From MUSTAFA KAMAL PASHA only for informatins for all

1. Dynamics of Rotating machinery with
Emphasis on Balancing
Technical Services

2. Dynamics of Rotating machinery with
Case studies
– Balancing fundamentals
– Critical Speeds and vibratory Modes- How to identify
and understand its significance.
– Slow Roll and Bow shaft -Rotor dynamic perspective.
– Damping
– Bearings and support structures
– Foundations
– Case Studies

3. F=m*r*ω2
A disk with a mass M having an
Unbalance weight m at a position
r from its center. This unbalance
causes an eccentric center of
gravity e and results in a centrifugal
force P when the disk is rotated at
an angular speed ω
Centrifugal Force F=mrω2
ω is angular velocity = 2πn/60 ; P is in Newtons
The centrifugal force P changes its direction as the rotor
rotates, which repeatedly acts on the bearing portion
and so causes vibration of the whole machine.

4. Rotor Unbalance should not represented by Centrifugal force F
since F changes as speed changes
Unbalance U is represented by U=mr
m : mass of unbalance r : radius of unbalance
Dimension of unbalance g ･ mm
Quality of Rotor Balance : ratio of unbalance U to rotor mass M
e=U/M=mr/M
Here e is a vector having a dimension of length which is given as μm
where m is expressed in [g], r in [mm] and M in [kg]
e is (eccentricity) of the center of gravity of the rotor.
Expression of unbalance

5. Single Plane balancing applied to thin disc
shaped rotors
Static unbalance

6. Unbalances U1,U2 and U3 distributed on a rotor which is long in
the axial direction can be substituted by two independent
Unbalance vectors Ua and Ub on correction planes A and B
respectively
Dynamic Unbalance

7. Balancing -First order mode is carried out on three correction planes
Balancing -Second order mode is carried out on four correction planes
Rotors become flexible when speed is increased
The boundary speed which separates the rigid rotor and the flexible
rotor is called the critical speed.
The number of additional correction planes necessary for eliminating
deformation of a rotor is the same as the order of the critical speed.
Three correction planes eliminating rotor deformation up to first-order
critical speed
Four correction planes eliminating deformation up to second-order
critical speed.
Multi Plane balancing of flexible rotors

8. Accuracy of balancing
Balancing to the achievable limit is uneconomical
Specific unbalance (e [μm]) expresses the unbalance state of a rotor
independently of its mass and shape.
Value of e is in inverse proportion to the maximum working revolution
speed N [min-1] of the rotor, which means that eN is a constant value.
(ISO) defines the product of specific unbalance and revolution speed as
the balance quality.
The balance quality has a dimension of [mm/s] because the
dimensions of revolution speed and specific unbalance are [rad/s] and
[mm] respectively.
The grade of the balance quality is expressed by putting a letter G
before a number which represents eN.

9. Procedure of determining allowable unbalance
Rotor speed N , Mass of the rotor m
Position of rotor bearings Position of correction planes
Set the grade of balance quality according to the type of the rotor.
Find allowable residual specific unbalance eper from rotor speed
Use equation or from diagram
Balance Quality = e*w
Calculate the allowable residual unbalance from the allowable residual
specific unbalance and mass of the rotor:
Allowable residual unbalance Uper = E per
* M(g ･ mm)
Allocate the allowable residual unbalance to unbalances on each
actual correction plane.

11. G6.3 6.3 ●Machines for processing plants ● Turbine blades for main
engines of merchant ships ●Drums for centrifugal separators
●Paper-making rolls and printing rolls ●Fans
●Completed gas turbine rotors for airplanes ●Flywheels
●Impellers of pumps ●Parts of machine tools and general
machinery
●Medium- and large-sized armatures having no specific
requirements for electric motors with axial center height of
80mm or more
●Small-sized armatures (mainly mass-production type)
either for use being insensitive to vibration or for use with
insulation against vibration
●Engine parts having specific requirements
G2.5 2.5 ●Gas turbines, steam turbines and main engine turbines for
merchant ships
●Rigid rotors for turbo generators
●Storage drums and disk turbo compressors for computers
●Main spindles for machine tools
●Medium- and large-sized armatures having specific
requirements
●Small-sized armatures (excluding those defined in G6.3 and
G1)
●Turbine-driven pumps,

12. Excessive Bearing Clearance
Bent Shaft
Misalignment or other Preload
Electrical Influence
Compliant Support or Foundation
Soft Foot
Mechanisms resulting in Syncronous 1X
vibration other than unbalance

