Question

Question 2 (a) A small electric vehicle is propelled by a motor with the performance data shown in Figure Q2 below. The motor drives a gear with 12 teeth, which in turn drives a larger gear, which is attached to the vehicle's driving wheels. The diameter of the driving wheels is 380 mm and the vehicle is designed for a speed of 30 km/h. (Note: Errors of +10% in reading data from the graphs are acceptable for the purposes of this question.) (i) Draw a simple diagram of the drive mechanism. (ii) What rotational speed should the motor run at, for maximum efficiency? Express your answer in revolutions per minute (rpm) and radians per second (rad/s). (iii) What is the rotational speed of the driving wheels when the car is at design speed? (iv) What gear ratio is required to ensure that the motor is operating at maximum efficiency when the car is at design speed? How many teeth are required on the large gear? (v) Calculate the torque and the traction force on the driving wheels when the car is moving at 30 km/h, if the car has the gear ratio described in (iv) above. (If you didn't determine the gear ratio, make a guess for the purposes of this exercise.) [12] 1.0 25 0.8 20 0.6 15 efficiency torque (Nm) 0.4 10 0.2 5 0.0 0 1000 4000 0 1000 4000 2000 3000 speed (rpm) 2000 3000 speed (rpm) Figure Q2: performance graphs for the electric motor mentioned in Question 2.

Answer 1