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Abstract

Main energy conversion machinery used and to be used in cogeneration systems are schematically described. Some assets of the distributed generation are pointed out and small-scale cogeneration systems designed for energy units of distributed cogeneration are described.

In the small scale, turbines and bearings are a source of specific problems connected with securing stable rotor operation. Accepted has been two kinds of high speed micro-turbines of electric power about 3 KW with multistage axial and radial rotors supported on foil bearings. A concept which becomes more and more attractive takes into account a low-boiling agent, which is normally used in the thermal cycle of the micro-turbine, as the lubricating liquid in the bearings (so-called ORC based systems). Of some importance is the operation of these machines at a low noise emission level, sine being parts of the household equipment they could disturb the calm of the residents. The scope of the present article is limited to the discussion of dynamic characteristics of the selected design. The properties of the rotor combined with slide bearings (foil bearings in this particular case) were taken under investigation. A combination of this type is a certain novelty since a typical modal analysis of such objects refers to a rotor itself. Analysing the dynamic state of the "home" power plants requires qualitatively novel research tools.

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Authors and Affiliations

Jan Kiciński
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Abstract

The considerations presented in the paper relate to one of the most intriguing phenomena, which is the development of oil whirls and oil whips in rotors with journal bearings. This effect is sometimes referred to as flutter, as its origin is in some relation to self-exciting vibrations of the system. Despite the fact that the flutter has been an object of investigation in numerous research centres all over the world, its nature has not been sufficiently recognized yet. The present paper delivers a description of particular phases of development of the hydrodynamic instability and proposes diagnostic determinants for this state. The object of investigations also included bearings with hybrid lubrication and siphon pockets in the oil gaps. The answer has been received to the question whether the self-exciting vibrations in rotating machines can be avoided, or reduced by means of additional oil supply having the form of siphon oil.

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Authors and Affiliations

J. Kiciński
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Abstract

Despite many years of development in the field of rotor dynamics, many issues still need to be resolved. This is due to the fact that turbomachines, even those with low output power, have a very complex design. The author of this article would like to signal these issues in the form of several questions, to which there are no precise answers. The questions are as follows: How can we build a coherent dynamic model of a turbomachine whose some subsystems have non-linear characteristics? How can we consider the so-called prehistory in our analysis, namely, the relation between future dynamic states and previous ones? Is heuristic modelling the future of rotor dynamics? What phenomena may occur when the stability limit of the system is exceeded? The attempt to find answers to these questions constitutes the subject of this article. There are obviously more similar questions, which encourage researchers from all over the world to further their research.
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Bibliography

