Breakout Force of Walking Draglines and Forces Impacting the
Stability of Equipment
Metin OZDOGAN*
Hakki OZDOGAN**
ABSTRACT
In this paper breakout geometry and forces effecting walking dragline bucket, break-out force,
and bucket fill mechanism are investigated. The relationship between the drag-in force
applied to the bucket and machine’s friction force with the ground surface is analyzed. In
addition, ground bearing pressures of some walking draglines are given. Equilibrium of
machine’s horizontal forces, vertical forces and moments, and conditions of not being
dragged and toppled are given and discussed. Additionally, measured break-out energies of
some draglines are presented.
Key Words: Breakout Force, Bucket Load, Equipment Sliding Force, Toppling Force
(*)
Dr. Mining Engineer, Consultant , İdeal Makina Danismanlik Ltd.Co., Ankara
(**) E&EE, MBA, Managing Partner, İdeal Makina Danismanlik Ltd.Co., Ankara
1. INTRODUCTION
In walking draglines major phases of digging comprises of penetration and breakout steps of
bucket. Penetration of bucket to the rock material is accomplished by the weight and
geometry of bucket, (Özdoğan, 2003). Upon penetration of teeth to the bench, bucket is
dragged towards to the machine via drag rope and rock material is broken out and thus it is
filled.
On well designed and balanced buckets, upon applying force on the drag rope the rear
section of the bucket lifts and the inclines to the penetration angle designed. The lift of rear
section of the bucket increases the penetration angle and thus increasing penetration of teeth
in the rock material. Thus, teeth can be mounted on the bucket lip with a smaller angle.
Penetration capability of buckets manufactured by well known manufacturers is higher; on
such buckets the whole weight of the bucket is transferred to the teeth with an optimum
cutting angle. Whilst the broken out rock material is getting (filling) into the bucket, the center
of gravity of the bucket shifts to the rear and becomes paralel to the surface, and the cutting
1
depth is preserved and digging action is kept on. Dug rock is pushed back to the rear of the
bucket as it is dragged, and center of gravity of the bucket shifts (moves) to the rear and rear
of bucket is dangle; as the filled in bucket lifted off the bench surface, thus, the material does
not spill off the bucket, (Ozdogan, 2003). The optimum bucket carry angle, β, should be 25º
≥β≥15º which can be achieved by adjusting the length of drag and hoist chains (Klink 2015).
A mine matched dragline bucket fills in at a distance of 1,5 to 3 bucket length distance (Grant
2014). According to Wood, (2013) the fill-in distance is 1,5 to 2 fold of bucket length;
according to Steidle (1976) bucket fills upon it travels twice (2) the length of the bucket on the
digging bench. Filling Distance (bucket filling time) is a function of skill and experience of the
operator, blasting performance at the bench, bench geometry, sharpness of bucket teeth and
suitability of the teeth to the formation being dug, specific digging power of the equipment etc.
B.F.D., m = (1,5 to 3) x B.L.
(1)
Where;
BFD
BL
= Bucket Fill Distance, m.
= Bucket length, m.
Average cycle times of walking draglines at 90 swing angle, vary from 65 seconds to 75
seconds, (Steidle, 1976). Cycle time durations depending on the bench digging type, blasting
performance, digging depth and the stripping method and skill and experience of the dragline
operator can be shorter or longer than the expected period. Erdem, (1996) gives an empirical
relationship for the cycle time as a function of bucket volume:
CT = 48.887 x V0.0483,
(r2 = 0.91)
(2)
Where ;
CT = Cycle Time, s
V = Bucket Volume, m3
Other rule of thumb facts and figures on estimation of bank measure hourly and annual
production of draglines are as follows in terms of per cu.m. of the bucket capacity;
Annual Production, Qa, per m3 of Bucket Capacity (bank measure) = 180,000 m3/year to
185,000 m3/year (Erdem 1996)
Hourly Production, Qh, per m3 of Bucket Capacity (bank measure)= 30 m3 /h (Steidle 1976)
Naturally, these figures are only for guidance; the actual production figures achieved depends
on operating conditions, working hours, availability of the equipment, efficiency of the
operation and management of the mining operation in question.
