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Turbine blade arc tenon/mortise structure and optimization method based on parameterized mesh deformation

Abstract

An arc tenon/mortise assembly is designed and optimized based on the free-form deformation (FFD) technique. Traditional tenon connection structure with planar-to-planar contact is prone to fretting fatigue due to the action of centrifugal loading and vibration. Therefore, a novel tenon connection structure with arc-to-arc contact is developed and its fretting fatigue is analyzed by using finite element (FE) method. The result shows that arc tenon structure can decrease the stress concentration and thus improve the fretting fatigue performance effectively. Then, an optimization method is applied to improve this merit of the arc tenon further. However, FE calculation is highly dependent on mesh quality, especially the mesh size of the contact region. In addition, the mesh quality of automatic mesh-regeneration in the optimization procedure has less controllability. To preserve the mesh quality during optimization process, a mesh parameterization method is presented by establishing mapping relationship between the control points and the geometry parameters based on FFD technique, and the quality of the morphed mesh is consistent with the original. Subsequently, with combination of the design of experiment (DOE) method and Kriging surrogate model, the designed arc tenon/mortise connection structure is optimized. The results show that the von Mises stress distribution in contact region become more uniform and the fretting fatigue is about twice as much as that of its counterpart with planar-to-planar structure. It is noted that the work developed in this paper can improve the fretting performance of connection structure effectively.

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References

  • Adjei RA, Fan C, Wang WZ, Liu YZ (2020) Multidisciplinary design optimization for performance improvement of an axial flow fan using free-form deformation. J Turbomach 143(1):1–25

    Google Scholar 

  • Agrawal M, Nandy A, Jog CS (2019) A hybrid finite element formulation for large-deformation contact mechanics. Comput Methods Appl Mech Eng 356(Nov 1):407–434

    MathSciNet  Article  Google Scholar 

  • Amargier R, Fouvry S, Chambon L, Schwob C, Poupon C (2010) Stress gradient effect on crack initiation in fretting using a multiaxial fatigue framework. Int J Fatigue 32(12):1904–1912

    Article  Google Scholar 

  • Amoiralis EI, Nikolos IK (2008) Freeform deformation versus B-spline representation in inverse airfoil design. J Comput Inf Sci Eng 8(2):13

    Article  Google Scholar 

  • Barrett R, Ning A (2018) Integrated free-form method for aerostructural optimization of wind turbine blades. Wind Energy 21(8):663–675

    Article  Google Scholar 

  • Beisheim JR, Sinclair GB (2003) On the three-dimensional finite element analysis of dovetail attachments. J Turbomach Trans ASME 125(2):372–379

    Article  Google Scholar 

  • Bhatti NA, Pereira K, Wahab MA (2019) Effect of stress gradient and quadrant averaging on fretting fatigue crack initiation angle and life. Tribol Int 131:212–221

    Article  Google Scholar 

  • Brujic D, Ristic M, Mattone M, Maggiore P, Poli GPD (2010) CAD based shape optimization for gas turbine component design. Struct Multidisc Optim 41(4):647–659

    Article  Google Scholar 

  • Calcaterra J, Naboulsi S (2005) Design methodology to investigate contact fatigue damage in turbine engine hardware. Int J Fatigue 27(9):1133–1141

    Article  Google Scholar 

  • Daxini SD, Prajapati JM (2017) Parametric shape optimization techniques based on meshless methods: a review. Struct Multidisc Optim 56(5):1197–1214

    MathSciNet  Article  Google Scholar 

  • Fleury R, Paynter R, Nowell D (2014) The influence of contacting Ni-based single-crystal superalloys on fretting fatigue of Ni-based polycrystalline superalloys at high temperature. Tribol Int 76:63–72

    Article  Google Scholar 

  • Frisch N, Ertl T (2002) Deformation of finite element meshes using directly manipulated free-form deformation. In: The seventh ACM symposium, 2002

  • Gagnon H, Zingg DW (2015) Two-level free-form and axial deformation for exploratory aerodynamic shape optimization. AIAA J 53(7):2015–2026

    Article  Google Scholar 

  • Goel T, Haftka RT, Shyy W, Queipo NV (2007) Ensemble of surrogates. Struct Multidisc Optim 33(3):199–216

    Article  Google Scholar 

  • Hahn Y, Cofer JI (2012) Design study of dovetail geometries of turbine blades using ABAQUS and ISIGHT. In: ASME turbo expo: turbine technical conference and exposition, 2012

  • He JX, Wang J, Yang QS, Han M, Deng Y (2021) Study on mechanical behaviors of loose mortise–tenon joint with neighbouring gap. Struct Eng Mech 77(4):509–521

    Google Scholar 

  • Hughes T, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194(39–41):4135–4195

    MathSciNet  Article  Google Scholar 

  • Jack D, Pontes JK, Sridharan S, Fookes C, Shirazi S, Maire M, Eriksson A (2019) Learning free-form deformations for 3D object reconstruction. In: Computer vision—ACCV 2018, 2019

  • Jin O, Mall S (2002) Influence of contact configuration on fretting fatigue behavior of Ti–6Al–4V under independent pad displacement condition. Int J Fatigue 24(12):1243–1253

    Article  Google Scholar 

  • John A, Shahpar S, Ning Q (2017) Novel compressor blade shaping through a free-form method. J Turbomach 139(8):081002.1-081002.11

    Article  Google Scholar 

  • Kircher S, Garland M (2008) Free-form motion processing. ACM Trans Graph 27(2):13

    Article  Google Scholar 

  • Leloudas SN, Strofylas GA, Nikolos IK (2018) Constrained airfoil optimization using the area-preserving free-form deformation. Aircr Eng Aerosp Technol 90(6):914–926

