474
a mathematical description for predicting field concentrations of methane in breakage face
(Borshchevich et al. 2010); the relationship that allows to predict the methane release from
the broken coal in the preparatory workings with the speed of face advance (Kachurin et al.
2014); the results of studies of gas emission from broken coal during high-performance treatment systems (Shevchenko & Livinskaya 2015); model parameter optimization of the extraction of the stratum “Fourth” mines of JSC “Vorkutaugol” (Kazanin & Sufiyarov 2014).
2 FORMALIZATION OF THE TASK
In practice, it is required quickly determine the modes of operation of complex-mechanized
faces in specific current conditions. Of particular importance is the correct choice of the
program of operational management and monitoring of technological operations for the
timely detection of deviations from the selected mode, adjustment of the established current
modes of operation of technological processes and the development, and if necessary, the
implementation of measures aimed at reducing the risks of accidents (Kopylov et al. 2016,
Kopylov et al. 2018, Kopylov et al. 2017). The analysis of the works considered above shows
that the results given in them are not suitable for the development of a model of the technological process characterizing the main operations of the extraction complex: the beating and
transportation of coal.
When creating a mathematical model of the excavation complex, the input factors are: the
feed rate of the combine, the speed of the flight conveyor, loader, crusher, belt conveyor, the
concentration of methane at the inlet and outlet of the treatment face, the relative methane
content of the developed layer; the output parameter is the performance of the combine. To
formalize the task, it is necessary to make the transition from verbal description to quantitative relations between input and output parameters. The first verbal description that needs to
formalize defines two actions – “the destruction of the coal seam and the movement of coal
to the flight conveyor.”
To represent these actions in a mathematical model, it is required to specify additional variables (the location and time of the combine relative to the face), which are determined based
on input parameters. When considering the problem, when the feed of the combine carried
out at a constant speed, there are no special problems. However, in practice, the harvester
along the lava moves at variable speed and often with stops. Therefore, in general case the
motion of the excavation of the harvester along the line of slaughtering is carried out with
the same velocity, V k , is given by an arbitrary (specified by the operator of the harvester) the
law V k = V k (t). Then the location of the harvester is determined as the x(t) coordinate and is
found from the solution of the differential equation
dx
dt
V k
V V
= ( )
t
(1)
With the constant movement of the harvester, its location changes with time x k = x k (t).
Using the parametric setting of the combine location coordinate, that is, expressing the time,
you can go through the coordinate to the equation
dx
dt
V x
k
V V
=
( )
t
( )
(2)
Thus, the number of additional variables reduced; however, this will not be correct, since if
the dependence x k = x k (t) is unambiguous, then the dependence t = t(x k ) is unambiguous only
with the constant movement of the harvester. If it stops or moves backwards, the certainty is
lost. This is the first feature of the task to taken into account.
The second feature arises when trying to quantitatively, using mathematical notation, formalize the second verbal description of the mechanized complex – “coal, getting on the flight
conveyor moves along the face.” At a constant rate of flow extraction processor, the amount
of repelling them coal will be permanent. The current filling of the flight conveyor with coal
a mathematical description for predicting field concentrations of methane in breakage face
(Borshchevich et al. 2010); the relationship that allows to predict the methane release from
the broken coal in the preparatory workings with the speed of face advance (Kachurin et al.
2014); the results of studies of gas emission from broken coal during high-performance treatment systems (Shevchenko & Livinskaya 2015); model parameter optimization of the extraction of the stratum “Fourth” mines of JSC “Vorkutaugol” (Kazanin & Sufiyarov 2014).
2 FORMALIZATION OF THE TASK
In practice, it is required quickly determine the modes of operation of complex-mechanized
faces in specific current conditions. Of particular importance is the correct choice of the
program of operational management and monitoring of technological operations for the
timely detection of deviations from the selected mode, adjustment of the established current
modes of operation of technological processes and the development, and if necessary, the
implementation of measures aimed at reducing the risks of accidents (Kopylov et al. 2016,
Kopylov et al. 2018, Kopylov et al. 2017). The analysis of the works considered above shows
that the results given in them are not suitable for the development of a model of the technological process characterizing the main operations of the extraction complex: the beating and
transportation of coal.
When creating a mathematical model of the excavation complex, the input factors are: the
feed rate of the combine, the speed of the flight conveyor, loader, crusher, belt conveyor, the
concentration of methane at the inlet and outlet of the treatment face, the relative methane
content of the developed layer; the output parameter is the performance of the combine. To
formalize the task, it is necessary to make the transition from verbal description to quantitative relations between input and output parameters. The first verbal description that needs to
formalize defines two actions – “the destruction of the coal seam and the movement of coal
to the flight conveyor.”
To represent these actions in a mathematical model, it is required to specify additional variables (the location and time of the combine relative to the face), which are determined based
on input parameters. When considering the problem, when the feed of the combine carried
out at a constant speed, there are no special problems. However, in practice, the harvester
along the lava moves at variable speed and often with stops. Therefore, in general case the
motion of the excavation of the harvester along the line of slaughtering is carried out with
the same velocity, V k , is given by an arbitrary (specified by the operator of the harvester) the
law V k = V k (t). Then the location of the harvester is determined as the x(t) coordinate and is
found from the solution of the differential equation
dx
dt
V k
V V
= ( )
t
(1)
With the constant movement of the harvester, its location changes with time x k = x k (t).
Using the parametric setting of the combine location coordinate, that is, expressing the time,
you can go through the coordinate to the equation
dx
dt
V x
k
V V
=
( )
t
( )
(2)
Thus, the number of additional variables reduced; however, this will not be correct, since if
the dependence x k = x k (t) is unambiguous, then the dependence t = t(x k ) is unambiguous only
with the constant movement of the harvester. If it stops or moves backwards, the certainty is
lost. This is the first feature of the task to taken into account.
The second feature arises when trying to quantitatively, using mathematical notation, formalize the second verbal description of the mechanized complex – “coal, getting on the flight
conveyor moves along the face.” At a constant rate of flow extraction processor, the amount
of repelling them coal will be permanent. The current filling of the flight conveyor with coal