D. Komljenovic, J. Paraszczak, K. Fytas, Canada and C. Drebenstedt, Germany
Methodology to Calculate the Effective Reclaiming Capacity of Rail-Mounted Boom-Type Bucket Wheel Reclaimer and Stacker/Reclaimer Summary This paper focuses on the methodology to calculate the effective reclaiming capacity of railmounted bucket wheel reclaimers, and stacker/reclaimers, for large-scale raw bulk material handling systems. Due to considerable gaps in the theory on this subject, a principal objective of the work presented here was to develop a methodology destined to determine reclaiming capacity of these machines. It reflects the relationship between the characteristics of the equipment and the parameters associated with its work environment. A function concerning the rule of the boom-slewing motion was defined. It was based on the particular shape of stockpiled material and the digging geometry of Fig. 1: Rail-mounted bucket wheel stacker/reclaimer with a slewing boom [21] the machines. This function was subsequently employed as a basis to work out a precise methodology for calthese operations has a considerable impact onto prices of final culating the effective reclaiming capacity of the equipment products. Therefore, bulk solids handling systems ought to be analysed. Successful validation of the model developed was perefficient, reliable, highly productive and must enable a good maformed for the Quebec Cartier Mining (QCM) port facilities in Port terial flow, at the least cost. This requires more efficient reclaimCartier. The paper concludes with some possible applications of ing and stacking machines. the results achieved in this study. The equipment employed to handle raw bulk materials in stockyards is referred to as a reclaimer (reclaiming operation only), and/or stacker/reclaimer (both functions: stacking and reclaim1 Description of the Problematic and ing). The most frequently used ones are the rail-mounted boomtype machines, such as a stacker/reclaimer shown in Fig. 1. To Objectives of the Research simplify the text that follows, from now on these machines will be referred to as “R&S/R”. 1.1 Introduction Handling and transhipment of bulk solid materials plays an important role in modern economy. It is due, among other things, to steadily increasing volume of raw materials being transported from often remote mine sites on all continents to plants and facilities in both industrialised and industrialising countries. Cost of
During the reclaiming operation the bucket of such machines follows a 3D trajectory defined by a combination of three elementary movements (Fig. 2): Fig. 2:
Elementary movements of a bucket wheel reclaimer or stacker/reclaimer in reclaiming operation [1]
DRAGAN KOMLJENOVIC, Ph.D., P.Eng., Production Advisor/Reliability Engineer, Hydro-Quebec, 4900, boul. Bécancour, Bécancour (Quebec) G9H 3X3, Canada Tel.: +1-819-298-2943 (Ext. 5032); Fax : +1-819-298-5092 E-Mail:
[email protected] Prof. Dr.-Ing., Dr.h.c. CARSTEN DREBENSTEDT, Professor in Opencast Mining Technische Universität Bergakademie Freiberg, Mining Institute, Gustav-Zeuner Str. 1, D-09596 Freiberg (Sachs), Germany. Tel.: +49-3731-393-373; Fax: +49-3731-392-524; E-Mail:
[email protected] JACEK PARASZCZAK, Ph.D., Full Professor, Dept. of Mining, Metallurgy and Materials, Laval University, Quebec G1K 7P4, Canada; Tel.: +1-418-656-5103; Fax: +1-418-656-5343; E-Mail:
[email protected] KOSTAS FYTAS, Ph.D., P.Eng., Full Professor, Dept. of Mining, Metallurgy and Materials, Laval University, Quebec G1K 7P4, Canada; Tel.: +1-418-656-5057; Fax: +1-418-656-5343; E-Mail:
[email protected] Details about the authors on page XXX.
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Reclaiming Capacity of Bucket Wheel Reclaimer
• rotation of the bucket around its own axis at speed vr, • slewing of the boom around a vertical axis to a yard plane at speed vzkr, and • travel of the machine on rails parallel to the pile at speed vtr.
ogy to calculate the performance of reclaiming and stacking operation of R&S/R, as well as the creation of a selection criterion for these machines.
The stacking (stockpiling), as the second operation, can be carried out only by stacker/reclaimers. The machine travels alongside the stockyard where bulk material is stockpiled. Therefore, one realizes the importance of developing a precise methodol-
1.2
Scope of the Work
At the early stage of the selection process of R&S/R, the amount of information available is limited. Specifications pro-
Nomenclature a
distance between the travelling axis of the R&S/R and the pile toe [m]
tg
acceleration time of the boom or the machine [h]
tk
digging time in a cut [h]
tk(mod)
total digging time in a module [h]
tktot
total digging time in a stockpile [h]
tm
manoeuvring time of R&S/R in the reclaiming operation [h]
tmtot
total of all manoeuvring times in all modules of a stockpile [h]
A
area of an individual cut in a reclaiming operation [m2]
a1i
distance between the travelling axis and the near bench edge [m]
a2i
distance between the travelling axis and the far bench edge [m]
a1p
distance between travelling axis of the R&S/R and the near bench edge, in the first reclaimed bench [m]
tod
returning time of the machine [h]
tpd
raising time of the boom [h]
distance between the travelling axis of the machine and the stockpile-middle [m]
tpr
advancement time of the machine [h]
tr-st
operating (reclaiming) time [h]
tsp
lowering time of the boom [h]
ttr
displacement (travelling) time of the machine [h]
ast b0
cutting width at the slewing angle 00 [m]
bβ
cutting width at the slewing angle β [m]
c0
cutting depth at the slewing angle 00 [m]
cβ
cutting depth at the slewing angle β [m]
D
bucket wheel diameter [m]
2d
distance between the rails of the runway [m]
dp
width of the pile top flat [m]
dpc
width of the pile top flat which is not still reclaimed [m]
di
width of the pile flat in the bench i [m]
dmp
width of the pile top flat – full reclaiming block [m]
Er
bucket volume [m3]
Vz
reclaimed volume [m3]
gu
maximal slewing acceleration/deceleration of the bucket wheel boom [m/s2]
X
distance between the rotating centre (slewing axis) and the boom fixation [m]
g
gravitational acceleration; g = 9.81 m/s2
Yk
Hmax
maximal height of stockpiled material [m]
height of the boom fixation at the rotating centre of the machine [m]
H
height of stockpiled material [m]
α
