For the conveyor system shown in Figure, the reducer reduces the motor speed by a factor of 2:1. The motor inertia is I1 = 0.003 kg-m2. Discount the inertias of the reducer and the tachometer, which is used to measure the speed for control purposes. Ignore the inertias of the two sprockets, the chain, and all shafts. The only significant masses and inertias arc the inertias of the four

drive wheels (0.01 kg-m2 each), the two drive chains (6 kg each), and the load mass (8 kg).
The radius of sprocket l is 0.04 m that of sprocket 2 is 0.12 m. The drive wheel has a radius of 0.1 m. The load friction torque measured at the drive shaft is 0.9 N-m.
a. Derive the equation of motion of the conveyor in terms of the motor velocity, with the motor torque T1 as the input.
b. Suppose the motor torque is constant at l.2 N.m Determine the resulting motor angular acceleration and load acceleration.

Transcribed Image Text:

Figure P3.27a Figure P3.27 Loat Drive chaim Tuchometer Drive wheels Sprocket 2 Daive shaf Speccket Reducer Motor