Indian J.Sci.Res.1(2) : 690-701, 2014

ISSN:2250-0138(Online)

ISSN : 0976-2876 (Print)

__________________________________ 1Corresponding author

DYNAMIC PROPERTIES OF TILTING-PAD JOURNAL BEARINGS IN POWER PLANT IRAN

(YAZD STATION)

ERFAN KHOSRAVIAN1a, SAM GHATREH

b

aFaculty Member Of Payam Noor University

bMechanical Department

ABSTRACT

Radial, tilting-pad journal bearings are usually applied in high speed rotating machines operating at small and mean motionless loads and

the peripheral speeds of journal reaching 150 m/s. These bearings have good stability at high speeds, are less responsive to the load direction

and shaft misalignment compared to the multilube bearings. Each pad tilts about its pivot making a hydrodynamic film that generates a

pressure reacting to the static load applied on the spinning journal. This type of bearing is typically installed to carry a static load on a pad

(LOP) or a static load in between pads (LBP).These bearings tender natural stability resulting from zero cross-coupling dynamic factor. It

has been establish that the dynamic properties of TPJBs are frequency dependent. on the other hand, in engineering tradition, laboratory

analysis of rotor dynamics is based on the values determined for the frequency which corresponds to the rotor speed .The paper analyzes

the conclusion of bearing stiffness and damping from experimental and investigational and theoretical investigations. It has been found that

the variations of tilting-pad bearings stiffness and damping properties with frequency of excitation depend on the bearing operating

situation,and can be very important.

KEYWORDS: Tilting Bearing Pads, Frequency, Dynamic Load, The Rotor Mass, Hydrodynamic Force Components

The tilting-pad bearings are the bearings, which have divide

pads and the space

between single tilting-pads effects the bearing act. The number

of tilting-pads can

be basically 3 to 5 depending on the required operating

parameters of rotating machine and the exitaton frequence in

system .The operating surfaces of tilting-pads are the

cylindrical ones with the spin around centred on the pad arc or

displaced in the direction of journal rotation from the pad

centre. The tilting 12-pad journal bearings have found

application in the turbines of hydroelectric power plants as the

radial bearings of vertical rotor.Tilting pad bearings is a partial

arc design. This configuration has individual bearing pads

which are allowed to pivot or tilt to conform with the dynamic

loads from the lubricant and shaft. This type of bearing is a

unidirectional design and is available in several variations

incorporating differing numbers of pads with the generated

load applied on a pad or between the pads.

A journal bearing, simply stated, is a cylinder which surrounds

the shaft and is filled with some form of fluid lubricant. In this

bearing a fluid is the medium that supports the shaft

preventing metal to metal contact. The most common fluid

used is oil, with special applications using water or a gas. This

application note will concentrate on oil lubricated journal

bearings.

Dynamics of high speed rotating equipment depend strongly

on journal bearings. Currently, tilting pad journal bearings

(TPJB) are leading as shaft support in such machinery in

power plant . This is mostly for the reason that of the

following two kind of the TPJBs: 1) freedom from self-

excited vibration, and 2) tolerance to misalignment.

Rotordynamic study is based on predicted bearing linear

dynamic factor, which are determined supposition

synchronous shaft vibrations (synchronously reduced stiffness

and damping factor). as regards, some investigational and

theoretical studies of tilting pad journal bearings illustrate a

positive effect of excitation frequency on the bearing stiffness

and damping factor (Parsell et al., 2005; Adams and

McCloskey, 1990). Other reported conclusions show quite

limited dependency on frequency, or are uncertain (Glienicke,

1967). If the bearing dynamic properties do depend on

destabilizing frequency, it is significant to also know the

properties, which match to the first usual frequency. In

totalling, non-synchronous forces, such as those related with

internal flow, or due to magnetic effects in generators, may

also affect rotor-bearing dynamics. getting a reliable guess of

the journal bearing dynamic properties has always been a

demanding task. The narrative documents moderately few

cases of such attempts. Using peripheral synchronous loads to

excite the test bearing, Glienicke (Cai, 2000) evaluated

stiffness and damping properties after measuring the applied

load and the resulting shaft path. A equivalent technique was

used by Morton (Parkins, 1979), who used non-synchronous

excitation in both the vertical and horizontal commands.