  1.  M.C. Shaw and T.J. Nussdorfer, “An analysis of the full-floating journal bearing,” NACA, Tech. Rep. RM-E7A28a, 1947.
  2.  C. Kettleborough, “Frictional experiments on lightly-loaded fully floating journal bearings,” Aust. J. Appl. Sci., vol. 5, pp. 211–220, 1954.
  3.  J. Dworski, “High-speed rotor suspension formed by fully floating hydrodynamic radial and thrust bearings,” J. Eng. Gas Turbines Power, vol. 86, no. 2, pp. 149–160, 1964.
  4.  M. Harada and J. Tsukazaki, “The steady-state characteristics of a hydrostatic thrust bearing with a floating disk,” J. Tribol., vol. 111, no. 2, pp. 352–357, Apr 1989, doi: 10.1115/1.3261921.
  5.  M. Fischer, A. Mueller, B. Rembold, and B. Ammann, “Numerical investigation of the flow in a hydrodynamic thrust bearing with floating disk,” J. Eng. Gas Turbines Power, vol. 135, 2013, doi: 10.1115/1.4007775.
  6.  S. Dousti and P. Allaire, “A thermohydrodynamic approach for single-film and double-film floating disk fixed thrust bearings verified with experiment,” Tribol. Int., vol. 140, p. 105858, Dec 2019.
  7.  H. Engel, “Berechung der Strömung, der Drücke und Temperaturen in Radial-Axialbund-Gleitlagern mit Hilfe eines Finite-Elemente-Programms,” Ph.D. thesis, Universität Stuttgart, 1992.
  8.  T. Hagemann, H. Blumenthal, C. Kraft, and H. Schwarze, “A study on energetic and hydraulic interaction of combined journal and thrust bearings,” in Proceedings of ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, no. GT2015‒43460, 2015, pp. 1–11.
  9.  G.H. Jang, S.H. Lee, and H.W. Kim, “Finite element analysis of the coupled journal and thrust bearing in a computer hard disk drive,” Tribol., vol. 128, pp. 335–340, 2006, doi: 10.1115/1.2162918.
  10.  G. Xiang, Y. Han, R. Chen, J. Wang, X. Ni, and K. Xiao, “A hydrodynamic lubrication model and comparative analysis for coupled microgroove journal-thrust bearings lubricated with water,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., vol. 234, no. 11, pp. 1755–1770, Nov 2019.
  11.  J.-C. Luneno, “Coupled vibrations in horizontal and vertical rotor-bearings systems,” Ph.D. thesis, Luleå University of Technology, 2010.
  12.  C. Ziese, C. Daniel, E. Woschke, and H. Mostertz, “Hochlaufsimulation eines semi-floating gelagerten ATL-Rotors mit schwimmender Axiallagerscheibe,” in 14. Magdeburger Maschinenbautage (24.–25.09.2019), Sep. 2019, pp. 105–112.
  13.  H.G. Elrod, “A cavitation algorithm,” J. Tribol., vol. 103, no. 3, pp. 350–354, 1981.
  14.  S. Nitzschke, E. Woschke, D. Schmicker, and J. Strackeljan, “Regularised cavitation algorithm for use in transient rotordynamic analysis,” Int. J. Mech. Sci., vol. 113, pp. 175–183, 2016.
  15.  S. Nitzschke, “Instationäres Verhalten schwimmbuchsengelagerter Rotoren unter Berücksichtigung masseerhaltender Kavitation,” Ph.D. thesis, Otto-von-Guericke Universität Magdeburg, 2016.
  16.  C. Daniel, “Simulation von gleit-und wälzgelagerten Systemen auf Basis eines Mehrkörpersystems für rotordynamische Anwendungen,” Ph.D. thesis, Otto-von-Guericke Universität Magdeburg, 2013.
  17.  C. Ziese, E. Woschke, and S. Nitzschke, “Tragdruck- und Schmierstoffverteilung von Axialgleitlagern unter Berücksichtigung von mas- seerhaltender Kavitation und Zentrifugalkraft,” in 13. Magdeburger Maschinenbautage, 2017, pp. 312–323.
  18.  A. Kumar and J.F. Booker, “A finite element cavitation algorithm,” J. Tribol., vol. 113, no. 2, pp. 279–284, 1991.
  19.  “MAN turbochargers TCA series floating disk thrust bearing,” https://turbocharger.man-es.com/docs/default-source/ shopwaredocuments/ tca-turbochargerf451d068cde04720bdc9b 8e95b7c0f8e.pdf, accessed: 2020‒10‒09.
  20.  “KBB turbochargers ST27 series f loating disk thrust bearing,” https://kbb-turbo.com/turbocharger-product-series/st27-series, accessed: 2020-10-09.
  21.  C. Irmscher, S. Nitzschke, and E. Woschke, “Transient thermohydrodynamic analysis of a laval rotor supported by journal bearings with respect to calculation times,” in SIRM 2019 – 13th International Conference on Dynamics of Rotating Machines, 2019, pp. Paper–ID SIRM2019–25.
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Authors and Affiliations

Jan Kiciński
1

  1. Institute of Fluid-Flow Machinery, Polish Academy of Sciences, ul. Fiszera 14, Gdańsk 80-231, Poland
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Abstract

