Final answer:
The synchronous speed of the induction motor is 4500 rpm, and the actual rotor speed at 4 percent slip is 4320 rpm, equivalent to 72 rps or 452.39 rad/s. Calculations for stator current, power factor, P_conv, P_out, and efficiency require additional motor impedance information. The specific values were not provided in the question.
Step-by-step explanation:
To find the performance metrics of the specified 530V, 86hp, 150Hz, four-pole, Y-connected induction motor at 4 percent rotor slip, we can use the given information and the following equations:
- The synchronous speed, N_s, of the motor in revolutions per minute (rpm) is given by N_s = (120 x Frequency) / Number of Poles. For a 150 Hz, four-pole motor, N_s = (120 x 150) / 4 = 4500 rpm.
- The actual rotor speed, N_r, in rpm is N_r = N_s x (1 - slip), which equals 4500 rpm x (1 - 0.04) = 4320 rpm.
- Convert N_r to revolutions per second (rps) by dividing by 60, resulting in 72 rps.
- To find the speed in radians per second (rad/s), multiply 72 rps by 2π, giving approximately 452.39 rad/s.
- Stator current, power factor, P_conv (power converted from electrical to mechanical) and P_out (output power) involve more complex calculations including the motor's impedance and can require additional information not provided in the question.
- Efficiency (η) is calculated by the equation η = (P_out / P_in) x 100%, where P_in is the input power and can be found when the stator current and power factor are known.
- The motor's actual speed, N_r, is already determined to be 4320 rpm.
The rotational and core losses are factored into the calculations for efficiency and output power, with P_out being the difference between P_conv and these losses.