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Rotational Mechanical Systems
Unit 2: Modeling in the Frequency Domain
Part 6: Modeling Rotational Mechanical Systems
Engineering 5821:
Control Systems I
Faculty of Engineering & Applied Science
Memorial University of Newfoundland
January 22, 2010
ENGI 5821 Unit 2, Part 6: Modeling Rotation Mechanical Systems
Rotational Mechanical System

Transcript

Rotational Mechanical Systems
Unit 2: Modeling in the Frequency DomainPart 6: Modeling Rotational Mechanical Systems
Engineering 5821:Control Systems I
Faculty of Engineering & Applied ScienceMemorial University of Newfoundland
January 22, 2010
ENGI 5821 Unit 2, Part 6: Modeling Rotation Mechanical Systems
Rotational Mechanical Systems
Rotational mechanical systems are modelled in almost the sameway as translational systems except that...We replace displacement,
x
(
t
) with angular displacement
θ
(
t
); Angular velocity is
ω
(
t
)We replace force with
torque
For a force
F
acting on a body at point
P
, torque is deﬁned as,
T
=
FR
sin
φ
where
R
is the distance from
P
to the body’s axis of rotation and
φ
is the angle the force makes to the ray from the axis of rotation to
P
. Hence, if the force is perpendicular to the axis of rotation then,
T
=
FR
Rotational Mechanical Systems Gears
A rotating body can be considered a system of particles withmasses
m
1
,
m
2
,
m
3
,
...
. The
moment of inertia
is deﬁned as,
J
=
m
1
R
21
+
m
2
R
22
+
m
3
R
23
+
···
The total kinetic energy is,
K
= 12
J
ω
2
Recall that the kinetic energy for a translational system is
12
mv
2
.So
J
is analagous to mass in translational motion. Also, similar tothe equation
F
=
ma
in translational systems, we can relate torqueand angular acceleration,
T
(
t
) =
J d
ω
dt
=
J d
2
θ
dt
2
We deﬁne the components of our rotational system as springs,viscous dampers, and rotating masses.
ENGI 5821 Unit 2, Part 6: Modeling Rotation Mechanical Systems

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