Squeeze film dampers (SFDs) are commonly used in turbomachinery in order to introduce external damping, thereby reducing rotor vibrations and acoustic emissions. Since SFDs are of similar geometry as hydrodynamic bearings, the REYNOLDS equation of lubrication can be utilised to predict their dynamic behaviour. However, under certain operating conditions, SFDs can experience significant fluid inertia effects, which are neglected in the usual REYNOLDS analysis. An algorithm for the prediction of these effects on the pressure build up inside a finite-length SFD is therefore presented. For this purpose, the REYNOLDS equation is extended with a first-order perturbation in the fluid velocities to account for the local and convective inertia terms of the NAVIER-STOKES equations. Cavitation is taken into account by means of a mass conserving two-phase model. The resulting equation is then discretized using the finite volume method and solved with an LU factorization. The developed algorithm is capable of calculating the pressure field, and thereby the damping force, inside an SFD for arbitrary operating points in a time-efficient manner. It is therefore suited for integration into transient simulations of turbo machinery without the need for bearing force coefficient maps, which are usually restricted to circular centralized orbits. The capabilities of the method are demonstrated on a transient run-up simulation of a turbocharger rotor with two semi-floating bearings. It can be shown that the consideration of fluid inertia effects introduces a significant shift of the pressure field inside the SFDs, and therefore the resulting damper force vector, at high oil temperatures and high rotational speeds. The effect of fluid inertia on the kinematic behaviour of the whole system on the other hand is rather limited for the examined rotor.
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Bibliography

  1.  M.B. Banerjee, R. Shandil, S. Katyal, G. Dube, T. Pal, and K. Banerjee, “A nonlinear theory of hydrodynamic lubrication,” J. Math. Anal. Appl., vol. 117, no. 1, pp. 48–56, 1986.
  2.  S. Hamzehlouia and K. Behdinan, “Squeeze film dampers supporting high-speed rotors: Fluid inertia effects,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., vol. 234, no. 1, pp. 18–32, 2020.
  3.  M. Ramli, J. Ellis, and J. Roberts, “On the computation of inertial coefficients in squeeze-film bearings,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., vol. 201, no. 2, pp. 125–131, 1987, doi: 10.1243/PIME_PROC_1987_201_095_02.
  4.  E. Reinhardt and J. Lund, “Influence of fluid inertia on the dynamic properties of journal bearings.” J. Lubr. Technol., vol. 97 Ser F, no. 2, pp. 159–167, 1975.
  5.  A.Z. Szeri, A.A. Raimondi, and A. Giron-Duarte, “Linear Force Coefficients for Squeeze-Film Dampers,” J. Lubr. Technol., vol. 105, no. 3, pp. 326–334, 07 1983.
  6.  A.Z. Szeri, Fluid Film Lubrication: Theory and Design. Cambridge University Press, 1998.
  7.  Z. Guo, T. Hirano, and R.G. Kirk, “Application of CFD analysis for rotating machinery: Part 1 — hydrodynamic, hydrostatic bearings and squeeze film damper,” in Volume 4: Turbo Expo 2003. ASME, 2003, doi: 10.1115/gt2003-38931.
  8.  C. Xing, M.J. Braun, and H. Li, “A three-dimensional navierstokes- based numerical model for squeeze film dampers. part 2—ef- fects of gaseous cavitation on the behavior of the squeeze film damper,” Tribol. Trans., vol. 52, no. 5, pp. 695–705, Sep 2009, doi: 10.1080/10402000902913311.
  9.  V. Constantinescu, Laminar Viscous Flow. Berlin Heidelberg: Springer Science & Business Media, 2012.
  10.  J. Gehannin, M. Arghir, and O. Bonneau, “Complete squeezefilm damper analysis based on the “bulk flow” equations,” Tribol. Trans., vol. 53, no. 1, pp. 84–96, 2009, doi: 10.1080/10402000903226382.
  11.  S. Lang and S. Verlag, Effiziente Berechnung von Gleitlagern und Dichtspalten in Turbomaschinen, ser. Forschungsberichte zur Fluidsys- temtechnik. Shaker Verlag, 2018.
  12.  H. Peeken and J. Benner, “Beeinträchtigung des Druckaufbaus in Gleitlagern durch Schmierstoffverschäumung,” in Gleit- und Wäl- zlagerungen: Gestaltung, Berechnung, Einsatz; Tagung Neu-Ulm, 14. und 15. März 1985 / VDI-Ges. Entwicklung, Konstruktion, Vertrieb. – (VDI-Berichte; 549), 2013, pp. 373–397.
  13.  Ü. Mermertas, “Nichtlinearer Einfluss von Radialgleitlagern auf die Dynamik schnelllaufender Rotoren, Dissertation,” Düren, Aachen, 2003.
  14.  E. Woschke, C. Daniel, and S. Nitzschke, “Excitation mechanisms of non-linear rotor systems with floating ring bearings – simulation and validation,” Int. J. Mech. Sci., vol. 134, pp. 15‒27, 2017, doi: 10.1016/j.ijmecsci.2017.09.038.
  15.  R. Eymard, G. Thierry, and R. Herbin, “Handbook of numerical analysis,” vol. 7, pp. 731–1018, 01 2000.
  16.  V.V. Moca, A. Nagy-Dăbâcan, H. Bârzan, and R. C. Mure¸san, “Superlets: time-frequency super-resolution using wavelet sets,” bioRxiv, 2019.
  17.  S. Hamzehlouia and K. Behdinan, “A study of lubricant inertia effects for squeeze film dampers incorporated into highspeed turboma- chinery,” Lubricants, vol. 5, p. 43, 10 2017, doi: 10.3390/lubricants5040043.
  18.  L. San Andrés and J. Vance, “Effects of fluid inertia and turbulence on the force coefficients for squeeze film dampers,” J. Eng. Gas Turbines Power, vol. 108, 04 1986, doi: 10.1115/1.3239908.
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Authors and Affiliations

