CC BY
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Electromechanics and Mechanical Engineering
UDC 620.172.2
REGULARITIES OF MATERIAL DESTRUCTION OF THE IMPACTOR IN REPEATED SINGLE PUNCH
Viktor I. BOLOBOV, LE TKHAN' BIN'
Saint-Petersburg Mining University, Saint-Petersburg, Russia
The technique and the results of experiments on the study of the laws of the process of the cone-shaped tip of a freely falling impactor made of 38HM, U8, H12MF steels, subjected to typical heat treatment and additionally treated with cold, when they apply multiple (up to 10000) single impacts on granite under conditions approaching hydraulic impactor peaks. To explain the processes, we used the values of stresses aK, arising at the contact area of the impactor and the rock, calculated using the developed mathematical model. It has been established that the process of wear
of an impactor with multiple single blows proceeds in three stages separated by critical values a*, a**, which correspond to the strength characteristics of the material of the impactor demonstrated in these dynamic conditions.
With a small number of strokes (n < n ) and the small size of the blunting area (stage I interaction) values ac
exceed a* of steel and it is exposed to local destruction at the contact site, which is recorded as a significant loss of the impactor's mass; with n* < n < n** (stage II) the resulting stresses are not enough to destroy the material, but it is enough for its plastic deformation, accompanied by the movement of metal from the central part of the contact area to the peripheral and the destruction of part of the deformed metal by rock; with n > n (stage III) arising aK do not
reach the level a** and the decrease in the mass of the impactor is determined by the resistance of the steel to abrasion by the products of rock destruction, displaced by the impactor from the well. The treatment of impactors from all tested steels with cold leads to an increase in their wear resistance; The total depth of the holes punctured by the cold-treated H12MF steel impactor at the time of the interruption of the rock penetration is four times higher than that of the 38HM steel impactor subjected to typical heat treatment.
Key words: multiple single blow; cone-type steel impactor; cold treatment; abrasive wear; metal wear
How to cite with article: Bolobov V.I., Le Tkhan' Bin'. Regularities of Material Destruction of the Impactor in Repeated Single Punch. Journal of Mining Institute. 2018. Vol. 233, p. 525-533. DOI: 10.31897/PMI.2018.5.525
Introduction. Impact breaking and chipping machines are widely used in mine workings, for dismantling refractory lining in the repair of domain and open-hearth furnaces, in the development of frozen and rocky soils, road pavement, destruction of concrete, reinforced concrete and brick structures, etc. [7]. As a working tool, these machines typically use cylindrical type of peaks in the form of a cone or wedge, sharpened at an angle, usually from 30 to 40° [5]. The process of destruction by such machines begins with the introduction of a tool into an array that has free surfaces close enough to each other, to such a depth that the tensile and shear stresses resulting from the insertion tear a piece of required size from the array. The efficiency of a machine is determined by its ability to inject a percussion instrument to a predetermined depth, and a performance indicator is the rate of penetration [5].
With the use of the tool due to the shock-abrasive wear of its material, the dimensions of the blunting area, which is present in the pointed part of the peak, increase. This leads to an increase in the contact area of the tool with the rock upon impact with a decrease in the intensity of impact destruction. As a result, starting from a certain point, the process of penetration of peak into the rock practically ceases, and its renewal requires replacement or regrinding of peaks. For example, as the experience of the DAEMO B180 hydraulic hammer shows, this moment for this machine occurs when the pointed part of the peak is worn out by about 50 %, as a result peak handles 4-5 regrindings. Taking into account the fact that the replacement of massive peaks and its regrinding are very time-consuming processes, the development of methods that increase the resistance of materials to the impactor and impact-abrasive wear and that, as a result, the peak-to-regrinding time, is an urgent task.
é Viktor I. Bolobov, Le Tkhan'Bin'
Regularities of Material Destruction of the Impactor..
A considerable amount of research is devoted to the problems of rock destruction by percussion tools and, in particular, hydraulic hammers. On the basis of the laws of mechanics and the classical Hertz theory, classical and wave theories of impact have been developed, connecting the energy, force and time of interaction between a impactor and destructible material with the depth of penetration of a impactor into a rock. Issues related to the mechanism of wear of the material of the impactor and the effect on the performance of hydraulic hammers on the magnitude of the area of the blunting of its tip, which varies with time depending on the wear resistance of the material, have not been studied sufficiently.