2. BUCKET BREAKOUT FORCE AND ANTI-SLIP EQUILIBRIUM OF EQUIPMENT
2.1. Bucket Breakout Force
Bucket Breakout Force, (K.K.K.), is the drag-in force applied to bucket by the drag rope. This
force has to overcome deadweight of the bucket, the rock material being fill in and filled in
2
materials’ weight, the friction force between the bench surface and the base of the bucket,
and the resistance of the rock mass to digging. Figure 1 depicts the forces impacting while
the bucket is filling. Well designed buckets minimise the base friction by transferring it to the
teeth with a good teeth angle so the base hardly touches the earth. Bucket density,
tonnes/m3, is defined as the ratio of the tare weight of the bucket to bucket volume.
Figure 1. Forces affecting the bucket during normal bench digging
Nomenclature in the figure above are;
K.K.K. = Bucket Breakout Force
Wk
= Weight of Bucket
Wm
= Weight of Rock Material in the Bucket
fs
= Friction Force
g
= Gravitational acceleration
α
= Bench Slope Angle
Table 1. Average breakout energies of some Turkish walking draglines measure by Gould
220 brush recorder (Ozdogan, 1994)
Model
and
Site
Bucket
Volume,
m3
Breakout
Time
(Bucket Fill
Time)
s
Breakout
Energy,
MJ
Normalised
Breakout
Energy,
MJ/s
0,41
Specific
Breakout
Energy
(Loose
Density),
MJ/m3
0,34
Specific
Breakout
Energy,
(Bank
Density)
MJ/m3
0,46
P&H 736
Tunçbilek
P&H 752
Milas
M7820
Tunçbilek
M8050
Yatağan
15
12,48
5,08
25
16,50
8,10
0,49
0,32
0,43
31
16,95
21,48
1,26
0,69
0,93
54
21,98
12,89
0,59
0,26
0,35
It is not easy to measure the breakout force directly as the bucket is digging. However, by
recording and processing the data of breakout energy consumptions of the buckets are
3
comperatively easier and gives an idea about the equipment’s breaking out difficulty
encountered, indirectly, (Figure 1). Table 1 shows average breakout energy consumptions of
various walking draglines operating at Turkish surface lignite mines; data were taken by
analog Gould 220 model brush recorder, (Ozdogan, 1994).
Swinging
4%
Hoisting
17%
Drag-in
79%
Figure 2. P&H 752 (Milas Yenikoy) fill-in energy consumption components of the bucket
When the bucket fill-in energy components are analysed it is seen that the major component
is drag-in and the minor component is swing motion whereas hoist motion is a secondary
motion Figure 2. depicts bucket fill-in energy constituents of P&H 752 model dragline in Milas
site.
Bucket breakout force is a function of specific digging power and specific breakout power of
the equipment. Specific Equipment Digging Power is the ratio of walking dragline’s total rated
motor powers to the bucket volume, HP (kW) / m3. Specific breakout power is the ratio of the
drag motor rated power to the bucket volume, HP (kW) / m3. Furthermore, it is affected by
drag gearbox reduction ratios and diameter of the drag rope drum. Specific digging powers
and specific breakout powers are given in Figure 3. and Figure 4. for some walking draglines
operating at Turkish coal mines.
The higher the density of the bucket “Specific Bucket Weight (bucket weight per unit
volume)”, the higher the durability is. The impact of bucket density on penetration and
breakout forces are as follows: The higher the density, the better the penetration of bucket at
the commence of digging. As far as breakout force is concerned, bucket density has no effect
on breakout force as seen Figure 1. However, in case of bench chopping the denser bucket
assists digging (drag force) with its horizontal component.
