Question

Assignment, due on Thursday Feb 1st 2018 n an underground mine, a 65 meters long conveyor belt is used to carry 100 Metric Ton per hour of crushed ore. The linear velocity of the conveyor belt is 1.4 m/s and it is installed with 9° inclination 1) Neglecting the velocity of the crushed ore just before it reaches the conveyor, calculate the mechanical power that the conveyor needs to operate. (hint; assume that mechanical power is needed to increase the kinetic energy and the potential energy of the crushed ore) Crushed ore 1.4 m/s L=65 m 2) The conveyor is mounted on a wheel with 0.4m diameter. A gear, with larger wheel diameter of 0.25 m and smaller wheel diameter of 0.032m, is used to transmit torque from an AC motor to the wheel. Calculate the torque and RPM of the AC motor. 21

Answer 1

Time taken to lift the core from one to other is, t = s/v = L/v = 65/1.4 = 46.428 sec Find the weight of the cole at any instant as, W = mt = 100/hr times hr/3600s times (46.28)s = 1.285 ton Apply the equation of motion to the conveyor F - W sin 9 degree = ma_x. F -1.285 times 9.81 times 10^3 sin 9 degree = m(0) F = 1971.99 N Find the power required to operate the conveyor. p = F.v = 1971.99(1.4) = 2760.786 W Find the speed of motor as, omega_wheel = v/r = v/d_1/2 = 1.4/0.4/2 = 7 rad/s omega_wheel = 2 pi N_2/60 = 7 N_2 = 66.845 rpm Considering the speed ratio, N_1/N_2 = D_2/D_1 N_1/66.845 = 0.25/0.032 N_1 = 522.22 rpm (motor speed) Find the torque on the motor as, p = 2 pi N_1 T/60 2760.786 = 2 pi times 522.22(T)/60 T = 50.483 N.m