Method for simulating the movement behaviour of a fluid in a closed, moving container
View Patent ↗A method for simulating the movement behavior of a fluid in a closed moving container is provided. The simulation is based on the determination of the potential movement path of the center of gravity of the volume of the fluid as an elliptical trajectory situated in a disturbance plane having certain semi-axes.
1. A method for controlling a vehicle comprising a closed container with a fluid, the container having a capacity (V T ) and the fluid having a volume (V L ), the method comprising the steps:
determining, using a simulation in a computing unit, a movement behavior of the fluid as a reaction to a planned movement change of the vehicle by determining, independent of a shape of the container, a potential movement path of a center of gravity of the volume (V L ) of the fluid as an elliptical trajectory;
determining expected trajectory data and forces of mass that will act on the container caused by the movement behavior of the fluid due to the planned movement change;
transmitting the expected forces of mass to a control computer of the vehicle; and
compensating, in real-time, for reactive effects on control of the vehicle induced by the expected forces of mass.
2. The method according to the claim 1 ,
wherein the elliptical trajectory is situated in a disturbance plane (E) and has the semi-axes
a
=
V
T
2
A
·
(
1
-
V
L
V
T
)
b
=
A
2
·
(
1
-
V
L
V
T
)
wherein (A) represents the largest cross-sectional area of the container perpendicular to the disturbance axis (E);
wherein the simulation of the movement behavior of the fluid in the container, with a temporally variable constant disturbance acting as a movement change on the container, which disturbance deflects the container from an idle position by an angle (φ 0 ) situated in the disturbance plane (E) having a container axis, involves the computing unit performing the further steps of
a) determining trajectory data of the expected disturbance-induced movement of the center of gravity as a function of time (t) according to the differential equation:
φ
¨
=
1
R
·
g
·
sin
δ
-
L
·
φ
.
which includes
the excitation:
φ
0
=
arctan
(
x
E
z
E
)
the force of gravity (g),
the tangential angle (δ) calculated according to
δ
=
arctan
(
-
x
E
·
b
2
z
E
·
a
2
)
,
wherein (x E ) and (z E ) are coordinates of the center of gravity on the elliptical trajectory having semi-axes (a) and (b);
a fluid-specific damping term (L) and
the distance (R) between the center of gravity and the center (M) of the elliptical trajectory,
wherein (R) is calculated according to
R
=
a
·
b
a
2
·
sin
2
φ
_
-
b
2
·
cos
2
φ
_
with
φ
_
=
90
°
-
φ
(
t
)
b) determining expected forces of mass (F) of the fluid, which act in the center of gravity, as a function of time (t) according to the equation:
F=m·g ·cos δ
which includes
the fluid mass (m),
the force of gravity (g) and
the tangential angle (δ) in (x E ) and (z E );
c) transmitting the determined trajectory data of the expected disturbance-induced movement and the expected force of mass (F) acting in the center of gravity from the computing unit to the processing unit arranged downstream thereof.
3. A method for dropping a load from vehicle, the load having a closed container with a fluid, the container having a capacity (V T ) and the fluid having a volume (V L ), the method comprising the steps:
determining, using a simulation in a computing unit, a movement behavior of the fluid as a reaction to a drop of the load from the vehicle by determining, independent of a shape of the container, a potential movement path of a center of gravity of the volume (V L ) of the fluid as an elliptical trajectory;
determining expected trajectory data and forces of mass that will act on the container caused by movement of the fluid when dropping the load;
transmitting the expected trajectory data and forces of mass to an on-board computer of the vehicle;
determining, using the on-board computer and accounting for an actual trajectory data of the movement path of the vehicle, whether dropping the load is permissible and authorized; and
dropping the load when it is determined that dropping is permissible and authorized.
