Reduced-Order Modeling for and Vibration Characteristics Analysis of a Hard-Coated Mistuned Blisk
Abstract
:1. Introduction
2. Theoretical Analysis of the HCM Blisk
2.1. Reduced-Order Modeling of the HCM Blisk Using ICMSM
2.2. Solution for the Vibration Characteristics of the HCM Blisk
3. Numerical Results of the Case Study
3.1. Description of the HCM Blisk and Experimental Test
3.2. Vibration Characteristics of the HCM Blisk and Verification
4. The Discussion of the Specific Influence of Hard Coating
4.1. The Influence of Hard Coating on Vibration Characteristics
4.2. The Influence of Coating Area on Damping Capacity
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
- Laxalde, D.; Thouverez, F.; Lombard, J.P. Forced response analysis of integrally bladed disks with friction ring dampers. J. Vib. Acoust. 2010, 132, 011013. [Google Scholar] [CrossRef]
- Chang, Y.Y.; Lai, H.M. Wear behavior and cutting performance of CrAlSiN and TiAlSiN hard coatings on cemented carbide cutting tools for Ti alloys. Surf. Coat. Technol. 2014, 259, 152–158. [Google Scholar] [CrossRef]
- Songbo, W.E.I.; Xiaohan, P.E.I.; Bairu, S.H.I.; Tianmin, S.H.A.O.; Tao, L.I.; Yiliang, L.I.; Yi, X.I.E. Wear resistance and anti-friction of expansion cone with hard coating. Pet. Explor. Dev. 2016, 43, 326–331. [Google Scholar]
- Shubin, A.Y.; Potekaev, A.I.; Savostikov, V.M.; Galsanov, S.V.; Dmitriev, V.S.; Stepanov, I.B.; Dammer, V.H. Comparative physical-tribological properties of anti-friction ion-plasma Ti-C-Mo-S coating on VT6 alloy or 20X13 and 40X steels//IOP Conference Series: Materials Science and Engineering. IOP Publ. 2017, 168, 012038. [Google Scholar]
- Ghidelli, M.; Sebastiani, M.; Collet, C.; Guillemet, R. Determination of the elastic moduli and residual stresses of freestanding Au-TiW bilayer thin films by nanoindentation. Mater. Des. 2016, 106, 436–445. [Google Scholar] [CrossRef]
- Doleker, K.M.; Karaoglanli, A.C. Comparison of oxidation behavior of YSZ and Gd2Zr2O7 thermal barrier coatings (TBCs). Surf. Coat. Technol. 2017, 318, 198–207. [Google Scholar] [CrossRef]
- Fayomi, O.S.S.; Popoola, A.P.P.; Aigbodion, V.S. Investigation on microstructural, anti-corrosion and mechanical properties of doped Zn-Al-SnO2 metal matrix composite coating on mild steel. J. Alloy. Compd. 2015, 623, 328–334. [Google Scholar] [CrossRef]
- Bakhsheshi-Rad, H.R.; Hamzah, E.; Ismail, A.F.; Daroonparvar, M.; Yajid, M.A.M. Preparation and characterization of NiCrAlY/nano-YSZ/PCL composite coatings obtained by combination of atmospheric plasma spraying and dip coating on Mg-Ca alloy. J. Alloys Compd. 2016, 658, 440–452. [Google Scholar] [CrossRef]
- Torvik, P.J. A slip damping model for plasma sprayed ceramics. J. Appl. Mech. 2009, 76, 061018. [Google Scholar] [CrossRef]
- Al-Rub, R.K.K.; Palazotto, A.N. Micromechanical theoretical and computational modeling of energy dissipation due to nonlinear vibration of hard ceramic coatings with microstructural recursive faults. Int. J. Solids Struct. 2010, 47, 2131–2142. [Google Scholar] [CrossRef]
- Torvik, P.J.; Langley, B. Material properties of hard coatings developed for high damping. In Proceedings of the 51st AIAA/SAE/ASEE Joint Propulsion Conference, Orlando, FL, USA, 27–29 July 2015. [Google Scholar]
- Yang, Z.X.; Han, Q.K.; Jin, Z.H.; Qu, T. Solution of natural characteristics of a hard-coating plate based on Lindstedt–Poincaré perturbation method and its valedictions by FEM and measurement. Nonlinear Dyn. 2015, 81, 1207–1218. [Google Scholar] [CrossRef]
