential: no

Initiator (university): prof.dr.ir. G. Lodewijks

Initiator (company): ir. D. Mooijman (EMO, Rotterdam) Supervisor: ir. T. van Vianen

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Delft University of Technology

FACULTY OF MECHANICAL, MARITIME AND MATERIALS ENGINEERING

Department of Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

Student: K. C. van Horssen Assignment type: Literature

Supervisor (TUD): Ir. T. van Vianen Report number: 2012.TEL.7724 Supervisor (Company): Ir. D. Mooijman (EMO)

Specialization: TEL Confidential: no

Creditpoints (EC): 12

Subject: Stacking and reclaiming methods

In dry bulk terminals, materials are temporarily stored in piles at the stockyard. For each type of material, a separate pile is formed. Huge machines stack the materials and mostly these machines are also equipped with a bucket wheel to reclaim the materials afterwards, see for example Figure 1 which shows two reclaiming bucket wheel stacker-reclaimers at the EECV terminal in Rotterdam.

These machines are able to luff the boom, slew the boom and

drive parallel to the stockyard piles. Based on combination of these rotations or movement, there can be derived several methods to stack or to reclaim materials. This literature assignment focuses on investigating existing stacking and reclaiming methods, generate alternative methods and evaluate all methods.

• Investigate and describe existing stacking and reclaiming methods based on literature but also based on practical experience of the EMO terminal in Rotterdam.

• What are the constraints; like the minimum and maximum stacking height, the maximum area pressure, width of the stockyard lanes, etc.

• Investigate and calculate other stacking and reclaiming methods and define selection criteria’s (f.e. energy consumption, reliability, surface occupation, productivity of the machine, etc.) to evaluate the different methods.

• Evaluate the different stacking and reclaiming methods

It is expected that you conclude with a recommendation for further research opportunities based on the results of this study.

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

Prof. dr. ir. G. Lodewijks

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Summary

Open storage of bulk solid material is mostly done in stockpiles. The material will be stored with a stacker, sometimes in combination with wheel loaders. To reclaim the material a reclaimer is used. Those two machines are often combined into one machine; a stacker/reclaimer. One of the most common stacker/reclaimer types is the bucket wheel stacker/reclaimer

There are different possible methods to store and reclaim bulk materials with those bucket wheel stacker/reclaimers.

The five most common methods for stacking are: • Cone-shell

• Chevron • Strata • Windrow • Advanced block

The four most common methods for reclaiming are: • Long travel

• Bench reclaim • Block reclaim • Pilgrim step

With the last 3 reclaim methods, the reclaimer uses a slewing movement during reclaiming. For the long travel method the travel movement is the most used movement of the machine.

The selection for a stacking method is normally based on the required blending efficiency. Whereby the cone-shell has the lowest blending efficiency and windrow the highest.

If the blending efficiency is an important selection criterion for the stacking method, then the selection of the reclaiming method will be based on the stacking method to avoid abolishing of the blending efficiency.

When blending is not important, than the capacity of a reclaim method is an important selection criterion. This capacity depends on the dimension of the stockpile.

At reclaim method the stockpile will be reclaimed in slices. The capacity can be calculated by determining the dimensions of those slices. This can be done in two manners:

1) The current reclaim capacity (Q [m3/s]) can be determined for a specific position and time with the cross sectional area of the slice at that point (A [m2]) multiplied with the current velocity (v [m/s]).

v

A

C

=

*

2) The reclaim capacity (Q [m3/s]) of each slice can be determined by: determine the volume (V [m3]) of each slice en divide it by the time (∆t [sec]) wherein the slice is reclaimed.

t

V

Q

=

_∆

When the reclaim velocity is inversely directly proportional with the cross sectional area of the slice results this in a constant capacity, which is shown in the figure below for a slewing reclaim method.

Capacity 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 Slewing angle: θ [o_] Q ( m 3/s )

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Summary (in Dutch)

De openopslag van stortgoederen wordt veelal gedaan in grote hopen. Deze hopen worden gestort met een opslag machine (stacker), al dan niet ondersteund door laadschoppen. Het afgraven wordt gedaan met een afgraafmachine (reclaimer). Veelal worden deze twee machines gecombineerd tot één machine; een stort- afgraaf machine (stacker/reclaimer). Één van de meest toegepaste varianten hiervan is een graafwiel stacker/reclaimer.

Om met deze graafwiel stacker/reclaimer stortgoederen op te slaan en af te graven zijn verschillende methodes mogelijk.

De meest bekende opslag methoden zijn: • Cone-shell

• Chevron • Strata • Windrow • Advanced block

De meest bekende afgraafmethode zijn: • Long travel

• Bench reclaim • Block reclaim • Pilgrim step

Hierbij wordt bij de laatste 3 afgraafmethode gebruik gemaakt van de zwenkbeweging van de graver en bij ‘long travel’ van de rijdende beweging van de gehele machine.

De keuze voor een stort methode wordt veelal gebaseerd op het meng effect. Waarbij cone-shell het laagste meng effect heeft en windrow het meest van de bovengenoemde stort methode.

Wanneer bij het storten het mengen van belang was, dan is bij de keuze van de afgraafmethode meestal de stortmethode de basis van de keuze, om te voorkomen dat het meng effect niet teniet gedaan wordt.

