6 Analysis of the Dynamic Response of Coupled Coaxial Rotors 59 Mode 1 (FW) Cylindrical IP 22.0Hz Mode 2 (BW) Cylindrical IP 22.0Hz Mode 3 (FW) Cylindrical OP 38.1Hz Mode 4 (BW) Cylindrical OP 38.1Hz Mode 5 (FW) Conical IP 56.4Hz Mode 6 (BW) Conical IP 56.4Hz Mode 7 (FW) ConcialOP 96.5Hz Mode 8 (BW) ConicalOP 96.5Hz (a) Mode 1 (FW) Static 4.1Hz Mode 2 (BW) Static 8.5Hz Mode 3 (FW) Flat IP 22.5Hz Mode 4 (BW) Flat IP 22.6Hz Mode 5 (FW) FlatOP 38.9Hz Mode 6 (BW) FlatOP 39.1Hz Mode 7 (FW) Precession 625.1Hz Mode 8 (BW) Precession 1235.9Hz (b) Fig. 6.4 Mode shapes of the counter-rotating dual-rotor system: rotor 1 ( ), rotor 2 ( ). (a) Mode shapes @ 0 rpm. (b) Mode shapes @ 20,000rpm 5,000 10,000 15,000 20,000 0 100 200 300 Ω(rpm) w (Hz) Mode 1 (FW) Mode 2 (BW) Mode 3 (FW) Mode 4 (BW) Mode 5 (FW) Mode 6 (BW) Mode 7 (FW) Mode 8 (BW) Fig. 6.5 Campbell Diagram of the counter-rotating dual-rotor system: FW modes ( ) and BW modes ( ); critical speeds from unbalances on rotor 1 ( ) and rotor 2 ( )
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