Dynamics of Rotating machinery with Emphasis on Balancing

Technical Services

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

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.

Rotor Unbalance should not represented by Centrifugal force Fsince 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

Single Plane balancing applied to thin disc shaped rotors

Static unbalance

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

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

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.

Procedure of determining allowable unbalance

Rotor speed N , Mass of the rotor mPosition 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.

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,

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

CROSS SECTIONAL ARRANGEMENT –TURBINE

VIBRATION MEASURING TRANSDUCERS

SHAFT VIBRATION - PROXIMITY PROBE

BEARING VIBRATION-VELOCITY PICK UP , ACCELEROMETER

PHASE

-OPTICAL PROBE , EDDY CURRENT PROBE

RECOMMENDED LOCATIONS OF VIBRATION MEASUREMENTS FOR PEDESTAL BEARINGS

(AS PER ISO)

RECOMMENDED LOCATIONS OF VIBRATION MEASUREMENTS FOR HOUSING TYPE

BEARINGS (AS PER ISO)

Measuring

Amplifier

45O 45O

Proximity Pick-up

L RSHAFT

RECOMMENDED LOCATIONS OF SHAFT VIBRATION MEASUREMENTS AS PER ISO

PROXIMITY PROBE & ACCELEROMETER

Natural FrequencyThe 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 speedCritical speeds are a special case of resonance in which the vibrating forces are caused by the rotation of the rotor

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I ,115 MW

Generator Front Vertical Coast up , Before Balancing

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Generator Rear Vertical Coast up , Before Balancing M

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 ROTOR AND BALANCE FORCE DETAILS GENERATOR ROTOR WEIGHT : 37000 KGGENERATOR ROTOR STATIC WEIGHT PER BEARING : 18500 KG

BALANCING RADIUS FAN PLANE : 310 MMRETAINING RING PLANE : 460 MM DISTANCE BETWEEN RETAINING RING PLANE : 4850 MMDISTANCE BETWEEN FAN PLANE : 5740 MMAPPROXIMATE WEIGHT OF TRIAL WEIGHT : 93 GRAMCENTRIFUGAL FORCE FOR 93 GRAMS AT BALANCE RADIUS AT 3000 RPM , FORCE UNITS : 430 KG RETAINING RING PLANE 

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115 MW Generator Rear Vertical Coast up

with 5x93 grams Couple correction weights M

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GENERATOR FAN BLADES-BALANCING PLANE

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

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.

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.

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

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

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

• 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

• 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

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.

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.

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.

• 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.

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

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.

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

Fig.1. Limit for Satisfactory Bearing Operation under Hydrodynamic

Condition.

Pressure Distribution in a Journal Bearing

Oil Ring Bearing

Different Oil Ring Designs

Cross Sectional View of Ring Lubricated Journal Bearing

RING LUBRICATED BEARINGS

Cylindrical and Multi-Lobe Journal Bearings

Pressure Fed Bearings

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

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

Active pads Inactive pads

Shims for axial position Shims for thrust float

Thrust Float

StationaryCasing

Thrust probe

Journalbearing

shaft NormalThrust

Thrust bearing ---Centrifugal compressors, small turbines

Active pads Inactive pads

Shims for axial position Shims for thrust float

Thrust Float

Thrust probe

Thrust cum Journal bearing

shaft NormalThrust

Thrust bearing ---Large Steam and Gas turbines

Active thrust collar Inactive thrust collar

Steam Turbine Design Philosophy

KWU Design

Russian Design

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 HP = IP – 0.085/870 IP = 0.205 / 740 = h3/6310 Gen = 0.158 / 760 h2= hH1 + 405 * HP h3 = 485* IP h5=1100*Gen h1= h2+3350* HP hH1=(485+3495)*IP h6=(1100+7810)*Gen Alignment correction of case 1

h1=h1-(6310+3900+3350)* h3=h3-6310* = 0 h5=h5-1575*

h2=h2-(6310+3900)* h4=0 h6=h6-(1575+7810)*

hG

Gen

IP

h3

HP

h2 h1

hH1

V 0.085 D870

0.205 D740

h5

V 0.158 D760

= Rotation angle of Shaft Alignment

h1 h2 h5 h6

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 HP = IP + 0.03 / 870 IP = 0.04 / 740 = h3/6310 Gen = 0.158 / 760 h2= hH1 + 405 * HP h3 = 485* IP h5=1100*Gen h1= h2+3350* HP hH1=(485+3495)*IP h6=(1100+7810)*Gen Alignment correction

h1=h1-(6310+3900+3350)* h3=h3-6310* = 0 h5=h5-1575*

h2=h2-(6310+3900)* h4=0 h6=h6-(1575+7810)*

hG

Gen

IP

h3

HP

h2 h1

hH1

0.03 D870

0.04 D740

h5

V 0.158 D760

= Rotation angle of Shaft Alignment

h1 h2 h5 h6

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

TIE ROD

SCHEMATIC FOR M/S GERB’S CONDENSER SPRING ASSEMBLY

SHIM

JACK BOLTS

CONDENSER FOUNDATION

CONDENSER BOTTOM PLATE

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