A program of equivalent tests for turbine blades under laboratory conditions

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    M. E. Kolotnikov and V. A. Solyannikov UDC 620.172.251.224

    A method of conducting equivalent tests of turbine blades under laboratory condi- tions, which ensures reproduction of the operational pattern of the loading in its most heavily loaded components, is proposed. A method for construction of the equivalent-test program is analyzed on a stage-I turbine blade of one of the high-temperature aviation gas-turbine engines.

    Modern aviation engine building has developed in the direction of increasing intensi- fication of the operating process; this has led to an increase in the temperature-force loading of basic components of the hot parts of gas-turbine engines. On the one hand, the rates of the development and precision sizing of engines have increased over the years, amounting to 4-5 years on average at the present time. This dictates the need for the development of new methods for the precision strength sizing of aircraft, which includes more precisely defined methods for the computational estimate of the strength and remaining life of engine components and also experimental methods of their precision sizing with re- spect to strength parameters under laboratory conditions.

    One of the critical and highly loaded components of gas turbine engines which requires a large volume of computational and experimental investigations is the turbine blade, which is subjected to multifactor nonisothermal loading during operation.

    The reliability and longevity of turbine blades are processed experimentally by methods of precision assembly sizing [I] and their testing in a full-scale engine in accordance with a program equivalent to an operational program [2]. In the first case, it is possible to obtain only a comparative estimate of blade strength; blade longevity, however, cannot be determined under real operating conditions; in the second case, the testing is extremely time-consuming and expensive.

    Owing to the development of experimental apparatus and testing machines that make it possible to simulate the operational character of blade loading under laboratory conditions, the possibility of working out the design and fabrication procedure for its components and also of confirming the efficiency of selected solutions by conducting equivalent-cyclic tests (ECT) of blades for an assigned service life under laboratory conditions has arisen.

    The method employed to conduct the ECT of blades includes the following basic steps.

    io Computational-experimental analysis of the loading of a blade during engine opera- tion in accordance with a generalized flight cycle (GFC), and the selection of the most heavily loaded components on the basis of this analysis.

    2. The formulation of laboratory regimes for the multifactor nonisothermal loading of each blade element investigated with assurance of the equality of maximum temperatures as well as the equivalence of the deformation mechanisms under laboratory and operation condi- tions.

    3. Determination of the duration of the ECT of blade components for a given service life on the basis of the conditions of their limiting state.

    4. Subsequent ECT of the blade elements for a given service life under laboratory con- ditions.

    A method of constructing the ECT program for a blade under laboratory conditions is proposed in this study for an uncooled stage-I blade of a turbine of one of the high-tempera- ture aviation gas turbine engines.

    Scientific-Production Union "Trud." Translated from Problemy Prochnosti, No. 7, pp. 89-92, July, 1991. Original article submitted October 25, 1990.

    828 0039-2316/91/2307-0828512.50 9 1992 Plenum Publishing Corporation

  • TABLE i. Characteristics of Temperature- Force Loading of Median Fin Section of Blade under Various Engine-Operating Modes

    Relativ( duratior of mode T, % B~ade components

    Load parameters

    I Tmax, ~ I O" h MPa aa, MPa d

    I 2,2



    Takeoff mode Leading edge 950 245 18 Trailing edge 935 223 15 Trough 945 181 -- Suction face 940 154 15

    N.omi.nal mode

    Leading edge 800 172 15 Trailing edge 785 152 16 Trough 790 157 -- Suction face 785 159 8

    flruising mode Leading edge 750 166 18 Trailing edge 740 146 16 Trough 752 151 - - Suction face 750 153 I0

    ~e.c.] , T Takeoff "--.I~--I Tstab


    I - J U ~ Tini , , . , ~.\,Tcool

    a b

    Fig. i. Generalized flight cycle of engine operation (a) and equivalent laboratory cycle (b): ~e.c.h) position of engine control handle; N) nominal regime; Cruis) cruising regime; I) idling.

