Chapter 3, Problem 3.24P

For the geared system discussed in Problem 3.23, shown in Figure P3.23, the inertias are given in $\text{kg}\cdot {\text{m}}^2$ as

$I_1={10}^{-3}{I}_2=3.84\times {10}^{-3}{I}_3=0.0148$

The speed ratios are

$\frac{{\omega }_1}{{\omega }_2}=\frac{{\omega }_2}{{\omega }_3}=1.6$

Derive the system model in terms of the speed ${\omega }_3$ , with the applied torque T as the input. The shaft inertias are negligible.

Figure P3.23

The speed ratios are

$\frac{{\omega }_1}{{\omega }_2}=\frac{{\omega }_2}{{\omega }_3}=1.6$

Derive the system model in terms of the speed ${\omega }_3$ , with the applied torque T as the input.