Analysis of an Outer Bearing Bush of a Hydropower Plant

Kaplan Turbine Using Finite Element Method

CALIN-OCTAVIAN MICLOSINA, CONSTANTIN VIOREL CAMPIAN,

DOINA FRUNZAVERDE, VASILE COJOCARU Center for Research in Hydraulics, Automation and Thermal Processes – CCHAPT

“Eftimie Murgu” University of Resita

Traian Vuia Square, No. 1-4, 320085 Resita

ROMANIA

c.miclosina@uem.ro http://www.cchapt.ro

Abstract: The paper presents the analysis of an outer bearing bush from a Kaplan turbine, using the finite

element method. The 3D model of the runner blade operating mechanism is shown. The motion is transmitted

from the fork head through connecting rod to the pin lever - trunion - blade subassembly. This subassembly is

borne on the hub by an outer bush and an inner one. A motion study is carried out, based on values of the fork

head displacement versus time and the forces acting on the blade. The action force values are determined over a

certain period of time. The dynamic loads on the outer bearing bush are imported in a static study. In this study

a stress calculus is done, using the finite element method, and maximum values and plots of Von Mises stress

are obtained. For modeling and simulation, SolidWorks 2010 software is used.

Key-Words: Outer bearing bush, Kaplan turbine, finite element, Von Mises stress

1 Introduction Currently, due to pollution generated by the

conventional energy sources, the increase of

renewable energy use is a global trend.

Hydroelectric energy is the most used of the

renewable energy types.

There are two different types of turbines in

hydropower plants: reaction turbines (Francis,

Kaplan) and impulse turbines (Pelton).

The rotors of Francis and Pelton turbines have

fixed blades.

The rotor of a Kaplan turbine has adjustable

blades; the blades may change the tilt angles. This

feature allows achievement of high efficiency in

different water flow conditions.

The runner blade operating mechanism consists

of a fork head driven by a hydraulic servomotor, a

connecting rod and the pin lever – trunnion - blade

subassembly. This subassembly is borne by the

rotor’s body through an outer bush and an inner

bush.

While functioning, failures occur due to high

loads or fatigue phenomenon.

Studies on the failure of different parts of Kaplan

turbines were made: runner blade [2], [3], [4], pin

lever [7].

The paper presents the analysis of an outer

bearing bush fixed on the rotor’s body, using the

finite element method.

2 3D Model of Runner Blade

Operating Mechanism The 3D model of runner blade operating mechanism

is shown in fig. 1.

Fig. 1. 3D model of runner blade operating

mechanism.

The component parts are as follows: 1 – hub;

2 – bush; 3 – fork head; 4 – connecting rod; 5 – pin

lever; 6 – trunnion; 7 – inner bearing bush; 8 – outer

bearing bush; 9 – blade.

The hub (1) is defined as a fixed element. The

bushes (2), (7) and (8) are locked together with the

hub.

The fork head (3) is linked to the pin lever (5) –

trunnion (6) – blade (9) subassembly through the

connecting rod (4).

1

2

3

5 6 7 8 9

4

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The relative positions of the part models are

defined using geometrical (coincidence,

concentricity) or dimensional constraints.

A section view through the pin lever - trunion -

blade subassembly is presented in fig. 2. The

notations have the same meanings as in fig. 1.

Fig. 2. Section view through the pin lever - trunion -

blade subassembly.

All parts have assigned materials.

From SolidWorks materials library, tin bearing

bronze iss chosen for the outer bearing bush.

3 Motion Parameters The displacement of fork head versus time is

defined in the motion study, as shown in fig. 3.

Akima interpolation type is used to obtain this

graphic representation.

Fig. 3. Displacement of fork head versus time.

The blade angle φ varies from the value 8,47 [º]

at the beginning of motion to 8,66 [º] at the end of

it.

4 Loads Acting on Mechanism Links The forces that act on the mechanism links are as

follows: action force Fa on the fork head, water axial

force on the blade Fax = 1,771·106 [N], water

tangential force on the blade Ft = 1,025·106 [N],

water torque on the blade M = 1,900·109 [N·mm]

centrifugal force of the pin lever – trunnion - blade

subassembly Fc = 4,070·106 [N] (fig. 4).

Fig. 4. Loads acting on mechanism links.

