Vorlesungen Mechatronik im WintersemesterSeminar EnergiforskVibrations in Nuclear ApplicationsStockholm, Sweden (13.11.2018)

Numerical Analysis of Influence Coefficients for On-Site Balancing of Flexible Rotors

Rainer NordmannTechnische Universität Darmstadt and Fraunhofer Institute LBF

Numerical Analysis of Influence Coefficients for On-Site Balancing of Flexible Rotors

1. Introduction: Balancing by means of Influence Coefficients

2. Experimental Determination of Influence Coefficients

3. Numerical Determination of Influence Coefficients

4. Modelling of the Complete Turbine Train

5. System Responses due to a Test Weight in a Balancing Plane

6. Calculated Results and Analysis of the Deviations

7. Conclusions

Balancing of Flexible Rotors by means of InfluenceCoefficients is a well-known method. An important prerequisite is the linear relationship between unbalance forces and the vibration responses and the ability to reproduce the dynamic behaviour. The method is applicable for single rotors, but also for rotor trains on-site.

For an application of the method, Influence Coefficients have to be determined in a first step.They are defined as the vibration response, at one measurement point excited by a single unbalance in one of the balancing planes.

Introduction: Balancing by means of Influence Coefficients

The experimental procedure to determine Influence Coefficientscan be very expensive, where several test runs with stops, restarts and cooling down processes will be needed.

However, Influence Coefficients can also be determined by means of a Numerical Analysis. This needs of course a very good model for the Rotordynamic System.

In this project a trial is made to determine Influence Coefficients by means of modelling and numerical simulation.

Influence Coefficients for the balancing process are usually determined by measurements in so called influence runs.

Introduction: Balancing by means of Influence Coefficients

Influence Coefficient: αik (Ω) = xi(Ω)/Uk = αik Re+ j∙αik Im

((K(Ω) – Ω2 M) + j∙Ω (D(Ω) + G(Ω)) x = Uk∙Ω2 F

Introduction: Balancing by means of Influence Coefficients

Test weight inBalancing plane kVibration response

in measurement plane i

Introduction: Balancing by means of Influence Coefficients

Simple Example for a Matrix of Influence Coefficients

Classic balancing

Model Based Balancing

Balancing needed

φ/°

0

330

30

60

300

umpp

60

40

20

270

90

240

120

150

210

180

3000 rpm

φ/°

0

330

30

60

300

umpp

60

40

20

270

90

240

120

150

210

180

3000 rpm

Balancing completed –

Measured influence coefficients

Calculated Influence coefficients

Calculation replaces physical runs

NO NEED to run the unit !

Influence coefficents runs

Selection of bolt weight final balancing

The Balancing Process by means of Influence Coefficients

Numerical Analysis of Influence Coefficients for On-Site Balancing of Flexible Rotors

1. Introduction: Balancing by means of Influence Coefficients

2. Experimental Determination of Influence Coefficients

3. Numerical Determination of Influence Coefficients

4. Modelling of the Complete Turbine Train

5. System Responses due to a Test Weight in a Balancing Plane

6. Calculated Results and Analysis of the Deviations

7. Conclusions

Vibration response amplitude to «residual» unbalance distribution @ e.g. 3000rpm

Balancing planes

Sensors planes

Example: Experimental Determination of Influence Coefficients

Balancing planes

Sensors planesTest weight

Response to «residual» unbalance @ e.g. 3000rpmResponse to resid. unbalance and test weight

Example:Experimental Determination of Influence Coefficients

Balancing planes

Sensors planesTest weight

Response to «residual» unbalance @ e.g. 3000rpmResponse to resid. unbalance and test weight Influence of test weight

Example: Experimental Determination of Influence Coefficients

Numerical Analysis of Influence Coefficients for On-Site Balancing of Flexible Rotors

1. Introduction: Balancing by means of Influence Coefficients

2. Experimental Determination of Influence Coefficients

3. Numerical Determination of Influence Coefficients

4. Modelling of the Complete Turbine Train

5. System Responses due to a Test Weight in a Balancing Plane

6. Calculated Results and Analysis of the Deviations

7. Conclusions

Numerical Analysis of Influence Coefficients with a Model

Numerical Analysis of Influence Coefficients for On-Site Balancing of Flexible Rotors