pile slope angle [°]
height of the bench i [m]
αc
angle of front slope [°]
Hr(g)
maximal positioning height of the bucket wheel axis [m]
αr
Hri
positioning height of the bucket wheel axis in the bench i [m]
angle between the bucket wheel and the boom in horizontal plan [°]
Lk
bucket wheel boom length [m]
β1i; β2i
slewing angles of the boom - auxiliary variables [°]
Lsr
length of cutting edges in contact with material [m]
βa1i
angle of the interval 3 [°] angle of the interval 4 [°]
n
number of reclaiming benches in the pile
βva2i
angle of the interval 2 [°]
ni
discharge frequency of buckets [1/min]
βua3i
nm
number of modules in the stockpile
βk1i
angle of a maximal acceleration/deceleration of the boom inner bench side [°]
nr(i)
number of cuts in a bench
βk2i
Qeff
effective reclaiming capacity [m3/h]
angle of a maximal acceleration/deceleration of the boom outer bench side [°]
Qex
exploitation capacity (reclaiming rate) [m3/h]
βmi
angle of a maximal slewing speed of the boom [°]
βt
current slewing angle [°]
βui
boom slewing angle - near side of the block in the bench i [°]
hi
Qt
theoretical capacity (reclaiming rate)
[m3/h]
[m3/h]
Tcal
total calendar time per year; Tcal = 8760 h
vkβ
slewing speed of the boom at the slewing angle β [m/min]
vkβ1i
slewing speed of the boom at the end of the interval 2 [m/min]
vkβ2i
slewing speed of the boom at the end of the interval 3 [m/min]
vr
peripheral speed of the bucket wheel [m/s]
vtr
travelling speed of the machine [m/h]
min/max minimal/maximal slewing speed of the bucket wheel boom at vzkr the bucket [m/min]
Qth
technical capacity (reclaiming rate)
r
bucket wheel radius; r = D/2 [m]
βvi
boom slewing angle - far side of the block in the bench i [°]
Rki
reclaiming outreach in the bench i [m]
βvn
Rkn
reclaiming outreach in the lowest bench (n) [m]
boom slewing angle - far side of the block in the lowest bench [°]
Sn
stockpile width on the ground [m]
βtxy
current slewing angle [°]
Snb
reclaiming block width - full block [m]
δi
inclination angle of the boom in the bench i [°]
Suk
total stockpile width [m]
ϕui
contact angle between the bucket wheel and the reclaimed material [°]
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vided by manufacturers specify (among others) linear dimensions of the machine, and its theoretical output rate, usually expressed in tonnes per hour. It is more convenient to have the later parameter in m3/h because the bucket volume Er and the number of bucket discharges per unit of time ni are usually known. In this case, the theoretical reclaiming rate is calculated as follows: Q t = 60 · Er · ni (1) The above value, however, is not the actual one that may be expected. Users should know the effective output rate (effective capacity) for their planning schedule. This represents the actual output of a reclaiming operation, and reflects influences of most important factors, such as: • design parameters of the machine, • geomechanical factors (properties of bulk material), and • technological parameters (block shape, mode of operation). These factors and influences may be presented in the manner shown in Fig. 3. Calculation procedures (models) used currently for R&R/S are those derived from Bucket Wheel Excavators (BWE) theory. BWE operates in blocks, in which only the cutting depth changes with an increasing slewing angle of the bucket wheel boom. This change may be described by the following rule (Fig. 4): c β = c 0 · cos β
vkβ
This is an important issue, since an inaccurate assessment of design parameters of a R&S/R at the pre-select stage may have negative (and expensive) consequences for a future user. Undesired excessive capacity usually involves higher capital and operating cost, whereas insufficient one may put in jeopardy the efficiency of the whole bulk material handling system. A precise assessment of the effective reclaiming capacity becomes then one of the crucial points of the selection process.
1.3
(3)
Principal Objective of the Work
Given some drawbacks and gaps of currently used models describing the reclaiming function of rail-mounted bucket wheel reclaimer and stacker/reclaimer (R&S/R), it is justifiable to investigate a new approach. In this context, the study presented here will focus on development of an accurate calculation methodology to determine R&S/R reclaiming capacity.
2
(2)
During the slewing operation, the height of cut remains unchanged. In order to compensate for this volume loss and to keep the buckets full, the slewing speed of the bucket wheel boom should increase reciprocally: v = k0 cos β
slewing angle (Fig. 5). Therefore, a new guiding rule, reflecting particularities of reclaiming should be developed.
Methodology to Calculate the Effective Reclaiming Capacity of Rail-Mounted Boom-Type Bucket Wheel Reclaimers and Stacker/Reclaimers (R&SR)
Reclaiming operation modes may be classified into two categories: a bench (more frequently used) or a modular-type (see Fig. 6) [12]. Fig. 5:
Typical block shape in reclaiming operation [16]
This approach is not adequate in the case of a reclaiming operation carried out by R&R/S, where cutting height varies with the Theoretical capacity
Input (main bucket wheel design parameters)
Transitional function
Influence factors on effective capacity - geomechanical/natural parameters - technological parameters - other design parameters
Effective capacity (Output) Fig. 3:
Influential factors on effective capacity
Fig. 4:
Change of cutting depth with an increasing slewing angle [3]
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The principal type of a reclaiming operation is the block work. There are two block shapes (Fig. 7): • narrow block, and • full block. A combination of these two block types may also occur. Fig. 7 that illustrates geometrical relationships is a basis for a detailed study presented below. 2.1.1 General Relationships
Fig. 6:
Types of reclaiming mode [12]; a) bench-type b) modular-type
In order to develop a precise methodology of the reclaiming performance of a rail-mounted bucket wheel R&S/R, it is necessary to investigate and define the rules governing cut dimensions variability both in horizontal and vertical plane. Following them, the rule for a bucket wheel slewing speed would be defined. This will enable determination of the transitional function (see Fig. 3), and an exact calculation of effective reclaiming capacity.