Thomas Drapatow
1
Oliver Alber
2
Elmar Woschke
1
ORCID: ORCID

  1. Institute of Mechanics, Otto von Guericke University Magdeburg, 39106 Magdeburg, Germany
  2. MAN Energy Solutions SE, 86153 Augsburg, Germany
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Abstract

Full-floating ring bearings are state of the art at high speed turbomachinery shafts like in turbochargers. Their main feature is an additional ring between shaft and housing leading to two fluid films in serial arrangement. Analogously, a thrust bearing with an additional separating disk between journal collar and housing can be designed. The disk is allowed to rotate freely only driven by drag torques, while it is radially supported by a short bearing against the journal. This paper addresses this kind of thrust bearing and its implementation into a transient rotor dynamic simulation by solving the Reynolds PDE online during time integration. Special attention is given to the coupling between the different fluid films of this bearing type. Finally, the differences between a coupled and an uncoupled solution are discussed.
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Bibliography

  1. M.C. Shaw and T.J. Nussdorfer, “An analysis of the full-floating journal bearing,” NACA, Tech. Rep. RM-E7A28a, 1947.
  2. C. Kettleborough, “Frictional experiments on lightly-loaded fully floating journal bearings,” Aust. J. Appl. Sci., vol. 5, pp. 211–220, 1954.
  3. J. Dworski, “High-speed rotor suspension formed by fully floating hydrodynamic radial and thrust bearings,” J. Eng. Gas Turbines Power, vol. 86, no. 2, pp. 149–160, 1964.
  4. M. Harada and J. Tsukazaki, “The steady-state characteristics of a hydrostatic thrust bearing with a floating disk,” J. Tribol., vol. 111, no. 2, pp. 352–357, Apr 1989, doi: 10.1115/1.3261921.
  5. M. Fischer, A. Mueller, B. Rembold, and B. Ammann, “Numerical investigation of the flow in a hydrodynamic thrust bearing with floating disk,” J. Eng. Gas Turbines Power, vol. 135, 2013, doi: 10.1115/1.4007775.
  6. S. Dousti and P. Allaire, “A thermohydrodynamic approach for single-film and double-film floating disk fixed thrust bearings verified with experiment,” Tribol. Int., vol. 140, p. 105858, Dec 2019.
  7. H. Engel, “Berechung der Strömung, der Drücke und Temperaturen in Radial-Axialbund-Gleitlagern mit Hilfe eines Finite-Elemente-Programms,” Ph.D. thesis, Universität Stuttgart, 1992.
  8. T. Hagemann, H. Blumenthal, C. Kraft, and H. Schwarze, “A study on energetic and hydraulic interaction of combined journal and thrust bearings,” in Proceedings of ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, no. GT2015‒43460, 2015, pp. 1–11.
  9. G.H. Jang, S.H. Lee, and H.W. Kim, “Finite ele- ment analysis of the coupled journal and thrust bearing in a computer hard disk drive,” J. Tribol., vol. 128, pp. 335–340, 2006, doi: 10.1115/1.2162918.
  10. G. Xiang, Y. Han, R. Chen, J. Wang, X. Ni, and K. Xiao, “A hydrodynamic lubrication model and comparative analysis for coupled microgroove journal-thrust bearings lubricated with water,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., vol. 234, no. 11, pp. 1755–1770, Nov 2019.
  11. J.-C. Luneno, “Coupled vibrations in horizontal and vertical rotor-bearings systems,” Ph.D. thesis, Luleå University of Technology, 2010.
