Problem #6 A cylindrical steel flywheel 10 cm in diameter and 1 cm thick is directly coupled to a DC servo motor (Pittman 9232S003, data sheet is available on the course Moodle page). Note that the density of steel is 8050 kg/m3 a) Calculate the mass moment of inertia of the flywheel. b) If a step input of 24V is applied directly to the motor terminals, analytically estimate how long it would take to reach 98% of steady-state motor velocity. Note: the simplest way to approach this problem is to assume a first-order motor model by neglecting the winding inductance (i.e.; assuming an electrical time constant of zero). c) Verify your results numerically with Matlab using the complete (i.e.; second order) Simulink motor model available on the course Moodle page. d) Does neglecting the electrical time constant of the motor introduce a significant error in your analytical estimate of the time to reach 98% of the steady-state motor velocity? Explain.
Problem #6 A cylindrical steel flywheel 10 cm in diameter and 1 cm thick is directly coupled to a DC servo motor (Pittman 9232S003, data sheet is available on the course Moodle page). Note that the density of steel is 8050 kg/m3 a) Calculate the mass moment of inertia of the flywheel. b) If a step input of 24V is applied directly to the motor terminals, analytically estimate how long it would take to reach 98% of steady-state motor velocity. Note: the simplest way to approach this problem is to assume a first-order motor model by neglecting the winding inductance (i.e.; assuming an electrical time constant of zero). c) Verify your results numerically with Matlab using the complete (i.e.; second order) Simulink motor model available on the course Moodle page. d) Does neglecting the electrical time constant of the motor introduce a significant error in your analytical estimate of the time to reach 98% of the steady-state motor velocity? Explain.
Related questions
Question
Transcribed Image Text:Assembly Data
Reference Voltage
No-Load Speed
Continuous Torque (Max.)
Peak Torque (Stall)²
Weight
Motor Data
Torque Constant
Back-EMF Constant
Resistance
Inductance
No-Load Current
Peak Current (Stall)²
Motor Constant
Friction Torque
Rotor Inertia
Electrical Time Constant
Mechanical Time Constant
Viscous Damping
Damping Constant
Maximum Winding Temperature
Thermal Impedance
Thermal Time Constant
Gearbox Data
Encoder Data
Symbol
E
SNL
Tc
TPK
WM
KT
KE
RT
L
INL
+2+36 30
Ip
KM
TF
JM
TE
TM
D
KD
MAX
RTH
TTH
Units
V
rpm (rad/s)
oz-in (N-m)
oz-in (N-m)
oz (g)
oz-in/A (N-m/A)
V/krpm (V/rad/s)
Ω
mH
A
A
oz-in/W (N-m/VW)
oz-in (N-m)
oz-in-s² (kg-m²)
ms
ms
oz-in/krpm (N-m-s)
oz-in/krpm (N-m-s)
°F (°C)
°F/watt (°C/watt)
min
7,015
2.4
14
10
4.40
3.25
Value
24
1.62
0.50
2.7E-04
0.027
1.9
311
72.9
7.38
4.64
0.16
3.25
(3.11E-02)
(3.11E-02)
7.2
(735)
(1.7E-02)
(9.7E-02)
(283)
0.63
14.4
(1.14E-02)
(3.5E-03)
(1.9E-06)
(1.8E-06)
(1.3E-04)
(155)
(22.7)
Channels
3
500
Resolution
CPR
1 - Specified at max. winding temperature at 25°C ambient without heat sink. 2- Theoretical values supplied for reference only.
Transcribed Image Text:Problem #6
A cylindrical steel flywheel 10 cm in diameter and 1 cm thick is directly coupled to a DC
servo motor (Pittman 9232S003, data sheet is available on the course Moodle page).
Note that the density of steel is 8050 kg/m3
a) Calculate the mass mor hent of inertia of the flywheel.
b) If a step input of 24V is applied directly to the motor terminals, analytically
estimate how long it would take to reach 98% of steady-state motor velocity.
Note: the simplest way to approach this problem is to assume a first-order
motor model by neglecting the winding inductance (i.e.; assuming an electrical
time constant of zero).
c) Verify your results numerically with Matlab using the complete (i.e.;
second order) Simulink motor model available on the course Moodle
page.
d) Does neglecting the electrical time constant of the motor introduce a
significant error in your analytical estimate of the time to reach 98% of the
steady-state motor velocity? Explain.
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