Free vibration analysis of the hard-coating splitter blisk using the energy-based finite element method

Abstract

This paper presents the free vibration analysis of the hard-coating splitter blisk (known as the splitter blisk deposited hard coating) and the damping-improved performance of the hard coating for vibration suppression of the splitter blisk. Based on the proposed energy-based finite element method by the energy considerations, complex modulus theory and composite Mindlin plate theory, the equations of motion of hard-coating splitter blisk are formulated. And, the complex solutions for free vibration problem are then solved, whose real and imaginary parts are closely related to natural frequencies and loss factors. Considering the academic splitter blisk deposited NiCoCrAlY+YSZ hard coating as the benchmark, the comparisons for vibration characteristics of hard-coating splitter blisk originating from different sources are performed for model validation, and the influence of hard coating on the dynamics of splitter blisk are also investigated. The numerical results reveal that the vibration amplitudes of splitter blisk are suppressed remarkably by the hard coating without altering natural frequencies significantly.

Keywords

Splitter blisk hard coating free vibration analysis energy-based finite element method complex modulus composite Mindlin plate theory

Get full access to this article

View all access options for this article.

References

Wennerstrom AJ and Frost GR. Design of a rotor incorporating splitter blades for a high pressure ratio supersonic axial compressor stage. Aerospace Research Labs Wright-Patterson AFB, USA, 1974.

Wennerstrom AJ, Buzzell WA and DeRose RD. Test of a supersonic axial compressor stage incorporating splitter blades in the rotor. Aerospace Research Labs Wright-Patterson AFB, USA, 1975.

Tzuoo

Hingorani

Sehra

. Optimization of a highly-loaded axial splittered rotor design. Revue Francaise de Mecanique 1992; 3: 235–246.

Opdyke

. Integrated high performance turbine engine technology (IHPTET). Gas Turbine Forecast 2006; 10: 1–8.

Younossi

Arena

Moore

et al.

Military jet engine acquisition: technology basics and cost-estimating methodology, Santa Monica, CA: Rand Corp., 2002.

Torvik PJ and Langley B. Material properties ofhard coatings developed for high damping. In: 51stAIAA/SAE/ASEE joint propulsion conference, Orlando, USA, July 27–29, 2015, vol. 4195.

Sun

Liu

. Analytical modeling of hard-coating cantilever composite plate considering the material nonlinearity of hard coating. Math Probl Eng 2015; 2015: 1–14.

Sun

Zhu

Wang

. Free vibration analysis of a hard-coating cantilever cylindrical shell with elastic constraints. Aerosp Sci Technol 2017; 63: 232–244.

Sun

Liu

. Vibration analysis of hard-coating composite beam considering the strain dependent characteristic of coating material. Acta Mech Sin 2016; 32: 731–742.

10.

Sun

Kari

. Coating methods to increase material damping of compressor blades: measurements and modeling. In: ASME turbo expo 2010: power for land, sea, and air, New York: American Society of Mechanical Engineers, 2010, pp. 1157–1165.

11.

Gounaris

Antonakakis

Papadopoulos

. Hysteretic damping of structures vibrating at resonance: an iterative complex eigensolution method based on damping-stress relation. Comput Struct 2007; 85: 1858–1868.

12.

Alati

Failla

Santini

. Complex modal analysis of rods with viscous damping devices. J Sound Vib 2014; 333: 2130–2163.

13.

Sun

Han

. Identification of mechanical parameters of hard-coating materials with strain-dependence. J Mech Sci Technol 2014; 28: 81.

14.

Wang

Inman

. Finite element analysis and experimental study on dynamic properties of a composite beam with viscoelastic damping. J Sound Vib 2013; 332: 6177–6191.

15.

Enemark

Santos

. Rotor-bearing system integrated with shape memory alloy springs for ensuring adaptable dynamics and damping enhancement - theory and experiment. J Sound Vib 2016; 369: 29–49.

16.

Chen

Zhai

Han

. Vibration and damping analysis of the bladed disk with damping hard coating on blades. Aerosp Sci Technol 2016; 58: 248–257.

17.

Gao

Sun

. Vibration characteristics and damping analysis of the blisk deposited hard coating using the Rayleigh-Ritz Method. Coatings 2017; 7: 108.

18.

Maturi

Ferreira

AJM

Zenkour

et al.

Analysis of laminated shells by Murakami's zig-zag theory and radial basis functions collocation. J Appl Math 2013; 2013: 123465.

19.

Tornabene

Fantuzzi

Bacciocchi

. Foam core composite sandwich plates and shells with variable stiffness: effect of the curvilinear fiber path on the modal response. J Sandwich Struct Mater 2017; 21: 320–365.

20.

Katili

Aristio

. Isogeometric Galerkin in rectangular plate bending problem based on UI approach. Eur J Mech-A/Solids 2018; 67: 92–107.

21.

Karami

Janghorban

. On guided wave propagation in fully clamped porous functionally graded nanoplates. Acta Astronaut 2018; 143: 380–390.

22.

Qin

Yang

et al.

Free vibration analysis of rotating cylindrical shells coupled with moderately thick annular plates. Int J Mech Sci 2018; 142: 127–139.

23.

Lee

Park

. Static test until structural collapse after fatigue testing of a full-scale wind turbine blade. Compos Struct 2016; 136: 251–257.

24.

Sun

Wang

Zhu

et al.

Identifying the mechanical parameters of hard coating with strain dependent characteristic by an inverse method. Shock Vib 2015; 2015: 1–15.

25.

Chandrashaker

Adhikari

Friswell

. Quantification of vibration localization in periodic structures. J Vib Acoust 2016; 138: 021002.