    Article  Google Scholar 

  • Li L, Jiao J, Sun S, Zhao Z, Kang J (2019a) Aerodynamic shape optimization of a single turbine stage based on parameterized Free-Form Deformation with mapping design parameters. Energy 169:444–455

    Article  Google Scholar 

  • Li L, Yuan TY, Li Y, Yang W, Kang J (2019b) Multidisciplinary design optimization based on parameterized free-form deformation for single turbine. AIAA J 57(5):2075–2087

    Article  Google Scholar 

  • Liang S, Wei DS, Wang YR, Tian AM, Li D (2016) An investigation of fretting fatigue in a circular arc dovetail assembly. Int J Fatigue 82(Pt 2):226–237

    Google Scholar 

  • Nascenzi T, Ha TH, Hwang JT (2019) A CAD-interoperable geometry parameterization for large-scale design optimization. In: AIAA Aviation 2019 Forum, 2019

  • Samareh JA (2004) Aerodynamic shape optimization based on free-form deformation. In: 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, 30 August–1 September 2004, Albany, New York

  • Sederberg TW, Parry SR (1986) Free-form deformation of solid geometric models. ACM SIGGRAPH Comput Graph 20:151–160

    Article  Google Scholar 

  • Sederberg TW, Goldman RN, Wang XH (2016) Birational 2D free-form deformation of degree 1 × n. Comput Aided Geom Des 44:1–9

    MathSciNet  Article  Google Scholar 

  • Shen X, Qi X, Wang R, Hu D,Liu H (2011) Shape optimization of aero engine fir-tree tenon/mortise structure. Eng Mech 28(12):231–237

    Google Scholar 

  • Shen Y, Huang W, Yan L, Zhang T (2020) Constraint-based parameterization using FFD and multi-objective design optimization of a hypersonic vehicle. Aerosp Sci Technol 100:12

    Article  Google Scholar 

  • Sinclair GB, Cormier NG, Griffin JH, Meda G (2002) Contact stresses in dovetail attachments: finite element modeling. J Eng Gas Turbines Power Trans ASME 124(1):182–189

    Article  Google Scholar 

  • Sun S, Li L, Yang W, Yue Z, Wan H (2019) RA-based fretting fatigue life prediction method of Ni-based single crystal superalloys. Tribol Int 134:109–117

    Article  Google Scholar 

  • Sun S, Li L, Yue Z, Yang W, Zhao Z, Cao R, Li S (2020) Experimental and numerical investigation on fretting fatigue behavior of Nickel-based single crystal superalloy at high temperature. Mech Mater. https://doi.org/10.1016/j.mechmat.2020.103595

    Article  Google Scholar 

  • Viana F, Venter G, Balabanov V (2010) An algorithm for fast optimal Latin hypercube design of experiments. Int J Numer Methods Eng 82(2):135–156

    MathSciNet  Article  Google Scholar 

  • Wang ZP, Abdalla M, Turteltaub S (2016) Normalization approaches for the descent search direction in isogeometric shape optimization. Comput Aided Des. https://doi.org/10.1016/j.cad.2016.06.002

    Article  Google Scholar 

  • Wei DS, Wang YR, Yang XG (2011) Analysis of failure behaviors of dovetail assemblies due to high gradient stress under contact loading. Eng Fail Anal 18(1):314–324

    Article  Google Scholar 

  • Yamazaki W, Mouton S, Carrier G (2010) Geometry parameterization and computational mesh deformation by physics-based direct manipulation approaches. AIAA J. https://doi.org/10.2514/1.J050255

    Article  Google Scholar 

  • Yang Q, Zhou W, Zheng X, Niu Z, Li Z, Zou B, Fu X (2019) Investigation of shot peening combined with plasma-sprayed CuNiIn coating on the fretting fatigue behavior of Ti–6Al–4V dovetail joint specimens. Surf Coat Technol 358:833–842

    Article  Google Scholar 

  • Yu D, Li F, Yang J, Kai C, Ming L (2016) Structural optimization of fir-tree root and groove for turbine blade with splines and genetic algorithm. In: ASME turbo expo: turbomachinery technical conference and exposition, 2016

  • Yuan R, Liao D, Zhu S, Yu Z, Correia J, Jesus AD (2021) Contact stress analysis and fatigue life prediction of turbine disc–blade attachment with fir-tree tenon structure. Fatigue Fract Eng Mater Struct. https://doi.org/10.1111/ffe.13410

    Article  Google Scholar 

  • Zhang B, Feng ZW, Xu BT, Yang T (2019) Free form deformation method applied to modeling and design of hypersonic glide vehicles. IEEE Access 7:61400–61413

    Article  Google Scholar 

  • Zhao ZC, Fu YC, Liu X, Xu JH, Wang J, Mao SJ (2017) Measurement-based geometric reconstruction for milling turbine blade using free-form deformation. Measurement 101:19–27

    Article  Google Scholar 

Download references

Acknowledgements

National Natural Science Foundation of China (Grant No. 51975471), Shaanxi Science Foundation for Distinguished Young Scholars (Grant No. 2022JC-36), National Science and Technology Major Project (2017-II-0006-0019), China Postdoctoral Science Foundation (2022M711777), National Natural Science Foundation of China (52105154), China National Postdoctoral Program for Innovative Talents (Grant No. BX20190285) support this work.

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Correspondence to Lei Li.

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Tan, C., Gao, H., Li, L. et al. Turbine blade arc tenon/mortise structure and optimization method based on parameterized mesh deformation. Struct Multidisc Optim 65, 239 (2022). https://doi.org/10.1007/s00158-022-03327-5

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  • DOI: https://doi.org/10.1007/s00158-022-03327-5

Keywords

  • Turbine blade
  • Arc tenon/mortise
  • Fretting fatigue life
  • Free-form deformation