2.1
Geometrical Relationships in Block-Reclaiming Operation
As mentioned before, development of the adequate methodology to calculate the effective capacity of a reclaiming operation is the main objective of this research.
This section gives equations for calculation of main geometrical relationship between the linear parameters of the machine such as: bucket wheel boom length, wheel diameter etc, and block geometry. Reclaiming outreach in the bench According to design parameters of the machine and block dimensions, this parameter is calculated in the following manner: R ki = Lk · cos δ i + X + r · cos α r · sinϕ ui
(4)
External slewing angles When the boom reaches the outer slope of the block, it is slewed at a certain angle from the travel axis of the machine. This “external slewing angle” of the boom in the bench i, is defined in the following manner: n
The first step consists of determining the main relationships between the linear dimensions of the machine and the geometry of the bulk material block to be reclaimed. Fig. 7:
(R kn − r · cos α r · sinϕ un ) · sinβvn − ∑ hj · cotα βvi = arcsin
j=i+1
R ki − r · cos α r · sinϕ ui
(5)
Block-types in a reclaiming operation; a) narrow block, b) full block
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Height change within the sector βvi ≤ β2it < β2i (outer slope side)
Internal slewing angles At the beginning of a bench at the inner side of the pile, the bucket wheel boom is slewed at an angle called “internal slewing angle”. It is also measured from the travel axis of the equipment. Its numerical value is: n
htβ2i = hi ·
j=i+1
R ki − r · cos α r · sinϕ ui
(6)
2.1.2 Variation of the Digging Height Due to the shape of the pile, the cutting height in a reclaiming operation varies. If the pile cross-section is triangular, the cutting height changes constantly in the first reclaimed bench. In the case of a trapezoidal cross-section, this height remains constant in the flat top area. Since this variation involves capacity losses, it is important to determine a rule to adjust the boom slewing speed to compensate for them. Although some losses are inevitable due to a machine design (for example due to a limit of maximum slewing speed), it is feasible to minimize them. Fig. 8 will be used to determine the rule of the digging height change. It is given as follows: Fig. 8:
5
(7)
Height change within the sector β1i ≤ β1it < βui (inner slope side)
a + ∑ hj · cotα βui = arcsin
βvi − βt2i βvi − β2i
htβ1i = hi ·
βt1i − βui β1i − βui
(8)
If the machine is operating in a full block, the cutting height changes only within the sector β1i ≤ β1it < βui (inner slope side) and Eq. (8) should be used. 2.1.3 Digging Geometry and the Technical Capacity In order to further develop the methodology to calculate reclaiming performance, the technical capacity Qth and digging geometry should be considered. The former depends on natural (geomechanical) characteristics of handled material, such as: digging resistance kL, swell factor of material kr, and bucket fill factor kpu, cut dimensions (height, depth, and width), and boom slewing speed.
Determining the cutting height change in reclaiming operation
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Relationships concerning the technical capacity and digging geometry, developed for BWE [3,8,13,14,15,19,22] remain applicable for the case of R&S/R. In this study, they are adopted after a slight modification, and integrated into the methodology. The rationale of these relationships may be found in the above mentioned references. Besides technical capacity and specific digging force, the following parameters of digging geometry are taken into consideration: • Total length of cutting bucket edges Lsr; • Optimal ratio between cutting depth and width (c/b)opt; • Actual cutting depth and width, as function of the technical capacity c0, b0; • Peripheral digging force of the bucket wheel Pk; • Optimal slewing speed at the beginning of a bench vk0.
speed” chart, see Fig. 9b. The slewing speed is defined by angle βmi . 6. Maximal linear acceleration/deceleration in the far side pile slope (Interval 6). The far side pile slope is defined by angle βk2i . Intervals 4, 5, and 6 cover the area of the inner pile slope (D - A in Fig 8). In order to maximise reclaiming capacity, it is necessery to optimise the boom slewing speed in intervals 2, 3, and 4. 2.2.2 Rule of Slewing Speed Change by Intervals Rule of slewing speed change at interval 2 (β1i < β1it ≤ βa3i ) Within this interval, both cutting depth and height vary. In order to maintain constant capacity, the slewing speed of a bucket wheel boom should then vary in a reciprocal manner. The formula is as follows:
There are two principal shapes of the bucket: trapezoidal and semi-rounded. For more details, consult above mentioned references.
vβ1t ki = vkβ1i · Fig. 9:
2.2
Rule of Slewing Speed Guidance in a Narrow Block
The next stage consists in determining the rule for boom slewing speed guidance. As mentioned before, the dimensions of a cut, dug by the bucket wheel, change in horizontal and vertical planes.