Als het mengen van product niet belangrijk is, dan is de capaciteit van de methode bepalend voor de keuze van de afgraafmethode. Waarbij de afmetingen van de hoop zijn van invloed op de capaciteit. Bij elke afgraafmethode wordt de hoop in sneden afgegraven. Met het bepalen van de afmetingen van de sneden kan de afgraafcapaciteit bepaald worden. Dit kan op twee manieren:

1) De lokale capaciteit (Q [m3/s]) op een bepaald punt (bepaald hoek) kan bepaald worden door doorsnede (A [m2]) van snede op dat punt te vermenigvuldigen met de lokale snelheid (v [m/s]).

v

A

Q

=

*

2) De capaciteit (Q [m3_{/s]) per snede kan bepaald worden door: het volume (V [m}3_{])van de snede te}

bepalen en te delen door de tijd waarin een snede afgegraven wordt (∆t [sec]).

t

V

Q

=

_∆

Wanneer de snelheid van afgraven omgekeerd evenredig is met de doorsnede van de snede resulteert dit in een constant afgraafdebiet. Zoals in onderstaand figuur afgebeeld voor een afgraafmethode met zwenkbeweging

Capacity

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Slew ing angle: θ [o_]

Q

(

m

3/s

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1 Introduction

A dry bulk terminal is used for the transshipment and storage of several bulk materials like coal, ore, and agriculture products. It is a buffer between incoming and outgoing bulk materials.

This research analyses the different methods to stack and reclaim materials on an open storage. 1.1 Stacking and reclaiming

Stacking is the process where bulk material is added to a pile. This pile can

be made longitudinal or circular (as shown in Figure 1.1 and Figure 1.2). This report is mostly based on a longitudinal stockpile, with a certain height (h), width (w) and length (L). Chapter 2.1 describes how a stockpile is formed.

Figure 1.3 Stockpile

Reclaiming is the process of removing the bulk material from a pile. This is mostly done by machines

that excavate the stockpile. The bulk material will be loaded in a transport facility like a vessel, train or truck for example.

Chapter 2.2 explains some reclaim methods. 1.2 Machines

Machines used for the stacking and reclaiming processes are mainly divided in three groups; (i) machines which only can stack (stacker), (ii) machines which only can reclaim (reclaimer) and (iii) machines which can perform both functions (stacker/reclaimer).

The motions of the stackers and reclaimers can be classified in three directions: luffing, slewing, and travelling. (See Figure 1.4)

Luffing is the motion whereby the boom rotates up or down. This is the height referring to a stockpile. Slewing is the horizontal rotation of the boom around the central axis of the stacker or reclaimer. Travelling is the motion of the entire stacker or reclaimer on the rails alongside the pile.

Figure 1.4 movements of a bucketwheel stacker/reclaimer

Figure 1.1 longitudinal

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Not each stacker or reclaimer can perform all these types of motions. There are three stacker types:

• Fixed stacker (no luffing and slewing. Mostly only travelling)

• Fixed luffing stacker (only luffing is possible and at some machines also travelling)

• Radial luffing stacker (slewing and luffing is possible and at some machines also travelling)

Figure 1.5 shows an example of a fixed stacker and Figure 1.6 an example of a redial luffing stacker.

Reclaimers can mainly be classified in three main groups: (i) Scrapers, (ii) Bridge reclaimers and (iii) bucket wheel reclaimers.

Scrapers reclaim from one side (side scraper) (as shown in Figure 1.8) or both sides (portal scraper)

(as shown in Figure 1.9 ) of a stockpile. The only possible motions are travelling and luffing.

Bridge reclaimers (as shown in Figure 1.10) reclaim the whole cross sectional area at once and travels perpendicular to the pile during reclaiming. The only motion is travelling.

Bucket wheel reclaimers are reclaiming with a wheel with buckets. (As the name mentioned). All the

three motions are possible. See Figure 1.11 for an example of those machines. Scrapers

Bridge reclaimers

Figure 1.8 Side scraper

Figure 1.10 examples of bridge reclaimers

Figure 1.7 an example of a scraper _{Figure 1.9 Portal scraper} Figure 1.5 fixed stacker Figure 1.6 Radial luffing stacker

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Bucket wheel reclaimer

1.3 Goal of the research The goal of this research is:

• Investigate which methods exists to stack and reclaim bulk materials on a stockpile. • How the stacking and reclaiming methods are related to each other.

• To give an estimation of the capacity of the different reclaim methods. (in m3/h)

The answers on those questions give more information about how to determine which method is most useful / efficient for a specific situation.

1.4 Structure of the report

This document will describe several stacking and reclaiming methods. The stacking methods are useful for different stacker types. The reclaim methods are mainly for bucket wheel reclaimers.

Chapter 2.1 describes the different stacking methods and Chapter 2.2 the different reclaim methods. Chapter 2.3 describes the relations between the stacking and reclaiming methods.

Chapter 3 compares the different reclaim methods based on capacity in m3/h

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2 Stacking and Reclaiming methods

Stacking and reclaiming of dry bulk materials is briefly material adding to and removing from a storage pile. For some reason it can be desirable to use a specific method for stacking and reclaiming. For instance to get a homogeneous bulk material or larger stacking/reclaiming capacities. This chapter describes different stacking and reclaiming methods and also the relations between those methods. The discussed stacking methods are applicable for the most common stacker types.

2.1 Stacking methods

Stacking is not only used to store material but can also been used to blend material to get a more homogeneous material over time. This is mostly the main reason to select a specific method. Generally a better method for blending is more expensive through time and energy consumption by more movements.

The five most common methods for stacking are: • Cone-shell (2.1.1) • Chevron (2.1.2) • Strata (2.1.3) • Windrow (2.1.4) • Advanced block (2.1.5) 2.1.1 Cone-shell

De cone-shell stacking method is the most straight forward method to stack material. As the name suggests, it starts with a cone, up to a certain height. Then the machine travels a small distance alongside the stock pile and makes a new ‘shell’ against the previous. This process is depicted in Figure 2.1

The advantage of the cone-shell is the low number of movements of the machine. When the height of the first cone is reached, the only movement that remains is the travel-movement for a new shell. In other words, a fixed stacker can do this method.

This method is often used when blending is not important.

2.1.2 Chevron (chevcon)

A chevron pile is build up in different layers. The first operation is to make a small stock pile with one material. The next step is covering this pile with another material, and so on. In theory a machine which only can travel can do this method, like the cone-shell method. To prevent dust, a stacker which can luff is used. This makes the drop height smaller. So the stacker travels alongside the stockpile during stacking, at the end it will rise the boom and travels back. If some blending is desirable this is also a simple way to stack, only the number of travel movements is more compared to the cone shell. Another name of chevron method used in a circular stockpile is chevcon.

