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**Unformatted text preview: **pm as shown in the graph below. Figure 12: Ideal Relation Between Motor Torque T, current i, and speed ω 17 The motor torque vs. motor current graph shows that as motor current increases
the motor torque increases. This plot allows us to determine the motor’s torque constant
from the slope of the line since T = k *i, where T is motor current, k is the motor
m t m t constant, and i is current. From the motor torque vs. motor current plot, we found the
following slopes corresponding to each motor voltage value:
Motor Voltage (V) Motor’s Torque constant (k )
t 22.7 0.5039 18.3 0.5176 11.7 0.5506 6.1 0.4785 Table 2: Torque Constant at Various Voltages Therefore, we can see that the average value for motor’s torque constant is k ~
t 0.51 Nm/A. From equation 4, we see that kt = 2NBLr. Similarly, from equation 9, ke =
2NBLr. Since the motor values of N, B, l, and r remain constant , the magnitude of the
back emf constant is equivalent to that of the torque constant obtained above. Thus, k ~
e 0.51V-s/rad.
For output power and motor efficiency, a quadratic relationship is obtained. The
output power response shows that there is an optimal value of rpm for which the
maximum power output can be obtained. The same behavior applies to the motor
efficiency response. Furthermore, these two relationships show that as the motor voltages
increase the corresponding optimal rpm values increase as well. Thus, we can see that the
output power and efficiency peaks shift to the right. A subtle difference between these 18 two relationships is that the output power peaks become higher as motor voltage
increases, but this is not the case for the efficiency peaks. The efficiency peak
corresponding to the 11.7 V motor voltage, seems to break the trend of higher peaks for
increasing voltages. This can be due to the fact that fewer increments of breaking force
were applied for this voltage and there seems to be big gaps between the values for the
corresponding output power values. Yet, these values incr...

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