    @, MPa 50g /,i I00

    g 0 ~ 60 ~ ~, see b

    F ig . 2. Pat tern of var ia t ion of normal s t ress in leading (i) and trailing (2) edges of blade fin during engine startup, and also on exiting from takeoff mode (a) and during laboratory load cycle (b).

    r J Z



  • The kinetics of the stress-strain state (SSS) of the blade under operating and labora- tory load conditions was analyzed using the developed software package (SP), which includes a program for calculation of the nonstationary thermal state and the kinetics of the inelastic deformation of a blade section under a cyclic nonisothermal load, and a program for calculat- ing the blade's longevity under a multifactor nonisothermal load, as well as programs for the automated processing and plotting of the computed results [3].

    The structural model of an elastoviscoplastic medium was adopted as a model of the mater- ial (high-temperature nickel alloy of the ZhS class) [4].

    We calculated the medium fin section of the blade, for whose discretization 120 repre- sentative points were selected. The calculation was performed for small time intervals, for which the GFC was divided into 200 increments (~ig. la). The base was I00 load cycles. The results of calculation of the thermal and stress states of the medium fin section of the blade for the different engine-operating modes and also the load parameters obtained by strain measurement of the blade fin with the engine in operation are given in Table I. The pattern of variation in the normal stress during engine startup and on exiting from the take- off mode as well as the evolution of creep strains in the edges - the most heavily loaded elements of the blade fin - are shown, respectively, in Figs. 2a and 3. The mechanism of edge deformation is an alternating asymmetric cycle with an elastic-strain swing Aees = 0.29% in the leading edge and Ame tra = 0.27% in the trailing edge, which is accompanied by an increase in creep strain on the tension side. The values of the accumulated creep strains after i00 load cycles were ~c s = 0.019% in the leading edge and Sc tra = 0.007% in the trailing edge.

    The values obtained for creep strain were small, and could be neglected. There were no plastic deformations.

    The operational load pattern of a blade under laboratory conditions was modeled on a VL-2 testing machine [5], which makes it possible to place the blade under a multifactor non- isothermal load.

    The blade was heated using a profiled working coil, whose shape and position relative to the blade's profile section were determined from the condition whereby the required tem- perature fields with maximum edge heating are ensured. In the cooling half cycle, the blade was blasted with a stream of air exiting from a nozzle. Vibrational loading was carried out, exciting resonant oscillations of the blade in accordance with the first bending mode by an electrodynamic vibrator.

    Laboratory loading regimes (Fig. ib) were distinguished by the heating and cooling rates. This made it possible to vary the swing of the elastic (or elastoplastic) deformation during the loading cycle. We investigated three loadregimes. The characteristics of the laboratory toad regimes and the computed SSS parameters of the blade edges are presented in Table 2. The pattern of varation in the normal stress in the edges of the blade fin during the labora- tory load cycle is shown in Fig. 2b.

    Proceeding from the operational mechanism of the blade's edge deformation and the maxi- mum loading within the framework of this mechanism, we selected two load regimes: the first regime for testing the trailing edge, and the second for the leading edge.

    The criterial equation proposed by Kolotnikov et al [6] was used to describe the limit- ing state of the blade edges under the multifactor nonisothermal load:

    / " mf \~qll=r /h f \v]it~

    \ Tf / J L \~v / J '

    where Zp is the thermal-cycling longevity under a deformation Ag and saw-like temperature zml

    curve in the assigned region, ~.rho is the total holding time at the maximum temperature

    and static stress in the load cycle to failure, mf is the time to failure in accordance with the long-term-strength curve under the static stress induced in the holding segments at the

    Zmf maximum cycle temperature, EN~ is the total number of vibratory-load cycles to failure


  • TABLE 2. Blade Edges under These Conditions

    Regime number




    Characteristics of Laboratory Load Regimes and Computed SSS Values for

    Blade element


    9 9 Holding Maximum I Coollng IHeatlng ]_. _ ~ i r~ tO ~winK of ~s inIAmplitude of - rateV - itlme aL ]elastic ~las~ic ~oldlng ~ibration- tempera- [o ~ cool, rate Vheat~T T- ~deform ~deform .~egment linaucea ture Tmax, C/sec i C/sec | max no, I^~ ~. " ~|~, ~ "%1o~, MPalstresses o a, o C ]sec l~p: , q~, ~ ]~u | MPa ,,