Figure 2.1 Cone-shell stacking

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2.1.3 Strata

The strata method is more or less the same idea as the chevron. The first step is also to start with a small stockpile. The next step is to cover one side instead of both sides by the chevron. Slewing (rotation) should be possible to realize this method with the stacking machine.

2.1.4 Windrow

A windrow stockpile is build up in several smaller stockpiles/layers on top of each other. The stacker travels along the stockpile. At the end the boom slews or luffs and after that the machine travels back. The layers are kept small to get a better distribution. Therefore a lot of movements are needed.

2.1.5 Advanced block

This method is a variation of the cone-shell method. The difference between those methods is that slewing is also possible during stacking. Instead of only stack in cones one after the other, also cones next to each other is a possibility.

Figure 2.5 shows the stacking process schematically. At first the machine will be placed such that a cone can be created at place A. After that the desired height is reached the boom slews to point B to stack a cone there. This process can be repeated till the maximum slewing angle, or the maximum stockpile width is reached. (point H in Figure 2.5). Slewing of the stackerboom is the only movement till this place H. To decrease the drop height it should also be possible to use the luffing movement of the stacker.

When the desired height of the cone at place H is reached, the stacker travels backwards and continues the stacking.

Figure 2.5 Movements advanced block operation (by ABB)

Figure 2.3 Strata stacking

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2.2 Reclaiming methods

The most important reason to choose a specific reclaim method is to prevent abolishing of a stacking method whereby blending was important. An other reason can be the reclaim capacity or area use. The discussed reclaiming methods are specific for a bucket wheel reclaimer.

The five most common methods for reclaiming are: • Long travel (2.2.1)

• Bench reclaim (2.2.2) • Block reclaim (2.2.3) • Pilgrim step (2.2.4) 2.2.1 Long travel

With the long travel reclaiming method a reclaimer moves along the stockpile without any other movements. The reclaim height and depth is set at the begin of a stockpile and wouldn’t change during travelling. At the end of the stockpile, the reclaim height and depth are set again and the reclaimer would travel backwards. Since a bridge reclaimer can only travels is this, is the only possible method to reclaim for that type reclaimer.

Figure 2.6 shows the process of reclaiming using the long travel method.

Figure 2.7 shows the path of the bucket wheel during reclaiming.

Figure 2.6 Long travel reclaiming

Figure 2.7 Path of the bucket wheel using the long travel reclaiming method

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2.2.2 Bench reclaiming

By the bench reclaiming method the stockpile is reclaimed slice by slice. The reclaimer only slews during reclaiming. When the reclaimer reached the maximum slewing angle, or when the max width of the stockpile is reached, the entire stacker/reclaimer travels one step forward. Than the reclaiming starts again during slewing back. When a whole layer (bench named) is reclaimed, the entire reclaimer travels back to the begin of the stockpile, to start with a new layer. This is necessary because the reclaimer cannot rotates more than +110o/-110o and therefore it is not possible to reclaim during backward travelling.

Figure 2.8 shows an overview of reclaiming with a bucketwheel stacker/reclaimer, using the bench reclaiming method.

Figure 2.9 shows the path of the bucket wheel during reclaiming.

Figure 2.9 Path of the bucket wheel using the bench reclaiming method.

2.2.3 Block reclaiming

The reclaimer uses the same movements with the block reclaiming method as the bench method. The difference between those two methods is that using the block reclaiming method, the reclaimer reclaims not till the end of the stockpile. There will be a layer reclaimed for a certain distance (for example a half length) of the stockpile. Then the stacker/reclaimer travels back and starts to reclaiming the next layer. The advantage of this method can be the use of area. For example, if a half stockpile has to be reclaimed the implementation both methods is: with the bench method is the half height of the stockpile reclaimed and the with block method the half length of a stockpile.

Figure 2.8 bench reclaim

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2.2.4 Pilgrim step

The pilgrim step method is a variation of the block method. The difference is that the block method reclaims a certain block length before the reclaimer travels back. (For example a half stockpile). The pilgrim step travels back after a certain slew movements. This number of slewings should be an even number because the reclaimer boom should be above the rails during travelling back. Mostly the number of slewing movements is 6, 8 or 10 (by ABB1)

Since the bench, block and pilgrim method are looking very similar (they use the same movements), are these terms sometimes used interchangeable. Figure 2.13 shows clearly the differences between those three methods. For example, if a half stockpile has to be reclaimed, then the numbers in the figure indicate the order of reclaiming.

Figure 2.13 differences between Bench, block and pilgrim step reclaiming method

1

See reference I

Figure 2.11 Pilgrim step method

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2.3 Relation between a stacking and reclaiming methods.

The selection for a stacking method is often based on blending. To avoid abolishing of the blending during reclaiming also the choice for a reclaiming method is indirectly based on blending.

The efficiency of blending can be calculated by:

) % 95 ( Re ) % 95 ( y probabilit at ng i claim after Variations y probabilit at Stacking before Variations Efficiency Blending =

The figures Figure 2.14 and Figure 2.15 give an indication of the blending efficiencies. Figure 2.14 indicates that for a boom-type machine (a bucket wheel reclaimer). The pilgrim step reclaiming method and the windrow stacking method result in the best blending efficiency. On the other hand, Figure 2.15 shows the blending efficiency for bridge-type reclaimers. Those numbers are higher then at the boom reclaimers.

So, if the blending efficiency is an important selection criterion for the stacking method, then the selection of the reclaiming method will be based on the stacking method to avoid abolishing of the blending efficiency.

For example, ash is stacked in windrow (because blending is important) with a stacking rate of 2000tph. A bucket wheel reclaimer with bench reclaiming method results in a blending efficiency of 2.01 On the other hand, if the reclaiming is performed by a bridge reclaimer, the blending efficiency is already 3.7. Almost twice as good.