- Sun, W.; Liu, Y.; Du, G. Analytical modeling of hard-coating cantilever composite plate considering the material nonlinearity of hard coating. Math. Probl. Eng. 2015, 2015, 978392. [Google Scholar] [CrossRef]
- Sun, W.; Zhu, M.; Wang, Z. Free vibration analysis of a hard-coating cantilever cylindrical shell with elastic constraints. Aerosp. Sci. Technol. 2017, 63, 232–244. [Google Scholar] [CrossRef]
- Sun, W.; Liu, Y. Vibration analysis of hard-coated composite beam considering the strain dependent characteristic of coating material. Acta Mech. Sin. 2016, 32, 731–742. [Google Scholar] [CrossRef]
- Sun, J.; Kari, L. Coating methods to increase material damping of compressor blades: Measurements and modeling. In Proceedings of the ASME Turbo Expo 2010: Power for Land, Sea, and Air, Glasgow, UK, 14–18 June 2010; American Society of Mechanical Engineers: New York, NY, USA, 2010; pp. 1157–1165. [Google Scholar]
- Yang, M.T.; Griffin, J.H. A reduced order model of mistuning using a subset of nominal system modes. J. Eng. Gas Turbines Power 1999, 123, 893–900. [Google Scholar] [CrossRef]
- Feiner, D.M.; Griffin, J.H. A fundamental model of mistuning for a single family of modes//ASME Turbo Expo 2002: Power for Land, Sea, and Air. Am. Soc. Mech. Eng. 2002, 124, 953–964. [Google Scholar]
- Lim, S.H.; Bladh, R.; Castanier, M.P.; Pierre, C. Compact, generalized component mode mistuning representation for modeling bladed disk vibration. AIAA J. 2007, 45, 2285–2298. [Google Scholar] [CrossRef]
- Hurty, W.C. Vibrations of structural systems by component mode synthesis. J. Eng. Mech. Div. 1960, 86, 51–70. [Google Scholar]
- Hurty, W.C. Dynamic analysis of structural systems using component modes. AIAA J. 1965, 3, 678–685. [Google Scholar] [CrossRef]
- Benfield, W.A.; Hruda, R.F. Vibration analysis of structures by component mode substitution. AIAA J. 1971, 9, 1255–1261. [Google Scholar] [CrossRef]
- MacNeal, R.H. A hybrid method of component mode synthesis. Comput. Struct. 1971, 1, 581–601. [Google Scholar] [CrossRef]
- Suarez, L.E.; Singh, M.P. Improved fixed interface method for modal synthesis. AIAA J. 1992, 30, 2952–2958. [Google Scholar] [CrossRef]
- Bai, B.; Bai, G.; Li, C. Application of improved hybrid interface substructural component modal synthesis method in vibration characteristics of mistuned blisk. Chin. J. Mech. Eng. 2014, 27, 1219–1231. [Google Scholar] [CrossRef]
- Johnson, C.D.; Kienholz, D.A. Finite element prediction of damping in structures with constrained viscoelastic layers. AIAA J. 1982, 20, 1284–1290. [Google Scholar]
- Zheng, H.; Tan, X.M.; Cai, C. Damping analysis of beams covered with multiple PCLD patches. Int. J. Mech. Sci. 2006, 48, 1371–1383. [Google Scholar] [CrossRef]
- Sinha, A. Reduced-order model of a bladed rotor with geometric mistuning. J. Turbomach. 2009, 131, 031007. [Google Scholar] [CrossRef]
- Curà, F.; Mura, A.; Scarpa, F. Modal strain energy based methods for the analysis of complex patterned free layer damped plates. J. Vib. Control 2012, 18, 1291–1302. [Google Scholar] [CrossRef]
- Yoon, Y.C.; Kim, K.H.; Lee, S.H. Dynamic particle difference method for the analysis of proportionally damped system and cracked concrete beam. Int. J. Fract. 2017, 203, 237–262. [Google Scholar] [CrossRef]
