Question-2: A DC electric motor is used to drive a turntable with a massless rigid shaft. Viscous damping is assumed to be at the bearings. The electromechanical system shown in the figure and system elements/parameters are described as follows: Mass moment of inertia (Rotational inertia) of the turntable Rotational damping coefficient at bearings Voltage source Inductive energy storage element (Inductance) of the DC motor Energy dissipation element (Resistance) of the DC motor The angular velocity of the shaft in the positive direction B : V(t) L R Ω Note: The electromechanical conversion of energy is represented Turntable J by an ideal two-port transformer with the electromechanical Bearing B coupling relating torque T to current i and angular velocity N to the motor internal voltage (back emf) Vm generated. The two-port transformer relationships are T = K * i V(t) 1 ww * Vm K Motor R The angular velocity of the shaft (N is the system output) is desired to be controlled by changes in the input voltage (V(t) is the system input). For the given system, a) Firstly, draw necessary free-body diagrams (FBD's) for the system. Then, write all elemental equations according to the given elements in the figure. | Note: Please pay attention to the positive and negative signs that indicate the direction.] b) Write out all structural equations for the electromechanical system. [ Continuity Equations: Torque equilibrium, Kirchhoff's current law] c) Obtain the equation of motion (EoM) for the system in terms of input & output parameters (i.e. standard differential eqn. form) using and combining Elemental & Structural Eqn's.
Question-2: A DC electric motor is used to drive a turntable with a massless rigid shaft. Viscous damping is assumed to be at the bearings. The electromechanical system shown in the figure and system elements/parameters are described as follows: Mass moment of inertia (Rotational inertia) of the turntable Rotational damping coefficient at bearings Voltage source Inductive energy storage element (Inductance) of the DC motor Energy dissipation element (Resistance) of the DC motor The angular velocity of the shaft in the positive direction B : V(t) L R Ω Note: The electromechanical conversion of energy is represented Turntable J by an ideal two-port transformer with the electromechanical Bearing B coupling relating torque T to current i and angular velocity N to the motor internal voltage (back emf) Vm generated. The two-port transformer relationships are T = K * i V(t) 1 ww * Vm K Motor R The angular velocity of the shaft (N is the system output) is desired to be controlled by changes in the input voltage (V(t) is the system input). For the given system, a) Firstly, draw necessary free-body diagrams (FBD's) for the system. Then, write all elemental equations according to the given elements in the figure. | Note: Please pay attention to the positive and negative signs that indicate the direction.] b) Write out all structural equations for the electromechanical system. [ Continuity Equations: Torque equilibrium, Kirchhoff's current law] c) Obtain the equation of motion (EoM) for the system in terms of input & output parameters (i.e. standard differential eqn. form) using and combining Elemental & Structural Eqn's.
Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
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![Question-2: A DC electric motor is used to drive a turntable with a massless rigid shaft. Viscous
damping is assumed to be at the bearings. The electromechanical system shown in the figure and
system elements/parameters are described as follows:
Mass moment of inertia (Rotational inertia) of the turntable
Rotational damping coefficient at bearings
Voltage source
Inductive energy storage element (Inductance) of the DC motor
Energy dissipation element (Resistance) of the DC motor
The angular velocity of the shaft in the positive direction
:
B
V (t)
L
:
Note: The electromechanical conversion of energy is represented
Turntable J by an ideal two-port transformer with the electromechanical
coupling relating torque T to current i and angular velocity N to
the motor internal voltage (back emf) Vm generated.
Bearing B
The two-port transformer relationships are
T = K * i
1
=- * Vm
K
V(t)
ww
Motor
The angular velocity of the shaft (N is the system output) is desired to be controlled by changes in
the input voltage (V (t) is the system input). For the given system,
a) Firstly, draw necessary free-body diagrams (FBD's) for the system. Then, write all
elemental equations according to the given elements in the figure.
| Note: Please pay attention to the positive and negative signs that indicate the direction.]
b) Write out all structural equations for the electromechanical system.
[ Continuity Equations: Torque equilibrium, Kirchhoff's current law]
c) Obtain the equation of motion (EoM) for the system in terms of input & output parameters
(i.e. standard differential eqn. form) using and combining Elemental & Structural Eqn’s.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb1546b5-c77d-439f-8243-9ae09415ca4b%2F798e8aea-b7a2-425a-9e44-a343f796ef1a%2Fzc2sevh_processed.png&w=3840&q=75)
Transcribed Image Text:Question-2: A DC electric motor is used to drive a turntable with a massless rigid shaft. Viscous
damping is assumed to be at the bearings. The electromechanical system shown in the figure and
system elements/parameters are described as follows:
Mass moment of inertia (Rotational inertia) of the turntable
Rotational damping coefficient at bearings
Voltage source
Inductive energy storage element (Inductance) of the DC motor
Energy dissipation element (Resistance) of the DC motor
The angular velocity of the shaft in the positive direction
:
B
V (t)
L
:
Note: The electromechanical conversion of energy is represented
Turntable J by an ideal two-port transformer with the electromechanical
coupling relating torque T to current i and angular velocity N to
the motor internal voltage (back emf) Vm generated.
Bearing B
The two-port transformer relationships are
T = K * i
1
=- * Vm
K
V(t)
ww
Motor
The angular velocity of the shaft (N is the system output) is desired to be controlled by changes in
the input voltage (V (t) is the system input). For the given system,
a) Firstly, draw necessary free-body diagrams (FBD's) for the system. Then, write all
elemental equations according to the given elements in the figure.
| Note: Please pay attention to the positive and negative signs that indicate the direction.]
b) Write out all structural equations for the electromechanical system.
[ Continuity Equations: Torque equilibrium, Kirchhoff's current law]
c) Obtain the equation of motion (EoM) for the system in terms of input & output parameters
(i.e. standard differential eqn. form) using and combining Elemental & Structural Eqn’s.
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