(β1i − βui ) · cos β1i (βt1i − βui ) · cos βt1i
(10)
Change of bucket wheel slewing speed a) maximal design speed is reached b) maximal design speed is not reached
a)
On a horizontal plane, the bucket wheel cuts a sickle shaped cut, which changes accordingly to the rule given by Eq. (2), see Fig. 4. On a vertical plane, the cut shape depends on the pile crosssection (triangular or trapezoidal). The rule of change is defined by Eqs. (7) and (8) (see Fig. 8). Since the objective is to maximise the capacity, the boom slewing speed ought to vary to compensate for changes in cut dimensions. Its general form is as follows: vkβ = ƒ(β, h)
(9)
For the purpose of this research, an original methodology for determining the rule of boom slewing speed change (guidance), as a function of the cut-dimension variations mentioned above, is developed. 2.2.1 Intervals of Slewing Speed Change With regard to the above, and design limits of R&S/R, such as the maximal slewing speed, and bucket dimensions, the following intervals may be distinguished (see Fig 9):
b)
1. Maximal linear boom slewing acceleration/deceleration in the inner slope (Interval 1). The inner slope is defined by angle βk1i . 2. Automatic slewing speed regulation in the area where the cutting height changes in the near-pile slope (Interval 2); intervals 1 and 2 cover the area of the inner slope marked by B - C in u Fig. 8. The near-pile slope is defined by angle βa3i . 3. Automatic slewing speed control in the area of a constant cutting height (Interval 3), where only the cutting depth varies. It is defined by angle βa1i . In Fig. 9, this interval is located at the area C - D. If the pile has a triangular shape, this interval is absent in the first /highest bench. 4. Automatic slewing speed regulation in the area where the cutting height changes in the outer slope (Interval 4). The v outer slope is defined by angle βa2i . 5. Maximal slewing speed limited by maximal design limit of the slewing speed (Interval 5). When such limit is not reached, this interval will disappear from “Slewing angle - slewing
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Rule of slewing speed change at interval 3 (β2i < βi ≤ β1i )
βa3i = βui +
Within this interval, only the cutting depth varies. As the cutting height remains constant, the slewing speed is as follows: v kβi = vkβ1i ·
cos β1i cos βi
A 1i (βa3i − βui )2 · COS2βa3i
(19)
where : (11) A 1i =
v2kβ1i · (β1i − βui )2 · cos 2β1i 7200 · gu · R ki
(20)
At the limit of this interval, the slewing speed reaches a value of: vkβ2i = vkβ1i ·
cos β1i cos β2i
(12)
Rule of slewing speed change at interval 4 (βa2i < βi ≤ β2i ) At this interval both the cutting depth and height vary. The slewing speed rule encompasses both variables: vβ2t ki = vkβ1i ·
(βvi − β2i ) · cos β1i (βvi − βt2i ) · cos βt2i
(13)
Determining angle βa2i , borderline between intervals 4 and 6 (βvi < β2it < β2i ) This angle (see Fig. 9 b) defines a borderline between intervals 4 and 6. If the interval 5 (maximal constant slewing speed, Fig. 9a) exists, the calculation of this angle is different and will be shown later. As in the previous case, one observes that the slewing speed at the limit of interval 4 must be equal to that at the beginning of interval 6. They coincide at point P. Therefore, the equations become: v3 = gu · t6
Following this analysis, the optimal rule of the boom slewing speed change defined for intervals 2, 3, and 4 allows to achieve maximal reclaiming capacity. In practice, if the reclaiming operation is automated, the guidance for the slewing speed is based on both the engaged power of the motor installed the bucket wheel and on the material output recorded on the boom conveyor.
v4 = vkβ1i ·
(22)
Since at the point P it is v3 = v4, the two equations can be compared and resolved with regard to t6:
2.2.3 Angles of Automatic Slewing Speed Guidance
t6 =
After the above analysis there still remain two transition points between intervals (borderlines) to be determined, namely: at the border of intervals 1 and 2, as well as 4 and 5 (Fig. 9 a), or 4 and 6 (Fig. 9 b). Other borderlines have been determined in the previous chapter.
(βvi − β2i ) · cos β1i 60 · (βvi − βa2i ) · cos βa2i
(21)
vkβ1i · (βvi − β2i ) · cos β1i 60 · gu · (βvi − βa2i ) · cos βa2i
(23)
where: t6 slewing-motion time in interval 6 [s] In interval 6, the following is the equation of slewing motion:
Angle βa3i , borderline between intervals 1 and 2 (β1i < β1it < βui ) This angle (see Fig. 9) defines a borderline between intervals 1 and 2. Obviously, the slewing speed at the limit of the acceleration (deceleration) interval 1 must be equal to that at the beginning of the interval 2. They coincide at point Q (Fig. 9). According to these, it may be written as follows: v1 = gu · t1 v2 = vkβ1i ·
(β1i − βui ) · cos β1i 60 · (βa3i − βui ) · cos βa3i
(14)
vkβ1i · (β1i − βui ) · cos β1i 60 · gu · (βa3i − βui ) · cos βa3i
βa2i = βvi − βk2i
(24)
(25)
Integrating Eqs. (23) and (24) into Eq. (25), the following equation is obtained: βa2i = βvi −
(16)
gu · t62 2 · R ki
The angle of the automatic speed control is calculated in the following manner (Fig. 9b):
(15)
Since at point Q it is v1 = v2, these two equations can be compared and resolved with regard to t1: t1 =
βk2i =
v2kβ1i · (βvi − β2i )2 · cos 2β1i 7200 · gu · Rki · (βvi − βa2i )2 · cos 2βa2i
(26)
It is also necessary to verify if the maximal design slewing speed max has been reached or exceeded of the bucket wheel boom vzkr at the angle βa2i. Note: Eqs. (19) and (26) should be solved by using a of numerical method.
where: t1 motion time in interval 1 [s]
2.3
In interval 1 (maximal linear acceleration or deceleration), the equation of slewing motion is as follows: βk1i
g · t2 = u 1 2 · R ki
(17)
The angle of the automatic speed control is calculated in the following manner (Fig. 9): βa3i = βui + βk1i
(18)
Integrating Eqs. (16) and (17) into Eq. (18), the following equation is obtained:
7
Digging Time in a Narrow Block Reclaiming Operation
Once the angles of automatic speed control are defined, it becomes possible to determine the digging time of the bucket wheel in a sickle cut. Digging time in interval 1 (defined by angle βk1i, see Fig. 9) Slewing speed at point Q on the borderline between intervals 1 and 2 (β1i − βui ) · cos β1i vQki = vkβ1i · (27) (βa3i − βui ) · cos βa3i
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This slewing speed at point Q is calculated using Eq. (10) by substituting.