- Sun, W.; Wang, Z.; Zhu, M.; Du, G. Identifying the mechanical parameters of hard coating with strain dependent characteristic by an inverse method. Shock Vib. 2015, 2015, 487457. [Google Scholar] [CrossRef]
- Chandrashaker, A.; Adhikari, S.; Friswell, M.I. Quantification of vibration localization in periodic structures. J. Vib. Acoust. 2016, 138, 021002. [Google Scholar] [CrossRef]
- Prudhomme, C.A.; Holtzinger, J.; Goldstein, G.H.; Tzivanis, M.J.; Noonan, W.E.; Austin, R.J. Thermal Spray Masking Tape. U.S. Patent 9,434,137, 6 September 2016. [Google Scholar]
Disk | Hard-Coated Blades | ||
---|---|---|---|
Inner radius of hub | 50 mm | Height of blade | 50 mm |
Outer radius of hub | 80 mm | Width of blade | 25 mm |
Thickness of hub | 19 mm | Thickness of blade | 3 mm |
Inner radius of rim | 182 mm | Number of blade | 18 |
Outer radius of rim | 200 mm | Coating thickness | 0.2 mm |
Thickness of rim | 20 mm | Coating area | 100% |
Thickness of sternum | 7 mm | Coating location | Both sides |
Type | Blisk | Hard Coating |
---|---|---|
Material | Aluminum | NiCoCrAlY + YSZ |
Young’s modulus (Gpa) | 70 | 54.494 |
Mass density (Kg/m3) | 2700 | 5600 |
Loss factor | 0.0003 | 0.0212 |
Poisson’s ratio | 0.33 | 0.3 |
Mode Order | ROM | FOM | Test | ER-F | ER-T |
---|---|---|---|---|---|
1 | 646.20 | 651.12 | 662.09 | 0.76% | 2.40% |
2 | 654.62 | 663.21 | 672.68 | 1.29% | 2.68% |
3 | 667.92 | 674.75 | 688.59 | 1.01% | 3.01% |
4 | 677.77 | 687.54 | 712.07 | 1.42% | 4.82% |
5 | 709.28 | 700.88 | 735.37 | −1.20% | 3.55% |
6 | 714.60 | 709.18 | 750.72 | −0.76% | 4.81% |
7 | 724.93 | 717.14 | 753.22 | −1.09% | 3.76% |
8 | 728.88 | 725.47 | 763.48 | −0.47% | 4.53% |
9 | 730.90 | 739.42 | 766.64 | 1.15% | 4.66% |
10 | 731.65 | 745.49 | 769.29 | 1.86% | 4.89% |
11 | 1149.10 | 1169.57 | 1193.26 | 1.75% | 3.70% |
12 | 1237.70 | 1251.40 | 1286.64 | 1.10% | 3.80% |
13 | 1332.60 | 1357.76 | 1394.69 | 1.85% | 4.45% |
Mode Order | ROM | Test | ||||
---|---|---|---|---|---|---|
Mistuned Blisk | HCM Blisk | Change Rate | Mistuned Blisk | HCM Blisk | Change Rate | |
1 | 655.99 | 646.20 | −1.52% | 701.07 | 662.09 | −5.89% |
2 | 668.38 | 654.62 | −2.10% | 710.80 | 672.68 | −5.67% |
3 | 676.34 | 667.92 | −1.26% | 721.54 | 688.59 | −4.79% |
4 | 690.33 | 677.77 | −1.85% | 737.30 | 712.07 | −3.54% |
5 | 716.70 | 709.28 | −1.05% | 764.01 | 735.37 | −3.89% |
6 | 725.95 | 714.60 | −1.59% | 780.04 | 750.72 | −3.91% |
7 | 733.27 | 724.93 | −1.15% | 783.49 | 753.22 | −4.02% |
8 | 741.11 | 728.88 | −1.68% | 794.87 | 763.48 | −4.11% |
9 | 743.69 | 730.90 | −1.75% | 798.59 | 766.64 | −4.17% |
10 | 745.74 | 731.65 | −1.93% | 801.76 | 769.29 | −4.22% |
11 | 1162.90 | 1149.10 | −1.20% | 1242.86 | 1193.26 | −4.16% |
12 | 1272.40 | 1237.70 | −2.80% | 1352.50 | 1286.64 | −5.12% |
13 | 1372.20 | 1332.60 | −2.97% | 1469.73 | 1394.69 | −5.38% |
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Gao, F.; Sun, W. Reduced-Order Modeling for and Vibration Characteristics Analysis of a Hard-Coated Mistuned Blisk. Coatings 2017, 7, 103. https://doi.org/10.3390/coatings7070103
Gao F, Sun W. Reduced-Order Modeling for and Vibration Characteristics Analysis of a Hard-Coated Mistuned Blisk. Coatings. 2017; 7(7):103. https://doi.org/10.3390/coatings7070103
Chicago/Turabian StyleGao, Feng, and Wei Sun. 2017. "Reduced-Order Modeling for and Vibration Characteristics Analysis of a Hard-Coated Mistuned Blisk" Coatings 7, no. 7: 103. https://doi.org/10.3390/coatings7070103