In the present work, in conditions approaching the working conditions of the peak of impact destruction machines by blasting and shearing, the regularities of the process of wear of the material of a freely falling impactor are investigated when they inflict single blows on the rock.
Experiment methodology. The object of the study was impactors with a length of L = 25 mm with a cylindrical part (D = 6 mm, l1 = 13.8 mm) and a cone-shaped point with a vertex angle P = 30 ° at a length of /2 = 11.2 mm, made of 38HM, U8 steels, H12MF, as the peak of hydraulic hammers characterized by durability and wear resistance. Some of the steels were subjected to typical heat treatment (THT) - quenched from 800-1000 °C in oil and tempering at 200 °C, practiced at the manufacturing plants of the peak, the other - additional processing [4] with cold (exposure at -75 °C) 5 hours) as an operation widely used to improve the wear resistance of tool steels [8, 10, 11, 13]. Using the Zwick / Roell ZHU universal hardness tester, the hardness of the materials of the impactor achieved as a result of thermal treatments was determined.
The tests were carried out on an installation (Fig.1) of a structure close to that described in [2].
Impactor 2, made of steel of one of these grades, after weighing on an analytical balance (±0.0001 g) was fixed in a vertical position in a massive impactor 3 (M = 2.8 kg). A fragment of rock 1 granite with a strength of 6.2 on the M.M. Protodyakonov scale with an aggregate hardness of ~ 450 HV and a hardness of its minerals up to 1200 HV (for quartz) exceeding the hardness of the used materials of the impactor was placed under the impactor.
When a impactor was struck with a pin from a certain height (H = 42 mm), a series of strikes n was carried out with the tip of the impactor to different points on the fragment surface, each hit to a different point. The kinetic energy A0 and the pre-impact velocity v0 of the impactor, calculated from the values of M and H, were 1.16 J and 0.91 m/s. After each impact, the impactor was reweighed and measured L (measurement accuracy ± 0.01 mm) with the determination of the mass loss Am and the length A/ of its tip; the diameter d of the formed blunting area was calculated from A/ taking into account p. When the number of strokes over 40, the establishment of Am and A/ was made through the interval n (from 10 to 100) and was calculated as the quotient of dividing the total value of the functions for this interval by the number of strokes in the interval. Analyzed the type of holes in the rock
4 5
Fig. 1. Installation for studying the process of impact destruction of rock and material of the impactor (a) and its schematic diagram (b) 1 - a fragment of rock; 2 - drummer; 3 - peen; 4 - roller; 5 - cam; 6 - reductor; 7 - electric motor
b
3
6
7
a
with the measurement of their depth h (measurement accuracy of 0.01 mm). Changing the material of the impactor, for each of them, dependences A/, d, h on the number of beats n were built.
Experiment results. As observations have shown, the process of hitting the granite is accompanied by a slight (by several millimeters) rebound of the impactor. The result of the first strike is the appearance on the pointed part of the impactor of a circular blunting area, the diameter d of which increases as the number of blows increases.
The destruction of granite is characterized by a departure from the zone of destruction of particles and dust-like fragments with the formation of holes of a shape that is close to the configuration of the penetrating part of a impactor of a larger diameter. At the bottom of the wells, a compacted core of powdered degradation products is found, which differs in color (white) from the rest of the rock.
It is established that with an increase in the number of impacts, the values of A/ and h monotonously decrease (Fig.2). Moreover, the curves A/ = f(n) for the analyzed steels are located on the graph relative to each other in a sequence opposite to the location of the curves h = f (n) for the same materials.