Parkins (Burrows, 1982), Brockwell and Dmochowski (Lund,

1964) used a more direct method of measuring the bearing

dynamic properties of journal bearings by generating two

different, straight line orbits of vibration. To obtain such

orbits, the magnitude of two oscillating forces, as well as the

Indian J.Sci.Res.1(2) : 690-701, 2014 - 691 -

phase difference between them, were carefully adjusted. The

main advantage connected with this method was that it passed

the measurement of the phase angle between the vectors of

shaft displacement and excitation force.

These methods signify time domain techniques. deplorably, it

was found that a small error in triggering or in the measured

phase angle could conclusion in large errors in the calculated

values. Frequency amplitude techniques overcome these

trouble. Burrows and Sahinkaya (Rouvas and Childs, 1993)

and Rodriguez and Childs (1) used frequency domain

algorithms for dynamic testing of bearings. This paper

analyzes the Changes of the stiffness and damping factor for

the tilting pad journal bearings with the frequency of

excitation and explainS the analytical and experimental

techniques used to evaluate these properties.

ASSESSMENT OF THE DYNAMIC FACTOR FOR

THE TILTING-PAD JOURNAL BEARINGS

Tilt Pad Bearing Preload

Fluid-film journal bearings offer the main support for

horizontal turbomachinery rotors. These bearings come in

many configurations from trouble-free, fixed geometry to

multifaceted tilt-pad units, such as the bottom-half bearing

assembly (Fig. 1).Bearing design is dependent upon criterion

such as load, speed, constancy, rotor dynamics, lubricants, and

price. Within the selection of design parameters, preload is

important in controlling bearing act, which finally impacts

preservation and operating costs. Tilting pad bearings usually

contain three to six pads. Orientation of the pads is distinct as

either load on pivot (LOP) or load between pivots (LBP). If a

horizontal rotor has a single pad centered at the bottom of the

bearing,an LOP condition exists. If two pads sit astride the

bottom centerline, then the bearing is referred to as an

LBP.The pad rotation of an LBP bearing results in a descend

of the shaft centerline below the LOP bearing (Fig. 1). The

amount of shaft drop is dependent on the bearing geometry.

Figure 1. Preload on tilting pad bearing

Bearing Preload

As the oil hold clearance changes,bearing stiffness and

damping are influenced. In order to give a ordinary method of

recitation these variations, the impression of preload is

applied. Preload is often used to adjust bearing factor in order

to obtain exact rotor response type. Since the translational

first-critical and the pivotal second-critical speeds depend on

bearing stiffness,proper range of preload may be required to

keep the rotor critical speeds out of the operating speed range.

Bearing preload is defined as follows:

The clearance value must be consistent either radial or

diametrical

−=

pad

brg

C

Ceload 1Pr

Where brgC is increase of the lift by the suitable factor

provides a good approximation of the bearing diametrical, or,

assembly clearance (Cbrg). It is identical to the assembly bore

diameter minus the journal diameter. It is also equal to the

diameter of the major mandrel that can be inserted into the

bearing minus the journal diameter.

Indian J.Sci.Res.1(2) : 690-701, 2014 - 692 -

An additional characteristic of journal bearings is damping.

This type of bearing provides much more damping than a

rolling element bearing because of the lubricant present. More

viscous and thicker lubricant films provide higher damping

properties. As the available damping increases, the bearing

stability also increases. A stable bearing design holds the rotor

at a fixed attitude angle during transient periods such as

machine startups/shutdowns or load changes. The damping

properties of the lubricant also provides an excellent medium

for limiting vibration transmission. Thus, a vibration

measurement taken at the bearing outer shell will not represent

the actual vibration experienced by the rotor within its bearing

clearances.

Bearing Linear Dynamic Factor

A major design consideration in the passive tilting-pad bearing

is the radial position of each pad/pivot pair. That is, the pads

can be located such that their centers of curvature (with zero

tilt angles) do not all necessarily coincide with the bearing

center. This is known as the preload factor, and directly affects

the dynamic stability properties of the bearing. The question is

then: How does one determine the “optimal” pad locations for

a given operating condition of the rotating machine?The

answer to this question naturally leads to the concept of the

active tilting-pad bearing. The idea of actively translating the

pads ofatilting-pad bearing was first proposed by. The

hypothesis is that it could further improve the stability

properties and performance of the bearing system.