Figure 2.14 Blending efficiencies boom-type machine (By A.T. Zador2)

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3 Determination of the reclaiming capacity

A selection criterion for a reclaiming method is the capacity. To make an estimation of the capacity for each reclaiming method, it is necessary to determine the shape of the reclaimed volume and the velocity of the motions of the reclaimer.

3.1 Reclaiming capacity with a slewing reclaiming method (m3_/hr)

This chapter describes the reclaiming capacity with a slewing reclaiming method. The reclaimer only slews during reclaiming, during the; bench, block and the pilgrim step reclaiming method.

3.1.1 Cross-sectional area of a slice

During bench, block and pilgrim reclaiming, the reclaimer is mostly slewing. This results in reclaiming the pile in slices. A slice has a so called moon shape, both seen from top- as from side view.

Figures 3.1 and 3.2 give an indication of this shape.

Figure 3.1 slice pattern (top view)

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Figure 3.33 slice

h = reclaim height [m] θ = slewing angle [rad]

∆x = travelling step of the reclaimer [m]

∆r = slice thickness (depending on slewing angle) [m]

The reclaimer boom rotates and the bucket wheel follows a circular path. After a maximum rotation (for example 900_{) , makes the reclaimer a (travel) step forward (∆x) and rotates back. The distance}

between the clockwise circular path and the counter clockwise path is a distance ∆x. Both paths are two overlapping circles.

This ensures that a moon shaped slice arises. See Figure 3.4.

Figure 3.4 slice, top view

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Figure 3.5 cross-sectional area of a slice

Figure 3.5 indicates a cross sectional area of a slice. Where;

rb = bucket wheel radius [m]

h = reclaim height [m]

∆r = slice thickness (depending on slewing angle) [m]

The cross-sectional area of a slice can be calculated4 in detail with:

))

2 (

cos

2 sin(

)

2 (

cos

2 (

(

1 1 2 b b b

r

A

⋅

∆

⋅

−

⋅

∆

⋅

−

=

_π

− − (3.1)

A simplification5 for the cross-sectional area is:

A

≈

h

⋅

∆

r

(3.2)

Since the thickness of slice varies with the slewing angle θ, ∆r = f(θ)6

∆

r

(

θ

)

≈

∆

x

⋅

cos(

θ

)

(3.3)

Formula (3.3) combined with (3.2):

A

≈

h

⋅

∆

x

⋅

cos(

θ

)

(3.4) 4 Elabored in Appendix A1 5_{Elabored in Appendix A2} 6_{Elabored in Appendix A3}

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The sides of the slice are slanting due to the angle of repose. This results in the reclaim height h = f(θ). Therefore equation (3.4) is not valid at the begin and end of the slice where the cutting height is not constant. The slewing angles where the condition of the height changes are:

θ1 = Slewing angle where reclaiming starts.

θ2 = Slewing angle where maximum reclaim height is reached

θ3 = Slewing angle where maximum reclaim height ends

θ4 = Slewing angle where reclaiming ends

These angles are shown in the figures 3.6 and 3.7:

Figure 3.6 slice, front view

Figure 3.7 top view

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At the sloping parts, the height can be calculated7 with:

h

(

θ

,

ϕ

)

=

R

⋅

tan(

ϕ

)

⋅

tan(

θ

)

(3.6)

Where;

R = Horizontal distance between slewing/rotation center to end of the bucket wheel(boom length) φ = angle of repose θ = slewing angle 4 4 3 3 2 2 1 1 max

0 )

tan(

)

tan(

)

tan(

)

tan(

0 )

,

(

θ

ϕ

θ

ϕ

θ

>

<













=

⋅

=

⋅

=

h

R

h

R

h

(3.7)

At some point there will be no slope anymore at the end of the slice. Then θ3 = θ4 = θmax

This occurs when the rotation center of the boom passes the begin of the stockpile. Figure 3.8 shows the cross sectional area as a function of the slewing angle.

The cross-sectional area increases during the first slewing degrees. Then it will decrease. The last few degrees it will decrease faster when θ3 > θ4 (as an effect of the slant side)

Figure 3.8 Cross –sectional area as function of the slewing angle

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3.1.2 Slice Volume

The volume of a slewing slice can be calculated with:

θ

π θ θ

d

r

A

V

=

∫

⋅

= = 2 0 (3.8)

[

]

[

]

[

]

4 3 3 2 2 1

)

sin(

4

2 )

2 sin(

8

1 )

sin(

4

2 )

2 sin(

4

1 )

sin(

4

2 )

2 sin(

8

1

θ θ θ θ θ θ

θ

⋅

−

⋅

∆

⋅

+

⋅

∆

⋅

−

+

⋅

−

⋅

∆

⋅

+

⋅

∆

⋅

−

+

⋅

−

⋅

∆

⋅

+

⋅

∆

⋅

−

=

R

x

h

R

x

h

R

x

h

V

Where; h = reclaim height [m]

∆x = travelling step of the reclaimer [m]

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3.1.3 Slewing Velocity

It is desirable to have a constant reclaiming capacity.

Therefore the slewing velocity has to be inversely directly proportional with the slice thickness. When the slice thickness (∆r) is halved, the velocity is doubled.

Since,

∆

r

≈

∆

x

⋅

cos(

θ

)

cos(

0

θ

v

=

8 _(3.9) V0= is the velocity at θ0 [m/s]

or in terms of angular velocity;

)

cos(

0

θ

ω

=

(3.10)

ω0= is the velocity at θ0 [rad/s]

Figure 3.9 shows the velocity (ω) as a function of the slewing angle (θ)

Equation (3.7) can lead to a higher velocity then the technically feasible velocity. The velocity becomes then constant. See Figure 3.10

(Accelerations and decelerations are not included in those figures)

Figure 3.9 velocity

Figure 3.10 velocity with maximum velocity

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3.1.4 Time

Time calculation9 for slewing

dt

d

θ

ω

=

ω = angular velocity

ds = change of angular displacement [m] dt = change in time [s]

[

sin(

)

sin(

)

]

1

0 1 0

θ

ω

−

=

∆

t

3.1.5 Capacity

The current capacity can be determined for a specific position and time. This can be done with multiplying the cross-sectional area of a slice, at that point, with the velocity at that point.

