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Journal of Engineering for Gas Turbines and Power | Volume 130 | Issue 3 | Research Paper
Research Papers: Gas Turbines: Structures and Dynamics

Damping Performance of Axial Turbine Stages With Loosely Assembled Friction Bolts: The Nonlinear Dynamic Assessment

[+] Author and Article Information
J. Szwedowicz

ABB Turbo Systems Ltd., Thermal Machinery Laboratory, CH-5401 Baden, Switzerlandjaroslaw.szwedowicz@ch.abb.com

Th. Secall-Wimmel

ABB Turbo Systems Ltd., Thermal Machinery Laboratory, CH-5401 Baden, Switzerland

P. Dünck-Kerst

Siemens AG, Power Generation/Industrial Applications, D-47053 Duisburg, Germanypeter.duenck-kerst@siemens.com

For X20Cr13 blade alloy, J=2×10−10 and η=2.1 at 500°C(34).

All static loads are normalized with the same constant factor nF.

All bending stresses are normalized by the same factor nσ.

Each stimulus is normalized with the same constant factor.

All frequencies are scaled by the same constant factor n0.

J. Eng. Gas Turbines Power 130(3), 032505 (Apr 03, 2008) (14 pages) doi:10.1115/1.2838998 History: Received July 03, 2007; Revised November 09, 2007; Published April 03, 2008
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Citing Articles

An entire family of twisted and tapered low pressure steam turbine fast rotating condensation blading (SK) blades with pinned radial root and loosely assembled conical bolts is designed by scaling the aerodynamic and mechanical properties of the smallest airfoil. For SK blades operating with variable speed, the friction bolts, mounted in the upper airfoil part, provide either damping or coupling capabilities for the blades with respect to resonance conditions. The damping and coupling performance have been proven experimentally in the test rig of the real turbine. The measurements of the smallest SK-disk assembly under different operating conditions have allowed us to understand the dynamic and damping behavior of the bolts that are either friction dampers or coupling devices for the vibrating blades depending on the excitation level. In this paper, nonlinear dynamic analyses of the smallest and large SK-turbine stage are performed and compared with the experimental data. The modal blade dynamics is defined by 30 complex finite element (FE) mode shapes of the freestanding blades coupled by the disk whereby the bolt’s motion is described by six rigid body modes. The sticking contact condition between the blades and bolts is represented by the normal and tangential contact stiffnesses. These values are firstly estimated analytically with Hertz’s formulas for the FE reaction forces and contact areas. More realistic contact stiffness values are obtained from the iterative process, in which the resonance frequencies are calculated with the steady-state simulations and compared to the FE nodal diameter curves for sticking contact conditions that meet the experimental frequencies very well (Szwedowicz, J., 2007, “Scaling Concept for Axial Turbine Stages With Loosely Assembled Friction Bolts: The Linear Dynamic Assessment Part 1  ,” Proceedings of ASME Turbo Expo 2007, Montreal, Canada, May 14–17, ASME Paper No. GT2007-27502). In nonlinear simulations, in case of exceeding the sticking contact condition, the induced friction forces are linearized by the harmonic balance method. In this manner, the microslipping and sticking contact behavior at all contact points are calculated iteratively for the specified excitation amplitudes, friction coefficient, contact roughness, and aerodamping values that are known from the experiment. The computed results of the tuned smallest SK blades agree with the experimental resonance stresses of 12 measured blades. Differences between the computed and measured stresses are caused by mistuning, which was not quantified in the experiment. The nonlinear dynamic analyses provide evidence of good damping performance for the smallest and large SK blades with respect to a wide range of excitation forces, different friction coefficients, and various aerodynamic damping values. For the analyzed resonances of the eighth engine order, the scalability of damping performance is found for the SK blades of different sizes.
Copyright © 2008 by American Society of Mechanical Engineers
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References