Typical shape of obtained dependencies Am = f(n) presented in Fig.3. As can be inferred from the type of curves in Fig.3, the process of an impactor mass loss Am depending on the number of
impacts n for all materials analyzed is characterized by three stages. At the first (stage I), including
*
several first strikes up to some critical, different for each steel, the number of strikes n = 8-10,
value Am it is calculated in tenth milligrams and decreases with each successive stroke with a no*
ticeable rate (0.3-0.4 mg / stroke). At stage II, starting at n > n and continuing to the second critical
value n = 3600-5400, value Am is only a few hundredths of a milligram, and its rate of decline
**
with increasing n slowing down dramatically. At stage III with n > n , continuing until the end of a series of experiments, the loss of mass Am becomes independent of the number of strokes. This value Am, determined for each steel, was taken as the speed of impact-abrasive wear K determined for each steel, was taken as the speed of impact-abrasive wear of K material at the steady-state stage
0.3
I 0.2
<
0.1
0.6 a °.4
-JC
0.2
10
20
30
10
20
30
Fig.2. Dependence of the length decrease of the hammer A/ (a) and the depths of the hole h (6) on the number of beats n
for different materials of a hammer 1 - steel 38HM; 2 - steel H12MFx (hereinafter index x indicates the processing of cold steel)
a 1.0 0.8
Ml
a
I 0.5 0.3
b 1.0 0.8
a
I 0.5 0.3
I n-1—''— II \ [{ III
) ) ( (
n ' 1__((
*v*
n* ,'■:■, , * * n
10
20
5090 5100
10
20
4890 4900
Fig.3. Dependence of the mass loss Am of the impactor from the 38HM (a) and X12MFx steels (b) on the number of impacts n
b
a
0
0
n
n
0
0
n
n
Viktor I. Bolobov, Le Tkhan' Bin'
Regularities of Material Destruction of the Impactor..
of the wear process, and the value of I, and the reverse of K, as shock-abrasive wear resistance of this impactor material.
To explain the processes occurring at each stage of wear of a impactor, we used the data on the magnitude of the stresses occurring at the contact area of the impactor and the types calculated using the developed mathematical model
Mathematical model of impact rock destruction process under experimental conditions. In
developing the model, it was assumed that the impactor, together with the pin, is a structure of relatively short length = 340 mm). It was believed that the influence of wave processes on the impact parameters can be neglected and the process of interaction between the impactor and the material being destroyed can be described by the equations of a two-element classical shock system [5]. As the results of the calculation showed, the condition of applicability of these equations is satisfied
tm > 3T,
where tm - stroke time, tm = 0,6-1,4 ms; T - oscillation period of impactor and pin, T = 0,13 ms.
Based on the outputs of [5] on the existing types of load characteristics of fracture, taking into account our observations of the impact process, it was assumed that the penetration of a impactor into the rock under the experimental conditions is characterized by three main stages:
• elastic deformation of the rock to achieve on the area of its contact with the impactor oK, at which the explosion-like destruction of the rock occurs under the contact area;
• by moving the impactor through the core of the destruction of the rock, displacing some of the products from the well and pressing the remaining products without reaching the bottom of the zone of destruction;
• discarding the impactor by the forces of residual elasticity of compacted fracture products.
The dependence of rock resistance force N on deformation a (Fig.4) for this case corresponds to the load characteristic of type V [5] and consists of three strength functions: loads Ni during elastic deformation of the rock under the contact area, loads N2 when the impactor is introduced into the products of rock destruction and discharge N3, each of which is characterized by its rigidity (g1, g2, g3). Wherein fuctions N1, N2, N3, as for the introduction of the body with a constant contact area, are linear type. The area of the figure in Fig.4 - the work of loading A, shaded area - work Ad, spent on destruction.
Maximum strength of rock resistance Nm and penetration apen, and also time strike tm for such a load characteristic [5]:
Nm - N„ 1 - +
g1
N2
a pen a m
Nm.
M 3
- N
1 1
, g 2 g 1
1 - Ml + 2Adg2 -1
g1
N2
M
tm -J-arctg
\M 2
2 A,g 2
N2
where M - falling object mass; Nd - force of contact destruction of rock,
Np = fca^cr,
fca = nd2/4 - contact area; ocr - stress at the point of contact at which tensile and shear stresses occur upon
Fig.4. Shape of load characteristic of the system, taken impact ^ in the rock lead to its explosion-like destruc-in the calculation of impact parameters tion under the contact area.
