An outliers-free isogeometric modeling method of rotating disk-shaft systems under elastic boundary conditions

Abstract

An outliers-free isogeometric modeling method for rotating disk-shaft systems is developed. The Timoshenko beam theory and artificial spring technique are employed for the rotating shaft and elastic boundary conditions. The nonlinear parameterization method is employed for the removal of outliers and three different nonlinear mappings are developed for the discussion of the accuracy of low modes. The energy coupling method between disks and shaft under nonlinear mapping is performed by using the Newton Raphson method. The results show that the isoparametric mapping has better performance in the accuracy of low modes than other nonlinear mapping and the outliers can also be removed, besides, the present method has good convergence rate for different boundary conditions. The accuracy of the proposed method shows good consistency with the Finite Element Method. The time cost of modeling is reduced by 71.4% compared to the traditional rotor model for a multiple disks rotor system, which indicates that the present approach has potential to provide more efficient optimization models of disk-shaft systems. The proposed method can provide a new modeling framework and can be easily extended to the prediction and optimization of vibration characteristics of complex rotor systems with multiple disks and supports.

Graphical abstract

Keywords

isogeometric analysis / outliers-free / non-linear mapping / disk-shaft coupling / rotor systems

References

[1] Ruhl R L, Booker J F. A finite element model for distributed parameter turborotor systems. Journal of Engineering for Industry, 1972, 94(1): 126–132

[2] Nelson H D, McVaugh J M. The dynamics of rotor-bearing systems using finite elements. Journal of Engineering for Industry, 1976, 98(2): 593–600

[3] Nelson H D. A finite rotating shaft element using Timoshenko beam theory. Journal of Mechanical Design, 1980, 102(4): 793–803

[4] Lee A S, Kim B O, Kim Y C. A finite element transient response analysis method of a rotor-bearing system to base shock excitations using the state-space Newmark scheme and comparisons with experiments. Journal of Sound and Vibration, 2006, 297(3–5): 595–615

[5] Gayen D, Chakraborty D, Tiwari R. Whirl frequencies and critical speeds of a rotor-bearing system with a cracked functionally graded shaft––Finite element analysis. European Journal of Mechanics. A, Solids, 2017, 61: 47–58

[6] Gayen D, Tiwari R, Chakraborty D. Finite element based stability analysis of a rotor-bearing system having a functionally graded shaft with transverse breathing cracks. International Journal of Mechanical Sciences, 2019, 157: 403–414

[7] Kulesza Z, Sawicki J T. Rigid finite element model of a cracked rotor. Journal of Sound and Vibration, 2012, 331(18): 4145–4169

[8] Bhowmick A, Ganguly S, Neogy S, Nandi A. A shaft finite element for analysis of viscoelastic tapered Timoshenko rotors. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2020, 42(1): 48

[9] Belhocine A, Afzal A. Computational finite element analysis of brake disc rotors employing different materials. Australian Journal of Mechanical Engineering, 2022, 20(3): 637–650

[10] Prabith K, Krishna I R P. The numerical modeling of rotor–stator rubbing in rotating machinery: A comprehensive review. Nonlinear Dynamics, 2020, 101(2): 1317–1363

[11] Kumar P, Tiwari R. Finite element modelling, analysis and identification using novel trial misalignment approach in an unbalanced and misaligned flexible rotor system levitated by active magnetic bearings. Mechanical Systems and Signal Processing, 2021, 152: 107454

[12] RogersD F. An Introduction to NURBS: With Historical Perspective. San Francisco, CA: Morgan Kaufmann, 2001

[13] Lee S J, Park K S. Vibrations of Timoshenko beams with isogeometric approach. Applied Mathematical Modelling, 2013, 37(22): 9174–9190

[14] Hughes T J R, Cottrell J A, Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 2005, 194(39–41): 4135–4195

[15] de BoorC. A Practical Guide to Splines. New York, NY: Springer-Verlag, 1978

[16] Cottrell J A, Reali A, Bazilevs Y, Hughes T J R. Isogeometric analysis of structural vibrations. Computer Methods in Applied Mechanics and Engineering, 2006, 195(41–43): 5257–5296

[17] Kheladi Z, Hamza-Cherif S M, Ghernaout M E A. Critical speeds analysis of spinning laminated composite shaft based on isogeometric analysis. International Journal for Computational Methods in Engineering Science and Mechanics, 2022, 23(6): 487–509

[18] Deng Q, Calo V M. A boundary penalization technique to remove outliers from isogeometric analysis on tensor-product meshes. Computer Methods in Applied Mechanics and Engineering, 2021, 383: 113907

[19] Hiemstra R R, Hughes T J R, Reali A, Schillinger D. Removal of spurious outlier frequencies and modes from isogeometric discretizations of second-and fourth-order problems in one, two, and three dimensions. Computer Methods in Applied Mechanics and Engineering, 2021, 387: 114115

[20] Manni C, Sande E, Speleers H. Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations. Computer Methods in Applied Mechanics and Engineering, 2022, 389: 114260

[21] Cheng L, Nicolas J. Free vibration analysis of a cylindrical shell-circular plate system with general coupling and various boundary conditions. Journal of Sound and Vibration, 1992, 155(2): 231–247

[22] Ertas B, John V. The influence of same-sign cross-coupled stiffness on rotordynamics. Journal of Vibration and Acoustics-Transactions of the ASME, 2007, 129(1): 24–31

[23] Cazzani A, Stochino F, Turco E. An analytical assessment of finite element and isogeometric analyses of the whole spectrum of Timoshenko beams. Journal of Applied Mathematics and Mechanics, 2016, 96(10): 1220–1244

[24] Genta G. Consistent matrices in rotor dynamic. Meccanica, 1985, 20(3): 235–248

[25] PieglLTillerW. The NURBS Book. Berlin: Springer Science & Business Media, 2012

[26] Yücel E, Saruhan H. Design optimization of rotor-bearing system considering critical speed using Taguchi method. Proceedings of the Institution of Mechanical Engineers Part E––Journal of Process Mechanical Engineering, 2017, 231(2): 138–146

RIGHTS & PERMISSIONS

Higher Education Press