STRUCTURAL AND VIBRATIONAL RESPONSE ANALYSIS OF H.P. BLADED DISC ASSEMBLY

Transcription

1 Intenational Jounal of Mechanical Engineeing and Technology (IJMET) Volume 7, Issue 3, May June 06, pp , Aticle ID: IJMET_07_03_08 Available online at Jounal Impact Facto (06): 9.86 (Calculated by GISI) ISSN Pint: and ISSN Online: IAEME Publication STRUCTURAL AND VIBRATIONAL RESPONSE ANALYSIS OF H.P. BLADED DISC ASSEMBLY Bhaath Bhaska, Anand. S. N. and D.T.Kishna Rao School of Mechanical Engineeing Reva Univesity, Bangaloe, Kanataka, India ABSTRACT In this aticle, an effot has been made to deal with stuctual behavio of the Steam tubine HP blade and disc assembly otating at 00% (6000 pm) optimum speed and 0% (700pm) ove speed conditions which in tun ceate lage amount of centifugal foce. This is the dominating foce in steam tubine blade assembly which is the cause fo all its behavio. Vibational analysis of this HP blade and disc assembly is also caied out using FEA methods to detemine and pedict the fatigue life of the blade and disc. The Stuctual analysis is caied out on the HP blade and disc to undestand the Stuctual behavios which comes on them in ode to find out the facto of safety of the HP blade and disc assembly due to high angula velocity. The Vibational analysis is then caied out on HP steam tubine blade and disc assembly to find out the Fequencies acting on them fo fist 5 modes and to pedict the safety of the blade and disc with the help of Campbell Diagam. Finally, the fatigue life analysis is caied out on the HP Blade and disc assembly with the help of S-N cuve diagam fo estimation of the fatigue life of the HP blade as well as the disc fo satisfactoy design of any steam tubine blade and disc assembly. Cite this Aticle: Bhaath Bhaska, Anand. S. N. and D.T.Kishna Rao, Stuctual and Vibational Response Analysis of H.P. Bladed Disc Assembly. Intenational Jounal of Mechanical Engineeing and Technology, 7(3), 06, pp INTRODUCTION In moden day wold, Application of steam tubine as a device that is used to tansfom the themal enegy of the steam into mechanical enegy by tuning the oto blades. Steam tubines ae used as pime moves in all themal and nuclea powe plants to poduce electicity, lage ships, pumps and fans at petochemical plants. The majoity of steam tubines have two essential components o sets of such components edito@iaeme.com

2 Stuctual and Vibational Response Analysis of H.P. Bladed Disc Assembly They ae Nozzle, Blade o Deflecto, The Simple Impulse Steam Tubine is shown diagammatically in fig... The top bit of the figue demonstates a longitudinal segment though the uppe potion of the tubine, the cente bit demonstates an development of the nozzles and blading, while the lowe pat of the outline indicates oughly how the absolute pessue end, the absolute velocity of the steam diffe fom point to indicating the enty of the steam though the tubine. Figue. Simple Impulse Steam Tubine and Its Component Figue. Oveview of Steam Tubine The steam movement though a tubine esults in change of enegy though blades; hence the tubine can be sepaated into thee stages. This can be odeed by use in the tubine as high, intemediate and low-pessue blades o stages (HP, IP and LP). The fig.. demonstates a diagam of the steam tubine. Blades ae one of the most cucial components in steam tubine powe plant. These ae the components acoss which flow of high-pessue steam takes place to poduce wok. The blade is subjected to foces in the thee diections, viz. Centifugal foces along the adial diection. Axial foces caused by the Steam flow, 3. Foces acting nomal to the shaft due to centifugal foces.. Blade and Disc mateials Scientists aound the wold ae tying to invent new mateials, which have stength and stability at lage tempeatues to meet the equiements of the steam tubine edito@iaeme.com

