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Research Papers: Gas Turbines: Structures and Dynamics

# Scaling Concept for Axial Turbine Stages With Loosely Assembled Friction Bolts: The Linear Dynamic Assessment

[+] Author and Article Information
J. Szwedowicz

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

Th. Secall-Wimmel

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

P. Dünck-Kerst

Power Generation/Industrial Applications, Siemens AG, D-47053 Duisburg, Germany

A. Sonnenschein

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

D. Regnery

Power Generation/Service Steam Turbines, Siemens AG, D-45473 Muelheim/Ruhr, Germanydavid.regnery@siemens.com

M. Westfahl

Power Generation, Siemens AG, D-10553 Berlin, Germanymartin.westfahl@siemens.com

All computations were done on IBM computer with two CPUs (EM64) with $8Gbyte$ RAM with LINUX SLES 9.0 system.

The MECHANICA code cannot be applied for nonlinear problems with large frictional sliding on contacts like the analyzed SK blades.

Degrees of freedom of the nodes on the bolt and airfoil contact area (Fig. 1) are tied rigidly in the normal and in two tangential contact directions.

Only in the normal direction of the contact, degrees of freedom of the nodes on the bolt and airfoil contact area (Fig. 1) are tied rigidly.

Because of spatial localization of the vibration energy, certain airfoils, which are disordered by manufacturing and assembling tolerances as well as by divergences in material properties, might experience substantially larger oscillations than the numerical response amplitudes of the tuned bladed disk.

J. Eng. Gas Turbines Power 130(3), 032504 (Apr 03, 2008) (12 pages) doi:10.1115/1.2838995 History: Received July 03, 2007; Revised November 09, 2007; Published April 03, 2008

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## Figures

Figure 13

Validation of the frequency scaling factors determined from the FE spin-pit Campbell diagrams of the smallest and large SK blades (Fig. 1), where the design scaling factor υ0 equals 4

Figure 14

Three lowest mode shapes of the blade coupled by (a) sticking and (b) slipping bolts, where SG#2 indicates the position of Gauge 2. Parameter E33MAX means the relative strain magnitude in the radial direction determined by {ε°}i,n=[{ε°i,n}c+j{ε°i,n}s]1∕2

Figure 15

(a) Position of Strain Gauge 1 (SG#1) instrumented on four adjacent blades for measuring the disk vibrations up to the 15th engine order (Fig. 1) and (b) Location of three gauges on four adjacent blades

Figure 10

FE normal contact stresses on the bolt of the large blade at (a) 100% and (b) 25% of its nominal speed Ωn

Figure 9

Computed final clearances at the ends of the bolts for (a) their maximum and (b) nominal dimensions of the large and small blades at their nominal speeds

Figure 8

Comparison of the centrifugal stresses between the smallest (a) and large (b) blades coupled by the friction bolts at their nominal speeds and T=20°C

Figure 7

The experimental resonance frequencies of eight large SK blades assembled to the rotor without bolts at standstill before the spin-pit test (T=20°C)

Figure 6

Relative errors of the FE blade frequencies computed with the contact root model illustrated in Fig. 5 in relation to the measurements at the hydraulic setup (Fig. 5) and at standstill (Fig. 7) before spin-pit tests

Figure 5

(a) Siemens’ setup for hydraulic pressing of two guide bolts to the second and third airfoil fingers of the radial root; (b) the FE normal contact stresses, where blue color refers to noncontact state

Figure 4

(a) FE model of (b) Siemens’ setup for hydraulic clamping of the airfoil root on its circumferential sides

Figure 3

(a) Siemens’ hammer setup with the airfoil measured at (b) 100 points for the mode shape identification of the large SK blade with (c) “long” and (d) “short” roots

Figure 2

Cyclic sector model representing one SK blade, the rotor part, and one bolt divided into two symmetrical halves

Figure 1

(a) The last LP stage of industrial Siemens steam SK turbine with (b) friction bolts, where the angle φ=2π∕N illustrates the geometrical periodicity of the disk sector for N number of blades in the row; (c) the considered scaled-up SK blades

Figure 16

The measured Campbell diagram of the four lowest eigenfamilies (ωC,i=1,…,ωC,i=4) of the large SK blades excited by air jet in vacuum at 20°C, where ΔΩC is the speed region while the bolts begin to couple the blades

Figure 11

Coupling bolt effect demonstrated by a frequency increase of the large SK disk assembly at 50% and 100% of the nominal speed n≡Ωn, where ωr,1, ωr,2, and ωr,3 are the resonances at Ω100%

Figure 12

The numerical Campbell diagrams of the freestanding (fi is the ith eigenfamily) and coupled large SK blade in the spin pit, where fi,n means the eigenfamily i vibrating with the nodal diameter n, and k={1,2,…,∞} is engine order

Figure 17

Order tracking of harmonic excitations of (a) k=7 for resonance i,n=1.7, (b) k=6 for resonance i,n=1.6 (Fig. 1) with the measured double resonances ω′ and ω″ due to mistuning effects, where Δω=ω″−ω′

Figure 18

The comparison of the computed and measured Campbell diagrams of the large SK blades, where the FE eigenfrequencies fi,n refer to eigenfamily number i={1,2,3} and nodal diameter numbers n={0,1,2,3,6,9,12,16,19}

Figure 19

The numerical and experimental Campbell diagrams for resonances of the first family excited by engine orders k of 6 and 7, where γ1,6 is the degree of blade coupling for disk mode i,n=1.6

Figure 20

The numerical and experimental Campbell diagrams for resonances of the second and third eigenfamilies, where γ2,11 and γ3,12 are coupling degrees of disk modes i,n of 2.11 and 3.12

Figure 21

(a) SK turbine train in the spin-pit chamber and (b) the pipe arrangement for the airfoil excitation, where κ is dimensionless polytropic constant and Tt, pt, ρt, and vt are the temperature, atmospheric pressure, air density, and flow velocity outside the bunker

Figure 23

Excitation amplitudes Fk and phase delays κk of engine orders k of the air jet excitation f

Figure 22

(a) The air jet excitation force f(α) and (b) blade mode shapes ϕ1.6, ϕ2.11, ϕ3.12, where α1 and α2 are angles at the entry and exit of the blade contours by the air gust at time t1 and t2 during one period T=2π∕Ω of the turbine rotation

Figure 24

A waterfall diagram of the spin-pit measurement of the large SK blade at strain gauge SG#1

Figure 25

The computed (the overall damping ξ=0.14%) and measured strain responses at SG#1 gauges on eight blades in the spin pin (Test Runs 08, 14, 20, and 41) for resonances (a) i,n=1.6 excited by k=6, (b) i,n=2.11 excited by k=11, and (c) i,n=3.12 excited by k=12

## Errata

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