A conveyor drive system to produce translation of the load is shown in Figure. The reducer is a gear pair that reduces the motor speed by a factor of 10:1. The motor inertia is I = 0.002 kg m2. The reducer inertia as felt on the motor shaft is I2 = 0.003 kg.m2. Neglect the inertia of the tachometer, which is used to measure the speed for control purposes. The properties of the remaining elements are given here.
Sprockets:
Sprocket 1: radius = 0.05 m mass = 0.9 kg
Sprocket 2: radius = 0.15 m mass = 8.9 kg
Chain mass: 10.7 kg
Drive shaft: radius = 0.04 m mass = 2.2 kg
Drive wheels (four of them): radius = 0.2 m mass = 8.9 kg each
Drive chains (two of them): mass = 67 kg each
Load friction torque measured at the drive shaft: 54 N.m
Load mass: 45 kg
a. Derive the equation of motion of the conveyor in terms of the motor velocity ω1, with the motor torque T1 as the input.
b. Suppose the motor torque is constant at 10 N.m. Determine the resulting motor velocity ω1 and load velocity v as functions of time, assuming the system starts from rest.
c. The profile of a desired velocity for the load is shown in Figure, where vo = 1 m/s, t1= t3 = 0.5s, and t2 = 2 s. Use the equation of motion found in part (a) to compute the required motor torque for each part of the profile.

Transcribed Image Text:

Figure P3.27a Figure P3.27b Load Drive chains Tachometer Drive wheels Sprocket 2 Drive shaft -Chain Sprocket I Reducer Motor