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Research Papers

Influence of Rotor Suspension Anisotropy on Oil Film Instability

[+] Author and Article Information
Francesco Sorge

DIID,
Polytechnic School,
University of Palermo,
Viale delle Scienze,
Palermo 90128, Italy
e-mail: francesco.sorge@unipa.it

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 24, 2017; final manuscript received December 15, 2017; published online February 9, 2018. Assoc. Editor: Patrick S. Keogh.

J. Vib. Acoust 140(3), 031010 (Feb 09, 2018) (13 pages) Paper No: VIB-17-1172; doi: 10.1115/1.4038946 History: Received April 24, 2017; Revised December 15, 2017

A crucial problem of turbomachinery is the oil film instability on increasing the angular speed, which is correlated with the asymmetry of the bearing stiffness matrix and resembles the hysteretic instability somehow. As a beneficial effect is exerted on the latter by the anisotropy of the support stiffness, some favorable effects have been recently found by the author also for the former, whence a systematic analysis has been undertaken. The instability thresholds may be detected by the usual conventional methods, but a detailed analysis may be carried out by closed-form procedures in the hypothesis of symmetry of the rotor-shaft-support system, which condition approaches the real working of turbomachines quite often. Altogether, the results point out an improvement of the rotor stability for low Sommerfeld numbers by softening and locking the support stiffness in the vertical and horizontal directions, respectively. Nonetheless, the partial support release on one plane implies lower instability thresholds for large Sommerfeld numbers, but this drawback may be obviated by a sort of “two-mode” stiffness management, with some vertical flexibility for heavy loads and full blocking for light loads. Otherwise, it is possible to combine the anisotropic supports with journal bearing types that offer favorable stability behavior in the range of large Sommerfeld numbers. Basing on approximate but realistic models, the present analysis elucidates the changes of the rotor-shaft unstable trend on varying the external stiffness of the supports and gives tools for a rapid calculation of the expected instability thresholds.

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References

Childs, D. , 1993, Turbomachinery Rotordynamics, Wiley, New York.
Rao, J. S. , 1996, Rotor Dynamics, New Age International, New Delhi, India.
Lund, J. W. , 1965, “ Rotor Bearings Dynamic Design Technology—Part III,” Design Hand Book for Fluid Film Type Bearings, Mechanical Technology Incorporated, Albany, NY.
Luneno, J. C. , and Aidanpää, J. O. , 2010, “ Use of Nonlinear Journal-Bearing Impedance Description to Evaluate Linear Analysis of the Steady-State Imbalance Response for a Rigid Symmetric Rotor Supported by Two Identical Finite Length Hydrodynamic Journal Bearings at High Eccentricities,” Nonlinear Dyn., 62(1–2), pp. 151–165. [CrossRef]
Sawicki, J. T. , and Rao, T. V. V. L. N. , 2004, “ A Nonlinear Model for the Prediction of Dynamic Coefficients in a Hydrodynamic Journal Bearing,” Int. J. Rotating Mach., 10(6), pp. 507–513. [CrossRef]
Qiu, Z. L. , and Tien, A. K. , 1997, “ Identification of Sixteen Force Coefficients of Two Journal Bearings From Impulse Responses,” Wear, 212(2), pp. 206–212. [CrossRef]
Meruane, V. , and Pascual, R. , 2008, “ Identification of Nonlinear Dynamic Coefficients in Plain Journal Bearings,” Tribol. Int., 41(8), pp. 743–754. [CrossRef]
Chasalevris, A. , and Papadopoulos, C. , 2014, “ A Novel Semi-Analytical Method for the Dynamics of Nonlinear Rotor-Bearing Systems,” Mech. Mach. Theory, 72, pp. 39–59. [CrossRef]
Kiciński, J. , and Zywica, G. , 2014, Steam Microturbines in Distributed Cogeneration, Springer, Berlin. [CrossRef]
Li, W. , Yang, Y. , Sheng, D. , and Chen, J. , 2011, “ A Novel Nonlinear Model of Rotor/Bearing/Seal System and Numerical Analysis,” Mech. Mach. Theory, 46(5), pp. 618–631. [CrossRef]
Gunter , E. I., Jr. , and Trumpler, P. R. , 1969, “ The Influence of Internal Friction on the Stability of High Speed Rotors With Anisotropic Supports,” ASME J. Eng. Ind., 91(4), pp. 1105–1113. [CrossRef]
Newkirk, B. L. , 1924, “ Shaft Whipping,” Gen. Electr. Rev., 27, pp. 169–178.
Sorge, F. , 2017, “ Stability Analysis of Rotor Whirl Under Nonlinear Internal Friction by a General Averaging Approach,” J. Vib. Control, 23(5), pp. 808–826. [CrossRef]
Sorge, F. , and Cammalleri, M. , 2012, “ On the Beneficial Effect of Rotor Suspension Anisotropy on Viscous-Dry Hysteretic Instability,” Meccanica, 47(7), pp. 1705–1722. [CrossRef]
Sorge, F. , 2016, “ Preventing the Oil Film Instability in Rotor-Dynamics,” J. Phys. Conf. Ser., 744(1), p. 012153. [CrossRef]
Ocvirk, F. , 1952, “Short-Bearing Approximation for Full Journal Bearings,” National Advisory Committee for Aeronautics, Washington, DC, Technical Note No. 2808.
Nicholas, J. C. , and Allaire, P. E. , 1978, “ Analysis of Step Journal Bearings–Finite Length, Stability,” ASLE Trans., 23(2), pp. 197–207. [CrossRef]
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Figures

