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**Unformatted text preview: **ease as the torque increase
which is correct and expected.
When the motor is stalled, it can be modeled as a resistor in series with an
inductor. The R and L values calculated from the dynamic measurements and shown in
table 1 correspond to this representation of the motor. The electrical time constant from
the solution to the differential equation can also be calculated from these data. It can be
approximated as the time it takes the system to reach 63% of its steady-state current when
a step voltage is applied. It is listed in table 1.
In a similar manner, we can calculate the intermediate time constant ts from the
angular velocity step response for the free wheel case. It is also included in table 1.
Knowing the steady-state angular velocity, we use equation 18 to find the viscous
damping constant b. At stall, b is calculated to be about 0.21, while the free wheel b is
0.03. From this, we can calculate J, the total inertia, using equation 17. To calculate J we
used the measurements obtained during the test. Additionally, since the material is made
up 3 different materials (aluminum, acrylic, and steel) we found the corresponding
volumes for each section of the disk and used the densities of each material to find the
disk’s total mass. The moment of inertia was calculated as 0.003 kg-m2. Subtracting this
from J gives the motor inertia Jm. Knowing the motor moment of inertia, we used 19 equation 19 to calculate the mechanical time constant tm. The result of the dynamic
response of the motor are summarized below:
J (kg-m2)
Free wheel 0.003 0.0005 0.019 0.03 0.02 0.122 Free wheel 0.01 0.008 0.248 Stall With disk Mechanical Time Constant Stall No disk Jm (kg-m2) 0.07 0.07 0.330 Table 3: Dynamic Measurements 7. Conclusions
The resulting plots confirm that motor torque is proportional to motor current, and
that as rotational speed (rpm) decreases, both torque and current increase. They also show
that there exist an optimal rpm value for maximum power output and efficiency. Beyo...

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