t 4i
vkβ1i · (βvi − β2i ) · cos β1i ·
∫ dt = 60 · R
· βvi · βa2i
−60 · R ki ·
vQki t1i = 60 · gu
(28)
Digging time in interval 2 (defined by angle βua3i, see Fig. 9)
(β1i − βui ) · cos β1i 60 · (βt1i − βui ) · cos βt1i
(29)
β1i
∫ dt = 60 · R · ∫ ki
0
βt1i
βa3i
· cos βt1i dβt1i
∫
β2i
∫β
t 2i
· cos βt2i dβt2i
60 · R ki · (βvi − βa2i ) · sinβa2i − cos βa2i vkβ1i · (βvi − β2i ) · cos β1i −
cos βt1i dβt1i
βa3i
60 · R ki · (β1i − βui ) · sinβ1i + cos β1i t2i = vkβ1i · (β1i − βui ) · cos β1i
(34)
60 · R ki · (βvi − β2i) · sinβ2i − cos β2i vkβ1i · (βvi − β2i ) · cos β1i
Eq. (34) represents the digging time in interval 4.
In interval 5, the slewing speed of the bucket wheel boom reaches the maximal design value νmax zkr (see also Fig. 9a). The angle βmi is calculated as follows: βm = βvi − βk2i − βm ki
β1i
−60 · Rki · βui ·
t t 2i dβ2i
Digging time in interval 5 (if the latter exists, it is defined by angle βmi)
whose solution is the following: t 2i
∫ cosβ
β2i
t4i =
The slewing motion of the bucket wheel boom in this interval (β1i < βt1i ≤ βa3i ) can be described by the following differential equation:
vkβ1i · (β1i − βui ) · cos β1i ·
ki
0
Acceleration (deceleration) time - digging time in interval 1
R ki · dβt1i = vkβ1i ·
βa2i
If an interval 5 exists, the angle βk2i defining the interval 6 (see Fig. 9a) is calculated according to the equation of slewing motion in this interval (6): t5i =
(30)
60 · R ki · (βa3i − βui ) · sinβa3i + cos βa3i − vkβ1i · (β1i − βui ) · cos β1i
(35)
vmax zkr 60 · gu
Rki · βk2i =
gu · t5i2 2
(36)
(37)
These equations give the following solution for the angle βk2i: Eq. (30) represents the slewing motion time (synonymous to digging time) of the bucket wheel boom in interval 2. Digging time in interval 3 (defined by angle βa1i = β2i - β1i, see Fig. 9) In this interval (β2i ≤ βi ≤ β1i ), the motion of the boom is described by the following differential equation: R ki · dβi = vkβ1i
cos β1i dt 60 · cos βi
(31)
The solution is obtained in the following manner: t 3i
β2i
60 · R ki ·
∫
cos βi dβi = vkβ1i · cos β1i ·
∫ dt
t5i =
60 · βmi · R ki vmax zkr
(βvi − β2i ) · cos β1i (βvi − βa2i ) · cos βa2i
(32)
The following differential equation describes the slewing motion:
The solution is as follows:
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(40)
This represents slewing speed at the point P (border of interval 6) calculated by means of Eq. (13), by substituting.
Digging time in interval 4 (defined by angle βva2i, see Fig. 9)
(βvi − β2i ) · cos β1i 60 · (βvi − βt2i ) · cos βt2i
(39)
It is the interval of maximal linear acceleration (deceleration) on the outer side of a stockpile. In the absence of interval 5, the calculation is carried out according to Fig. 9b. The slewing speed at the point P has the following value:
The digging time is calculated in the following manner: t6i =
R ki · dβt2i = vkβ1i ·
(38)
Digging time in interval 6 (defined by angle βk2i)
vPki = vkβ1i ·
and finally, the digging time in this interval: 60 · R ki · (sinβ2i − sinβ1i ) vkβ1i · cos β1i
2 (vmax zkr ) 7200 · gu · R ki
The digging time in interval 5 is expressed as:
0
β1i
t3i =
βk2i =
(33)
vPki 60 · gu
(41)
If the interval of maximal slewing speed (interval 5) exists, this time becomes: vmax t6i = zkr (42) 60 · gu Total digging time in a cut The total digging time is given as the sum of individual digging times by sectors. It is calculated as follows:
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6
tk(i) =
∑t
ji
Reclaimed volume of a cut in a narrow block (43)
j=1
With total digging time in a sickle cut determined, an important stage in development of methodology to calculate the reclaiming performance (capacity) is achieved.
According to Figures 7a and 8, it may be written that: Vz(i) =
R ki · hi · c β1i · sinβvi + sinβ2i − (sinβui + sinβ1i ) (45) 2 · cos β1i
Full block reclaiming operation
Reclaimed volume in a cut in a full block
The rule of slewing speed guidance in a full block may be determined in a similar manner. In this case (see also Fig. 9b), a R&S/R operates in the block where the cutting height on the outer side of a pile remains constant. The variation in the cutting height on the inner side of a stockpile follows the same pattern as in a narrow block. Consequently, the slewing speed rule changes must be defined. Intervals of slewing speed change in a full block operation are determined using the same approach as the one employed for the narrow-block reclaiming operation.
Regarding figure 9b, reclaimed volume is as follows:
2.4
Effective Reclaiming Capacity
Effective capacity in reclaiming operation expresses a real output of a system with a working reclaimer or stacker/reclaimer (R&S/R). It depends on equipment design, technological parameters, as well as geomechanical properties and characteristics of material handled. A general formula is as follows: Q eff =
V tk + tm
(44)
Vz(i) =
At the beginning, a study concerning the effective capacity in a sickle cut will be done. The next stage will consist in determining of effective reclaiming capacity in an entire stockpile. 2.4.1 Effective Reclaiming Capacity in a Cut Reclaimed volume in a cut It corresponds to the volume dug by the bucket wheel during a slewing cycle – from the inner to the outer side of a stockpile. In a narrow-block, it is calculated differently than in a full block. Fig. 10: Plan for determining the manoeuvring time of a R&S/R in a modular reclaiming type
(46)
After calculating the volume reclaimed in a cut, the manoeuvring time must be determined. Manoeuvring time in a cut As previously mentioned, this is the time elapsed on manoeuvring motions of a machine in a digging cut (with digging time excluded). It does not depend on the block-type (narrow or full block) in a reclaiming operation. In the following, all components of this time will be defined. Manoeuvring time in the bench-type reclaiming operation In a bench-type of reclaiming operation (see also Fig. 6a), a R&S/R performs only one manoeuvre: an advance for a cutting depth. It is calculated as follows:
Eq. (44) represents the mathematical form of the transitional function shown in Fig. 3. The manoeuvring time tm accounts for manoeuvres of a given machine in a digging cut, such as positioning a R&S/R during a reclaiming operation. Depending on reclaiming mode (bench or modular-type), this time is calculated differently. It does not depend on the block-type (narrow or full block) in a reclaiming operation.