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Fig. 1

Scheme of the rotor-shaft-support system. The shaft segments are massless and flexible; the two rotors are heavy and rigid.

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Fig. 2

Maps (Ω,ε) of instability regions for cylindrical and conical modes (indicated by circles and triangles, respectively). Data: 3EI/l3 = 100khe, 3EI/(χGAl2) = 0.3, ti/l = 1.5, te/l = 1, re/l = 1.5 (a) kex = kix = 100khe, key = kiy = 100khe and (b) kex = kix = 100khe, key = kiy = 0.1khe.

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Fig. 3

Thresholds of Ω and Γ for cylindrical and conical modes (indicated by circles and triangles, respectively). Data: 3EI/(l3khe) = ∞, kex/khe = kix/khe = ∞, key/khe = kiy/khe = 0.1 (other data like in Fig. 2).

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Fig. 4

Correlation between Ky and values of Ω and Γ at the starting point (ε = 0) of the critical curves for cylindrical modes (all data like in Fig. 3, save Ky)

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Fig. 5

Correlation between Ky and values of ε and Γ at the asymptotes (Ω → ∞) of the critical curves for cylindrical modes (all data like in Fig. 3, save Ky)

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Fig. 6

Correlation between Ky and values of Ω and Γ at the starting point (ε = 0) of the critical curves for conical modes (all data like in Fig. 3, save Ky)

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Fig. 7

Correlation between Ky and values of Ω and Γ at the final point (ε = 1) of the critical curves for conical modes (all data like in Fig. 3, save Ky)

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Fig. 8

Map of instability thresholds (Ω versus modified Sommerfeld number), for the cylindrical and conical modes of plain bearings (continuous line) and step bearings (dots). Circles: cylindrical mode. Triangles: conical modes. Data: 3EI/(l3khe) = ∞, kex/khe = kix/khe = ∞, key/khe = kiy/khe = 0.1. Other data of plain bearing like in Fig. 2. Data of step bearing: see Fig. 6 of Ref. [17].

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Fig. 9

Map of instability thresholds (Ω versus modified Sommerfeld number), for the cylindrical and conical modes of step bearings. Circles: cylindrical mode. Triangles: conical modes. Data: 3EI/(l3khe) = ∞, kex/khe = kix/khe = ∞, key/khe = kiy/khe = 0.1 (full circles and triangles) or key/khe = kiy/khe = ∞ (empty circles and triangles). Other data: see Fig. 6 of Ref. [17].

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Fig. 10

(a) Transient motion around the equilibrium position of the left rotor of Fig. 1 and (b) final steady orbits. Data: eL/ce = 1, Ω = 0.7, ε = 0.7, u2x,equil./ce = 0.438, u2y,equil./ce = –1.546, 3EI/(l3khe) = ∞, kex/khe = kix/khe = 5, key/khe = kiy/khe = 1.

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