The assumptions adopted in the calculations:
• for the value of the critical contact stress oc the value of the dynamic hardness of the rock can be accepted (for granite 1305 MPa [9]);
• to establish the contact stiffness of the system gi, as for the circular contact area with a diameter d, following formula is occurred [5]:
1.6
1.2
0.8
0.4
0.0
/3
1
2 ■ \ r ' '—* ■ * *m mrn^^m-ui. a
/ " 4 1 1 1
0.6
0.8
gi =
2Epd
3(1 P)
1.0
d, mm
1.2
with
Fig.5. Estimated single impact parameters tm (1), Nm (2), ac (3), apen (4) depending on the diameter of the contact area d in comparison with the experimentally established depth of the holes obtained for impactors from the steels being analyzed
Ep = 50 GPa
modulus of elasticity and Poisson's ratio p,p = 0.2 of granite [5];
• by analogy with the stiffness ratio g2/g1 and g3/g1, which can be established from the analysis of the experimental strength characteristics of contact fracture of fragile rocks given in [6], for the rigidity g2 in our case, a value equal to 0,16 g1, and for g3 - value g1;
• only about half of the kinetic energy A0 of the impactor is expended on elastic deformation and destruction of the rock (for granite 58.6 % [5]), the rest of the energy is expended on heat losses to the environment, elastic and plastic deformation of the impactor, and wear of its contact surface [9]), so they took value Ai = 0.586, A0 = 0.68 J.
Fig.5 presents the values of the impact time. tm (cuve 1), maximal rock resistance force Nm (curve 2), contact stress oc = Nm/nd2/4 (curve 3) and penetration apen of impactor in the breed (curve 4), calculated by value Np for the interval of diameters d of contact areas taking place in experiments (blunting areas). In Fig.5, for the corresponding values of d, the depths h of the wells, established experimentally (see Fig.2, b), are given.
As can be seen from the graph in Fig.5, with a constant impulse of forceM v0 = Nm tm with an increase in the diameter d of the contact area (padding of the impactor), the maximum force of resistance of the rock Nm increases monotonically, and the time of impact tm, maximum contact stress oc and depth of penetration apen of indenter are dropping. As can be inferred from comparing the location of experimental points and curve 4, the regression line is apen = f (d) shows satisfactory convergence with experimental data for all steels.
The obtained satisfactory convergence of the calculation results and experiment can serve as confirmation of the proposed mathematical model and the validity of the accepted assumptions.
Patterns of destruction of the material of the impactor. Set values K u I, arranged in increasing order of wear resistance of impactors from analyzed steel grades, as well as experimentally determined hardness values HV and calculated yield strengths [12]. oT and strength oB of steels for the conditions of static stretching of the samples are presented in table 1. It also shows the number of strokes n , n , at which for a impactor from each steel there is a transition to the next stage of interaction, the corresponding diameters d*, d** blunting area, stress o*, 0** on the contact area of the impactor with the rock from curve 3 (Fig.5) for d*, d**.
As follows from the data of Table 1, the installed shock-abrasive wear resistance of steels correlates, in general, with their hardness and strength indicators oh, cs, amplifying with the increase of these parameters. In this case, the lowest wear resistance is observed for steel 38XM after a typical heat treatment, the highest, 2.7 times greater - for steel X12MF after cold treatment. It can be noted that cold treatment leads to an increase in wear resistance of all other steels (from 11 to 26 %).
8
6
4
2
0
ё Viktor I. Bolobov, Le Tkhan'Bin'
Regularities of Material Destruction of the Impactor..
Table 1
Shock-abrasive wear resistance of the studied materials of the impactor in comparison with their strength characteristics and critical parameters of interaction between the impactor and the rock
Steel brand of hummer K, mg/stroke I, stroke/mg HV ah, MPa os, Mpa n n" d*, mm d", mm a*, MPa ac**, Mpa
38HM 0.0027 370 529 1933 1478 10 ~ 5100 1.011 2.114 3643 1651
38HM* 0.0023 435 536 1953 1529 10 ~ 5400 0.986 2.047 3767 1691
U8 0.0019 526 707 2540 1943 8 ~ 3600 0.889 1.763 4340 1915
U8, 0.0017 588 717 2577 1971 8 ~ 3900 0.876 1.724 4435 1955
H12MF 0.0013 741 694 2492 1905 8 ~ 4100 0.866 1.680 4502 2003
H12MF* 0.0010 1000 708 2544 1946 8 ~ 4900 0.836 1.620 4729 2076
It can be seen that as the strength and wear resistance of steels increases, the magnitude of contact voltage a**, aC, corresponding to the transition from stage to stage of interaction, increase. At the same time between the values oc* and oh, and aC* and os there is a definite correlation: first (aC, a**) about the same number of times than the second. From the facts of the presence of three characteristic stages of interaction (see Fig.3) and the existence of this proportion for all steels, it can be assumed that the critical values established by calculation and experimentally are aC, aС contact stresses correspond to the voltage in the layer of a given material of the impactor adjacent to the contact area, starting from which it is able to collapse under dynamic conditions aC or plastically deform a**. For the conditions of static stretching of the samples, the analogue stress aC is the parameter «true breaking stress Sc», and stress aC* - yield threshold os of material with values less than the corresponding dynamic characteristics of steels. It can be noted that approximately the same excess of the values of the yield strength os (to 1,1 times) and strength threshold oh (до 2 раз), determined at high strain rates, above those established under static compression and tension of the samples, are described in works [2, 6] for technical iron and medium carbon alloyed steel.