R ki · hi · c β1i · sinβvi − 0.5 · (sinβui + sinβ1i ) cos β1i
tm(i) = tg +
c max (i) vtr
(47)
where: cmax(i) depth of the machine’s advance (see Fig. 4). c max(i) =
c β1i cos β1i
(48)
Manoeuvring time in the modular-type reclaiming operation In a modular-type reclaiming operation (see also Fig. 6), the machine performs several manoeuvres (see Fig. 10). The machine begins at the top of a stockpile by taking a cut. The cut depth varies from case to case. At the completion of a bench, the reclaimer moves back at the distance of the advance, plus an additional distance to clear the angle of a lower bench face, and to assure a longitudinal terrace geometry which is stable for reclaimed material. The boom is then lowered to the next bench and a new reclaiming cycle begins. This sequence is repeated for each bench in a reclaiming module. When the last cut in the last bench (the lowest bench) has been completed, the bucket wheel boom is raised to the highest (first) bench to recommence a new cycle in a new module. According to the above description, the total manoeuvring time is composed of the following individual actions (see also Fig. 10): • raising the boom tpd (between points 8 and 9); • displacement of the machine ttr (see an explanation below); • advance of the machine tpr (between points 1-2, 4-5, and 7-8); • return of the machine tod (between points 2-3, and 5-6); • lowering the boom tsp (between points 3-4, and 6-7). These time components may easily be determined using Fig. 10. Total manoeuvring time in a module It is equal to the sum of all individual manoeuvring times:
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Vol. 24 (2004) No. 3 • bulk solids handling
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n
tm = ttr + tpd +
n−1
∑t
pr(i)
+
i=1
n
∑t
od(i)
i=1
+
2.5
∑t
(49)
sp(i)
i=2
It may be defined as a real performance of a R&S/R over a period of time (usually one year) in actual local conditions. Besides the factors related to effective reclaiming capacity (design, geomechanical and technological), it may also be affected by organizational, climatic, subjective, market, etc. factors [15]. It may be said that it depends on equipment availability and its contributing factors (corrective and preventive maintenance, delays, etc.), its utilization during working hours (operational delays, statutory breaks, standby-time, etc.) as well as work scheduling (working hours/shifts per day, workdays per year, etc.). An example of equipment time split for a calendar year may follow a pattern given in Fig. 11 [2].
With total manoeuvring time expressed as a function of the type of reclaiming operation, effective reclaiming capacity may be calculated according to Eq. (44). 2.4.2 Effective Reclaiming Capacity If a R&S/R operates in a bench-type of operation, its effective reclaiming capacity in a cut can now be calculated according to Eq. (44) where the cut volume is given by Eqs. (45) or (46). If, however, a R&S/R carries out reclaiming operation of a modular-type, the effective reclaiming capacity of this machine in a cut, may now be calculated according to Eq. (44). However, for this type of operation, one talks rather about the effective capacity in a module than in a cut. The volume of a module may be calculated as follows:
In order to increase the efficiency of operations, delay times (operation, maintenance) and idle time should be minimised. The yearly reclaiming productivity (operational capacity) is given as follows: Q eff = Q eff · T0 (52)
n
Vmod =
∑n
r(i)
· Vz(i)
(50)
where:
i=1
Qeff effective reclaiming capacity in a cut or in a module [m3/h]
The reclaimed volume depends on stockpile shape, digging time changes with the block form (narrow or full), whereas manoeuvring time depends on the reclaiming mode (bench-type or modular-type operation). The formulas to calculate these parameters are developed above.
To actual operating time of the machine per year [h/year] The level of working and operating time depends on internal and external conditions in a location: • External conditions - Needs for material handled - Market fluctuation - Input capacity from consumers (end-users) - Frequency of reclaiming operation within a period of time - Climate and weather conditions - Type and properties of material handled - Requested level of the environmental protection • Internal conditions - Synchronisation between material inflow and outflow - Effective reclaiming capacity - Organisational efficiency of reclaiming and maintenance operations - Stockpile layout - Skills and training of the personnel
2.4.3 Reclaiming Performance in the Entire Stockpile The methodology to calculate reclaiming performance determined previously takes into consideration the effective reclaiming capacity of a R&S/R in a cut, or in a module. However, in order to calculate a real output from a stockpile, the entire manoeuvring and digging times concerning this stockpile, have to be considered. The effective reclaiming capacity regarding the entire stockpile is calculated as follows: Q eff− st = 3600 ·
Average Operational Performance Over a Period of Time
Vd tr − st
(51)
where: Vd volume of a stockpile [m3] tr-st operating time in a stockpile [s] Fig. 11: Diagram showing basic equipment time elements
Total calendar time Tcal 8760 hours
Working time Tw
Operating delays Td
Down time Tdw
Operating time To
Pure digging time Tk
bulk solids handling • Vol. 24 (2004) No. 3
Maintenance delays Tmd
Manoeuvring time Tm
Idle time Tidl
Corrective and preventive meintenance time Tr
Scheduled repair Tsr
Unscheduled repair Tdw
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These conditions may also vary from case to case and depend on the location of a stockpile, as well as its purpose and organisational level. Productivity can be improve by acting on internal conditions and optimisation ought to be done at the local, internal, and organisational level. By determining relationships connecting the most important influence parameters (design, technological, natural, organizational), a R&S/R user or designer will be able to improve performance of the machine in reclaiming operation. Obviously, by increasing the performance (capacity), a lower operation cost will be reached.