)

(

)

cos(

)

(

)

(

)

(

θ

v

r

h

v

A

Capacity

⋅

∆

⋅

=

⋅

=

(3.11)

The capacity over the entire slice can be plot as a function of the slewing angle, like the figure below (Figure 3.8 multiplied by Figure 3.9)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 angle (degrees) Q ( m 3 /m in )

Figure 3.11 Capacity (as function of the slewing angle)

The capacity can also be calculated as an average over time with the volume divided by the time.

t

V

Capacity

∆

=

(3.12) For the capacity over a longer time or distance can the volume of more slices be summed. Also the time for travelling can be included.

t

V

Capacity

∆

=

∑

(3.13)

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3.2 Reclaiming capacity using the long-travel reclaiming method)

Using the long travel method, the reclaimer reclaims only during travelling and only slew/luff the boom at the end or begin of the stockpile.

Figure 3.12 indicates a long travel reclaiming situation.

Figure 3.12 Reclaiming bulk materials using the Long travel reclaiming method

3.2.1 Capacity

The capacity calculation of the long travel reclaiming method can be done in the same way as capacity calculation for slewing reclaiming methods.

The differences are the shape of a slice and the direction of motion.

3.2.2 Cross-sectional area of a slice

The cross-sectional area of a slice (A [m2]) is the same as described in chapter 3.1.1.

r

h

A

≈

⋅

∆

(3.14)

The difference is that the slice thickness is constant and therefore the cross-sectional area is constant during reclaiming. Except the begin and end where the stockpile slant is.

3.2.3 Slice volume

The volume of a slice of the long travel reclaiming method can be calculated with:

)

tan(

(

ϕ

h

L

A

V

≈

⋅

−

10 (3.15) Where;

A = cross sectional area of the slice [m2] L = length of the reclaimed layer [m] h = reclaim height [m]

φ = angle of repose [o]

The longitudinal slant sides and the corners of the stockpile influence this volume. The corners can be include by decrease the length.

The longitudinal slant side can be include by a decrease of the height. (the first slice at the edge of the stockpile is not reclaimed with a maximum reclaim height)

(25)

3.2.4 Travel Velocity

Since the cross sectional area is constant, the travel velocity is also constant.

3.2.5 Travel Time

Since the travel velocity is constant the time for one slice can be calculate with:

v

L

t

=

∆

(3.16) Where; L= length of a slice [m] v = travelling velocity [m/s]

(26)

3.3 Example situations.

3.3.1 Example 1 determination of the capacity Assume a stockpile with:

Length = 150m Width = 80m Height = 24m

Angle of repose: φ=400

Which is reclaimed from two sides. Reclaimer specifications:

Slew velocity: ω = (n = 0,0132 - 0,0928 min-1) = 0.083 – 0.583 rad/min Travel velocity: v = 3-30 m/min

Length of the boom: R=50m Bucket wheel diameter: rb=4.5m

Reclaim depth: ∆x=1m (maximum)

Reclaim height: h=4.8 (this results in 24/4.8= 5layers Distance from rails center to pile: Y=10m

Distance reclaimer from begin of the pile: X = 12m Acceleration is neglected for now.

Assume ω0 = ωmin

Question:

Using the Bench reclaiming method. What is the capacity of the reclaimer at this position as an average for this slice? Reclaiming the 4th layer (height: 4.8 – 9.6m)

This slice is the hatched area.

12 5 ,7 1 0 5 ,7 5 ,7 150 8 0 R= 50

Figure 3.13 example situation

The distances of the slant sides are: x = y =5.7m (4.8/tan(40)) Y = 10 + 5.7 = 15.7m X = 12 + 5.7 = 17.7m 4 ,8 4 0_° 5,7

(27)

Determine the slewing angles:

)

7 .

18 (

32 .

0 )

1 2400

7 .

15 arctan(

)

1

10

50

7 .

5

10 arctan(

)

arctan(

0 2 2 2 2 1

=

−

=

−

+

=

∆

−

=

rad

x

Y

R

Y

θ

)

8 .

25 (

45 .

0 )

1 )

7 .

5

7 .

15 (

50 )

7 .

5

7 .

15 (

arctan(

)

(

arctan(

0 2 2 2 2 2

=

−

+

−

+

=

∆

−

+

=

rad

x

y

Y

R

y

Y

θ

)

8 .

61 (

07 .

1 )

7 .

17

7 .

5 )

7 .

17

7 .

5

1 (

50 arctan(

)

(

arctan(

0 2 2 2 2 3

₊

=

+

−

=

+

∆

−

=

rad

X

x

X

x

R

θ

)

2 .

68 (

16 .

1 )

7 .

17 )

7 .

17

7 .

5 (

50 arctan(

)

(

arctan(

0 2 2 2 2 4

=

+

−

=

+

∆

−

=

rad

X

x

R

θ

Determine the volume:

[

]

[

]

[

]

4 3 3 2 2 1

)

sin(

4

2 )

2 sin(

8

1 )

sin(

4

2 )

2 sin(

4

1 )

sin(

4

2 )

2 sin(

8

1

θ θ θ θ θ θ

θ

⋅

−

⋅

∆

⋅

+

⋅

∆

⋅

−

+

⋅

−

⋅

∆

⋅

+

⋅

∆

⋅

−

+

⋅

−

⋅

∆

⋅

+

⋅

∆

⋅

−

=

R

x

h

R

x

h

R

x

h

V

[

]

[

]

[

]

1.18 07 . 1 07 . 1 45 . 0 45 . 0 32 . 0

)

sin(

50

4

1

2 )

2 sin(

1

8 .

4

8

1 )

sin(

50

4

1

2 )

2 sin(

1

8 .

