Question

Rotating unbalance is also important in rotorcraft such as helicopters and prop planes. The tail rotor of a helicopter (the small rotor rotating in a vertical plane at the back of a helicopter used to provide yaw control and torque balance) as sketched in Figure 2.21 can be modeled as a rotating-unbalance problem discussed in this section with stiffness k 1 x 105 N/m (provided by the tail section in the vertical direction) and mass of 20 kg.The tail section providing the vertical stiffness has a mass of 60 kg. Suppose that a 500-g mass is stuck on one of the blades at a distance of 15 cm from the axis of rota tion. Calculate the magnitude of the deflection of the tail section of the helicopter as the tail rotor rotates at 1500 rpm. Assume a damping ratio of 0.01.At what rotor speed is the deflection a maximum? Calculate the maximum deflection. Schematic of a helicopter tail section illustrating a tail rotor. The Figure 2.21 tail rotor provides a "counterclockwise thrust (when looking at the top of the helicopter) to counteract the "clockwise" thrust created by the main rotor, which provides lift and horizontal motion. An out-of-balance rotor can cause damaging vibrations and limit the helicopter's performance. 60 kg 20 kg

Answer 1

Rotox System ts modeled as mochins of m 20. sprinemo m. concapt yields that ro l eu OS N/m rnck mo 53-923 Equivalent mass meg-m+ms= 34.54 18 Maximum dellection ocaurs ot about In caje of max, detlection becomes x = (0-518) :15 34.34k9 2000) This reprexensa lasgesunacceptable dageadhon -s sxotun Thuus he tl votur should not be allo to ruttde od 53-1 pm