Final answer:
Calculations for a long shunt compound motor involve determining the armature current, developed torque, output torque, and constant losses based on nameplate data and efficiency. To safeguard the motor during startup, a starting resistor is calculated to limit inrush current to 250% of the rated armature current.
Step-by-step explanation:
A long shunt compound motor has various nameplate parameters that allow us to calculate the necessary values like armature current, developed torque, output torque, and constant losses. Given the data: rated line voltage = 380V, rated speed = 1200 rpm, output power = 24hp, armature resistance = .3 ohm, shunt field resistance = 47.5 ohm, and series field resistance = .1 ohm, and the efficiency at the rated load is 80%, we aim to find the armature current, converted power, developed torque, output torque, and constant losses for this motor when it is driving a constant torque load. Additionally, we are tasked to compute the value of the starting resistor needed to limit the initial armature current to no more than 250% of its rated armature current.
First, we need to find the motor's output power in watts. Since 1 horsepower equals 746 watts, the motor's output power is 24hp * 746W/hp = 17904W. With an efficiency of 80%, the input power is 17904W / 0.8 = 22380W. The armature current can then be determined by using the input power and dividing it by the line voltage: 22380W / 380V = 58.9A.
To find the developed torque, we use the relationship between power (P), torque (T), and angular velocity (ω), where P = Tω. The angular velocity in radians per second is found by converting the given RPM to rad/s using the conversion factor 2π/60. Therefore, the developed torque can be calculated.
For the output torque, it can be deduced that it will be less than the developed torque due to losses, which are accounted for in the machine's efficiency. The constant losses are typically associated with friction and windage and can be estimated as the difference between input power and developed power.
The starting resistor is required to limit the inrush current during startup. To find the value, we first need to determine the permissible starting current, which is 250% of the rated armature current, and then calculate the required additional resistance to drop the initial voltage to this level, ensuring that the motor is protected from excessive starting current.