With small diameters of blunting area (n < n , d < d , stage I) contact stresses developed upon impact ок are exceeding true dynamic breaking stress aK this steel and on the contact area there are cracks, the development of which leads to chipping of significant volumes of metal, which is recorded in the form of a noticeable loss of the impactor mass. With large diameters (d < d < d , n < n < n , stage II) of the resulting stresses it is not enough to destroy the material of the impactor, but it is sufficient for its plastic deformation, accompanied by the movement of metal from the central part of the contact area to the peripheral one. Based on the fact that there is a noticeable loss in the mass of the impactor at this stage, it can be concluded that a significant part of the metal volume deformed and weakened by cracks is carried away by the moving products of rock destruction.
Such a conclusion about the destruction and significant plastic deformation of the tip of the impactor in the early stages of interaction is supported by the results of tests specially carried out by the authors, in which strikes by the impactor were applied not to the abrasive, but to a smooth plate of a harder material that is not destroyed. As can be inferred from the results of this experiment, shown in Figure 6, with a small number of blows, chipping off of the parts of the impactor tip occurs with the appearance of deformed metal waves directed from the center to the periphery at the contact area. Fig.6 shows the manifestation of the edge effect - chipping of the peripheral areas of the contact area.
The greater the number of beats n in the early stages of interaction and the larger the area of the dumbness of the impactor, the smaller the resulting contact voltage oK and its excess over aC or a**
steel used, and, accordingly, a thinner metal zone on the contact area subjected to destruction or deformation and, therefore, less Am. With n > n**, d > d* (stage III), arising contact stresses oc do not reach the level aC* and the tip of the impactor is not subjected to plastic deformation. The appear-
Fig.6. View of a steel hammer blunting area of U8 after striking a solid metal substrate at the stage I of engagement (a) and granite at stage III (b)
ance of parallel scratches on this site during the transition to impact on the rock suggests that in this case the metal of the site is exposed to moving abrasive particles. The result of scratching is a significantly smaller, compared with stages I, II, loss of metal mass, the value of which is determined by the abrasive wear resistance of the steel used to manufacture the impactor, depending on its hardness and structural features [3]. It should be noted that the presence of holes on the contact area, along with scratches, may indicate that, in addition to wear by the moving abrasive particles, the material of the impactor undergoes impact and the introduction of stationary abrasive particles into it [2], which takes place at the stage of compaction products of rock destruction.
The proportion of energy expended in the destruction of a rock to wear a impactor at the steady (third) stage of its wear was estimated based on the established wear rates of K materials and critical stresses c corresponding steels. It was assumed that, since in our case, the wear of the material occurs mainly due to the destruction (scratching) of its surface with an abrasive, the specific work Asp this process can be estimated by the formula proposed in [1] for the destruction of metals by stretching samples
A -
sp - p ,
where Sc - true destructive stress of the metal, in accordance with the above assumptions of the authors, for dynamic conditions, equals Cc of particular steel from Table 1; p - density, p = 7.85 103 kg/m3 for all steels.
Then the work spent on the wear of the material of the impactor per blow,
A - KA - KCc
mw ^^^sp
p
and the amount of Amw for wear metal in impact energy A0
A
mw%
Amw Kcc
Ao Aop
The work Aei, spent on the elastic deformation of the impactor in the course of a single injection into granite at the steady-state stage of interaction III, was calculated as the product of the maximum resistance of the rock Nm for d = d by the total decrease in the lengths AlSel cylindrical Aliel and the conical Al2el parts of the impactor when it is elastic, when
Al - Nml
1 el -
S1E '
where S1 - sectional area of the cylindrical part; E - Young's modulus, E = 200-10 MPa for all steels.
b
a
ê Viktor I. Bolobov, Le Tkhan'Bin'
Regularities of Mäerial Destruction of the Impactor..