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Ewins, D. J., 1973, “Vibration Characteristics of Bladed Disc Assemblies,” J. Mech. Eng. Sci.  [CrossRef], 15 (3), pp. 165–186.
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Filsinger, D., Szwedowicz, J., and Schäfer, O., 2002, “Approach to Unidirectional Coupled CFD-FEM Analysis of Axial Turbocharger Turbine Blades,” ASME J. Turbomach.  [CrossRef], 124 , pp. 125–131.
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Sextro, W., 2002, “Dynamical Contact Problems With Friction: Models, Methods, Experiments and Applications,” "Lecture Notes in Applied Mechanics", Springer-Verlag, Berlin, Vol. 3 .
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Petrov, E. P., 2006, “Direct Parametric Analysis of Resonance Regimes For Nonlinear Vibrations of Bladed Discs,” ASME Paper No. GT2006-90147.
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Szwedowicz, J., Slowik, S., Mahler, A., and Hulme, C. J., 2005, “Nonlinear Dynamic Analyses of a Gas Turbine Blade for Attainment of Reliable Shroud Coupling,” ASME Paper No. GT2005-69062.
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Treyde, T., 1994, “Koppeldaempfungen Und-Steifigkeiten Zwischen Den Kontakflaechen Der Deckplatten Von Laufschaufeln (Contact Damping and Stiffness Between the Interfaces of the Shrouds of Rotating Turbine Blades,” FVV Report No. 525, BMWi/AIF Report No. 8803.
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34
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38
Matveev, V. V., Chaikoskii, B. S., and Rzhavin, L. N., 1970, “Damping Capacity of the Hinged Locking Joint of Turbomachine Compressor Blades (in Russian),” Problemy Prochnosti, 12 , pp. 106–109.
39
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Figures

Grahic Jump Location
+(a) The last LP steam turbine SK blades. (b) FE static bending stresses. (c) The test rig with the SK turbine (16), where Λ is the position of the excitation force at the radius hΛ.
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(a) The last LP steam turbine SK blades. (b) FE static bending stresses. (c) The test rig with the SK turbine (16), where Λ is the position of the excitation force at the radius hΛ.
Figure 1

(a) The last LP steam turbine SK blades. (b) FE static bending stresses. (c) The test rig with the SK turbine (16), where Λ is the position of the excitation force at the radius hΛ.

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+Variation of the order tracking of the eighth engine order of the first resonance frequencies5 at blade 4 for different service conditions A, B, C, D with full steam loading and P with partial arc admission, where ω′ and ω″ are resonance amplitudes of the mistuned bladed disk
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Variation of the order tracking of the eighth engine order of the first resonance frequencies5 at blade 4 for different service conditions A, B, C, D with full steam loading and P with partial arc admission, where ω′ and ω″ are resonance amplitudes of the mistuned bladed disk
Figure 2

Variation of the order tracking of the eighth engine order of the first resonance frequencies5 at blade 4 for different service conditions A, B, C, D with full steam loading and P with partial arc admission, where ω′ and ω″ are resonance amplitudes of the mistuned bladed disk

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+Numerical representation of the bolt contact, where mode shapes at points CS and CP, contact areas, and static reaction forces RS3 and RP3 are obtained from the cyclic FE computation of the disk sector
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Numerical representation of the bolt contact, where mode shapes at points CS and CP, contact areas, and static reaction forces RS3 and RP3 are obtained from the cyclic FE computation of the disk sector
Figure 3

Numerical representation of the bolt contact, where mode shapes at points CS and CP, contact areas, and static reaction forces RS3 and RP3 are obtained from the cyclic FE computation of the disk sector

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+Illustration of the three lowest mode shapes of the smallest SK blade without bolt coupling used for the modal transformation of the FE disk vibrations of the nodal diameter n=9 (see also Appendix)
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Illustration of the three lowest mode shapes of the smallest SK blade without bolt coupling used for the modal transformation of the FE disk vibrations of the nodal diameter n=9 (see also Appendix)
Figure 4

Illustration of the three lowest mode shapes of the smallest SK blade without bolt coupling used for the modal transformation of the FE disk vibrations of the nodal diameter n=9 (see also Appendix)

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+Comparison of the FE and modal diameter curves of the smallest SK blade for the determination of the resulting normal cn and tangential ct contact stiffness at the bolt at (a) 0.625Ωn and (b) at Ωn nominal speed
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Comparison of the FE and modal diameter curves of the smallest SK blade for the determination of the resulting normal cn and tangential ct contact stiffness at the bolt at (a) 0.625Ωn and (b) at Ωn nominal speed
Figure 5

Comparison of the FE and modal diameter curves of the smallest SK blade for the determination of the resulting normal cn and tangential ct contact stiffness at the bolt at (a) 0.625Ωn and (b) at Ωn nominal speed