4
Figure 3. Specific machine digging powers of some Turkish draglines
2.2. Calculation of Bucket Breakout Force
Bucket breakout force is calculated as follows for a Standard dragline bench shown in Figure
1., bench slope being, 90  0 :
K.K.K. = F (MG, W k, W m , , c, , s , fs )
(3)
Where ;
K.K.K.
MG
Wk
Wm

c

s
fs
g
= Bucket breakot force, N
= Drag motor power, kW
= Tare weight of bucket and bucket rigging, kg
= Rock mass in the bucket, kg
= Slope of dig bench, 
= Compressive strength of the rock, MPa
= Loose unit weight of the rock in the bucket, kg/m3
= Coefficient of friction between bucket and the rock
= Friction force between bucket base (floor) and the rock surface, N
=Accelaration of gravity, m/s2
fs
= s (Wk + Wm ).g. cos 
(4)
5
K.K.K.  (Wk + Wm).g. sin  + fs
(5)
K.K.K.  (Wk + W m).g. sin  + s (W k + Wm ).g. cos 
(6)
K.K.K.  (Wk + Wm).g. (sin  + s cos  )
(7)
K.K.K.  (Wk.g +  W mt.g. dt) (sin  + s cos  )
(8)
Figure 4. Specific breakout powers of some Turkish draglines
2.3. Anti-slip Equilibrium of Equipment
Equilibrium of forces involved during digging is illustrated in Figure 5. Forces involved are the
friction force between the tub and the bench surface, horizontal component of bucket
breakout force and digging phase equilibrium of the machine. Equipment’s drag motor power
and the magnitude of the force applied to the drag rope should be such that the drag force
exerted should not overcome the friction force between the bottom of the tub and the bench
surface. This is an important design feature to be taken into account. On the contrary, the
dragline drags itself off the bench and topples. In the USA such a case story is reported at a
surface coal mine (Gray,1986). Precipitation reduces the the value of friction coefficient in
clayey formations and increases the risk of sliding of the dragline towards to the dig bench.
The friction force in question may be calculated by the equation given below:
fs = s W d .g
(9)
Where :
6
fs = Friction force between the equipment and the earth, N
s = Coefficient of friction between tub and earth
Wd = Working mass of the equipment, kg
g = Gravitational acceleration, m/s2
K.K.K. horizontal component = [(wk + wm ).g. sin  + fs] . cos
= [(wk + wm ).g. sin  +s (wk + wm ).g. cos ] . cos
(10)
(11)
The condition that the tub not to be dragged towards to the dig bench is as follows:
fs  K.K.K. cos
s.W d .g  [(wk + wm ).g. sin  +s (wk + wm ).g. cos . cos
(a)
(12)
(13)
(b)
Figure 5. Friction force of the tub and bucket breakout force
Walking draglines’ ground pressures (the pressure exerted to the bench surface) are smaller
than the ground pressure of electric mining shovels. Tub ground pressure varies from 84,34
kPa (0,86 kg/cm2) to 111,80 kPa (1.14 kg/cm2). The pressure exerted by the walking shoes
vary from 163,77 kPa to 181,42 kPa (1,67 -1,85 kg/cm2), seeTable 2.
