A rotor, having three eccentric masses in different planes, is shown in Fig. 9.43. The axial, radial,

Question:

A rotor, having three eccentric masses in different planes, is shown in Fig. 9.43. The axial, radial, and angular locations of mass $m_{i}$ are given by $l_{i}, r_{i}$, and $\theta_{i}$, respectively, for $i=1,2,3$. If the rotor is to be dynamically balanced by locating two masses $m_{b 1}$ and $m_{b 2}$ at radii $r_{b 1}$ and $r_{b 2}$ at the angular locations $\theta_{b 1}$ and $\theta_{b 2}$, as shown in Fig. 9.42, derive expressions for $m_{b 1} r_{b 1}, m_{b 2} r_{b 2}, \theta_{b 1}$, and $\theta_{b 2}$.

Figure 9.43:-