13. CROSS SECTIONAL ARRANGEMENT –TURBINE

14. VIBRATION MEASURING
TRANSDUCERS
SHAFT VIBRATION
- PROXIMITY PROBE
BEARING VIBRATION
-VELOCITY PICK UP , ACCELEROMETER
PHASE
-OPTICAL PROBE , EDDY CURRENT PROBE

15. RECOMMENDED LOCATIONS OF VIBRATION
MEASUREMENTS FOR PEDESTAL BEARINGS
(AS PER ISO)

16. RECOMMENDED LOCATIONS OF VIBRATION
MEASUREMENTS FOR HOUSING TYPE BEARINGS
(AS PER ISO)

17. Measuring
Amplifier
45O 45O
Proximity
Pick-up
L RSHAFT
RECOMMENDED LOCATIONS OF SHAFT
VIBRATION MEASUREMENTS AS PER ISO

18. PROXIMITY PROBE & ACCELEROMETER

19. Natural Frequency
The frequency of free vibration of a system. The frequency at which an
undamped system with a single degree of freedom will oscillate upon
momentary displacement from its rest position.
Resonance
Resonance is the condition which occurs when such forcing frequencies do in
fact coincide with one or more natural frequencies. These may be a natural
frequencies of the rotor, but often can be a natural frequency of the support
frame, foundation . Forcing frequencies include those from sources such as
unbalance, misalignment, looseness, bearing defects, gear defects, belt wear, etc.
Critical speed
Critical speeds are a special case of resonance in which the vibrating forces are
caused by the rotation of the rotor

20. 0
10
20
30
40
50
60
70
80
90
0 300 600 900 1200 1500 1800 2100 2400 2700 3000 3300
RPM
0
60
120
180
240
300
360
0 300 600 900 1200 1500 1800 2100 2400 2700 3000 3300
I ,115 MW
Generator Front Vertical Coast up , Before Balancing
Micronspk-pkPhasedegrees

21. 0
10
20
30
40
50
60
70
80
0 300 600 900 1200 1500 1800 2100 2400 2700 3000 3300
RPM
0
60
120
180
240
300
360
0 300 600 900 1200 1500 1800 2100 2400 2700 3000 3300
115 MW
Generator Rear Vertical Coast up , Before Balancing
Micronspk-pkPhasedegrees

22. ROTOR AND BALANCE FORCE DETAILS
GENERATOR ROTOR WEIGHT : 37000 KG
GENERATOR ROTOR STATIC WEIGHT PER BEARING : 18500 KG
BALANCING RADIUS
FAN PLANE : 310 MM
RETAINING RING PLANE : 460 MM
DISTANCE BETWEEN RETAINING RING PLANE : 4850 MM
DISTANCE BETWEEN FAN PLANE : 5740 MM
APPROXIMATE WEIGHT OF TRIAL WEIGHT : 93 GRAM
CENTRIFUGAL FORCE FOR 93 GRAMS
AT BALANCE RADIUS AT 3000 RPM , FORCE UNITS : 430 KG
RETAINING RING PLANE

23. 0
10
20
30
40
50
60
70
80
0 300 600 900 1200 1500 1800 2100 2400 2700 3000 3300
RPM
0
60
120
180
240
300
360
0 300 600 900 1200 1500 1800 2100 2400 2700 3000 3300
115 MW Generator Rear Vertical Coast up
with 5x93 grams Couple correction weights
Micronspk-pkPhasedegrees

25. GENERATOR FAN BLADES-BALANCING PLANE

26. Dynamics of Rotating machinery
• Critical Speeds are dependent upon:
– Rotor Flexibility - Mass and Stiffness ( D-dia
of rotor, L- Bearing Span)
– Support Stiffness which also includes the
foundation stiffness.
– The damping from the bearings dictates the
amplification factor

27. To Summarize on critical speeds
• It is always due to synchronous excitation.
• Critical speeds in horizontal and vertical
direction called as horizontal and vertical
Modes depend on stiffness in those
directions.
• Horizontal mode is predominantly effects the
vibration in horizontal direction and so in case
of vertical mode. Can be measured by
seismic in that direction only.
• Since we also measure shaft vibrations at 45
deg so it is measuring both.