  12. C. Ziese, C. Daniel, E. Woschke, and H. Mostertz, “Hochlaufsimulation eines semi-floating gelagerten ATL-Rotors mit schwimmender Axiallagerscheibe,” in 14. Magdeburger Maschinen- bautage (24.–25.09.2019), Sep. 2019, pp. 105–112.
  13. H.G. Elrod, “A cavitation algorithm,” J. Tribol., vol. 103, no. 3, pp. 350–354, 1981.
  14. S. Nitzschke, E. Woschke, D. Schmicker, and J. Strackeljan, “Regularised cavitation algorithm for use in transient rotordynamic analysis,” Int. J. Mech. Sci., vol. 113, pp. 175–183, 2016.
  15. S. Nitzschke, “Instationäres Verhalten schwimmbuchsengelagerter Rotoren unter Berücksichtigung masseerhaltender Kavitation,” Ph.D. thesis, Otto-von-Guericke Universität Magdeburg, 2016.
  16. C. Daniel, “Simulation von gleit-und wälzgelagerten Systemen auf Basis eines Mehrkörpersystems für rotordynamische Anwendungen,” Ph.D. thesis, Otto-von-Guericke Universität Magdeburg, 2013.
  17. C. Ziese, E. Woschke, and S. Nitzschke, “Tragdruckund Schmierstoffverteilung von Axialgleitlagern unter Berücksichtigung von masseerhaltender Kavitation und Zentrifugalkraft,” in Magdeburger Maschinenbautage, 2017, pp. 312–323.
  18. A. Kumar and J.F. Booker, “A finite element cavitation algorithm,” J. Tribol., vol. 113, no. 2, pp. 279–284, 1991.
  19. “MAN turbochargers TCA series floating disk thrust bearing,” https://turbocharger.man-es.com/docs/default-source/ shopwaredocuments/tca-turbochargerf451d068cde04720bdc9b 8e95b7c0f8e.pdf, accessed: 2020‒10‒09.
  20. “KBB turbochargers ST27 series f loating disk thrust bearing,” https://kbb-turbo.com/turbocharger-product-series/ st27-series, accessed: 2020-10-09.
  21. C. Irmscher, S. Nitzschke, and E. Woschke, “Transient thermohydrodynamic analysis of a laval rotor supported by journal bearings with respect to calculation times,” in SIRM 2019 – 13th International Conference on Dynamics of Rotating Machines, 2019, pp. Paper–ID SIRM2019–25.
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Authors and Affiliations

Steffen Nitzschke
1
Christian Ziese
1
Elmar Woschke
1
ORCID: ORCID

  1. Institute of Mechanics, Otto-von-Guericke University, 39106 Magdeburg, Germany
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Abstract

Electro-dynamic passive magnetic bearings are now viewed as a feasible option when looking for support for high-speed rotors. Nevertheless, because of the skew-symmetrical visco-elastic properties of such bearings, they are prone to operational instability. In order to avoid this, the paper proposes the addition of external damping into the newly designed vibrating laboratory rotor-shaft system. This may be achieved by means of using simple passive dampers that would be found among the components of the electro-dynamic bearing housings along with magnetic dampers, which satisfy the operational principles of active magnetic bearings. Theoretical investigations are going to be conducted by means of a structural computer model of the rotor-shaft under construction, which will take into consideration its actual dimensions and material properties. The additional damping magnitudes required to stabilize the most sensitive lateral eigenmodes of the object under consideration have been determined by means of the Routh-Hurwitz stability criterion.

