Stockholm, Sweden (13.11.2018) · 2018. 11. 14. · Stockholm, Sweden (13.11.2018) Numerical...
Transcript of Stockholm, Sweden (13.11.2018) · 2018. 11. 14. · Stockholm, Sweden (13.11.2018) Numerical...
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