28. Let us understand the vibratory
modes.
• The modes below the first flexural critical
speed are called as rigid modes.
• Rigid modes are bouncing or translatory have
same phase on both bearings while in conical
modes the phase is 180 deg.
• In bending modes also the phase relationship
in first and second modes is similar.
• We need to study the phase angle vis a vis
the design critical speed in overhung modes.

29. Rocking mode
Conical mode
First bending mode
Second bending mode
Overhungcantilever
bending mode
Rocking mode
Conical mode
First bending mode
Rocking mode
Conical mode
Second bending mode
First bending mode
Rocking mode
Conical mode
Overhungcantilever
bending mode
Second bending mode
First bending mode
Rocking mode
Conical mode

30. A typical shaft bow Bode’s Plot of a 120 MW generator.

31. Turbo machinery damping
• Viscous damping – Proportional to velocity
Bearings and Oil seals of large rotating machinery
damping provided by lubricating oil
Rotor system process fluids
Pumps significant
Gas turbines, Centrifugal compressors – insignificant

32. • Coulomb damping
Sliding friction – rub
Coulomb friction force is constant , depends on
1. Nature of sliding surfaces and
2. Perpendicular pressure between surfaces
Turbo machinery damping

33. • Structural damping
Internal friction in material due to vibratory
stress and strain
Proportional to maximum stress and
therefore deflections
Independent of frequency – vibratory stress
Rotating machinery small compared to viscous
damping
Turbo machinery damping

35. Hydrodynamic bearingsHydrodynamic bearings
•One of the basic purposes of a bearing is to
provide a frictionless environment to support
and guide a rotating shaft.
•Industrial machinery with high horsepower
and high loads, such as steam turbines,
centrifugal compressors, pumps and motors,
utilize journal bearings as rotor supports.

36. TO Develop Hydro Dynamic Pressures the following
three parameters are required :
1) Load,
2) Speed and
3) Oil Wedge
•Hydrodynamic principles, which are active as the shaft
rotates, create an oil wedge that supports the shaft and
relocates it within the bearing clearances.
• Hydrodynamic bearings have relatively a low frictional
resistance to turning but more importantly provide
viscous damping to reduce lateral vibrations.

37. All heavy industrial turbo-machines use fluid film
journal bearings of some type :
• To support the shaft weight
• To control the motions caused by
I) unbalanced forces
II) aerodynamic forces
III) external excitations from seals and couplings.

38. • The damping is very important in many
types of rotating machines where the fluid
film bearings are often the primary source of
the energy absorption needed to control
vibrations.
• Fluid film journal bearings also play a major
role in determining rotor dynamic stability,
making their careful selection and
application a crucial step in the development
of superior rotor-bearings systems.

39. Journal bearings have many differing designs to
compensate for differing load requirements,
machine speeds, cost, or dynamic properties.
•Cylindrical Journal Bearings with & without oil
rings .
• Multi lobe Journal Bearings:
2 Lobe , 2 Lobe with loading arc, 2 Lobe Offset
& 4 Lobe type
• Tilting Pad Journal Bearings
4 Pad and 5 Pad type

40. CAPACITY OF HYDRODYNAMIC BEARINGSCAPACITY OF HYDRODYNAMIC BEARINGS
Under operation, the capacity of hydrodynamic
bearings is restricted by:
• Minimum oil film thickness &
• Babbitt temperature.
• The critical limit for low-speed operation is
minimum oil film thickness. In high-speed
operation, babbitt temperature is usually the
limiting criteria.

41. FLUID FILM JOURNAL BEARINGS
SLOW SPEED HIGH SPEED
RING LUBRICATED
BEARINGS
PRESSURE FED
BEARINGS
RADIAL
LOADS
RADIAL AND
THRUST LOADS
MULTI LOBE BEAINGS TILTING PAD
BEARINGS
CYLINDRICAL 2- LOBE 3- LOBE 4- LOBE
4- PAD 5-PAD
VERTICAL
ELLIPTICITY
HORIZONTAL
ELLIPTICITY
SYMME-
TRICAL
4- LOBE
TILTED
4- LOBE

42. Fig.1. Limit for Satisfactory Bearing Operation under Hydrodynamic
Condition.

43. Pressure Distribution in a Journal Bearing

44. Oil Ring Bearing

45. Different Oil Ring Designs

46. Cross Sectional View of Ring Lubricated Journal Bearing
RING LUBRICATED BEARINGS

47. Cylindrical and Multi-Lobe Journal Bearings
Pressure Fed Bearings

48. Fluid film Thrust bearings
1. Supports Axial Forces
Constant thrust loads
Differential pressure across wheels (Turbines and
Compressors)
Gears – Axial force components
Dynamic axial loads
Bent rotors , Misaligned shafts
2. Maintains rotor in fixed axial position with respect to
Casing
Axial clearances between Blade rows determine Turbine efficiency
Wheels and diaphragms in Compressors

