a dc motor is powered with ea 400v the armature resistance is ra 2 the torque constant of the mo

a) To draw the torque speed curve, we need to use the equation 𝑇 = 𝐾𝑡𝐼 and 𝐸𝑎 = 𝐼𝑅𝑎 + 𝐾𝑡𝜔. We ca

Question

A DC motor is powered with $E_a = 400V$. The armature resistance is $R_a = 2Omega$ and the torque constant of the motor is $K_t = 1 Nm/A$. a) Draw the torque-speed curve of this motor, indicating $T_{stall}$ and $omega_{no-load}$. b) The motor is directly connected to a load with a constant torque given by $T_L(omega) = 80 Nm$. At what operating speed $omega_{op}$ will the load be driven? c) A gear ratio of $G = 3$ is used to drive the load. What is the new operating speed $omega_{op}$? d) What gear ratio $G$ is required to drive this load at its maximum operating speed? Hint: you will need to solve $domega_{op}/dG = 0$. e) The load is changed to a fan which has a load characterized by $T_L(omega) = 0.0001omega^2$. At what operating speed $omega_{op}$ will the fan be driven? f) What gear ratio $G$ is required to drive this load at its maximum operating speed? Hint: The load torque intercepts the motor torque in two places, only one will be positive. You will again need to solve $domega_{op}/dG = 0$.

          A DC motor is powered with $E_a = 400V$. The armature resistance is $R_a = 2Omega$ and the torque constant of the motor is $K_t = 1 Nm/A$.

a) Draw the torque-speed curve of this motor, indicating $T_{stall}$ and $omega_{no-load}$.

b) The motor is directly connected to a load with a constant torque given by $T_L(omega) = 80 Nm$. At what operating speed $omega_{op}$ will the load be driven?

c) A gear ratio of $G = 3$ is used to drive the load. What is the new operating speed $omega_{op}$?

d) What gear ratio $G$ is required to drive this load at its maximum operating speed? Hint: you will need to solve $domega_{op}/dG = 0$.

e) The load is changed to a fan which has a load characterized by $T_L(omega) = 0.0001omega^2$. At what operating speed $omega_{op}$ will the fan be driven?

f) What gear ratio $G$ is required to drive this load at its maximum operating speed? Hint: The load torque intercepts the motor torque in two places, only one will be positive. You will again need to solve $domega_{op}/dG = 0$.

Added by Jose Luis S.

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