477
of each portion. This approach leads, firstly, to a sharp increase in the dimension of the
problem by several orders of magnitude. Secondly, a need to constantly generate dependencies describing the movements along the face of the newly repulsed portion of coal by the
flight conveyor, and after the overload of the elementary portion from the flight conveyor
to remove these dependencies. All this leads to the fact that the discrete formulation of the
problem of describing the process of complex-mechanized face today is not solved.
All these circumstances leave only one way to represent the length-distributed loading of
the scraper conveyor in the form of selective different actions on the elements of the function ϕ. This should increase the dimension of the distribution function of coal on the scraper
conveyor, adding time t presenting it as ϕ = ϕ (x, t).
Then, the increase in the volume of coal by the extraction combine on the flight conveyor
is written by the expression ϕ = ϕ(x k , t) = ϕ(x ki , t i ) + dM = ϕ(x ki , t i ) + hγ lVk dt. Moving
cargo flight conveyor (with speed V sk ) – shift operation – transformation function ϕ (x, t),
which is described by the expression ϕ(x i , t + dt) = ϕ(x i – V sk dt, t). In this case, the part of the
conveyor, which is located at the top of the road, and is a section that appeared in the time
interval dt and remains empty ϕ(x n ÷ x n – V sk dt, t + dt) = ϕ(x i – V sk dt, t) = 0.
Coal, which was on the flight conveyor at the bottom of the bay, is overloaded to the following process equipment. This volume of coal is ϕ out (x k , t) = ϕ(x 1 ÷ x 1 + V sk dt, t). Similar to
the flight conveyor as a streaming device for moving the rock mass, a loader, a crushing plant,
and a belt conveyor work.
The ratios describing the technological process of moving the combine harvester, rock
mass, with the help of technological equipment of complex-mechanized face the following.
Submission of the combine along the face (1).
The flow of coal
ϕ
ϕ
γ
ϕ
ϕ
sk
ϕ ϕ
sk
ϕ
k
p
i
ϕ ϕ
i
p
ϕ
n
dM
hlV k
V dt
dM
x x
n
ϕ sk
ϕ
( )
i i
t + dM
( )
i i
x t
i i
x i
+ γ hl
γ V d
k t(
)
i
k
x
=
i
x
( )
i i
t + dM
n
p
n n
i
s k
sk
p
d
d
V d
p t t
V s
V p
dM
−
(
) = k (
)
sk
i
x x V d
k t t
x
+
( )
i i
( )
t + dM
sk sk
sk k
, i
t
ϕ
ϕ d
ϕ d ( )
i i
x t
i
+
=
dM
x x V dt t
V
V
dM
p
p
i
p
V V
d
V V
lk
lk
,
V dt
p
V V
x x
p
(
)
n
n
x x
n
−
x V d
V V t t
d
i
V d
V V V t t i
t
x x
=
+
( (
)
( )
t
i i + dM
ϕ
ϕ
d
ϕ lk
l
( )
x t
i i
t +
=
dM
1
x x x
V
V
d
d
V V
lk
V V
d
(
)
x x V
n
n
x
lk
V V
−
x
dt d d t i
,t i
(
)
x x V dt t
d
i
V dt t
V d
V V dt
x ÷
x x
⎧
⎨
⎪
⎧ ⎧
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎨ ⎨
⎪ ⎪
⎩
⎪
⎨ ⎨
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎩ ⎩
⎪ ⎪
x x
÷
(8)
Coal movements
ϕ
ϕ
ϕ
sk
ϕ ϕ
s
ϕ k
sk
ϕ
if i
s
ϕ k
,
(
)
i t dt
+
ϕ k (
)
i
sk
x V
i
dt t
,
i
sk
V
i
s dt
x
(
)
i
n
sk
x x V
n
s dt
,
, ,
i
, f
i
x V dt i
,
t
p
i
i
p x
p
(
)
n
n
sk
x x
n
V d
sk t
−
x
, , ,t dt
i
, f
i (
)
x x V dt
i
n
x
sk
V V
≥
x i
⎧
⎨
⎧ ⎧
⎨ ⎨
⎧ ⎧ ⎧ ⎧
⎩
⎨ ⎨
⎩ ⎩
⎨ ⎨ ⎨ ⎨
)
i
(
)
t dt
+
x
( (
)
0
ϕ
ϕ p (
)
,
x t
, dt
i
x +
=
f x
f f
i
x V dt
x x V dt t dt
if x x V dt
i
n
x
p
V V
n
x
p
n
p
V V
i
n
x
p
V V
d
≺
(
)
−
x
+
(
)
≥
x
= if
−
(
)
⎧
⎨
⎪
⎧ ⎧
⎨ ⎨
⎩ ⎪
⎨ ⎨
⎩ ⎩ ϕ
ϕ d
,
,
t dt
+ ) 0
d
d
d
if
d d
,
(
)
x i i i t dt
d (
)
i
d
x V d
d t t
,
i
d
x
d
d t
−
x
(
)
i
n
d
x x
i
V d
d t
−
(
)
n
n
d
x x
n
V d
d t t dt
,
−
x
+
=
d d
ϕ d
0, 0 0
,
if
i
, f
i
lk
lk l l
(
)
x
V dt
i
n
x
d
V V
≥ −
x n
x
⎧
⎨
⎧ ⎧
⎨ ⎨
⎧ ⎧ ⎧ ⎧
⎩
⎨ ⎨
⎩ ⎩
⎨ ⎨ ⎨ ⎨
(
)
i
(
)
t dt
+
lk l (
)
,
x V dt t
i
x
lk
V V
x x
ϕ l
ϕ lk (
)
x t dt
i ,t , dt
+
= l
(
)
x x
i
n
x
≺ − −
(
)
−
+
=
(
)
≥ −
⎧
⎨
⎧ ⎧
⎨ ⎨
⎧ ⎧ ⎧ ⎧
⎩
⎨ ⎨
⎩ ⎩
⎨ ⎨ ⎨ ⎨
⎧
⎨
⎪
⎧ ⎧
⎪
⎪ ⎪
⎪
⎪ ⎪
÷
if
≥
lk
≥
ϕ l
,
)
+
0
⎪ ⎪
⎪ ⎪ ⎪ ⎪
⎪
⎪ ⎪ ⎪ ⎪
⎪
⎪ ⎪
⎪
⎨ ⎨
⎪ ⎪
⎩
⎪
⎨ ⎨
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎩ ⎩
⎪ ⎪
(9)
Transshipment of coal to the following process equipment
of each portion. This approach leads, firstly, to a sharp increase in the dimension of the
problem by several orders of magnitude. Secondly, a need to constantly generate dependencies describing the movements along the face of the newly repulsed portion of coal by the
flight conveyor, and after the overload of the elementary portion from the flight conveyor
to remove these dependencies. All this leads to the fact that the discrete formulation of the
problem of describing the process of complex-mechanized face today is not solved.
All these circumstances leave only one way to represent the length-distributed loading of
the scraper conveyor in the form of selective different actions on the elements of the function ϕ. This should increase the dimension of the distribution function of coal on the scraper
conveyor, adding time t presenting it as ϕ = ϕ (x, t).
Then, the increase in the volume of coal by the extraction combine on the flight conveyor
is written by the expression ϕ = ϕ(x k , t) = ϕ(x ki , t i ) + dM = ϕ(x ki , t i ) + hγ lVk dt. Moving
cargo flight conveyor (with speed V sk ) – shift operation – transformation function ϕ (x, t),
which is described by the expression ϕ(x i , t + dt) = ϕ(x i – V sk dt, t). In this case, the part of the
conveyor, which is located at the top of the road, and is a section that appeared in the time
interval dt and remains empty ϕ(x n ÷ x n – V sk dt, t + dt) = ϕ(x i – V sk dt, t) = 0.
Coal, which was on the flight conveyor at the bottom of the bay, is overloaded to the following process equipment. This volume of coal is ϕ out (x k , t) = ϕ(x 1 ÷ x 1 + V sk dt, t). Similar to
the flight conveyor as a streaming device for moving the rock mass, a loader, a crushing plant,
and a belt conveyor work.
The ratios describing the technological process of moving the combine harvester, rock
mass, with the help of technological equipment of complex-mechanized face the following.
Submission of the combine along the face (1).
The flow of coal
ϕ
ϕ
γ
ϕ
ϕ
sk
ϕ ϕ
sk
ϕ
k
p
i
ϕ ϕ
i
p
ϕ
n
dM
hlV k
V dt
dM
x x
n
ϕ sk
ϕ
( )
i i
t + dM
( )
i i
x t
i i
x i
+ γ hl
γ V d
k t(
)
i
k
x
=
i
x
( )
i i
t + dM
n
p
n n
i
s k
sk
p
d
d
V d
p t t
V s
V p
dM
−
(
) = k (
)
sk
i
x x V d
k t t
x
+
( )
i i
( )
t + dM
sk sk
sk k
, i
t
ϕ
ϕ d
ϕ d ( )
i i
x t
i
+
=
dM
x x V dt t
V
V
dM
p
p
i
p
V V
d
V V
lk
lk
,
V dt
p
V V
x x
p
(
)
n
n
x x
n
−
x V d
V V t t
d
i
V d
V V V t t i
t
x x
=
+
( (
)
( )
t
i i + dM
ϕ
ϕ
d
ϕ lk
l
( )
x t
i i
t +
=
dM
1
x x x
V
V
d
d
V V
lk
V V
d
(
)
x x V
n
n
x
lk
V V
−
x
dt d d t i
,t i
(
)
x x V dt t
d
i
V dt t
V d
V V dt
x ÷
x x
⎧
⎨
⎪
⎧ ⎧
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎨ ⎨
⎪ ⎪
⎩
⎪
⎨ ⎨
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎩ ⎩
⎪ ⎪
x x
÷
(8)
Coal movements
ϕ
ϕ
ϕ
sk
ϕ ϕ
s
ϕ k
sk
ϕ
if i
s
ϕ k
,
(
)
i t dt
+
ϕ k (
)
i
sk
x V
i
dt t
,
i
sk
V
i
s dt
x
(
)
i
n
sk
x x V
n
s dt
,
, ,
i
, f
i
x V dt i
,
t
p
i
i
p x
p
(
)
n
n
sk
x x
n
V d
sk t
−
x
, , ,t dt
i
, f
i (
)
x x V dt
i
n
x
sk
V V
≥
x i
⎧
⎨
⎧ ⎧
⎨ ⎨
⎧ ⎧ ⎧ ⎧
⎩
⎨ ⎨
⎩ ⎩
⎨ ⎨ ⎨ ⎨
)
i
(
)
t dt
+
x
( (
)
0
ϕ
ϕ p (
)
,
x t
, dt
i
x +
=
f x
f f
i
x V dt
x x V dt t dt
if x x V dt
i
n
x
p
V V
n
x
p
n
p
V V
i
n
x
p
V V
d
≺
(
)
−
x
+
(
)
≥
x
= if
−
(
)
⎧
⎨
⎪
⎧ ⎧
⎨ ⎨
⎩ ⎪
⎨ ⎨
⎩ ⎩ ϕ
ϕ d
,
,
t dt
+ ) 0
d
d
d
if
d d
,
(
)
x i i i t dt
d (
)
i
d
x V d
d t t
,
i
d
x
d
d t
−
x
(
)
i
n
d
x x
i
V d
d t
−
(
)
n
n
d
x x
n
V d
d t t dt
,
−
x
+
=
d d
ϕ d
0, 0 0
,
if
i
, f
i
lk
lk l l
(
)
x
V dt
i
n
x
d
V V
≥ −
x n
x
⎧
⎨
⎧ ⎧
⎨ ⎨
⎧ ⎧ ⎧ ⎧
⎩
⎨ ⎨
⎩ ⎩
⎨ ⎨ ⎨ ⎨
(
)
i
(
)
t dt
+
lk l (
)
,
x V dt t
i
x
lk
V V
x x
ϕ l
ϕ lk (
)
x t dt
i ,t , dt
+
= l
(
)
x x
i
n
x
≺ − −
(
)
−
+
=
(
)
≥ −
⎧
⎨
⎧ ⎧
⎨ ⎨
⎧ ⎧ ⎧ ⎧
⎩
⎨ ⎨
⎩ ⎩
⎨ ⎨ ⎨ ⎨
⎧
⎨
⎪
⎧ ⎧
⎪
⎪ ⎪
⎪
⎪ ⎪
÷
if
≥
lk
≥
ϕ l
,
)
+
0
⎪ ⎪
⎪ ⎪ ⎪ ⎪
⎪
⎪ ⎪ ⎪ ⎪
⎪
⎪ ⎪
⎪
⎨ ⎨
⎪ ⎪
⎩
⎪
⎨ ⎨
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎪ ⎪
⎪
⎩ ⎩
⎪ ⎪
(9)
Transshipment of coal to the following process equipment