3 Bhaath Bhaska, Anand. S. N. and D.T.Kishna Rao designes. Vaious alloy compositions ae developed which have a good stability to withstand the themal stesses, these alloys have been modified to give good eosioncoosion chaacteistics to the blade. Among these vaious mateials, the few which have found to be apt fo use in blades ae steels, titanium alloys and nickel-based alloys. All the thee types of alloys, which ae mainly used, have vaiations in the popotion of chomium and aluminum to impove the stength and coosion at high tempeatue. Nickel alloys have also been developed extensively and ae cuently being used fo steam tubine engine. These alloys have supeio stength and oxidation esistance even though nickel by itself has poo oxidation esistance. This weakness is ovecome by alloying with chomium. In alloys, chomium is geneally 0 30 % and foms chomium oxide (C O 3) potective laye and chomium cabide. Othe elements geneally added ae aluminum, titanium and niobium to impove the stength at high tempeatue. Cuent alloys also use cobalt, hafnium, boon, ziconium, molybdenum etc. Blades ae mounted on a disc in seies, hence cae must be taken in design and mateial selection to avoid the catastophic failue of the disc, based on yield and ultimate stength at diffeent tempeatues, esistance to ceep elaxation and good factue toughness at ambient tempeatue conditions and opeating tempeatues. Steel based alloy pefomed these chaacteistics and lowe levels of sulfu and phosphoous esults in the attainment of a high stength, tempeed, lowe bainite stuctues having high toughness. In the pesent wok chomium vanadium steel alloy with diffeent popotion is used fo Disc. The fig..3 shows a conventional bladed disc assembly used in tubines..4. MATHEMATICAL MODELLING.4.. Stesses induced Rotating Disk: The Mathematical modeling of disk wheel otating at high speed in steam tubines ae consideed. The lage stesses ae due to centifugal foces of the otating disk which acts adially outwads. Since disk is symmetic, Let the centifugal foce in tangential diection is R =, R θ = 0 () We know that, the diffeential equation of motion fo otating disk at equilibium is ( ) R 0 () Whee = Radial stess = Tangential Stess By solving the above two equation, ( ) Aiy s stess function is (3) edito@iaeme.com

4 Stuctual and Vibational Response Analysis of H.P. Bladed Disc Assembly Afte simplification of eq.3, we get The compatibility equation fo otational disk is ( ) (4) Afte substituting the Genealized Hook s law, the elations fo the plane stess condtion in the above equation, ( ) E = Radial Stain, = Tangential stain By solving the above two equation, ( ) E Radial stain E Tangential stain E Substituting above two equations in compatibility equation eqn. (4) and simplifying it, We get d d(, ) (3 ) d d Upon integating the above equation d d(, ) (3 ) d d The Aiy s stess function 3 C C (3 ) 8 Whee C and C ae constant of integation and can be found by initial conditions. Substitute the Aiy s stess function in the above equation, we get C C The Radial stess is (3 ) (5) 8 C C The Tangential Stess is ( 3 ) (6) Hollow Disk Conside the hallow disk with cental inne hole of inne adius a and oute adius b. By initial bounday condition to eqn. (5) and eqn. (6) i.e edito@iaeme.com

5 Bhaath Bhaska, Anand. S. N. and D.T.Kishna Rao At = a, = 0, = b, = 0 We can find the constant of integation i.e. C and C. The Radial Stess induced is and a b (3 ) ( a b ) 8 a b (3 ) ( a b ) 8 The Tangential Stess induced is 3 3 the maximum adial stess ( ) max and maximum ( ) max and minimum ( ) min tangential stess fo the otating disk due to centifugal load, Diffeentiating the above equation with espects to adius The maximum adial stess at = ab is (3 ) ( a b ) ( ) max= 8 Induced Maximum tangential stess at = a, ) max a (3 ) b 4 3 b ( Minimum tangential stess at = b i.e. ( ) min is ( ) min b (3 ) a 4 3 a. NUMERICAL METHODOLOGIES:. Geometic Modeling of Blade and Disc Assembly Fo the pesent analysis the blades of the HP stage ow wee consideed. Geneally the HP stage blades ae tip shouded, because they have to esist huge bending foces poduced by the steam loads. The geomety of the blade disc secto is modeled using commecially available modeling softwae CatiaV5. A minimum of 30 co-odinate points at each section ae selected fom the list to epesent the geomety as accuately as possible. These coodinates ae used to geneate the aeofoil suface. T-oot of the blade is epoduced with best possible fillet to avoid shap cone of the blade fo analysis. The geometic model of HP stage bladed disc is as shown in fig... Blade Dimention: Blade height= 6.mm Thickness of leading edge = 3 to 5mm Thickness of tailing edge= 0.9 to 0.mm Numbe of blades = 60 Secto angle = 6 0 Mean diamete = 50 to 350mm 30 edito@iaeme.com

