APPENDIX 5

Gyroscopic Rotor Responses to Synchronousand Nonsynchronous Forward and

Backward Perturbation

the synchronous and nonsynchronous forward and backward perturbation, using differentialtechniques. This data was used for identification of the system parameters.

The differential technique was used in order to eliminate the effect of any possibleunknown residual unbalance in the main rotor. During the first startup of the rotor the inputunbalance weight with mass ‘‘m’’ is installed in the perturbation disk at radius r at 0�. Duringthe second startup the same unbalance weight is installed at the same radius but at 180�

orientation. The filtered 1� response vector data from the first and the second runs are then

thus with the magnitude 2mr!2 and located at 0�.The full spectrum cascade plots were obtained from the rotor direct response data

while long rotor was unstable. The threshold of instability occurred at about 2200 rpm,and with increase of rotational speed was followed by the oil whirl self-excited vibrations

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© 2005 by Taylor & Francis Group, LLC

The data presented in Figures A5.1–A5.12 illustrate short and long rotor responses to

vectorially subtracted, providing a clean 1� response of the rotor to the double input force,

(Figures A5.2, A5.4, A5.6, A5.8, A5.10 and A5.12). The short rotor system was stable,

(see Figure A5.8).

Figure A5.1 Bode and polar plots of synchronous perturbation of gyroscopic rig in stable (short rotor)

configuration: (a) Vertical and (b) Horizontal responses. Data reduced using differential technique.

Unbalance mass¼ 0.4 g at 0� and 114 mm radius. Disk mounted on the shaft at 51 mm from

centerline of rolling element support bearing (driver end). Nonsynchronous perturbator wheel

mounted on the rotor at 95mm from centerline of rolling element support bearing (driver end). Oil

pressure¼14 kPa. Shaft diameter¼ 25.3 mm, length to center of fluid bearing¼ 147 mm from

centerline of rolling element support bearing (driver end). An apparent decrease of phases at low

speed is associated with very low amplitude level, thus an inaccurate phase reading.

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© 2005 by Taylor & Francis Group, LLC

Figure A5.2 Direct orbits at various speeds (a) and full spectrum cascade plot (b). Synchronous perturbation of

rig in stable configuration. Unbalance mass¼0.4 g at 0� and 114 mm radius. Disk mounted to the

shaft at 51 mm from centerline of rolling element support bearing (driver end). Nonsynchronous

perturbator wheel mounted to the shaft at 95mm from centerline of rolling element support

bearing (driver end). Oil pressure¼14 kPa, shaft diameter¼ 25.3 mm, length to center of fluid

bearing¼147 mm from centerline of rolling element support bearing (driver end).

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© 2005 by Taylor & Francis Group, LLC

Figure A5.3 Bode and polar plots of nonsynchronous forward perturbation of gyroscopic rig in stable configura-

tion; (a) Vertical and (b) Horizontal responses. Data reduced using differential technique. Shaft

speed¼ 200 rad/s. The whirl resonance occurs at about 1000 rpm. Unbalance mass¼ 3.53 g

at 0� and 38 mm radius. Disk mounted on the shaft at 51 mm from centerline of rolling element

support bearing (driver end). Nonsynchronous perturbator wheel mounted on the rotor at 95 mm

from centerline of rolling element support bearing (driver end). Oil pressure¼ 14 kPa, shaft

diameter¼25.3 mm, length to center of fluid bearing¼ 147 mm from centerline of rolling element

support bearing (driver end).

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Figure A5.4 Direct orbits at various speeds (a) and full spectrum cascade plot (b). The same data as in

rotation 200 rad/s. The higher harmonics of these vibrations are also in the spectrum.

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© 2005 by Taylor & Francis Group, LLC

Figure A5.3. The vibrations at frequency slightly lower than 2000 cpm correspond to rotor constant

Figure A5.5 Bode and polar plots of nonsynchronous backward perturbation of gyroscopic rig in stable

configuration. (a) Vertical and (b) Horizontal responses. Data reduced using differential technique.

