As shown in Figure 1.P8, there is a commuter train consisted with four motor cars (M car) and four trailer cars (T car).

The mass of T car is 28 metric tons, and that of M car is 30 metric tons. The maximum payload of each car is 20 metric tons. The rolling resistance of the train is given by the following equation:

Where the unit of R is kg-G/ton = 9.8 N/ton, ya is the speed of the train, and its unit is km/h. The train accelerates up to 35 km/h with the maximum acceleration, 3.0 km/h/s. The maximum speed of the train is 100 km/h. During acceleration, the inertia of the rotating parts of the train such as wheels, gears, and electric machines can be converted to an equivalent mass in calculating of the traction force. The converted inertia to the mass is called “inertia mass.” The compensation factor of the inertia mass to consider the traction force due to the rotating parts of each car is 6% in the case of a T car and 14% in the case of an M car. Hence, the equivalent total mass (including the inertia mass) to consider the torque due to the rotating parts of the car can be given by following equation. Equivalent mass at acceleration = Total mass of car including payload þ (Compensation factor for the inertia mass * Mass of each car itself) Only 97% of the mechanical torque from the machine is transfered to the rail and that is used as the tractive force to move the train. Each M car has four traction motors.

(1) Calculate the power rating of the motor in kilowatts. The power rating of the motor is decided at the operating speed where the tractive force is the maximum (in this problem it is 35 km/h).

(2) The gear ratio between motor and wheel is 7.07:1 and the gear is reducing gear. When the average speed of the train is 48 km/h, the rotating speed of the motor is the rated value. The diameter of the wheel is 0.82 m constant.

(a) What is the rated rotating speed (revolutions/min) of the traction motor?

(b) At maximum train speed, 100 km/h, what is the rotating speed (revolutions/min) of the motor?

(c) At the operating condition given in part 1, if the efficiency of the AC traction motor is 92% and the power factor is 85%, then calculate the apparent input power (kVA) to the machine.