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+(a) The partial arc admission arranged for the amplification of the eighth engine order within the stator of 40 vanes at the setup in Fig. 1 (c). (b) Its idealized pressure alteration from 0 up to 1 with nozzle effects (from 0.7 up to 1) from unblocked stator pitches modeled as sinus wave (see zoom).
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(a) The partial arc admission arranged for the amplification of the eighth engine order within the stator of 40 vanes at the setup in Fig. 1 (c). (b) Its idealized pressure alteration from 0 up to 1 with nozzle effects (from 0.7 up to 1) from unblocked stator pitches modeled as sinus wave (see zoom).
Figure 6

(a) The partial arc admission arranged for the amplification of the eighth engine order within the stator of 40 vanes at the setup in Fig. 1 (c). (b) Its idealized pressure alteration from 0 up to 1 with nozzle effects (from 0.7 up to 1) from unblocked stator pitches modeled as sinus wave (see zoom).

Grahic Jump Location
+The estimated relative excitation spectrum for the assumed pressure distribution of the partial arc admission shown in Fig. 6
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The estimated relative excitation spectrum for the assumed pressure distribution of the partial arc admission shown in Fig. 6
Figure 7

The estimated relative excitation spectrum for the assumed pressure distribution of the partial arc admission shown in Fig. 6

Grahic Jump Location
+The experimental overall modal damping ratios where ξm denotes the damping value for blade m. (a) Freestanding blades for the excitation of the partial arc admission. (b) Freestanding blades under the nominal service condition with the ordinary stator arrangement. (c) Blades with bolts for the excitation arranged by the partial arc admission. (d) Blades with bolts under the nominal service condition with the ordinary stator arrangement.
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The experimental overall modal damping ratios where ξm denotes the damping value for blade m. (a) Freestanding blades for the excitation of the partial arc admission. (b) Freestanding blades under the nominal service condition with the ordinary stator arrangement. (c) Blades with bolts for the excitation arranged by the partial arc admission. (d) Blades with bolts under the nominal service condition with the ordinary stator arrangement.
Figure 8

The experimental overall modal damping ratios where ξm denotes the damping value for blade m. (a) Freestanding blades for the excitation of the partial arc admission. (b) Freestanding blades under the nominal service condition with the ordinary stator arrangement. (c) Blades with bolts for the excitation arranged by the partial arc admission. (d) Blades with bolts under the nominal service condition with the ordinary stator arrangement.

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+The measured mass flow rate in the smallest SK turbine at the test rig with respect to the break load (39), where 80 kp≈800N
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The measured mass flow rate in the smallest SK turbine at the test rig with respect to the break load (39), where 80 kp≈800N
Figure 9

The measured mass flow rate in the smallest SK turbine at the test rig with respect to the break load (39), where 80 kp≈800N

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+The comparison of the numerical results of the tuned model with the measured stresses of the real mistuned smallest SK blades excited by the partial arc admission for the resonance frequency (a) ω′ and (b) ω″ shown in Fig. 2
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The comparison of the numerical results of the tuned model with the measured stresses of the real mistuned smallest SK blades excited by the partial arc admission for the resonance frequency (a) ω′ and (b) ω″ shown in Fig. 2
Figure 10

The comparison of the numerical results of the tuned model with the measured stresses of the real mistuned smallest SK blades excited by the partial arc admission for the resonance frequency (a) ω′ and (b) ω″ shown in Fig. 2

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+The numerical resonance frequency responses of the smallest SK blade rotating with Ωs=0.625Ωn in service at the setup with the arranged partial arc admission (aerodamping ξ0=0.3%, μ=0.15)
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The numerical resonance frequency responses of the smallest SK blade rotating with Ωs=0.625Ωn in service at the setup with the arranged partial arc admission (aerodamping ξ0=0.3%, μ=0.15)
Figure 11

The numerical resonance frequency responses of the smallest SK blade rotating with Ωs=0.625Ωn in service at the setup with the arranged partial arc admission (aerodamping ξ0=0.3%, μ=0.15)

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+Comparison of the numerical resonance stresses and frequencies with the experimental Campbell diagram of the first eigenfamily of the smallest SK blades with the bolt coupling excited by the partial arc admission, where f1–f4 show frequencies of the freestanding blade
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Comparison of the numerical resonance stresses and frequencies with the experimental Campbell diagram of the first eigenfamily of the smallest SK blades with the bolt coupling excited by the partial arc admission, where f1–f4 show frequencies of the freestanding blade
Figure 12