4

1 )

sin(

50

4

1

2 )

2 sin(

1

8 .

4

8

1 θ

θ

⋅

−

⋅

+

⋅

−

+

⋅

−

⋅

+

⋅

−

+

⋅

−

⋅

+

⋅

−

=

V

V=116.65m3

This number is checked with a 3d-cad program. Which gives a result of 117.42m3 (See figure below) The calculation has an error of 0.7% compared with the

3dcad-program.

(28)

Check ωmax

min

/

583 .

0 min

/

22 .

0 )

19 .

1 cos(

083 .

0 )

cos(

max 4 0

=

_rad

≤

=

_rad

=

ω

_θ

ω

The velocity does not exceed the maximum velocity.

Time:

[

sin(

)

sin(

)

]

1

1 4 0

θ

ω

−

=

∆

t

[

sin(

1 .

19 )

sin(

0 .

33 )

]

7 .

3 min

083 .

0

1 =

−

=

∆

t

Capacity:

The average capacity for this slice is:

hr

m

t

V

₁₅

_.

₅₅

_/

_min

₉₃₃

_/

5 .

7

65 .

116 ₌

2

₌

3

=

∆

This number is very low compared to a real situation. This is explainable because the max slewing velocity is not reached. For example, a higher value for ω0 can be chosen.

(29)

3.3.2 Example 2: determination reclaim efficiency Assume a stockpile with:

Length = 150m Width = 80m Height = 24m

Angle of repose: φ=400

Which is reclaimed from two sides.

The volume of this stockpile is approximately 150677 m3_{The half stockpile is 75338.5 m}3.

Reclaimer specifications:

Slew velocity: ω = (n = 0,0132 - 0,0928 min-1) = 0.083 – 0.583 rad/min

Travel velocity: v = 3-30 m/min (acceleration for 5sec) (assume 10m/min during reclaiming and 30m/min during travel back)

Length of the boom: R=50m Bucket wheel diameter: rb=4.5m

Reclaim depth: ∆x=1m (maximum)

Reclaim height: h=4.8 (this results in 24/4.8= 5layers Distance from centor of the rails to pile: Y=10m The maximum reclaiming capacity therefore will be:

60 /

50

1

8 .

4 min

/

10

60 /

max

v

h

x

R

m

C

=

⋅

∆

⋅

=

⋅

Assume ω0=0.145rad/min

An efficiency for bench reclaiming and long travel reclaiming can be determined as follows: For each slice the volume is calculated as described in chapter 3.1.2 and the time for each slice is calculated as described in 3.1.4. summed with 5 seconds for acceleration and 5 seconds deceleration. The average capacity is the summation of the volume of all the slices (

∑

V

[m3]) divided by the summation of the times for all slices (

∑

t

[hr]).

∑

=

t

V

Q

avg (3.17)

This average capacity divided by the maximum capacity results in a reclaim efficiency (

ε

)

max

Q

avg

=

(30)

Bench reclaiming results in an efficiency of 44.3% Time reclaiming travel-back layer 1 358.5 6.1 minutes layer 2 518.7 6.6 minutes layer 3 698.1 7.1 minutes layer 4 891.5 7.6 minutes layer 5 1098.5 Total 3592.626 Minutes max capacity 2880 m3/hr total volume 75338.5 m3 total time 59.9 hr avg. Capacity 1258.219 m3/hr efficiency 44.3%

The figure below shows the reclaim capacity during the first hour.

reclaim capacity bench reclaim. Layer 1 (top layer) slice 1-35

0 500 1 000 1 500 2 000 2 500 3 000 3 500 0 10 20 30 40 50 60 70 80 Time (minutes) C a p a c it y ( m 3 /h r)

(31)

Long travel reclaiming results in an efficiency of 87.3% layer 1 149.8 minutes layer 2 237.0 minutes layer 3 339.8 minutes layer 4 468.7 minutes layer 5 603.5 minutes total 1798.9 minutes

max capacity 2880 m3/hr (=4.8m*1m*10m/min) total volume 75338.5 m3

total time 30.0 hr avg. Capacity 2512.856 m3/hr efficiency 87.3%

Is this case is the long travel-method more efficient then the bench reclaiming method. It is plausible that this efficiency varies with the dimensions of the stockpile and the reclaimer parameters.

The figure below shows the reclaim capacity during the first layer.

Reclaim capacity long-travel method

0 500 1000 1500 2000 2500 3000 3500 0 50 100 150 200 250 300 350 400 450 Time [minutes] Q [ m 3 /h r]

(32)

Conclusions

The goal of this literature study was:

• To investigate which methods there exist to stacking and reclaiming bulk materials on a stockpile.

• How the stacking and reclaiming methods are related to each other.

• To give an estimation of the capacity of the different reclaim methods. (in m3/h)

The five most common methods for stacking are; Cone-shell, Chevron, Strata, Windrow and Advanced block. The choice for a method is based on blending efficiency and stacking capacity.

The five most common methods for reclaiming are: Long travel, Bench reclaiming, Block reclaiming, Pilgrim step. The choice for a reclaiming method is based on the stacking method, to avoid abolishing of blending during stacking. If blending is not important, the capacity or area use can be a factor. For example, if a stockpile is reclaimed for 50% , this results in a stockpile with half the length if the pilgrim or block reclaiming method is performed or a stockpile with half the height if the bench or long travel reclaiming method is performed.

The capacity of all the reclaiming methods can be calculated by dividing the stockpile in reclaimed slices and can be determined for a specific point or as an average over time.

The capacity on a local point can be calculated by multiplying the current cross sectional area of the slice by the current velocity. Except the long travel method, are the cross sectional area (A [m2]) of a slice and the velocity (v [m/s]) dependent on the slewing angle θ.

v

A

Capacity

=

*

The capacity over time can be calculated by determining the volume (V [m3]) of a slice and the required time to reclaiming that slice (∆t [sec]).

t

V

Capacity

=

_∆

At a curtain length of the stockpile, will be the reclaim capacity/efficiency of the long travel reclaiming method the best. Up to 97.8% 11 instead of 75% - 88% for bench/block reclaiming method and 80% for the pilgrim step method. This is explainable by less repositioning times for the reclaimer.