Specifically, the dynamic damping-stiffness effects of the

bearing could be adjusted due to the variation in the fluid film

thickness caused by the pad/pivot pair translation. The

reasoning behind this hypothesis can be understood by

examining the Reynolds equation for laminar, incompressible,

Newtonian, inertialess, thin-film flows For a rigid shaft we

may inscribe the following two equations of motion (Figure

1):

t

hh

z

P

z

Ph

R ∂∂

+∂∂

=

∂∂

∂∂

+

∂∂

∂∂

µθ

µωθθ

1261 3

2

0)(

0)(

2

2

2

2

=++

=++

yyS

xxS

wtfdt

yjdM

wtfdt

xjdM

(1)

Indian J.Sci.Res.1(2) : 690-701, 2014 - 693 -

Figure 2. Organize System For Estimate Of Journal Bearing Dynamic Factor

For a little vibration approximately the shaft symmetry position, we may consider that the resultant bearing force is linearly relative to

the journal movement x j and y j , and velocities x j and y j . The equations (1) can then be written as follows:

0

0

2

2

2

2

=++++

=++++

jyyjyxjyyjyx

j

S

jyyjxxjxyjxx

j

S

ycxcykxkdt

ydM

ycxcykxkdt

xdM

(2)

The factor with the index xx and yy are called direct stiffness

and damping factor, while those with the indices xy and yx are

referred to as cross-coupling factor.

The last symbolize a connection of the hydrodynamic force

part in the horizontal or vertical direction and the journal

movement in the way perpendicular to this component. Figure

1 illustrates the journal centre pathway resulting from changes

to the bearing static load. The action of the cross-coupling

stiffness factor is accountable for instability of hydrodynamic

bearings (half-frequency spin, oil whip).

For each of the pads of tilting-pad journal bearing its

hydrodynamic force passes through has zero cross-coupling

rigidity, and thus is naturally stable.

Indian J.Sci.Res.1(2) : 690-701, 2014 - 694 -

Figure 3. Tilting-pad journal bearing

Computer Model

Calculations of the bearing dynamic properties have been

based on a three-dimensional model of tilting-pad journal

bearings, though all the main equations are summary to a two-

dimensional form. The model has been described somewhere

else (Dmochowski and Brockwell, 1995). Here, only a brief

explanation is given.

A limited length pressure equation (circumferential and axial

directions) allows for viscosity variations in circumferential

direction and across the oil film. Turbulent flow is also

accounted for by counting Reynolds number effect. The

temperature and viscosity fields are obtained from a two-

dimensional energy equation, which accounts for heat

conduction in radial direction and heat convection

circumferentially. Oil mixing in the bearing cavities as well as

hot-oil carry over is also built-in in the analysis. Heat

conducted through the pad is calculated from the Laplace

equation, which accounts for heat conduction in

circumferential and radial directions. The model also

calculates both the thermal and elastic distortions of the

individual pads.

Figure 4. Typical pivot stiffness of a 120 mm TPJB

The above hydrodynamic considerations allow for calculation

of the stiffness and damping factor for fixed pads. They have

been used to compute the factor for tilting pads applying the

technique described by Lund (Kirk and Reedy, 1988). This

technique takes into considerations the mass and the excitation

frequency of the tilting pad. naturally, calculated bearing

dynamic properties are obtained after assuming that shaft mass

can be deserted and that both shaft and pad motions are

synchronous with shaft rotary speed. certainly, mass forces

associated with tilting of the pads are negligible when

compared with viscous forces. However, pivot stiffness can be

of the same order of magnitude as the oil film stiffness, and

thus can engage in recreation an important function in the

bearing dynamic properties. Figure 3 shows pivot stiffness for

a typical 140 mm diameter bearing calculated using the

formulae given by Kirk and Reedy (Flack and Zuck, 1988).

Thus, each pad can be represented by the mass, spring, and

damper elements, as shown in Figure 5.