1. Introduction: Balancing by means of Influence Coefficients

2. Experimental Determination of Influence Coefficients

3. Numerical Determination of Influence Coefficients

4. Modelling of the Complete Turbine Train

5. System Responses due to a Test Weight in a Balancing Plane

6. Calculated Results and Analysis of the Deviations

7. Conclusions

m1 m2 m3 m4 m5 m6 m8m7

Modelling: Mass and Stiffness Matrix of the Shaft Train

Stiffness- and damping coefficients for Bearings and Pedestal

Oil Film bearings

Pedestals

Stiffness, damping and mass of pedestals

Modelling: Foundation of the SteamTurbine

typical for Foundations:− many modes in speed range− significant cross-coupling

Foundation couples with the shaft train

The Equations of Motion of the Turbogenerator with the Inertia, stiffness and damping information of the shaft train, the bearings and the supports (Pedestal and foundation)

Model and Equations of Motion of a Turbogenerator

Balancing Planes and Weights for the Turbine Train

Balance weights

Numerical Analysis of Influence Coefficients for On-Site Balancing of Flexible Rotors

1. Introduction: Balancing by means of Influence Coefficients

2. Experimental Determination of Influence Coefficients

3. Numerical Determination of Influence Coefficients

4. Modelling of the Complete Turbine Train

5. System Responses due to a Test Weight in a Balancing Plane

6. Calculated Results and Analysis of the Deviations

7. Conclusions

F1 (t) = M·e·Ω2 · cos (Ωt + β) = M·e·Ω2 Im ( j· exp (j·(Ωt + β))

F2 (t) = M·e·Ω2 · sin (Ωt + β) = M·e·Ω2 Im ( 1·exp (j·(Ωt + β))

Unbalance Forces in Balancing Plane

Unbalance Forces in a Balancing Plane

Complex System Response contains Amplitude and Phase for each location

Complex Equations for Unbalance Response

Unbalance Response of the Turbogenerator Saft Train

Influence Coefficient: αik (Ω) = xi(Ω)/Uk = αik Re+ j∙αik Im

((K(Ω) – Ω2 M) + j∙Ω (D(Ω) + G(Ω)) x = Uk∙Ω2 F

Numerical Calculation of the Influence Coefficients

Numerical Analysis of Influence Coefficients for On-Site Balancing of Flexible Rotors

1. Introduction: Balancing by means of Influence Coefficients

2. Experimental Determination of Influence Coefficients

3. Numerical Determination of Influence Coefficients

4. Modelling of the Complete Turbine Train

5. System Responses due to a Test Weight in a Balancing Plane

6. Calculated Results and Analysis of the Deviations

7. Conclusions

Results for 4 LP planes: phase comparison (Deviations)

50°

-50°

Results for 4 LP planes: amplitude comparison (Deviations)

2

1

0

Calculated Critical Speeds of RinghalsTurbogenerator by GE

GEN 1.Bending900 rpm

LP3 1.Bending1350 rpm

Critical Mode Shape Amplitude Unbalance Force Speed rpm in Shaft Train Excitation

900 rpm GEN 1.Bending 100 um Center of GEN

1350 rpm LP3 1.Bending 100 um Center of LP3

1550 rpm LP2 1.Bending 40 um Center of LP2

1160 rpm LP1 1.Bending 40 um Center of LP11000 rpm 25 um

2100 rpm HP 1.Bending 35 um Center of HP1700 rpm 20 um

Calculated Critical Speeds of RinghalsTurbogenerator

Critical Mode Shape Amplitude Unbalance Force Speed rpm in Shaft Train Excitation

2500 rpm GEN 2.Bending+..>100 um Opp. Force GEN 1950 rpm 45 um

2500 rpm LP3 2.Bending +.. 45 um Opp. Force LP3 1950 rpm 20 um

2500 rpm LP2 2.Bending+.. 20 um Opp. Force LP21950 rpm 10 um

2500 rpm LP1 2.Bending +.. 28 um Opp. Force LP1

Calculated Critical Speeds of RinghalsTurbogenerator

Measured Critical Speeds of RinghalsTurbogenerator

Critical Mode Shape Amplitude Unbalance Force Speed rpm in Shaft Train Excitation