7
Figure 6. Pressures exerted by tub, walking shoes and crawler shoes of equivalent electric
shovel
Table 2. Ground pressures exerted in some walking draglines
Machine Model
Bucket Volume,
m3
Tub Ground
Pressure,
kPa
Walking Shoe
Ground
Pressure,
kPa
Ground
Pressure of
Equivalent
Electric mining
Shovel,
kPa
P&H 736
15
84,34
169,66
319,70
P&H 752
30
85,32
163,77
383,44
P&H 757
50
100,03
169,66
388,35
P&H 9100
75
111,80
181,42
-------
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3. BUCKET LIFTING FORCE (RATED SUSPENDED LOAD) AND ANTI-TOPPLING
EQUILIBRIUM OF THE EQUIPMENT
3.1. Bucket Hoisting Force
Bucket lifting force is governed by the following factors; boom angle, boom length, boom
weight, weight of the machine and counterweight, hoist motor power and hoist gear box, rock
density, weight of the bucket and rigging, weight of the hoist rope etc.. Equipment
manufacturer specifies the maximum allowable load based on the above parameters. As a
rule of thumb, the safety limit is the twice the maximum allowable load (Steidle, 1976). In
order to equalise the moment generated because of the bucket hoisting force, counterweight
is placed in the rear section of the machinery house (revolving frame); for the models
investigated, the counterweights vary from 13 % to 23 % of the net weight of the machine,
see Table 3. The operating weight of the machine is the weight obtained by adding the
counterweight to the net machine weight, Table 3. Erdem, (1996) gives an ampirical
relationship between the maximum allowable suspended load and equipment’s operating
weight:
Maximum Allowable Suspended Load = 0.2123 x W d0.8954
(14)
Where;
W d = Equipments Operating, kg
Table 3. Bucket hoisting capacities and counterweights of some Turkish draglines
Equipment
Model
Bucket
Volume,
m3
Net
Machine
Weight,
Tonnes
Counterweight,
Tonnes
Machine
Operating
Weight,
Ton
Counterweight %
(Net MC
Weight)
%
Counterweight %
(MC Op.
Weight)
%
15
Max
Allowable
Load,
(suspended
load)
Tonnes
52
P&H 736
859
195
1054
23
19
P&H 752
30
91
1751
249
2000
14
12
P&H 757
50
147
3236
411
3647
13
11
P&H 9100
75
227
5239
726
5965
14
12
9
Figure 7. Weights of P&H 752 walking dragline
3.2. Moment Equilibrium of Equipment
Anti-toppling condition of the equipment is that the sum of the weight of bucket and its rigging
and the weight of the rock material in it should be smaller than the maximum allowable load.
The function of the counterweight installed on the rear section of the revolving frame is to
balance out the suspended load of the equipment, Table 3. Anti-toppling equilibrium of the
machine is given by the following torque equation:
M = 0
(W d.g + Fs) . r  (Wk+W m)g . R
(15)
(16)
Where :
r
R
= Radius of tub, m
= Operating radius of equipment, m
In mining literature, there are some torque parameters are being used for walking draglines
(Chironis, N.P., 1980 and 1990). These parameters are MUF (Machine Utilization Factor) and
K-Factors. MUF is the multiplication of operating radius of the equipment by the volume of the
bucket (m x m3). Whereas, K-Factor is the multiplication of the operating radius by maximum
allowable load (m x ton) see Figure 8.
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3.3. Moment of Inertia of Equipment
Walking draglines have higher moment of inertia because of bigger working radius they have.
Moment of inertia of a dragline is the multiplication of operating radius by the square of
maximum allowable load. The higher moment of inertia of walking dragline ease the swing
motion once initiated; One of the reasons of smaller energy consumption in swinging because
of this fact, Table 4.
Moment of inertia equation is given below:
I= (Wk+Wm).g.R2
(17)
Where ;
I
Wk
Wm
R
= Moment of Inertia, N.m2
= Mass of bucket and its rigging, kg
= Mass of rock in the bucket, kg
= Operating radius of the equipment, m
Wd. g.r≥(W k+Wm).g.R
Figure 8. Moment (torque) equilibrium of equipment
In practice, there is another indicator of machine stability which is the ratio of the equipment
weight over bucket volume (ton/m3). The higher this ratio, the higher the operating stability of
the machine is.
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Figure 9. Normalised MUF values of some Turkish draglines
Normalised MUF, which is obtained by dividing the dragline torque parameter MUF to
operating weight of the machine is an indicator of equipment’s digging capability (breakout
force) (m x m3/tonnes). The lower the normalised MUF, the higher the digging power of the
equipment.