3
3.1
Model Validation on Site with a Working Stacker/Reclaimer Example: The Québec Cartier Mining Company General Overview
The validation of the developed model was carried out at the Québec Cartier Mining company (QCM), or more precisely at its deep sea port in Port Cartier (province of Quebec, Canada). General data have been obtained by courtesy of the communication department. QCM is one of the leading producers of iron ore products in North America, and exporter to the USA, Europe and Asia. It operates an open-pit mine and a crusher/concentrator facility capable of producing 18 million metric tonnes of iron ore concentrates annually at Mont-Wright, close to the city of Fermont in Northern Québec. The company operates also a pellet-plant in Port-Cartier, Québec on the north shore of the Gulf of St.
Lawrence. Its annual production capacity is about nine million metric tonnes of iron ore pellets. Iron ore concentrates and pellets are subsequently loaded on ships and delivered to customers. Pellets at Port Cartier stockpiles are handled by a 3ST46x140 stacker and a 3RP26x168 reclaimer, both from Stephens Adamson. Iron ore concentrates are handled (stockpiled and reclaimed) by a ThyssenKrupp’s Ldc (360x1000)/52 combined stacker/reclaimer. Stacking of concentrates is performed using a chevron method, whereas a windrow method is used for pellets. The latter is employed to avoid a segregation of pellets having various corn sizes. Dimensions of a typical stockpile cross-section are shown in Fig. 12. The reclaiming operation is performed using a modular type operation.
3.2
Validation of the Calculating Methodology
Validation of the methodology has been performed for the ThyssenKrupp machine. A typical shape of a reclaimed block is shown in Fig. 13. It is necessary to mention that the machine operates in a combined narrow/full block, modular-type reclaiming operation. A usual depth of the machine advance in a module is L = 15 m. However, other depth advances may occur as well. Benches 1 and 2 are reclaimed in a narrow block, while benches 3, 4 and 5 in a full block operation (see Fig. 13). This way, a maximal efficiency of the reclaiming operation is assured. Height of the first bench is usually 4.4 m (according to the rule h1 ≈ 0.7·D), whereas that of the others 3.9 m. For the conditions and dimensions specified above, effective reclaiming capacity, calculated accordingly to a newly developed
North side
South side 44
21
10 5
84
60 90
Fig. 12: Typical stockpile cross-section Fig. 13: Usual block shape during the reclaiming operation of the KRUPP machine at Port Cartier
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• geomechanical properties of bulk material (including its digging resistance), and • technological parameters (block shape and mode of operation).
methodology is Qeff = 766.2 m3/h. However, this capacity varies with a changing depth of the advance (see Table 1). It is due to a relative increase of manoeuvring time in total operating time.
3.3
First, the influence of the main design and geomechanical parameters was defined. Subsequently, effective reclaiming capacity was determined. In addition to design and geomechanical parameters, the influence of technological factors should be taken into consideration. These are related to the digging and manoeuvring time in a block. A complex mathematical analysis was used to develop an appropriate methodology for calculating effective reclaiming capacity.
Actual Achieved Performance of the Machines
Records of operating performance exist for each machine at the site for their whole operating life. Moreover, the records for the last 12 months, and the period of time since the last overhaul of the machine, are displayed separately. All data is kept on a computer system which manages the entire operating data. Detailed information has been collected from 1997 to August 2000. Tab. 2 gives reached results of the KRUPP machine.
Validation of the methodology performed on the operating ThyssenKrupp stacker/reclaimer at QCM’s Port Cartier harbour facilities clearly confirms the applicability of this approach in actual conditions. The difference between calculated and actual capacity, recorded over four years varies within a margin of ±1.5 %. Based on these results, it may be concluded that the developed methodology is fully applicable for this purpose.
Validation of the methodology performed on the KRUPP stacker/reclaimer operating in Port Cartier (QCM), clearly shows the applicability of this approach in actual conditions. The difference between calculated and actual capacity, recorded over four years varies within a margin of ±1.5% (compare results in Tables 1 and 2).
4
Anticipated Research Benefits Final research results are applicable for the following purposes: 1. Pre-selection of a machine with regard to its acquisition; a future user should accurately calculate effective reclaiming rate of a R&S/R, and make sure whether the machine under consideration matches capacity targets.
Conclusions
The research presented here has been focused primarily on reclaiming capacity calculation of rail-mounted bucket wheel reclaimers, and stacker/reclaimers (R&SR). The effective reclaiming capacity represents an actual output of this operation with regard to its influencing factors, such as:
2. The follow-up of R&S/R in the reclaiming operation; if large capacity variations and deviations from planned capacity exist, verification ought to be performed to determine possible roots of problems, and solve them. This also helps maintain operating cost of the machine low.
• design parameters of the machine,
3. Production scheduling; for operating R&S/R, the effective capacity may be calculated precisely for production scheduling purposes over an analysed time period. This enables a maximisation of the machine’s performance.
Table 1: The change of the effective reclaiming capacity as a function of the depth of the advance L (ThyssenKrupp stacker/reclaimer)
Qeff (m3/h)
Li (m)
Qeff(L =15 m)/Qeff(Li) Difference (%) (%)
4. Analysis of potential benefits and assessment of impact of possible design modifications onto performance of an existing machine leading to a choice of the best alternative.