Indian J.Sci.Res.1(2) : 690-701, 2014

ISSN:2250-0138(Online)

ISSN : 0976-2876 (Print)

__________________________________ 1Corresponding author

Figure 5. Mass, spring, and damper elements for tilting pad

Figure 6. Mass-spring-damper model for pads with flexible pivot (a) and equivalent bearing-shaft system (b)

The schematic shown in Figure 5 illustrates the mass-spring-

damper arrangement for the pad as well as the the same

system to calculate the effective pad factor. The shaft

experiences the combined action of all the elements of the

system represented by equivalent stiffness and damping factor.

From the deliberation of the systems shown in Figure 5 the

equivalent factor can be evaluated from equaition (5).

Indian J.Sci.Res.1(2) : 690-701, 2014

ISSN:2250-0138(Online)

ISSN : 0976-2876 (Print)

__________________________________ 1Corresponding author

pivexcpz

ijexczij

ijzeq

ij

ijexczij

ijzexczijzijeq

ij

kmk

where

ckk

ckc

ckk

ckkKKKK

+−=

++=

++

−+=

2

222

2

)(

222

22

)(

)(

)(

)(

ω

ω

ω

ω

(3)

Experimental Investigation

The NRC’s test fix, which is shown in Figure 7, utilizes the

scheme of a fixed rotating shaft (1) and a free vibrating test

bearing (2). Two orthogonal electro-magnetic shakers (3) and

(4) apply dynamic loads to the stator, and the bearing’s reply

is measured. Each shaker is attached to the bearing housing

through a steel rod and a flexible element assembly (5) that

prevents any constraints of the housing in a path at a 90 degree

angle to the shaking force. The shaft is supported on high

accuracy, angular ball bearings. A tensioned cable (6) applies

a static load. Soft springs (7) minimize the effect of bearing

vibration on the applied static load.

Indian J.Sci.Res.1(2) : 690-701, 2014 - 697 -

Figure 7. Journal bearing dynamic test rig

Table 1. Rig specifications

Shaft speed 0-16500 rpm

Journal diameter Up to 0.09843 m

Static load Up to 20 KN

Lubricant flow Up to .44 sm /

3

Lubricant inlet temperature

Up to Co

70

Power of motor 50 KW

The shakers have been automaticly to give a multifrequency excitation. In the presence of external excitation, equations of motions (2)

become

)()()()()()(

)()()()()()(

,

,

tftyctxctyktxktym

tftyctxctyktxktxm

ydyvyxyyyxb

xdxvxxxyxxb

=++++

=++++

&&&&

&&&&

(4)

The quantity of the bearing/shaft displacement within the

bearing clearance is contaminated by noise. Collecting a

certain number of accounts, and using their average can

minimize this effect. However, averaging in time field is not

suitable for random signals, and frequency domain techniques

should be applied. estimate of the bearing dynamic properties

using frequency domain techniques allows for minimization of

noise effects and the errors related with triggering.

After introducing Fourier transforms, equations (6) become

ijijij

xyxxxbx

xyxxxbx

cikH

where

YHXHAmf

YHXHAmf

ω

ωωωω

ωωωω

+=

+=−

+=−

)()()()(

)()()()(

(5)

Indian J.Sci.Res.1(2) : 690-701, 2014

ISSN:2250-0138(Online)

ISSN : 0976-2876 (Print)

__________________________________ 1Corresponding author

is the frequency response purpose, and Fx , Fy , Ax , Ay , X

,Y are Fourier transforms of excitation forces in the horizontal

and vertical directions, accelerations in the horizontal and

vertical directions, and displacements in the horizontal and

vertical directions, respectively.

The two Equations (7) contain four unknowns H ij . so, an

extra self-determining excitation is required to find two more

formulae, needed to calculate the bearing dynamic properties.

The Power Spectral Density method, which is described in

(Brockwell et al., 1990), has been used to evaluate the bearing

stiffness and damping factor. The bearing dynamic properties

have been determined from 16 following records. Each record

consisted of 256 samples of each measured variable (6

channels), collected over a period of 0.1 s

RESULTS AND DISCUSSION

In order to appraise the frequency effects on the bearing

dynamic properties calculations, an experimental examination

has been carried out for two effective conditions, which are

typical for high speed rotating machinery in power plant. The

bearing parameters and operating conditions are shown in

Table 2. For both suitcases pivot stiffness is similar and its

variation with load is shown in Figure 3.

