Derive the governing equation for the above. Must show free body
diagrams and each step.
Consider...
Consider the rotor with the gear train driving a propeller through a flexible shaft, as shown in Fig An external motor (not shown) delivers the input torque T(t) to the Rotor with inertia ½. The Rotor is connected to the gear wheel n, of the gear train with a very short and very stiff shaft. Gear n2 is larger tharn gear n1, and their gear ratio is n2/n1 = N: similarly, gear n3 is larger than gear n2, and their gear ratio is the same: na/n2 -N. Inertia of gears n1, n2, and n3 can be neglected. The rotor is supported by bearings with damping coefficient b,. Gear Train and Propeller are connected by a flexible shaft. The elastic property of this shaft is represented by torsional spring with stiffness coefficient of k The Propeller has inertia ½, and is supported by bearings with damping coefficient b2 T(t) 1 n Rotor 113 83 Gear Tra in Propeller Figure 1