Question

The tail rotor section of a Black Hawk helicopter consists of four blades, each has a mass of 2 [kg), and a gear box that weights 38 [kg]. The center of gravity of each blade is 0.4 [m] from the rotational axis. The tail section is connected to the main body of the helicopter by an elastic structure. The natural frequency of the tail section is observed as 135 [rad/s]. During flight, the rotor operates at 850 [r/min). 1- Calculate the total mass of the rotor. 2- Calculate the equivalent stiffness. 3- Calculate the natural frequency. 4- Calculate the frequency ratio. 5. What is the vibration amplitude of the tail section if one of the blades falls off during flight? Assume a damping ratio of 0.05. 6- Write a paragraph intended to be part of a technical report for your nation's air force to describe how safe is it to fly the helicopter with such conditions and do you propose any design suggestions. It is known that a machine with a rotating unbalance experiences a frequency squared harmonic excitation.

Answer 1

1.

Total mass of the rotor =4*2 +38= 46 kg

2.

Given Natural frequency of tail section=135 rad/sec

$\omega_n =\sqrt{\frac{k}{m}} => k= \omega_n^2 *m$

K=135^2 *46 = 838.35 kN/m

3.

Given Natural frequency as 135 rad/sec already

4.

Frequency of rotation is w.

$\omega=\frac {2*\pi*N}{60} = \frac{2*3.14*850}{60} = 89.01 rad/sec$

$r=\frac{\omega}{\omega_n}$

r is frequency ratio. = 89.01/135 = 0.659