Table 4. Torque and moment of inertia figures of some Turkish draglines
Equipment
Model
Bucket
Volume,
m3
Operating
Radius,
M
Equipment
Torque
(M x MN)
15
Max.
Allowable
Load,
kN
510 kN
65
33,15
Equipment
Moment of
Inertia,
(MN x m2)
2155
P&H 736
P&H 752
30
892 kN
80
71,36
5709
P&H 757
50
1442 kN
98
141,32
13849
P&H 9100
75
2226 kN
100
222,60
22260
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6. CONCLUDING REMARKS
For an optimum bucket filling time, the bucket filling distance should be 1,5 to 2 times the
bucket length, as a rule of thumb. Factors influencing the time are as follows; sharpness of
the teeth, type of the teeth, level of applied drag force, and blasting performance at the
bench. The result of optimum bucket breakout force is easier fill-in (shorter bucket fill time),
higher productivity and lower energy consumption.
Heavy duty dragline buckets have higher densities; and they have better penetration to the
ground and contribute to the brakout force in bench chopping applications. However, size of
the heavy duty bucket have to be smaller compared to the medium to light-weight buckets for
a specific dragline size. The compression generated by the drag-in force on the dipper teeth
tips should overcome the resistance of the rock mass to digging.
During digging operation, dragline should not drag itself off the dig bench and topples. In
other words, the horizontal component of the drag force should not overcome the friction
force between the tub and the ground. There are such case stories reported in the mining
literature, in rainy seasons and in clayey formations.
Another danger is the overloading of the bucket which may exceed the maximum allowable
load and may endanger the equipment and cause toppling. So it is extremely important to
grasp the bucket lifting force and equipment’s anti-toppling equilibrium. During operation of
the equipment equilibrium of vertical forces, horizontal forces and moments should never be
spoiled by the generated dynamic and static loads. Payload should never exceed the
maximum allowable load for the well being of the equipment and for safety reasons. It is beter
to have onboard loadweighing instrument, to ensure the recording of bucket overloads and
bucket critical overloads so that precautions may be taken prior to damages..
REFERENCES
1. Chironis. N.P., 1980; ‘’ Draglines: Kings of Strippers’’, Coal Age, January, s. 128-138.
2. Chironis. N.P., 1990; ‘’ Utilization Factors Help Estimate Diggability of Excavators’’, Coal
Age, October, s. 58-59.
3. Deslandes, J.V. and et al, 1990; ‘’Dragline Performance Monitoring and Control at N.B.
Coal Ltd.’’ International Symposium on Mine Planning and Equipment Selection in Surface
Mining, Calgary, Canada, s.1-10.
4. Erdem, B., 1996; ‘’ Development of an Expert System for Dragline and Stripping Method
Selection in Surface Mines’’, Ph.D. Thesis, METU, 1996, 383 s.
5.Grant, I., 2014; ‘’ Personnel Communications”, Joy Global, Wigan, England
13
6. Gray, L.B., 1986; ‘’ Analysis of a Dragline Slip Failure to Establish Preventure Measures’’.
A paper presented at 1986 American Mining Congress Coal Convention, Washington DC,
USA, 9s.
7. Klink, D., 2015; ‘’ Personnel Communications”, Joy Global, Milwaukee, WI, USA
8. Özdoğan, M., 1994; ‘’ Gould Brush Yazıcı ile Bazı TKİ Dragline Yerkazarlarında Yapılan
Ölçümler’’, (Yayımlanmamış)
9. Özdoğan, M., 2003; ‘’ Dragline Yerkazarlarda Kepçe Saplanış Mekanizması ve Kuvveti’’
Madencilik, Cilt 42, Sayı 1, Mart 2003, Ankara, s. 17-26.
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No.1, Ohio, USA
11. Wood, A., 2013; ‘’ Personnel Communications”, Joy Global, Wigan, England
14