5.0
743.14
96.99 %
7.5
753.88
98.39 %
-1.61 %
10.0
759.59
99.14 %
-0.86 %
12.5
763.97
99.71 %
-0.29 %
15.0
766.19
100.00 %
0.00 %
17.5
767.81
100.21 %
0.21 %
20.0
769.05
100.37 %
0.37 %
5
22.5
770.40
100.55 %
0.55 %
[1]
25.0
771.14
100.65 %
0.65 %
Tab. 2:
5. Development of a new machine (model) by manufacturers of reclaimers and stacker/reclaimers. Performance of the new model can be calculated precisely for different conditions of application in order to optimise its design. This way, the best alternative may be identified.
References BERGONZOLI, A. and C. FERRETTI: Calculation Program for the Analysis of the Performance of Boom-Type Reclaimers; Stacking, Blending & Reclaiming of Bulk Materi-
Operating parameters of the KRUPP stacker/reclaimer
Item
1997
1998
1999
2000 – 8 months (yearly basis)
Mean value
Standard deviation
A
Working time (h)
1 450
1 058
1 429
2 223
1 540
490
B
Material handled (metric tons)
2 875 862
2 132 834
2 528 075
4 404 372
2 985 286
993 562
C
Material handled (m3)
1 106 101
820 321
976 337
1 693 989
1 148 187
382 139
D
Performance (tm/h) (B/A)
1 983
2 017
1 769
1 982
1 938
114
E
Performance (m3/h) (C/A)
763
776
680
762
745
44
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als, Volume B/94,Trans Tech Publications, 1994, pp. 95108. [2]
[3] [4]
[5]
COLLINS, J.-L.: Simple ways for reducing equipment queuing time at a repair shop in an open pit operation; CIM Bulletin, October, 1988. DURST, W. and W. VOGT: Bucket Wheel Excavator; Trans Tech Publications, 1988, 378 pp. FARIA DE, R., W. KIKUTI and M. MILANI: Stacker/Reclaimer Design Using CAE, Stacking, Blending & Reclaiming of Bulk Materials; Volume B/94, Trans Tech Publications, 1994, pp. 109-114. GERLACH, K.-H.: Unmanned Operation of Stockyard Machines; Siemens AG (Internal document), 1999, Erlangen, 12 pp.
[6]
KENNEDY, B.A.: Surface Mining, 2nd Edition, Society for Mining, Metallurgy and Exploration, Publications Sales ME, P.O. Box 625002, Littleton, CO 80162-5002, USA, 1990 (ISBN 0-87335-102-9).
[7]
KOMLJENOVIC, D.: Mathematical model of functioning and technical selection of bucket wheel reclaimers and stacker/reclaimers (PhD Thesis), Laval University, Quebec City, 2002, 179 pp.
[8]
KOMLJENOVIC, D.: Izbor osnovnih parametara sistema hidraulicni rotorni bager – samohodni transporter u slozenim rudarsko-geoloskim uslovima (na primjeru PK Dubrave) (MSc Thesis), University of Belgrade, 1991, 136 pp.
[9]
KORZEN, Z. and K. DUDEK: Mechanics of Gravitational Discharge of Cell-Less Bucket Wheels in Reclaiming Machines; Stacking, Blending & Reclaiming of Bulk Materials, Volume B/94,Trans Tech Publications, 1994, pp. 121-132.
[19] STRZODKA, K., J. SAJKIEWICZ and A. DUNIKOWSKI: Tagebautechnik-Band I; VEB Deutscher Verlag für Grundstoffindustrie, Leipzig, 1979. [20] WIECZOREK, A.: Schwenkgeschwindigkeitregelung bei Schaufelradrückladern (Internal Information); Company Sandvik Roxton, Finland and Austria, 2000, p.1. [21] WÖHLBIER, R.H.: Stacking, Blending, Reclaiming, Trans Tech Publications, 1977, 858 pp. [22] ZIVKOVIC, S.: Istrazivanje osnovnih parametara kompaktnog rotornog bagera i tehnologije njegovog rada u slozenim rudarsko-geoloskim uslovima (PhD Thesis), University of Tuzla, Tuzla, 1992. [23] Technical documentation of the mining company «Québec Cartier», Port Cartier, Quebec, Canada.
[10] KULWIEC, R.A.: Materials Handling Handbook, John, Wiley&Sons, 2nd Edition, Sponsored by The American Society of Mechanical Engineers and The International Material Management Society, New York, Chichester, Brisbane, Toronto, Singapure, 1985. 1485 pp. [11] MÜLLER, D.: Kohlenversorgungsmanagement – Betriebserfahrungen mit einer voll-automatisierten Haldenbewirtschaftung, 6th International Symposium Continuous Surface Mining, Freiberg, 2001, pp. 399-410. [12] OYLER, J.F.: The Basis for Bucket Wheel Stacker/Reclaimer Design Philosophy; Stacking, Blending, Reclaiming, Trans Tech Publications, 1977, pp. 141-160. [13] PAJER, G., M. PFEIFFER and F. KURTH: Tagebaugrossgeräte und Universalbagger, VEB Verlag Technik, Berlin, 1979. [14] PARTZ, K.E.: Kräftmessung an Schneiden von Schaufelradbaggern (Dissertation); Fakultät für Bergbauingenieur- und Vermessungswesen, University of Karlsruhe, Karlsruhe, 1985. [15] POPOVIC, N.: Naucne osnove projektovanja povrsinskih kopova, NIRO Zajednica – NISRO Oslobodjenje, Sarajevo, 1984, 971 pp. [16] PRINS, G., J. VAN LADESEIJN and R. FORTMAN: Concept of a Walled-in Storage System for an Import Coal Terminal; Stacking, Blending & Reclaiming of Bulk Materials, Volume B/94, Trans Tech Publications, 1994, pp. 175-186. [17] SCHMITZ, E.: Automatic Reclaiming of Bulk Solids; Stacking, Blending, Reclaiming, Trans Tech Publications, 1977, pp. 285-292. 18] SCHNEIDERSMANN, E.O.: Design and Function of the Bucket Wheel; Stacking, Blending, Reclaiming, Trans Tech Publications, 1977, pp. 161-170.
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