900 rpm GEN 1.Bending 80/100 um Unknown980 rpm 100/160 um

1400 rpm LP3 1.Bending 150/230 um Unknown1100 rpm 100/130 um

1400 rpm LP2 1.Bending 200 um Unknown1150 rpm 130/160 um

1180 rpm LP1 1.Bending 40/150 um Unknown1250 rpm 50/100 um

Measured Critical Speeds of RinghalsTurbogenerator

GEN 1. Bending900 rpm

LP3 1. Bending1400 rpm

Critical Mode Shape Amplitude Unbalance Force Speed rpm in Shaft Train Excitation

2700 rpm GEN 2.Bending+.. 50 um Unknown2250 rpm 50 um

2700 rpm LP3 2.Bending +.. 25 um Unknown2250 rpm 25 um

2500 rpm LP2 2.Bending+.. 25 um Unknown

2600 rpm LP1 2.Bending +.. 50 um Unknown

Measured Critical Speeds of RinghalsTurbogenerator

Calculated Measured Delta Mode ShapeCriticals Criticals in Shaft Train

900 rpm 900 rpm 0 rpm GEN 1.Bending980 rpm +80 rpm

1350 rpm 1400 rpm +50 rpm LP3 1.Bending1100 rpm -250 rpm

1550 rpm 1400 rpm -150 rpm LP2 1.Bending

1160 rpm 1400 rpm +240 rpm LP1 1.Bending

Based on the deviations support stiffnesses will bemodified in order to improve the model!

Comparison of Calculated and Measured Critical Speeds

Calculated Measured Delta Mode ShapeCriticals Criticals in Shaft Train

2500 rpm 2700 rpm +200 rpm GEN 2.Bending1950 rpm 2250 rpm +300 rpm

2500 rpm 2700 rpm +200 rpm LP3 2.Bending1950 rpm 2250 rpm +300 rpm

2500 rpm 2500 rpm 0 rpm LP2 2.Bending

2500 rpm 2600 rpm +100 rpm LP1 2.Bending

Comparison of Calculated and Measured Critical Speeds

Based on the deviations support stiffnesses will be modified in order to improve the model!

Numerical Analysis of Influence Coefficients for On-Site Balancing of Flexible Rotors

1. Introduction: Balancing by means of Influence Coefficients

2. Experimental Determination of Influence Coefficients

3. Numerical Determination of Influence Coefficients

4. Modelling of the Complete Turbine Train

5. System Responses due to a Test Weight in a Balancing Plane

6. Calculated Results and Analysis of the Deviations

7. Conclusions

Conclusions

For an application of the Balancing method Influence Coefficientshave to be determined in a first step.They are defined as the vibration response, at one measurement point excited by a single unbalance in one of the balancing planes.

Such Influence Coefficients can also be determined by means of a Numerical Analysis. This needs of course a very good model for the rotor train, including all important rotor dynamic effects.

In this project a trial was made to determine Influence Coefficients by means of modelling and numerical simulation.

First results obtained with the model have some deviations! Trials will be made to improve the results by changing parameters of the supporting system (Pedestals).

Statement from GE: Open Items and Next Steps

Ping Tests Results of the Pedestals:• Results are available for Pedestals 5..8 only.• Available Results require additional postprocessing in

progress• GE will extract (if possible) dynamic stiffness and update the

shaft train models accordingly. Then GE will run an additional calculation with updated dynamic characterstics and conclude. expected to be completed by end of November

• Other Items not covered by the current project: • Generate Test Specification for Ping Test of Pedestals• Perform ping test of Pedestals 1...4. Pedestals are believed

to be a major source of uncertainty. The ping tests will deliver realistic dynamic properties of the pedestals.

• Update of the rotordynamic model and recalculate IC’s-

Vorlesungen Mechatronik im WintersemesterSeminar EnergiforskVibrations in Nuclear ApplicationsStockholm, Sweden (13.11.2018)

Numerical Analysis of Influence Coefficients for On-Site Balancing of Flexible Rotors

Rainer NordmannTechnische Universität Darmstadt and Fraunhofer Institute LBF