6 Stuctual and Vibational Response Analysis of H.P. Bladed Disc Assembly Figue. Geometic Modeling of the Blade Disc secto.. F.E Model of HP Blade The FE model of the HP stage blade disc secto is discetized by the choosing solid bick element with 8 nodes. In ode to achieve the convegence the aspect atio of blade fillet and disc fillet potions ae consideed less than 5%, wheeas aspect atio in the disc is consideed less than 0%. To geneate the contact between blade and disc, contact 73 element fo the blade contact egion and taget 70 element fo the disc egion is consideed in the pesent wok. Fo the pesent analysis nodes and 0943 elements ae geneated to achieve the convegence. The blade and disc at T-oot ae discetized with such a magin that the blade and disc consideed ae of simila numbe of element division. In ode to achieve continuity, fine mesh is consideed in this zone. The FE model of geomety is as shown in fig.., fig..3 and fig..4. Fig.. FE Model of Blade Fig..3 FE Model of Disc Fig..4 FE Model of Blade Disc Secto.3 Bounday Conditions Fo the pupose of analysis a secto of the blade disc is consideed. The consideed model as secto angle of 6 0 and the model is cyclic-symmetic in natue. The hoop displacement at low edge and high edge of the blade and disc ae aested. In ode to avoid the igid body motion one of the node is aested in the axial diection as shown in the fig.5.8. Contact 73 and Taget 70 elements ae used to geneate the blade and disc contact. In the contact zones of blade and disc, it is assumed fictionless suppot 3 edito@iaeme.com

7 Bhaath Bhaska, Anand. S. N. and D.T.Kishna Rao i.e., nomal contact with axial motion is esticted and sliding motion is possible with othe diections. In the analyses otational speed of 6000 pm and 700 pm is consideed fo opeating and ove speed conditions espectively Figue.5 Bounday Conditions.4. Mateial Popeties The Chomium-Vanadium alloy mateials at oom tempeatue 7 0 c have been consideed and shown in the Table. Table. Mechanical Popeties Mechanical Popeties Blade Disc (C 3MoV 59 ) (8CMoV 55 ) Young s Modulus (E).8e5MPa.e5 MPa Density(ρ) 7750 Kg/m Kg/m 3 Poison s atio(ν) Yield stength(σ y ) 540Mpa 590Mpa 3. RESULTS AND DISCUSSIONS 3.. HP bladed disc In pesent wok, the following obsevations wee made petaining to the HP bladed disc secto of steam tubine at 6000pm with appopiate bounday conditions as explained ealie with ove speed conditions as pe API standads. The esults of the same classified unde two goup one fo stuctual analysis and othe petaining to coupled fequencies. Finally some obsevations ae also made fo low cycle fatigue life and stuctual safety magins. The output of the stuctual analysis is done as following ways. The HP blade is categoized fom stuctual point of view into thee zones, hub, tip and mean. The tip is consideed to be most cucial because the ubbing of blade against the casing duing opeating conditions. The aveage stess in aeofoil is vey impotant fom blade bending stess point of view which cause due to both selfweight of blade and steam loads. The last pat of blade disc assembly is the hub, the blade and disc inteface and which happens to be the most citical zone of assembly. 3 edito@iaeme.com

8 Stuctual and Vibational Response Analysis of H.P. Bladed Disc Assembly 3... Displacement Analysis Fom the analysis it is found that the adial gowth of blade at 00% speed vaied fom 0mm to mm and ove speed conditions the displacements wee 0mm to 0.094mm indicating clealy the absence of allowing adial gowth of blade fo tip ubbing conditions. The fig.3. shows the adial gowth of blade at 6000pm 3... Stess Analysis Figue 3. Radial Gowth of Blade at 6000pm 3... Stesses in the blade Fom the analysis it is found that the von-mises stess in the blade vaied fom MPa at the tip to maximum MPa at blade oot is as shown in fig.3.. The stesses in the tang egion is appeas to be 300 to 350MPa. The pinciple stesses which ae highly tensile in natue play a vital ole in deciding Low cycle fatigue life of the blade which is found to be 57.3MPa at the blade oot. The blade neck which esist the centifugal pull at opeating condition as developed an aveage equivalent von-mises stess equal to 0.04 MPa at 00% speed is as shown fig.7.5 and 46.07MPa at 0% speed fo ove speed condition, since stesses developed wee with in the design limit. The blade stesses at the neck egion is Mpa to 58.93Mpa wee also consideed as safe fom goss yielding point of view. The maximum aveage centifugal stess developed in the aeofoil is equal to 0.44Mpa. The yield stess of the blade at oom tempeatue is 590MPa. Hence the stesses developed ae well within the yield stess; hence the blade is vey much safe fom failue edito@iaeme.com