(33)

Recommendations and Discussion

Plausible is that the accelerations, during a motion, have big influences on the velocity. It is recommended to investigate what there accelerations are. This should result in refined results for the reclaiming capacity. The time of reclaiming will be higher than calculated in the example and therefore the capacity will be lower.

To investigate the capacity over a longer time it would be necessary to determine the time to set the reclaimer for a new slice. For example to determine the travel time for one step at a slewing reclaiming method or the luffing time of the boom to switch to the next layer. Those times can also be included in the time calculation.

For longer reclaiming times it can be useful to calculate more then one slice and sum them. It should be noticed that at the begin of reclaiming the stockpile (at the corner of a stockpile) the value’s for θ1

- θ4 differ for each slice. Therefore it can be recommended to script this in a computer program.

At the end of a slice, the velocity of slewing motion is the highest. It would be interesting to investigate what this means for the energy consumption. It can be interesting to slew the second part of the slice with a constant velocity like shown in Figure 3.10.

According to W. Knappe 12 The velocity curve should be as shown in the figure below to get a constant reclaiming capacity. To get a more detailed velocity equation then eq. 3.10, a specified equation can be determined for the first and last part of the slice (the sloping parts from θ1 – θ2 and

θ3 – θ4) .

The question that remains is, if it interesting to accelerated to a high velocity, to get a constant reclaiming capacity, or is a decrease of reclaiming capacity no issue. The last one results in a lower maximum velocity and energy save.

At a curtain length of the stockpile, will be the reclaim capacity/efficiency of the long travel reclaiming method the best. Due to less repositioning times of the reclaimer. A next question is to proof the numbers given by W. Knappe:

Long travel : up to 97.8% (travelling time include) Block / bench : 75% - 88%

Pilgrim step reclaiming : up to 80%

Figure 0.1 ideal velocity pattern for constant capacity (By W. Knappe12₎

(34)

References

I. ABB: S/SR Reclaiming/stacking methods, November 5th 2012 from

http://www.abb.com/industries/db0003db002806/e29095140f8c008fc12573b1002d9a69.aspx ?tabKey=6

II. Knappe, W: Performance of bucket wheel reclaimer, November 5th 2012 from

http://www.saimh.co.za/beltcon/beltcon8/paper820.html

III. Zador, AT: Technology and economy of blending and mixing, 1991 IV. ABB: bucket wheel excavator, November 24th 2012 from

http://www.abb.com/industries/db0003db002806/8482fbf32c5c2411c1257315001df1f1.aspx? productLanguage=nl&country=NL&tabKey=6

V. Trans Tech Publications: Stacking, Blending & Reclaiming of bulk materials, 1994 ISBN 0-87849-088-4

VI. FAM: Stockyard systems, November 29th 2012 from

http://fam.de/english/Products/Stockyard%2520systems/index.html

VII. Thyssenkrupp-materialshandling: Stockyard equipment, November 29th 2012 from

http://www.thyssenkrupp-materialshandling.co.za/web/TLN_19.asp

VIII. Bulkonline: Oktober 13th_{2012 from}

www.bulkcn.com

IX. aumund: Fördertechnik. November 29th 2012 from

http://www.aumund.de/de/schade/products/longitudinal-stockyards

X. Metso: Mining and construction. January 13th 2013 from

http://www.metso.com/miningandconstruction/mm_bulk.nsf/WebWID/WTB-041103-2256F-F999B

(35)

Appendix A1

(Detailed calculation cross-sectional area of a reclaiming slice) The cross sectional area of a reclaimed slice arises by the movement of the bucket wheel.

This area is hatched in the figure below. The surface of this area can be calculated as described below in this appendix. A B C D O C1 _C2

The overlapping area of two circles C1 and C2 can be determined with the “intersection area of two circles theory”. A B C D O C1 _C2

The shaded area part ACD can be calculated with:

∠

ABO = arccos(OB/AB)

∠

ABC = 2*

∠

ABO

Area ABCD =

⋅

AB

2

⋅

∠

ABC

=

⋅

AB

2

⋅

∠

ABO

=

AB

2

⋅

∠

ABO

2

2 π

π

(1) A B C D O C1 _C2

(36)

Area ABC =

sin(

2 *

)

2

1 )

sin(

2

1

2 2

ABO

AB

ABC

AB

⋅

∠

=

⋅

∠

⋅

(2) A B C O C2

Area ADC = area ABCD (1) – area ABC (2)

)

2 sin(

2

1 (

)

2 sin(

2

1

2 2 2

ABO

AB

ABO

AB

ABO

AB

⋅

∠

−

⋅

∠

=

∠

−

⋅

∠

(3) A B C O C2

The shaded area between ABCD is 2* area ADC The non shaded area of the circle C1 will be

))

(

cos

2 sin(

)

(

cos

2 (

(

)

2 sin(

2 (

)

2 sin(

2

1 (

2

1 1 2 2 2 2

AB

OB

AB

OB

AB

ABO

AB

ABO

AB

− −

₋

_⋅

⋅

−

=

∠

⋅

−

∠

⋅

−

=

∠

⋅

−

∠

−

π

(4) A C D O C1

Formula (4) describes the non shaded area of circle C1. When,

(37)

AB = rb (radius bucket wheel)

))

2 (

cos

2 sin(

)

2 (

cos

2 (

(

1 1 2 b b b

r

A

⋅

∆

⋅

−

⋅

∆

⋅

−

=

_π

− −

(38)

Appendix A2

(Simplification cross-sectional area of a slice)

On each height of the cross-sectional area the slice thinness (∆r) is identical. Except from the point where the circles intersect each other.

Therefore the area can be calculate with

r

h

A

≈

⋅

∆

(1)

The point where ∆r becomes smaller is the intersection point.

