Chapter 6, Problem 6.44P

A conveyor drive system to produce translation of the load is shown in Figure P6.44. Suppose that the equivalent inertia felt at the motor shaft is $0.05\text{kg}\cdot {\text{m}}^2$ , and that the effect of Coulomb friction in the system produces an opposing torque of $3.6\text{N}\cdot \text{m}$ at the motor shaft. Neglect damping in the system. It is desired to have the motor shaft rotate through 11 revolutions in a total time of 3 s, using a trapezoidal speed profile with $t_1=0.5\text{s}$ and $t_2=2.5\text{s}$ .

The given motor parameters are $R_a=3\Omega$ , $L_a=4\times {10}^{-3}\text{H}$ , and $K_T=0.4\text{N}\cdot \text{m/A}$ . Compute the energy consumption per cycle; the maximum required torque, current, and voltage; the rms torque; and the rms current.