Comparison of the numerical resonance stresses and frequencies with the experimental Campbell diagram of the first eigenfamily of the smallest SK blades with the bolt coupling excited by the partial arc admission, where f1–f4 show frequencies of the freestanding blade

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+Performance curves of the smallest and large SK blades excited by the eighth engine order at Ωs=0.625Ωn under the service condition for the assumed aerodamping ξ0 of 0.5%, where a stimulus of 100% is equal to the static steam bending load at speed Ωs=0.625Ωn
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Performance curves of the smallest and large SK blades excited by the eighth engine order at Ωs=0.625Ωn under the service condition for the assumed aerodamping ξ0 of 0.5%, where a stimulus of 100% is equal to the static steam bending load at speed Ωs=0.625Ωn
Figure 14

Performance curves of the smallest and large SK blades excited by the eighth engine order at Ωs=0.625Ωn under the service condition for the assumed aerodamping ξ0 of 0.5%, where a stimulus of 100% is equal to the static steam bending load at speed Ωs=0.625Ωn

Grahic Jump Location
+Sensitivity curves of the resonance frequencies of the smallest and large SK blades excited by the eighth engine order at Ωs=0.625Ωn under service conditions for the assumed aerodamping ξ0=0.5%
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Sensitivity curves of the resonance frequencies of the smallest and large SK blades excited by the eighth engine order at Ωs=0.625Ωn under service conditions for the assumed aerodamping ξ0=0.5%
Figure 16

Sensitivity curves of the resonance frequencies of the smallest and large SK blades excited by the eighth engine order at Ωs=0.625Ωn under service conditions for the assumed aerodamping ξ0=0.5%

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+Validation of the scaling factors of the resonance frequencies υω=ωsmall∕ωlarge determined from the nonlinear dynamic simulations of the smallest and large SK blade scaled by the design factor υO of 4
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Validation of the scaling factors of the resonance frequencies υω=ωsmall∕ωlarge determined from the nonlinear dynamic simulations of the smallest and large SK blade scaled by the design factor υO of 4
Figure 15

Validation of the scaling factors of the resonance frequencies υω=ωsmall∕ωlarge determined from the nonlinear dynamic simulations of the smallest and large SK blade scaled by the design factor υO of 4

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+The FE Campbell diagram of the freestanding smallest SK blade coupled by the rotor and the lowest natural frequencies of the friction bolt with unrestrained (free-free) boundary condition, where EO denotes the engine order and f1̱blade and f1̱bolt are the fundamental natural frequencies of the blade and bolt, respectively
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The FE Campbell diagram of the freestanding smallest SK blade coupled by the rotor and the lowest natural frequencies of the friction bolt with unrestrained (free-free) boundary condition, where EO denotes the engine order and f1̱blade and f1̱bolt are the fundamental natural frequencies of the blade and bolt, respectively
Figure 18

The FE Campbell diagram of the freestanding smallest SK blade coupled by the rotor and the lowest natural frequencies of the friction bolt with unrestrained (free-free) boundary condition, where EO denotes the engine order and f1̱blade and f1̱bolt are the fundamental natural frequencies of the blade and bolt, respectively

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+Resonance responses of the smallest SK blade with the full sticking and with the sliding bolt coupling excited by the eighth engine order for a reference viscous aerodamping damping ξ0 of 0.3% and a friction coefficient μ of 0.15
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Resonance responses of the smallest SK blade with the full sticking and with the sliding bolt coupling excited by the eighth engine order for a reference viscous aerodamping damping ξ0 of 0.3% and a friction coefficient μ of 0.15
Figure 13

Resonance responses of the smallest SK blade with the full sticking and with the sliding bolt coupling excited by the eighth engine order for a reference viscous aerodamping damping ξ0 of 0.3% and a friction coefficient μ of 0.15

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+Example of coatless contact conditions of SK blade (a) in airfoil holes and (b) on friction bolt after 20years in service
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Example of coatless contact conditions of SK blade (a) in airfoil holes and (b) on friction bolt after 20years in service
Figure 17

Example of coatless contact conditions of SK blade (a) in airfoil holes and (b) on friction bolt after 20years in service

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