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Authors and Affiliations

T. Szolc
F. Falkowski
M. Henzel
P. Kurnyta-Mazurek
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Abstract

In this paper, a new application of the Numerical Assembly Technique is presented for the balancing of linear elastic rotor-bearing systems with a stepped shaft and arbitrarily distributed mass unbalance. The method improves existing balancing techniques by combining the advantages of modal balancing with the fast calculation of an efficient numerical method. The rotating stepped circular shaft is modelled according to the Rayleigh beam theory. The Numerical Assembly Technique is used to calculate the steady-state harmonic response, eigenvalues and the associated mode shapes of the rotor. The displacements of a simulation are compared to measured displacements of the rotor-bearing system to calculate the generalized unbalance for each eigenvalue. The generalized unbalances are modified according to modal theory to calculate orthogonal correction masses. In this manner, a rotor-bearing system is balanced using a single measurement of the displacement at one position on the rotor for every critical speed. Three numerical examples are used to show the accuracy and the balancing success of the proposed method.
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Bibliography

  1.  J. Tessarzik, Flexible rotor balancing by the exact point speed influence coefficient method. Latham: Mechanical Technology Incorporated, 1972.
  2.  P. Gnielka, “Modal balancing of flexible rotors without test runs: An experimental investigation,” Journal of Vibrations, vol. 90, no. 2, pp. 152–170, 1982.
  3.  K. Federn, “Grundlagen einer systematischen Schwingungsentstörung wellenelastischer Rotoren,” VDI Bericht, vol. 24, pp.  9‒25, 1957.
  4.  A. G. Parkinson and R. E. D. Bishop, “Residual vibration in modal balancing,” Journal of Mechanical Engineering Science, vol. 7, pp. 33–39, 1965.
  5.  W. Kellenberger, “Das Wuchten elastischer Rotoren auf zwei allgemeinelastischen Lagern,” Brown Boveri Mitteilungen, vol. 54, pp. 603– 617, 1967.
  6.  A.-C. Lee, Y.-P. Shih, and Y. Kang, “The analysis of linear rotor bearing systems: A general Transfer Matrix Method,” Journal of Vibration and Accoustics, vol. 115, no. 4, pp. 490–497, 1993.
  7.  J.-S. Wu and H. M. Chou, “A new approach for determining the natural frequency of mode shapes of a uniform beam carrying any number of sprung masses,” Journal of Sound and Vibration, vol.  220, no. 3, pp. 451–468, 1999.
  8.  J.-S. Wu, F.-T. Lin, and H.-J. Shaw, “Analytical solution for whirling speeds and mode shapes of a distributed-mass shaft with arbitrary rigid disks,” Journal of Applied Mechanics, vol. 81, no. 3, pp. 034 503–1–034 503–10, 2014.
  9.  M. Klanner, M.S. Prem, and K. Ellermann, “Steady-state harmonic vibrations of a linear rotor- bearing system with a discontinuous shaft and arbitrarily distributed mass unbalance,” in Proceedings of ISMA2020 International Conference on Noise and Vibration Engineering and USD2020 International Conference on Uncertainty in Structural Dynamics, 2020, pp. 1257–1272.
  10.  M. Klanner and K. Ellermann, “Steady-state linear harmonic vibrations of multiple-stepped Euler-Bernoulli beams under arbitrarily distributed loads carrying any number of concentrated elements,” Applied and Computational Mechanics, vol. 14, no. 1, pp. 31–50, 2019.
  11.  M.B. Deepthikumar, A.S. Sekhar, and M.R. Srikanthan, “Modal balancing of flexible rotors with bow and distributed unbalance,” Journal of Sound and Vibration, vol. 332, pp. 6216‒6233, 2013.
  12.  O.A. Bauchau and J.I. Craig, Structural Analysis – With Applications to Aerospace Structures. Heidelberg: Springer Verlag, 2009.
  13.  R.E.D. Bishop and A.G. Parkinson, “On the isolation of modes in balancing of flexible shafts,” Proc. Inst. Mech. Eng., vol. 117, pp. 407– 426, 1963.
  14.  X. Rui, G. Wang, Y. Lu, and L. Yunm, “Transfer Matrix Method for linear multibody systems,” Multibody Syst. Dyn., vol.  19, pp. 179–207, 2008.
  15.  I.N. Bronstein, K.A. Semendjajew, and E. Zeidler, Taschenbuch der Mathematik. Stuttgard: Teubner, 1996.
  16.  D. Bestle, L. Abbas, and X. Rui, “Recursive eigenvalue search algorithm for transfer matrix method of linear flexible multibody systems,” Multibody Syst. Dyn., vol. 32, pp. 429–444, 2013.
  17.  B. Xu and L. Qu, “A new practical modal method for rotor balancing,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., vol. 215, pp.  179–190, 2001.
  18.  J. Tessarzik, Flexible rotor balancing by the influence coefficient method. Part 1: Evaluation of the exact point speed and least squares procedure. Latham: Mechanical Technology Incorporated, 1972.
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Authors and Affiliations