9 Bhaath Bhaska, Anand. S. N. and D.T.Kishna Rao Fig.3. Avg.Von-Mises Stess in the Blade at 6000pm Fig.3.3 Avg. Von-Mises Stess in the disk at 6000pm 3... Stesses developed in the steam tubine disc The stesses developed in the disc is vaies fom 7.8 to MPa.The peak stess developed in the disc at blade disc inteface is MPa is as shown in fig.3.6.the stess developed at fillet egion of bladed disc inteface is maximum because the stess concentation will be moe at this egion. Hence the stess developed is safe fom net yielding point of view. The aveage sectional stess at less coss section of the disc which has huge centifugal foce happens to be 5.54 MPa at 00% speed is as shown in fig.3.4 and 80.77MPa at 0% speed. The yield stess of the disc consideed fo analyses is 540MPa. Hence the stess developed is vey much safe fom design limits. Fig.3.6 shows the stesses developed in blade disc secto, the stess developed is maximum at blade disc inteface that is MPa. The table: 3. shows the aveage vonmises stess developed and facto of safety in the blade and disc

10 Stuctual and Vibational Response Analysis of H.P. Bladed Disc Assembly Figue 3.4 Stesses Distibution in the Disc at 6000pm Figue 3.5 Aveage Von-Mises Stess Distibution at Minimum Coss Section of Disc Figue 3.6 Stess in Blade Disc Secto at 6000pm 35

11 Bhaath Bhaska, Anand. S. N. and D.T.Kishna Rao Minimum cosssection Table 3. Avg Von-mises stesses in Blade and disc with FOS 00% speed in MPa 0% speed in MPa Design limit in MPa Blade Disc Vibation Analysis The fundamental natual fequencies of bladed disc assembly ae computed to evaluate the pobable esonance conditions at opeating speed. Fist five modes of the blade wee taken into consideation and the most citical one happens to be bending, axial and tosional modes as pe the published liteatues. The fundamental fequencies computed fo the coupling between blade and disc and coupled fequencies due to tang contact between blade and the disc. The elated fundamental fequencies ae tabulated in the tabula fom in Table: 3. and fig.3.7 shows the natual fequencies and fundamental mode shapes at 6000pm. The natual fequencies obtained ae epesented in the Campbell diagam to check safety magin fo vibatoy stesses. The concept of Campbell diagam has been discussed in the ealie chapte. Natual fequencies obtained ae well within the safety limits. The fist five engine ode lines dawn elated 00% and 0% speed ae not cossing the mode hence the blade is vey much safe fom vibation point of view. It also indicates the blade will be unde low cycle fatigue. The fig.3.8 shows the Campbell diagam dawn fo fundamental modes. The foced fequencies ae not expected to coss the fundamental fequencies fo esonance to occu, which play a vital ole in deciding the High Cycle Fatigue life of the blades due to the vibatoy stesses developed at esonant conditions. Speed (pm) Table 3. Natual Fequencies fo Blade Disc Secto Mode (Hz) Mode (Hz) Mode3 (Hz) Mode4 (Hz) Mode5 (Hz) FOS at 00% speed Mode Mode Mode edito@iaeme.com

12 Stuctual and Vibational Response Analysis of H.P. Bladed Disc Assembly Mode 4 Mode 5 Figue 3.7 Natual Fequencies and Mode Shapes at 6000pm Figue 3.8 Campbell Diagam fo Obtained Natual Fequencies Low Cycle Fatigue Life Estimation In the pesent wok, to compute the low cycle fatigue life of the blades fo expected 4000 cycles which oughly comes aound 30 to 40 yeas at the expected life of the tubine, though many components in the tubine ae fequently changed. The blade is expected to meet equiement since HP stage blade happens to be the key component in a steam tubine hence the stess developed at blade oot ae taken into the S-N cuve data is shown in fig.3.9 and fig.3.0 esulting the life of blade happens to be infinite numbe of cycles at 00% speed and infinite numbe of cycles at 0% speed fo blade. The peak stess developed in disc is MPa at 00% speed esults in.89e5 numbe of cycles is as shown and peak stess at 0% speed esult in.94e5 numbe of cycles, though the fatigue life estimated fo 0% fo all pactical pupose. The estimated life to be taken at 00% speed, the expected life to calculated based on (Zeo maximum Zeo) aveage stess based theoy fom the analysis 37 edito@iaeme.com

