1

Physical Asse autical EngineeringUniversity of Pretoria

�

A Comparative Study of Finite Element Methodologies for Torsional Vibration Response Calculations of Bladed Rotors

R Scheepers

Supervisor: Prof. PS Heyns

19 February 2014

2

Overview

� Background

� Research contribution

� Experimental testing

� Modelling methodologies

� Measured and calculated results

� Conclusions

Background

3

� Torsional excitation of turbo-generator trains• Short circuits• Line switching• Out of phase• Resonance

Background

4

� Conventional modelling• 1D lumped mass/distributed parameter FE models• LP blade participation – rigid blades• Sudden diameter change• Blade-to-disk rigidity

� Improved accuracy required� Move towards full 3D, 3DCS

Research Contribution

5

� Effect of blade stagger angle• Level of blade participation• Response frequencies• Damping

� Direct comparison of different FE methodologies• Solution time• Accuracy

90° stagger angle

Experimental testing

6

� Small scale test rotor

Modelling Methodologies

7

� Full 3D FEA

� 3D Cyclic symmetric

� 1D lumped mass

Modelling Methodologies

8

� 1D lumped mass – blade coupling

Results

9

� Effect of blade stagger angle

90 deg 45 deg 0 deg no blades0

0.5

1

1.5

2

2.5

3

3.5

4

dam

ping

(%

)

blade stagger angle

F2

F3b

F3a

F4

0 rpm 0 rpm

90deg 45deg 0deg no blade100

150

200

250

300

350

400

450

500

550

blade stagger angle

freq

uenc

y (H

z)

F2 1D

F3b 1D

F3a 1D

F4 1D

F2 meas

F3b meas

F3a meas

F4 meas

0 500 1000 1500

150

200

250

300

350

400

450

500

550

angular velocity (rpm)

freq

uenc

y (H

z)

F2 3D

F3b 3D

F3a 3D

F4 3D

F2 meas

F3b meas

F3a meas

F4 meas

Results

10

� Effect of centrifugal force

0° blade stagger angle

0 500 1000 1500

150

200

250

300

350

400

450

500

550

angular velocity (rpm)

freq

uenc

y (H

z)

F2 3D

F3b 3D

F3a 3D

F4 3D

F2 meas

F3b meas

F3a meas

F4 meas

45° blade stagger angle

Results

11

� Effect of stagger angle on mode shapes

0 0.2 0.4 0.6 0.8 1 1.2 1.4

-0.5

0

0.5

1

normalized shaft length

norm

aliz

ed to

rsio

nal d

ispl

acem

ent

geometryF

2 0deg

F3b

0deg

F3a

0deg

F4 0deg

F2 45deg

F3b

45deg

F3a

45deg

F4 45deg

F3b

90deg

F3a

90deg

F4 90deg

Results

12

� Blade response

Results

13

� Accuracy

� Solution times• 3DCS – 80% reduction• 1D – 99% reduction

Conclusions

14

� Stagger angle affects level of blade participation� Torsional frequencies and damping is affected by stagger

angle� FE approaches are all usable depending on required

accuracy and available resources� Field testing must be done under dynamic conditions� DC motor & controller can be used for torsional excitation

of small scale test rotors

Acknowledgements

15

� Prof. PS Heyns� Dr. Abrie Oberholster� Mr. Francesco Pietra� Dr. Mark Newby � Mr. George Breitenbach� Mr. Herman Booysen� Eskom Power Plant Engineering Institute

(EPPEI)� NRF Technology and Human Resources

Programme (THRIP)