The shaded area in de figure below is also included by calculation with formula (1) and should be subtracted for an exact answer.

Since this shaded area is very small compared to the rest of the cross-sectional area, it can also be neglected.

When the radius of the bucket wheel is a lot bigger then the slice thickness (

r

_bucketwhee_l

>>>

∆

r

) The cross sectional area can be calculated with

r

h

A

≈

⋅

∆

For example,

Bucket wheel diameter rb= 9 m (9000mm)

Reclaim depth ∆r = 1m (1000mm)

(39)

4 5 0 0 1000 R4500 1000 1000 R4500 Calculated with:

A

≈

h

⋅

∆

r

2 2

5 .

4 4500000

1000

4500

m

mm

A

=

⋅

≈

Calculated with the more detailed method:

2 2 1 1 2 1 1 2

49 .

4 4490723

))

9000

)

0 cos(

1000

(

cos

2 sin(

))

9000

)

0 cos(

1000

(

cos

2 (

(

4500

))

2 )

cos(

(

cos

2 sin(

))

2 )

cos(

(

cos

2 (

(

m

mm

r

A

b b b

=

⋅

−

⋅

−

=

⋅

∆

⋅

−

⋅

∆

−

=

− − − −

π

θ

π

(40)

Appendix A3

(Calculation slice thickness ∆r)

∆r = slice thickness [m]

∆x = travelling ‘step’ of the reclaimer [m] R = length of the reclaimer boom [m] r + ∆r = R

θ = slewing angle [rad]

(41)

α

cos

2

2 2 2

=

+

−

⋅

bc

c

b

a

)

(

sin

)

cos(

)

1 )

(

(cos

)

cos(

)

(

cos

)

cos(

)

(

)

(

cos

)

cos(

2 )

(

4 )

(

cos

2 )

cos(

2

2 )

(

4 ))

cos(

2 (

)

cos(

2 )

cos(

)

cos(

2 )

(

4 ))

cos(

2 (

)

cos(

2

0 )

cos(

2 )

cos(

2

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

θ

π

θ

π

θ

π

θ

π

θ

π

⋅

∆

−

±

⋅

∆

−

=

+

−

⋅

∆

±

⋅

∆

−

=

∆

−

+

⋅

∆

±

⋅

∆

−

=

∆

+

−

⋅

∆

±

⋅

∆

−

=

∆

+

−

⋅

−

⋅

∆

⋅

±

⋅

∆

⋅

−

=

∆

+

−

⋅

−

⋅

∆

⋅

±

⋅

∆

⋅

−

=

−

=

−

∆

+

−

⋅

−

⋅

∆

⋅

−

±

−

⋅

∆

⋅

−

=

∆

+

−

⋅

−

⋅

∆

⋅

−

⋅

∆

⋅

−

∆

+

=

x

R

x

r

R

x

r

x

R

x

r

x

R

x

r

x

R

x

r

x

R

x

r

x

R

x

r

x

R

r

x

r

x

r

x

r

R

))

(

sin

1

1 (

)

cos(

)

(

sin

)

cos(

)

(

sin

)

cos(

(

2 2 2 2 2 2 2

θ

R

x

R

x

R

x

R

x

R

x

R

r

R

r

∆

−

±

+

⋅

∆

=

⋅

∆

−

±

⋅

∆

+

=

⋅

∆

−

±

⋅

∆

−

=

−

=

∆

Source: www.bulkcn.com

)

cos(

)

(

))

(

sin

1

1 (

)

cos(

₂ 2 2

θ

⋅

∆

≈

∆

−

≥≥

⋅

∆

x

r

Then

R

x

R

x

if

(42)

Appendix A4

(Calculation h(θ))

h = maximum reclaim height [m] φ = angle of repose [o_]

ϕ

tan

⋅

=

b

h

b

h

b ? if R>>b then,

ϕ

θ

tan

⋅

=

⋅

=

R

h

R

b

(43)

Appendix A5

(Calculation slewing angles)

θ0 =0

θ1

(44)

Y = (width) distance from center of the reclaimer till the start point of reclaiming of a layer. ∆x= step distance of the reclaimer

R = Horizontal distance between slewing/rotation center to end of the bucket wheel r = R - ∆r (∆r = slice thickness)

θ2

Slewing angle where maximum reclaim height is reached

)

arctan(

)

arctan(

2 2 1 2 2

x

Y

R

Y

x

X

Y

R

X

∆

−

=

∆

−

=

−

=

θ

(45)

Y = (width) distance from center of the reclaimer till the start point of reclaiming of a layer. y = distance where h varies

∆x= step distance of the reclaimer

R = Horizontal distance between slewing/rotation center to end of the bucket wheel r = R - ∆r (∆r = slice thickness) φ = angle of repose

)

(

arctan(

)

arctan(

)

(

2 2 2 2 2

x

y

Y

R

y

Y

x

X

y

Y

y

Y

R

X

∆

−

+

−

+

=

∆

−

+

=

+

−

=

θ

(46)

θ3

(47)

)

arctan(

)

(

3 2 2

X

x

Y

X

x

R

Y

+

=

+

∆

−

=

θ

X = (length) distance from center point of the reclaimer till reclaimed layer. [m] x = distance where h varies [m]

∆x= step distance of the reclaimer [m]

R = Horizontal distance between slewing/rotation center to end of the bucket wheel [m] r = R - ∆r (∆r = slice thickness) [m]

φ = angle of repose

θ4

(48)

)

arctan(

)

(

4 2 2

X

Y

X

x

R

Y

=

+

∆

−

=

θ

X = (length) distance from center point of the reclaimer till reclaimed layer [m] ∆x= step distance of the reclaimer [m]

R = Horizontal distance between slewing/rotation center to end of the bucket wheel [m] r = R - ∆r (∆r = slice thickness) [m]

Bucketwheel stacker/reclaimers: an analysis of stacking/reclaiming methods

Specialization:

Transport Engineering and Logistics

Report number: 2012.TEL.7724

Title: