Method for conveying container, device for conveying container, and method for conveying ladle
A method for calculating a conveyance velocity at which oscillation of a liquid surface is suppressed in conveying a container in which a liquid is accommodated, e.g., a ladle in which molten metal is accommodated. In a graph of conveyance velocity versus conveyance time, an upwardly convex parabola and a downwardly convex parabola having vertical symmetry are prepared in advance, the downwardly convex parabola and the upwardly convex parabola are smoothly connected to form an acceleration curve, the upwardly convex parabola and the downwardly convex parabola are smoothly connected to form a deceleration curve, and the conveyance velocity is obtained from the acceleration curve and the deceleration curve smoothly connected where the slope thereof is zero.
1. A method for conveying a container, comprising:
starting a conveyance by accelerating the container containing a liquid in a horizontal direction; and
decelerating the container to complete the conveyance, wherein
a conveyance velocity v(t) of the container, which is a function of time t, is represented by:
Formula 1 when 0≤t≤(t 0 /4)
v ( t )= a·t 2 [Formula 1]
Formula 2 when (t 0 /4)≤t≤(3t 0 /4)
v
(
t
)
=
-
a
·
[
(
t
-
t
0
2
)
2
-
t
0
2
8
]
[
Formula
2
]
Formula 3 when (3t 0 /4)≤t≤(t 0 )
v ( t )= a ·( t−t 0 ) 2 [Formula 3]
wherein ‘t 0 ’ represents a time for conveying the container and ‘a’ represents a constant, and the method further comprises determining the conveyance velocity v(t) of the container by using Formulae 1 to 3, and driving a motor that rotates a plurality of wheels of a trolley on which the container is placed and conveying the container in accordance with the determined conveyance velocity v(t) such that liquid surface oscillations after conveying the container are within a tolerable range.
2. The method for conveying a container according to claim 1 , wherein:
the conveyance velocity v(t) of the container, which is a function of time t, is also represented by:
Formula 4 when 0≤t≤(t 1 /4)
v ( t )= b·t 2 [Formula 4]
Formula 5 when (t 1 /4)≤t≤(t 1 /2)
v
(
t
)
=
-
b
·
[
(
t
-
t
1
2
)
2
-
t
1
2
8
]
[
Formula
5
]
Formula 6 when (t 1 /2)≤t≤(t 1 /2)+t 2
v
(
t
)
=
1
8
b
·
t
1
2
[
Formula
6
]
Formula 7 when (t 1 /2)+t 2 ≤t≤(3t 1 /4)+t 2
v
(
t
)
=
-
b
·
[
(
t
-
t
1
2
-
t
2
)
2
-
t
1
2
8
]
[
Formula
7
]
Formula 8 when (3t 1 /4)+t 2 ≤t≤t 1 +t 2
v ( t )= b ·( t−t 1 −t 2 ) 2 [Formula 8]
wherein ‘t 1 ’ represents a total time for conveying the container in acceleration and in deceleration, ‘t 2 ’ represents a time for conveying the container at a constant speed, and ‘b’ represents a constant, and
the method further comprises:
setting the conveyance time v(t) of the container by using Formulae 1 to 3 when a maximum value of the conveyance velocity v(t) among Formulae 1 to 3 is equal to or less than a velocity limit V max for the container, which is tolerable in conveying the container; and
setting the conveyance time v(t) of the container by using Formulae 4 to 8 and calculating the conveyance time t 1 and the conveyance time t 2 from the constant a, the velocity limit V max , and a conveyance distance L of the container where the constant b is equal to the constant a and the constant speed of Formula 6 is the velocity limit V max when the maximum value of the conveyance velocity v(t) among Formulae 1 to 3 is more than the velocity limit V max .
3. The method for conveying a container according to claim 2 , wherein
the liquid is a molten metal and the container is a tilting ladle.
4. The method for conveying a container according to claim 1 , wherein
the constant a is determined α max /2 wherein α max represents a maximum value of a rate of change of acceleration of the container at which liquid surface oscillations after conveying the container is suppressed within a tolerable range.
5. The method for conveying a container according to claim 4 , wherein
a conveyance distance of the container is L and a velocity limit of the container that is tolerable in conveying the container is V max ;
the conveyance velocity v(t) of the container is set by Formulae 1 to 3 when a maximum value of the conveyance velocity v(t) among Formula 1 to 3 is equal to or less than the velocity limit V max ; and
when the maximum value of the conveyance velocity v(t) among Formulae 1 to 3 is more than the velocity limit V max , a total time for conveying the container in acceleration and in deceleration is t 1 , a time for conveying the container at a constant speed is t 2 , and the constant is b, and, in addition, the conveyance velocity v (t) of the container, which is a function of time t, is represented by:
Formula 4 when 0≤t≤(t 1 /4)
v ( t )= b·t 2 [Formula 4]
Formula 5 when (t 1 /4)≤t≤(t 1 /2)
v
(
t
)
=
-
b
·
[
(
t
-
t
1
2
)
2
-
t
1
2
8
]
[
Formula
5
]
Formula 6 when (t 1 /2)≤t≤(t 1 /2)+t 2
v
(
t
)
=
1
8
b
·
t
1
2
[
Formula
6
]
Formula 7 when (t 1 /2)+t 2 ≤t≤(3t 1 /4)+t 2
v
(
t
)
=
-
b
·
[
(
t
-
t
1
2
-
t
2
)
2
-
t
1
2
8
]
[
Formula
7
]
Formula 8 when (3t 1 /4)+t 2 ≤t≤t 1 +t 2
v ( t )= b ·( t−t 1 −t 2 ) 2 [Formula 8]
wherein the conveyance velocity v(t) is set from the conveyance time t 1 and the conveyance time t 2 that are calculated from the constant a, the velocity limit V max , and the conveyance distance L where the constant b is the constant a and the constant speed of Formula 6 is the velocity limit V max .
6. The method for conveying a container according to claim 1 , wherein
the liquid is a molten metal and the container is a tilting ladle.
7. A conveyor control device for conveying a container, which starts conveying by accelerating the container containing a liquid in a horizontal direction and completes the conveyance after deceleration, the conveyor control device comprising:
a computer, wherein
the computer stores a conveyance time t 0 of the container, a constant a, a maximum value of a rate of change of acceleration of the container α max at which liquid surface oscillations after conveying the container are suppressed within a tolerable range;
the computer also stores a conveyance velocity of the container v(t), which is a function of time t as:
Formula 1 when 0≤t≤(t 0 /4)
v ( t )= a·t 2 [Formula 1]
Formula 2 when (t 0 /4)≤t≤(3t 0 /4)
v
(
t
)
=
-
a
·
[
(
t
-
t
0
2
)
2
-
t
0
2
8
]
[
Formula
2
]
Formula 3 when (3t 0 /4)≤t≤(t 0 )
v ( t )= a ·( t−t 0 ) 2 [Formula 3]
the computer is programmed to calculate the constant a from the stored rate of change of acceleration α max and determine the conveyance velocity v(t) of the container by using Formulae 1 to 3; and
the computer is programmed to drive a motor that rotates a plurality of wheels of a trolley on which the container is placed and convey the container in accordance with the determined conveyance velocity v(t) such that the liquid surface oscillations after conveying the container are within the tolerable range.
8. The conveyor control device unit for conveying a container according to claim 7 , wherein
the computer stores a conveyance distance L, a velocity limit V max for the container, which is tolerable in conveying the container, a total time t 1 for the container to be conveyed in acceleration and deceleration, a constant speed time t 2 , and a constant b;
the computer also stores the conveyance velocity of the container v(t), which is a function of time t as:
Formula 4 when 0≤t≤(t 1 /4)
v ( t )= b·t 2 [Formula 4]
Formula 5 when (t 1 /4)≤t≤(t 1 /2)
v
(
t
)
=
-
b
·
[
(
t
-
t
1
2
)
2
-
t
1
2
8
]
[
Formula
5
]
Formula 6 when (t 1 /2)≤t≤(t 1 /2)+t 2
v
(
t
)
=
1
8
b
·
t
1
2
[
Formula
6
]
Formula 7 when (t 1 /2)+t 2 ≤t≤(3t 1 /4)+t 2
v
(
t
)
=
-
b
·
[
(
t
-
t
1
2
-
t
2
)
2
-
t
1
2
8
]
[
Formula
7
]
Formula 8 when (3t 1 /4)+t 2 ≤t≤t 1 +t 2
v ( t )= b ·( t−t 1 −t 2 ) 2 [Formula 8]
and
when a maximum value of the conveyance velocity v(t) among Formulae 1 to 3 is equal to or less than the velocity limit V max , the computer is programmed to set the conveyance time v(t) of the container by using Formulae 1 to 3; and
when the maximum value of the conveyance velocity v(t) among Formulae 1 to 3 is more than the velocity limit V max , the computer is programmed to set the conveyance time v(t) of the container by using Formulae 4 to 8, and, in addition, the computer is programmed to calculate the conveyance time t 1 and the conveyance time t 2 from the constant a, the velocity limit V max , and the conveyance distance L where the constant b is equal to the constant a and the constant speed of Formula 6 is the velocity limit V max .