Shaft speed¼200 rad/s. Unbalance mass¼3.53 g at 0� and 38 mm radius. Disk mounted on the

shaft at 51 mm from centerline of rolling element support bearing (driver end). Nonsynchronous

perturbator wheel mounted on the rotor at 95 mm from centerline of rolling element support

bearing (driver end). Oil pressure¼ 14 kPa, shaft diameter¼ 25.3 mm, length to center of fluid

bearing¼ 147 mm from centerline of rolling element support bearing (driver end). Note that fluid

whirl resonance does not occur for this backward perturbation.

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Figure A5.6 Direct orbits at various speeds (a) and full spectrum cascade plot (b). The same data as in

on the backward side of the plot. It corresponds to the constant rotational speed 200 rad/s of

the rotor.

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Figure A5.5. Note the constant amplitude vibration component with frequency about 2000 cpm

Figure A5.7 Bode and polar plots of synchronous perturbation of gyroscopic rig in unstable configuration.

(a) Vertical and (b) Horizontal response. Data reduced using differential technique. Unbalance

mass¼ 1.18 g at 0� and 114 mm radius. Disk mounted on the shaft at 259 mm from centerline of

rolling element support bearing (driver end). Nonsynchronous perturbator wheel mounted

on the rotor at 229 mm from centerline of rolling element support bearing (driver end). Oil

pressure¼7 kPa, shaft diameter¼ 25.3 mm, length to center of fluid bearing¼300 mm from

centerline of rolling element support bearing (driver end).

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Figure A5.8 Direct orbits at various speeds (a) and full spectrum cascade plot (b). The same data as in

occurs at about 2000 rpm.

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© 2005 by Taylor & Francis Group, LLC

Figure A5.7. Note fluid whirl self-excited vibrations with frequency 0.48O. Instability threshold

Figure A5.9 Bode and polar plots of nonsynchronous forward perturbation of gyroscopic rig in unstable

configuration: (a) Vertical and (b) Horizontal response. Data reduced using differential techni-

que. Shaft speed¼200 rad/s. Unbalance mass¼ 2.20 g at 0� and 38 mm radius. Disk mounted

on the shaft at 259 mm from centerline of rolling element support bearing (driver end).

Nonsynchronous perturbator wheel mounted on the rotor at 229 mm from centerline of

rolling element support bearing (driver end). Oil pressure¼7 kPa, shaft diameter¼ 25.3 mm,

length to center of fluid bearing¼300 mm from centerline of rolling element support bearing

(driver end). Note fluid whirl resonance at the perturbation speed slightly lower than 1000 rpm.

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Figure A5.10 Direct orbits at various speeds (a) and full spectrum cascade plot (b). The same data as in

rotor rotation at 200 rad/s and its 1x vibrations, due to imbalance. The use of the differential

technique did not perfectly eliminate the rotor imbalance.

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Figure A5.9. The large amplitude and constant frequency, about 2000 cpm, corresponds to the

Figure A5.11 Bode and polar plots of nonsynchronous backward (Y�X) perturbation of gyroscopic rig in

unstable configuration. (a) Vertical and (b) Horizontal responses. Data reduced using differential

technique. Shaft speed¼200 rad/s Unbalance mass¼ 2.20 g at 0� and 38 mm radius. Disk

mounted on the shaft at 259 mm from centerline of rolling element support bearing (driver end).

Nonsynchronous perturbator wheel mounted on the rotor at 229 mm from centerline of rolling

element support bearing (driver end). Oil pressure¼7 kPa, shaft diameter¼25.3 mm, length to

center of fluid bearing¼300 mm from centerline of rolling element support bearing (driver end).

No fluid whirl resonance at backward perturbation.

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Figure A5.12 Direct orbits at various speeds (a) and full spectrum cascade plot (b). The same data as in

synchronous vibrations.

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© 2005 by Taylor & Francis Group, LLC

Figure A5.11. The constant frequency (around 2000 cpm) component corresponds to the rotator