Table 2. Bearing parameters and test conditions

parameter Case 1 Case 2

Bearing type 4 pad TPJB 4 pad TPJB

Pad configuration Load-between-pads(LBP) Load-on-pad(lop)

Nominal diameter 98.5 mm 100 mm

Length/diameter ratio (L/d) 0.4 1.0

Preload 0.3 0.3

Bearing load 4.0 KN 4.5 KN

Shaft speed 9000 rpm 9000 rpm

Case 1 represents a reasonably loaded bearing.

Figure 7 illustrates the deliberate and calculated

variations of the actual part of the frequency

response function, equation (6), which represents

bearing stiffness. The conclusions show a convinced

frequency effect on the bearing stiffness properties;

the factor decrease with the excitation frequency. For

the excitation frequencies up to that of the shaft

rotary motion (150 Hz), factor of stiffness are

comparatively constant. This effect is mainly clear

for the vertical bearing stiffness, kyy=Re(Hyy), at

higher frequencies of excitation.

Indian J.Sci.Res.1(2) : 690-701, 2014 - 699 -

Figure 8. Bearing direct stiffness factor: Case 1. a. horizontal b. vertical

The direct bearing damping factor for Case 1 are

represented by the angle of the imaginary part of the

frequency answer off function Hi,j (Eq. 8) illustrated

in Figure 8. Constant angle indicates insignificant

effects of both the pivot flexibility and the pad’s

mass. even though the trends of the experimental

results shown in Figures 7 and 8 are well defined, a

sure spread of the conclusions can be seen. earlier

analysis has shown that the doubt for the stiffness

and damping factor can exceed 10% and 15% in that

order (Rodriguezand Childs, 2004). in addition, the

results can be affected by the shaft flexibility.

Figure 9. 1 Bearing direct damping properties: Case 1. a. Horizontal b.vertical

With the validated model from Case 1, a different

bearing dynamic actions has been experiential in

Case 2 (Table 2), which deals with similar bearing

operating conditions and bearing geometry as those

of Case 1, apart from the bearing width. With a L/d

(length-to-diameter ratio) of 1.0, the bearing is

considered to be lightly loaded, as the operating

unconventional behaviour was just about 0.1 of the

bearing radial clearance. At such a low eccentricity,

and with the preload of 0.3, each pad of the bearing

operates under load. In this situation, both the

horizontal and vertical bearing direct stiffness factor

raise ith the frequency of excitation.

Indian J.Sci.Res.1(2) : 690-701, 2014

ISSN:2250-0138(Online)

ISSN : 0976-2876 (Print)

__________________________________ 1Corresponding author

Figure 10. Calculated bearing stiffness factor: Case 2.

a. horizontal b. cross-coupling c. vertical

As different to Case 1, frequency of excitation very

strongly affected the bearing damping properties.

Figure 10 shows that the fantasy part of the

frequency response function levels out, which means

a important reduce in bearing damping, even at

subsynchronous (with respect to the shaft turning

frequency) frequencies.

Figure 11. Calculated bearing damping properties: Case 2.

a. horizontal b. cross-coupling c. Vertical

Figures 10 and 11 also compare the result of (enabled

by pivot suppleness). It is the pad radial motion and

pivot stiffness that lead to variations of the dynamic

properties with frequency of excitation. Bearings

with inflexible pivots have steady stiffness and

damping factor for the entire range of measured

frequencies. Figures 10b and 11b show that the pad

flexibility and associated inertia forces do not affect

the cross coupling factor for tilting-pad journal

bearings.

4.0 CONCLUDING REMARKS

a. An insufficient knowledge of the bearing dynamic

properties is following many of the vibration

problems in rotating machinery in abadan power

plant ( iran ) . This study points at frequency effects

Indian J.Sci.Res.1(2) : 690-701, 2014 - 701 -

on the stiffness and damping factor of the tilting-pad

journal bearings as one of the potential issues in

rotordynamic stability analysis.

b. Pivot flexibility can have a important effect on the

TPJB’s dynamic behavior, in exacting at higher

frequencies of excitations.

c. As a result of pivot flexibility, the bearing stiffness

factor can boost or reduce with the frequency of

excitation, depending on functional conditions and

bearing design.

d. In the attendance of pivot flexibility, an increase in

frequency of excitation can lead to a important

reduce in bearing damping in the horizontal as well

as in the vertical directions.

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