13 Bhaath Bhaska, Anand. S. N. and D.T.Kishna Rao consideing size facto, shape facto, suface finish facto etc. The safety facto fo the blade and disc is as shown in fig.3. and fig 3. is vaying fom.3074 to 5. This also ensues the safety of the blade at opeating conditions. Figue 3.9 Stess Life(S-N) Cuve fo Blade Figue 3.0 Stess Life(S-N) Cuve fo Disc Figue 3. Fatigue Life of Blade Figue 3. Fatigue Life of Disc Figue 3.3 Facto of Safety fo Blade and Disc unde Fatigue Loading 4. CONCLUSIONS The consideations fo stuctual, vibation and fatigue analysis is obtained the following conclusions fo the pesent wok

14 Stuctual and Vibational Response Analysis of H.P. Bladed Disc Assembly. The adial expansion of blade at opeating conditions is safe and found within the safe limit. Hence thee is no wea and tea of blade with the tubine casing even at highe speeds.. The aveage stess developed in the blade, neck and the minimum disc coss section at 00% and 0% is also shows the complete safety of the blade and the disc fom total yielding point of view. 3. The calculated natual fequencies should not match with any of the foced fequency esulting fom the unning speed of tubine, NPF (nozzle passing fequency), patial steam admission in the tubine at opeating speed. 4. The peak stess developed at blade oot filet due to centifugal spin as esulted in the LCF of.97e5 and.89e5 numbe of cycles in blade and disc espectively by meeting the impotant design equiements fom both local stess-stain appoach and stess based (Zeo-Max- Zeo) fatigue analysis. Theefoe, with this novel wok gives an appoach fo evaluation of a HP stage Blade in a steam tubine is established in a methodical way and an effot has been made to fomulate the best method to undestand and apply the same pocedues fo estimation of the stength of the blade and the disc in egula design pactice. REFERENCES [] Pof. W.S. Rathod and Khalid Ansai, Modal and Hamonic analysis of Tubochage tubine using Finite Element Method, (7), July 03. [] Mahajan Vandana N, analysis of blades of axial flow fan using ansys, Depatment of Mechanical Engg. S.S.B.T s College of Engg. and Technology, Bambhoi, Jalgaon. [3] R.D.Banpuka, Stuctual Analysis of Mico Compesso Blades, Dept. of Mechanical Engineeing, Abha Gaikawad Patil Engineeing College, Nagpu, Mahaashta, India. [4] Sheik Ghouse.M, P. Manivannan, Computational Analysis of Compesso Blade, Intenational Jounal of Innovative Reseach in Science, Engineeing and Technology, 4(3), Mach 05. [5] C. S. Kishnamoothy, (987).Finite Element Analysis, Theoy and Pogamming, Tata McGaw-Hill Publishing Company Ltd., New Delhi. [6] Leonid Shabliy and Aleksand Cheniaev, Optimization of Gas Tubine Compesso Blade Paametes fo Gas-dynamic Efficiency unde Stength Constaints, Samaa State Aeospace Univesity, Moskovskoe, Samaa, Russia JSC, CADFEM-CIS, Avoa st., Samaa, Russia [7] Ahmed abdulhussein jabba, a. k. ai, p. avinde eedy & mahmood hasan dakhil, Intenational Jounal of Mechanical and Poduction Engineeing Reseach and Development (IJMPERD) 4(), Feb 04, [8] Naixing Chen, Hongwu Zhang, Yanji Xu, Weiguang Huang, Blade Paameteization and Aeodynamic Design Optimization Fo a 3D Tansonic Compesso Roto, Poceedings of the 8th Intenational Symposium On Expeimental and Computational Aeothemodynamics of Intenal Flows Lyon, July 007. [9] Sanket Kothawade, Aditya Patanka, Rohit Kulkani and Samee Ingale, Detemination of Heat Tansfe Coefficient of Bake Roto Disc Using CFD Simulation. Intenational Jounal of Mechanical Engineeing and Technology, 7(3), 06, pp edito@iaeme.com