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

(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.

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

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

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)

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

(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).

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

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.

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

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

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)

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

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

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

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

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%

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

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