Bearings and Fluid-Induced Instability in Rotordynamics

Dr. Mehmet Sunar

ME 562

Fluid Induced Instabilities

Fluid induced Instability is self-excited vibrations induced by internal mechanism that transfers rotational energy into the shaft as lateral vibrations.

Properties of fluid induced instability

Created and controlled by fluid flow around the rotor.

Self excited. Non synchronous. Considered more destructive in fatigue view

point.

Categories of fluid induced instability

Fluid Induced Instability

Lube OilProcess Fluid

(Pumps or Compressors)Cooling Fluids

(like air in turbines)

Areas to control Fluid Induced Instability

Possible Areas

Bearing Rotor

Design Lube Oil

Flow rate

Viscosity

Preload

Clearance

Bearing type

Mathematical complexity due non-linearities in the bearing properties. Specially, in post instability conditions.

Modeling of bearing mechanical properties. Transient rotor response changes the fluid film bearing properties.

•Average Circumferential Velocity Ratio.

•Complex Dynamic Stiffness.

Fluid average circumferential velocity ratioIt is the ratio of average

fluid velocity to the average rotor velocity

Lambda ( λ )= ū/ω

Eccentricity (e)

It is the distance from the center of bearing to the center of rotor.

Ratio=e/c. Sometimes

called radial deflection.

e

Effect of eccentricity on stability in fluid film bearings

Higher eccentricity leads to lower fluid average velocity.

Lower fluid average velocity leads to better stability.

Bearing Stiffness

Higher eccentricity leads to higher stiffness.

Higher stiffness leads to better stability.

Complex dynamic stiffness

Total stiffness of fluid film bearings is considered to be complex and dynamic. Real part is called direct stiffness Imaginary part is called quadrature stiffness. KT=KD+jKQ

KT=[KS-Mrω2]+j[ω(DS+D)-λDΩ]

Dynamic since it is speed dependant.

Threshold of instability

The speed at which fluid induced instability commences. (e.g. 1900 rpm)

Two types of Fluid Induced Instabilities

Whirl. Forward precession. Usually starts earlier. Frequency holds a

constant order of rotor speed. (dependent on rotor speed)

Whip. Forward precession. Starts after whirl dies.

(it may exist without being preceded by whirl)

Frequency holds constant value (independent on rotor speed).

Fluid Induced Instability

Stable

Whip

Whirl

Orbit= 2D shaft vibration

FII Vibration symptoms:

* Large Amplitude * Subsynchronous

* Circular Orbit * Forward Precession

Experimental Setup

Experiments have been carried out at KFUPM MED Advanced Mechanics Lab.

Setup consists of Bently Nevada rotor kit with fluid film bearing

option. Speed controller. Oil pump. Vibration pickups and ADRE software.

Rotor kit

Fluid film bearing

Speed controller

Oil pump

Effect of fluid wedge support CCW rotation

Effect of fluid wedge support CW rotation

Typical experimental test results:

Vibration spectrum

Shaft average centerline, clearance circle and average eccentricity ratio. Gradual concentricity.

Zoomed run-up cascade. Instability threshold and frequency.

Threshold of instability change with oil pressure during start up

0

2150 2250

1620

2070

2500

0

500

1000

1500

2000

2500

3000

0.6 0.8 1 1.2 1.4 1.6

Pressure (psi)

Speed

(rp

m)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0.6 0.8 1 1.2 1.4 1.6

Pressure (psi)

Speed

(rp

m)

Threshold of instability change with oil pressure during shutdown

How oil behaves at the threshold of instability

1. Disk Location (A)

2. Shaft Length (B)

3. Disk Unbalance (Unb)

Unbalance effect (as function of rpm).

-9.3

-9.2

-9.1

-9

-8.9

-8.8

-8.7

-8.6

-8.5

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

C0930001

C0930101

C0930201

Unb=2g

Unb=0g

Conclusions from experimental work

Higher flow rate of lubricating oil should raise the threshold of instability.

The unbalance has effect on instability.

THERORITICAL WORK

System response at P=0.6 psi at 1800 rpm

Displacement Transient Response

-15

-10

-5

0

5

10

15

0 0.5 1 1.5 2

Time, sec

Dis

pla

cem

ent,

mils

D(2)x

D(2)y

Pressure is 0.6 psi at 1800 rpmStn (2): Fluid Film Bearing

Displacement Transient Response

-15

-10

-5

0

5

10

15

-15 -5 5 15 25 35

D(2)x, mils

D(2

)y, m

ils

D(2)x

Pressure is 0.6 psi at 1800 rpmStn (2): Fluid Film Bearing

System response at P=0.6 psi at 1800 rpm (Cont’d)

Displacement Transient Response

0

1

2

3

4

5

6

7

0 50 100 150 200

Frequency, Hz

Dis

pla

cem

ent,

mils

D(2)x

D(2)y

Pressure is 0.6 psi at 1800 rpmStn (2): Fluid Film Bearing

System response at P=0.6 psi at 1800 rpm (Cont’d)

F=30 Hz=1800 cpm

F=11.72 Hz=703 cpm

Displacement Transient Response

-4

-3

-2

-1

0

1

2

3

4

0 0.5 1 1.5 2

Time, sec

Dis

pla

cem

ent,

mils

D(2)x

D(2)y

Pressure is 0.6 psi at 1700 rpmStn (2): Fluid Film Bearing

System response at P=0.6 psi at 1700 rpm

Displacement Transient Response

-4

-3

-2

-1

0

1

2

3

4

-4 -2 0 2 4 6 8 10

D(2)x, mils

D(2

)y, m

ils

D(2)x

Pressure is 0.6 psi at 1700 rpmStn (2): Fluid Film Bearing

System response at P=0.6 psi at 1700 rpm (Cont’d)

System response at P=1.2 psi at 2300 rpm

Displacement Transient Response

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 0.5 1 1.5 2 2.5 3 3.5

Time, sec

Dis

pla

cem

ent,

mils

D(2)x

D(2)y

Pressure is 1.2 psi at 2300 rpmStn (2): Fluid Film Bearing

System response at P=1.2 psi at 2300 rpm (Cont’d)

Displacement Transient Response

-10

-5

0

5

10

-8 -3 2 7 12 17 22 27

D(2)x, mils

D(2

)y, m

ils

D(2)x

Pressure is 1.2 psi at 2300 rpmStn (2): Fluid Film Bearing

System response at P=1.2 psi at 2300 rpm (Cont’d)

Displacement Transient Response

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 50 100 150 200

Frequency, Hz

Dis

pla

cem

ent,

mils

D(2)x

D(2)y

Pressure is 1.2 psi at 2300 rpmStn (2): Fluid Film Bearing

F=38.4 Hz=2300 cpm

F=13.67 Hz=820 cpm

System response at P=1.2 psi at 2200 rpm

Displacement Transient Response

-4

-3

-2

-1

0

1

2

3

4

0 0.5 1 1.5 2 2.5 3 3.5

Time, sec

Dis

pla

cem

ent,

mils

D(2)x

D(2)y

Pressure is 1.2 psi at 2200Stn (2): Fluid Film Bearing

System response at P=1.2 psi at 2200 rpm (Cont’d)

Displacement Transient Response

-4

-3

-2

-1

0

1

2

3

4

-4 -2 0 2 4 6 8 10

D(2)x, mils

D(2

)y, m

ils

D(2)x

Pressure is 1.2 psi at 2200Stn (2): Fluid Film Bearing

Conclusions from theoretical work

Effect of Viscosity on the stability is expected. Higher bearing pressure leads to higher

threshold of instability.