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 ------- 8 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. 10 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. 11 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 12 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. 10. Steidle, E., 1976; ‘’Role of Draglines and Shovels in Modern Mining’’, Groundhog Vol.77 No.1, Ohio, USA 11. Wood, A., 2013; ‘’ Personnel Communications”, Joy Global, Wigan, England 14