To determine A/2el a truncated cone with bases equal to the areas of the cylindrical part of the impactor and the blunting area, the height-varying area of its cross section Si expressed through the distance x from the top of the cone and the angle ß = 30°
o 2.2 ß
Si = nx tg
and the differential equation of the relative change in the height of the cone due to the elastic deformation as a function of x was solved
dx
G
E
N_
Etcx 2tg ß 2
which was integrated at the current x coordinate from the top of the cone to the blunting area x1 (Al at d**) and to seat x2 (l2), as a result, the final equation had the form
A/2el =-
N„
Etc tg2
x2
/ x2
~2dx = -
N
2
Etc tg2
x2 _
N
2
Etc tg
1 1
V xi
2 J
2
Accordingly, the value Ae%0 equals Ael/A0.
Assuming that the established rates of impact-abrasive wear of the steels K from Table 2 are maintained with further shocks up to a diameter of 3.55 mm, at which the formation of the well is stopped, the number of impacts n was calculated and the resulting depth of holes hs to this moment for the hammer of each steel.
Tab/e 2
Energy parameters of the process of shock-abrasive wear and elastic deformation of a impactor of various steel grades
Steel brand Asp, J/mg Amw) J Amw, % Ae/, J Ae/, % n'" hi, mm
38HM 0.464 0.0013 0.108 0.114 9.8 ~68500 3410
38HM 0.480 0.0011 0.095 0.107 9.3 ~ 79900 4219
U8 0.553 0.0011 0.091 0.085 7.3 ~ 93800 6352
U8x 0.565 0.0010 0.083 0.082 7.1 ~104700 7376
H12MF 0.574 0.0008 0.067 0.080 6.9 ~131000 9569
H12MFx 0.602 0.0006 0.052 0.076 6.6 ~176200 13623
1
ß
ß
ß
x
As can be concluded from Table 2, the work Amw%%, spent on the destruction of the material of the impactor in the process of a single injection into the granite, is ~ 0.1 % of the impact energy. At the same time, with an increase in the wear resistance of the steel used to manufacture the impactor, Amw% decreasing. The work Ael% on the elastic deformation of the impactor is a few percent of the impact energy and, as Amw%, decreases with increasing wear resistance of the impactor material. So, if for the least durable steel 38HM it is 9.8% (d**= 2.11 mm, Nm = 5.80 kN, Md = 0.0182 mm, Ml = 3.94 mm, Al2el = 0.0211 mm), then for the most durable (H12MFx) - 6.6 % (d** = 1,62 mm, Nm = 4.28 kN, Ml1ynp = 0.0127 mm, Ml = 3.02 mm, Ml2el = 0.0229 mm). As calculations show, with a further increase in the number of strokes (above n ) and a corresponding increase in the diameter of the blunting area (above d ) work quantity Ael% increases and reaches for all steels by the time of complete blunting of the tip of the impactor of ~ 36 %.
From Table 2 it follows that by the time of the termination of the introduction of the impactor into the rock, the total depth of the holes hs, embossed by a impactor from steel H12MFx after cold treatment is four times higher than the same figure for a impactor from steel 38XM due to the significantly greater wear resistance of the impactor from steel H12MFx.
Conclusion. Thus, as shown by calculations and experiments, the wear process of a cone-shaped steel impactor during its single impacts on granite is characterized by the existence of three stages of interaction, each of which is determined by the ratio of the strength characteristics a , a , demonstrated by the material of the impactor under dynamic conditions, with the magnitude of the stress ak arising at the contact area of the impactor with the rock and decreasing as the number of impacts n increases. At the last established stage of the interaction, the decrease in the impactor mass with increasing number of impacts practically does not change and is determined by the wear resistance of the steel used, as a result of which the number of impacts until the tip of the impactor is completely blunt and the total depth of holes for the analyzed steels differ by 2.6 and 4.0 times, respectively.
Gratitude. The authors express deep gratitude to Associate Professor A.P.Batalov for the assistance rendered in the preparation of this article.
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Authors: Viktor I Bolobov, Doctor of Engineering Sciences, Professor, boloboff@mail.ru (Saint-PetersburgMining University, Saint-Petersburg, Russia), Le Tkhan' Bin', Postgraduate Student (Saint-Petersburg Mining University, Saint-Petersburg, Russia).
The paper was received on 10 January, 2018.
The paper was accepted for publication on 25 May, 2018.