    950 I O0 50 30 O, 53 0 200 16 935 0,56 0 215 20

    950 150 ! O0 30 O, 60 0 220 20 935 O, 57 0 205 26

    950 200 150 30 O, 67 O, 05 225 20 935 0,62 0 215 26

    Leading edge Trailing edge Leading edge Trailing edge

    Leading edge Trailing edge

    1 2 ~c tO , ?,




    f . . . I - -


    2 I

    0 ~ O0 80 Nicycles

    Fig. 3. Evolution of creep strain in leading (i) and trailing (2) edges of blade fin under operating conditions.

    at the variable-stress amplitude Ovmax , N v is the limiting number of cycles for the variable stress with the amplitude Ovmax at the maximum cycle temperature, which is established from the multicycle-fatigue curve, and ~, $, g, and 7 are constants defining the extent of the mutual effect of the active load factors on the exhaustion of longevity, which can be de- termined either from two series of experiments - during thermal-cyclic loading with holding and under saw-like thermal-cycling and vibratory loads, or in processing experimental data for the case of the complex effect of these factors.

    Using the latter approach to determine the constants ~, $, ~, and 7 in the temperature region under investigation, we obtain the following values: ~ = 0.6, $ = 0.2, $ = 0.5, and u = 0.i. In this case, the longevities to the appearance of cracks under a multifactor iso- thermal load, which were calculated from Eq. (I), differed from the experimental values by no more than 70%.

    To conduct equivalent blade tests under laboratory conditions, it is necessary to ensure the equality of the accumulated damages in the blade over the service life under laboratory and operating conditions. In this case, the duration of the equivalent blade tests under laboratory conditions was determined from the relationship

    O a

    ~l = 7r R, (2)

    where R is the service life of the engine on which the ECT of the blade is being conducted, and is expressed in load cycles, a ~ and a Z are the damage portions accumulated in the blade during one load cycle under operating and laboratory conditions, respectively; they are evaluated from expression (I) in the following manner:

    a . . . . . z~ 1 - - 1 - - Zmf


    Substituting the values of the parameters of the operating and laboratory loadings of the blade edges (Tables 1 and 2) in expression (3) and determining the damage portions a O


  • and a~,l we can calculate the duration of the ECTifor the blade edges under laboratory con- ditions for an engine life R = 15000 h (or R = 7500 cycies), using relationship (2): Rs 735 cycles for the leading edge with the blade tested in accordance with the second load regime; Rs 920 cycles for the trailing edge with the blade tested in accordance with the first load regime.

    The corrosion and erosion damages incurred over the life of the blade are not defined more precisely in the proposed approach. For this purpose, the coefficients of Eq. (i) should be corrected on the basis of the results of special tests conducted under single-factor loads.

    Equivalent tests of blade elements under laboratory conditions make it possible in the early stages of the engine's precision sizing to work out optimal structural-production solu- tions for a multifactor nonisothermal load, which models the pattern of the operating load~ and to confirm the blade's sericeability experimentally for an assigned engine life.


    i. D. S. Elenevskii, "Problems of the development of methods for the precision assembly sizing of gas turbine engines for structural strength," in: Vibrational Strength and Reliability of Engines and Aircraft Systems [in Russian], Kuibysheskii Aviatsionnyi institut, Kuibyshev (1986), pp. 33-44.

    2. N. D. Kuznetsov and V. I. Tseitlin, Equivalent Tests of Gas-Turbine Engines [in Russian], Mashinostroenie, Moscow (1976).

    3. V. A. Solyannikov, "Modeling the inelastic deformation and limiting state of turbine blades subjected to combined thermal-cycling and vibration loads," in: Structural Strength of Engines: Theses of Papers Presented at the Twelveth All-Union Scientific- Technical Conference (12-14 November 1990), Kuibyshevskii Aviatsionnyi institut, Kuibyshev (1990), pp. 136-137.

    4. D. A. Gokhfel'd and O. S. Sadakov, Plasticity and Creep of Structural Components Sub- jected to Repeated Loads [in Russian], Mashinostroenie, Moscow (1984).

    5. Scientific Bases and Methods of Improving the Reliability and Longevity of Gas-Turbine Engines [in Russian], V. T. Troshchenko and G. S. Pisarenko (eds.), Naukova Dumka, Kiev (1979).

    6. M. E. Kolotnikov, K. G. Svyatyshev, and V. A. Solyannikov, "Estimating the safety factor of turbine blades under thermal-cycling and vibration loads," Probl. Prochn., No. 8, 97-100 (1990).



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