Actually, forces Fax and Ft act on the upper

surface of the blade. Be these forces applied so in

the model, their point of application is

undetermined.

In theory, the forces could be applied in an

application point; in this case they determine a

torque M versus the rotation axis of the blade. If the

forces are applied in a point on the blade model, the

possibility of high stresses appears. To avoid this,

the forces are applied on the cylindrical surface S2

of the blade base. To maintain the rotation effect of

these forces, the torque M is applied on the same

surface S2 (fig. 4).

The centrifugal force Fc of the pin lever - trunion

- blade subassembly is applied on the same surface

S2.

The action force Fa is applied on the plane upper

surface S1 of the fork head (fig. 4).

The magnitude of action force Fa is computed by

SolidWorks software on the basis of other acting

forces, previously presented. The variation of

magnitude of action force on the fork head is shown

in fig. 5.

Fig. 5. Variation of action force magnitude.

9

8

1

5 6 7

S1

S2

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5 Analysis of the Outer Bearing Bush

Using Finite Element Method The loads on the outer bearing bush are imported in

static studies from the motion study file, for the

entire period of motion.

In numerical analysis using finite element

method, stress values depend on mesh parameters

[1], [5]. The accuracy of the results depends on the

quality of the mesh [8], [9].

In order to make the stress calculus, the outer

bearing bush is meshed using standard mesh with

automatic transition option.

This option offers the possibility of automatic

change of the mesh size to small features, holes,

fillets, and other fine details of the model [9].

Different values of global mesh size (GMS) are

used: 22, 25, 28, 31, 34 and 37 [mm].

The meshed model of outer bearing bush is

presented in fig. 6, for value of 37 [mm] of global

mesh size.

Fig. 6. The meshed model of outer bearing bush,

for value of 37 [mm] of global mesh size.

Examples of standard mesh with automatic

transition, with different global sizes are presented

in fig. 7.

a) b)

Fig. 7. Standard mesh with automatic transition,

with different global sizes:

a) 22 [mm]; b) 37 [mm].

After the mesh is done, numerical calculus (using

FFEPlus solver) for Von Mises stress is performed

and plots are obtained.

The plot of Von Mises stress for global mesh

size of 28 [mm] is shown in fig. 8.

Fig. 8. Plot of Von Mises stress for

global mesh size of 28 [mm].

Maximum values of Von Mises stress depend on

global mesh size, as seen in fig. 9.

Fig. 9. Von Mises stress depending on

global mesh size (GMS).

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6 Conclusions The 3D model of runner blade operating mechanism

is presented. For the motion study, loads are applied

on surfaces of fork head and blade.

Plots and maximum values of Von Mises stress

for the outer bearing bush are computed using

SolidWorks Simulation module.

The maximum values of Von Mises stress vary

between 39,8 and 59,8 [MPa] and are lower than

yield strength (110,3 MPa) for global mesh sizes

between 22 and 37 [mm].

As further research, a fatigue analysis of outer

bearing bush is to be accomplished.

7 Aknowledgement The work has been co-funded by the Sectoral

Operational Programme Human Resources

Development 2007-2013 of the Romanian Ministry

of Labour, Family and Social Protection through the

Financial Agreement POSDRU/89/1.5/S/62557.

References:

[1] Bordeasu I., Popoviciu M. O., Marsavina L.,

Voda M., Negru R., Pirvulescu L. D.,

Numerical Simulation of Fatigue Cracks

Initiation and Propagation for Horizontal Axial

Turbines Shafts, Annals of DAAAM for 2009 &

Proceedings of the 20th International DAAAM

Symposium, 25-28th November 2009, Vienna,

Austria, pp. 407-408.

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Marginean G., Failure Analysis of a Kaplan

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IAHR Symposium on Hydraulic Machinery and

Systems, 27-31st October 2008, Foz do

Iguassu, Brazil.

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[7] Pittner A.-M., Campian, C.V., Nedelcu D.,

Frunzaverde D., Cojocaru V., Stress

Concentration Factors for Pin Lever of Runner

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Proceedings of 3rd WSEAS International

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’10), 22-24th July 2010, Corfu Island, Greece,

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[8] Yinong L., Guiyan L., Ling Z., Influence of

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[9] *** http://help.solidworks.com – SolidWorks

Help, Accessed on: 2011-05-04

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