Georg Quinz
1
Marcel S. Prem
1
Michael Klanner
1
ORCID: ORCID
Katrin Ellermann
1

  1. Graz University of Technology, Institute of Mechanics, Kopernikusgasse 24/IV, 8010 Graz, Austria
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Abstract

Vibration in rotating machinery leads to a series of undesired effects, e.g. noise, reduced service life or even machine failure. Even though there are many sources of vibrations in a rotating machine, the most common one is mass unbalance. Therefore, a detailed knowledge of the system behavior due to mass unbalance is crucial in the design phase of a rotor-bearing system. The modelling of the rotor and mass unbalance as a lumped system is a widely used approach to calculate the whirling motion of a rotor-bearing system. A more accurate representation of the real system can be found by a continuous model, especially if the mass unbalance is not constant and arbitrarily oriented in space. Therefore, a quasi-analytical method called Numerical Assembly Technique is extended in this paper, which allows for an efficient and accurate simulation of the unbalance response of a rotor-bearing system. The rotor shaft is modelled by the Rayleigh beam theory including rotatory inertia and gyroscopic effects. Rigid discs can be mounted onto the rotor and the bearings are modeled by linear translational/rotational springs/dampers, including cross-coupling effects. The effect of a constant axial force or torque on the system response is also examined in the simulation.
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Bibliography

  1.  J.W. Lund and F.K. Orcutt, “Calculations and Experiments on the Unbalance Response of a Flexible Rotor,” J. Eng. Ind., vol. 89, no. 4, pp. 785–796, 1967.
  2.  A. Vollan and L. Komzsik, Computational Techniques of Rotor Dynamics with the Finite Element Method. Boca Raton: CRC Press, 2012.
  3.  J.S. Rao, Rotor Dynamics. New Delhi: New Age International, 1996.
  4.  A.-C. Lee and Y.-P. Shih, “The Analysis of Linear Rotor-Bearing Systems: A General Transfer Matrix Method,” J. Vib. Acoust., vol. 115, no. 4, pp. 490–497, 1993.
  5.  T. Yang and C. Lin, “Estimation of Distributed Unbalance of Rotors,” J. Eng. Gas Turbines Power, vol. 124, no. 4, pp. 976‒983, 2002.
  6.  J.-S. Wu and H.-M. Chou, “A new approach for determining the natural frequencies and mode shapes of a uniform beam carrying any number of sprung masses,” J. Sound Vib., vol. 81, no. 3, pp.  1–10, 1999.
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Authors and Affiliations

Michael Klanner
1
ORCID: ORCID
Marcel S. Prem
1
Katrin Ellermann
1

  1. Graz University of Technology, Institute of Mechanics, Kopernikusgasse 24/IV, 8010 Graz, Austria

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