49. Thrust bearing assembly should fulfill requirement for
Axial position
Axial float
Axial location – axial position shims behind active thrust shoes
Axial float – Total thrust float shims behind inactive thrust shoes
Motors and Generators no thrust bearing
Magnetic forces across air gap center the rotor within the
stator
Fluid film Thrust bearings
Dynamics of Rotating machinery

50. Active pads Inactive pads
Shims for axial position Shims for thrust float
Thrust Float
Stationary
Casing
Thrust probe
Journal
bearing
shaft Normal
Thrust
Thrust bearing ---Centrifugal compressors, small turbines

51. Active pads Inactive pads
Shims for axial position Shims for thrust float
Thrust Float
Thrust probe
Thrust cum Journal bearing
shaft Normal
Thrust
Thrust bearing ---Large Steam and Gas turbines
Active thrust collar Inactive thrust collar

54. Steam Turbine Design Philosophy
KWU Design
Russian Design

69. Run-out Diagram , Rotation angle of Shaft alignment and Bearing Height Correction
(Before Initial Correction for BKTPP unit 2 )
405 3495 485 5825 475 1100
3350 3900 6310 1575 7810
θ HP = θ IP – 0.085/870 θ IP = 0.205 / 740 ψ = h3/6310 θ Gen = 0.158 / 760
h2= hH1 + 405 * θHP h3 = 485* θIP h5=1100*θGen
h1= h2+3350* θHP hH1=(485+3495)*θIP h6=(1100+7810)*θGen
Alignment correction of case 1
h1=h1-(6310+3900+3350)*ψ h3=h3-6310* ψ = 0 h5=h5-1575*ψ
h2=h2-(6310+3900)*ψ h4=0 h6=h6-(1575+7810)*ψ
hG
θ Gen
θIP
h3
θHP
h2
h1
hH1
V 0.085 D870
Λ 0.205 D740
h5
V 0.158 D760
ψ = Rotation angle
of Shaft Alignment
h1
h2 h5 h6

70. Run-out Diagram , Rotation angle of Shaft alignment and Bearing Height Correction
(Before Secondary Correction for BKTPP unit 2 )
405 3495 485 5825 475 1100
3350 3900 6310 1575 7810
θ HP = θ IP + 0.03 / 870 θ IP = 0.04 / 740 ψ = h3/6310 θ Gen = 0.158 / 760
h2= hH1 + 405 * θHP h3 = 485* θIP h5=1100*θGen
h1= h2+3350* θHP hH1=(485+3495)*θIP h6=(1100+7810)*θGen
Alignment correction
h1=h1-(6310+3900+3350)*ψ h3=h3-6310* ψ = 0 h5=h5-1575*ψ
h2=h2-(6310+3900)*ψ h4=0 h6=h6-(1575+7810)*ψ
hG
θ Gen
θIP
h3
θHP
h2
h1
hH1
Λ 0.03 D870
Λ 0.04 D740
h5
V 0.158 D760
ψ = Rotation angle
of Shaft Alignment
h1
h2 h5 h6

72. SCHEMATIC FOR GERB SPRING
TIE ROD
SHIM
TG DECK
TG COLUMN
NOTE:
1. THESE READINGS ARE IN
ADDITION TO READING
TAKEN BY GERB ON THE
PROTOCOL DOCUMENT.
2 TURBINE ENGINEER
ALONG WITH CIVIL
ENGINEER TO ASSOCIATE.
A. STICK MICRO METER READING AT FOUR
LOCATIONS BETWEEN DECK AND
COLUMN. MARK THE LOCATION OF
READING (USE METAL MARKER).
B. STICK MICROMETER READING AT FOUR
LOCATION OF EACH SPRING ASSEMBLY.
C RECORD TOTAL THICKNESS OF SHIM
HEIGHT AND NUMBER OF SHIMS.
A AB B
C

73. TIE
ROD
SCHEMATIC FOR M/S GERB’S CONDENSER SPRING ASSEMBLY
SHIM
JACK
BOLTS
CONDENSER
FOUNDATION
CONDENSER
BOTTOM PLATE
BACK

76. THANK YOU