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Three Rotor System

Unit 3<br>Dynamics of Machines<br>Free Vibration

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Three Rotor System

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  1. Three Rotor system

  2. Three rotor system • Consider , the two rotors A and B are fixed to the ends of the shaft. and the rotor C is in between. Let the rotors A !nd B rotate in the same direction and C in the opposite direction and the node points lie at D and E as shown in

  3. Three rotor system • When A and C are rotating in same direction and B is rotating in opposite direction, node is formed in between C and B

  4. Three rotor system • When B and C are rotating in same direction and A is rotating in opposite direction, node is formed in between C and A

  5. 3 Rotor 2 Rotor 1 1 1 1 Iala Iclc

  6. 1. A single cylinder oil engine drives directly a centrifugal pump. The rotating mass of the engine, flywheel and the pump with the shaft is equivalent to a three rotor system as shown in Fig. The mass moment, of inertia of the rotors A, B and C are 0.15, 0.3 and 0.09 kg-m2. Find the natural frequency of the torsional vibration. The modulus of rigidity for the shaft material is 84 kN/m2 Given : IA = 0.15 kg-m2 ; IB = 0.3 kg-m2 ; IC = 0.09 kg-m2 ; d = 70 mm =0.07 m; l1= 1.5 m; l2 = l m; C= 84 kN/mm2 = 84 x 109 N/m2

  7. Position of nodes

  8. Position of nodes

  9. Polar moment of inertia • Natural frequency of single node system

  10. Natural frequency of two node system

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