4. The method according to the claim 3 ,
wherein the elliptical trajectory is situated in a disturbance plane (E) and has the semi-axes
a
=
V
T
2
A
·
(
1
-
V
L
V
T
)
b
=
A
2
·
(
1
-
V
L
V
T
)
wherein (A) represents the largest cross-sectional area of the container perpendicular to the disturbance axis (E);
wherein the simulation of the movement behavior of the fluid in the container, with a temporally variable constant disturbance acting as a movement change on the container, which disturbance deflects the container from an idle position by an angle (φ 0 ) situated in the disturbance plane (E) having a container axis, involves the computing unit performing the further steps of
a) determining trajectory data of the expected disturbance-induced movement of the center of gravity as a function of time (t) according to the differential equation:
φ
¨
=
1
R
·
g
·
sin
δ
-
L
·
φ
.
which includes
the excitation:
φ
0
=
arctan
(
x
E
z
E
)
the force of gravity (g),
the tangential angle (δ) calculated according to
δ
=
arctan
(
-
x
E
·
b
2
z
E
·
a
2
)
,
wherein (x E ) and (z E ) are coordinates of the center of gravity on the elliptical trajectory having semi-axes (a) and (b);
a fluid-specific damping term (L) and
the distance (R) between the center of gravity and the center (M) of the elliptical trajectory,
wherein (R) is calculated according to
R
=
a
·
b
a
2
·
sin
2
φ
_
-
b
2
·
cos
2
φ
_
with
φ
_
=
90
°
-
φ
(
t
)
b) determining expected forces of mass (F) of the fluid, which act in the center of gravity, as a function of time (t) according to the equation:
F=m·g ·cos δ
which includes
the fluid mass (m),
the force of gravity (g) and
the tangential angle (δ) in (x E ) and (z E );
c) transmitting the determined trajectory data of the expected disturbance-induced movement and the expected force of mass (F) acting in the center of gravity from the computing unit to the processing unit arranged downstream thereof.
5. A method for dropping a load from an vehicle, the load having a closed container with a fluid, the container having a capacity (V T ) and the fluid having a volume (V L ), the method comprising the steps:
determining, using a simulation in a computing unit, a movement behavior of the fluid as a reaction to a drop of the load from the vehicle by determining, independent of a shape of the container, a potential movement path of a center of gravity of the volume (V L ) of the fluid as an elliptical trajectory;
determining expected trajectory data and forces of mass that will act on the container caused by movement of the fluid when dropping the load;
transmitting the expected trajectory data and forces of mass an on-board computer of the vehicle; and
generating, using the on-board computer, a suggested a movement procedure of the vehicle to allow a safe drop of the load; and
executing the suggested movement procedure while dropping the load.
6. The method according to the claims 5 ,
the elliptical trajectory is situated in a disturbance plane (E) and has the semi-axes
a
=
V
T
2
A
·
(
1
-
V
L
V
T
)
b
=
A
2
·
(
1
-
V
L
V
T
)
wherein (A) represents the largest cross-sectional area of the container perpendicular to the disturbance axis (E);
wherein the simulation of the movement behavior of the fluid in the container, with a temporally variable constant disturbance acting as a movement change on the container, which disturbance deflects the container from an idle position by an angle (φ 0 ) situated in the disturbance plane (E) having a container axis, involves the computing unit performing the further steps of
a) determining trajectory data of the expected disturbance-induced movement of the center of gravity as a function of time (t) according to the differential equation:
φ
¨
=
1
R
·
g
·
sin
δ
-
L
·
φ
.
which includes
the excitation:
φ
0
=
arctan
(
x
E
z
E
)
the force of gravity (g),
the tangential angle (δ), calculated according to
δ
=
arctan
(
-
x
E
·
b
2
z
E
·
a
2
)
,
wherein (x E ) and (z E ) are coordinates of the center of gravity on the elliptical trajectory having semi-axes (a) and (b);
a fluid-specific damping term (L) and
the distance (R) between the center of gravity and the center (M) of the elliptical trajectory,
wherein (R) is calculated according to
R
=
a
·
b
a
2
·
sin
2
φ
_
-
b
2
·
cos
2
φ
_
with
φ
_
=
90
°
-
φ
(
t
)
b) determining expected forces of mass (F) of the fluid, which act in the center of gravity, as a function of time (t) according to the equation:
F=m·g ·cos δ
which includes
the fluid mass (m),
the force of gravity (g) and
the tangential angle (δ) in (x E ) and (z E );
c) transmitting the determined trajectory data of the expected disturbance-induced movement and the expected force of mass (F) acting in the center of gravity from the computing unit to the processing unit arranged downstream thereof.