Analysis of a complete model of rotating machinery excited by magnetic actuator system

Abstract

Rotating machines have a wide range of application involving shafts rotating at high speeds that must have high confidence levels of operation. Therefore, the dynamic behavior analysis of such rotating systems is required to establish operational patterns of the equipment, providing the basis for controller development in order to reduce vibrations or even to control oil instabilities in lubricated bearings. A classical technique applied in parameter identification of machines and structures is the modal analysis, which consists of applying a perturbation force into the system and then to measure its response. However, there are mainly two problems in modal analysis concerning the excitation of rotating systems. First, there are limitations to the excitation of systems with rotating shafts when using impact hammers or shakers, due to friction, undesired tangential forces, and noise that can be introduced in the system response. The second problem relies in the difficulty of exciting backward whirl modes, an inherent characteristic from these systems. Therefore, the study of a non-contact technique of external excitation, also capable of exciting backward whirl modes, becomes of high interest. In this sense, this article deals with the study and modeling of a magnetic actuator, used as an external excitation source for a rotating machine, mainly in backward whirl mode. Special attention is given to the actuator model and its interaction with the rotor system. Differently from previous works with similar proposal, which uses current and air gap measurements, here the external excitation force control is based on the magnetic field directly measured by hall sensor positioned in the pole center of the magnetic actuator core. The magnetic actuator design was completely developed for this purpose, opening different paths to experimental application of this device, for example, fault detection analysis based on directional modes. It is also presented a comparison between the numerical simulations and practical tests obtained from a rotor test rig and an experimental evidence of the backward whirl was accomplished based on the numerical simulation results.

Keywords

Directional frequency response function forward whirl backward whirl magnetic actuator lubricated bearings

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References

Vance

. Rotordynamics of turbomachinery, 1st edn. New York, United States: John Wiley & Sons, 1988, p.400–400.

Krämer

. Dynamics of rotors and foundations, 1st edn. New York: Springer-Verlag, 1993, p.383–383.

Childs

. Turbomachinery rotordynamics: phenomena, modeling, and analysis, 1st edn. New York: Wiley-Interscience, 1993, p.496–496.

Nelson

McVaugh

. The dynamics of rotor-bearing systems using finite elements. Trans ASME J Eng Ind 1976; 98: 593–600.

Nelson

. A finite rotating shaft element using timoshenko beam theory. J Mech Des 1980; 102: 793–803.

Lund

. Spring and damping coefficients for the tilting pad journal bearing. ASLE Trans 1964; 7: 342–352.

Silva EL. Dinâmica de rotore: modelo matemático de mancais hidrodinâmicos. Dissertation, Federal University of Paraná, Brazil, 2004. In Portuguese.

Machado TH and Cavalca KL. Evaluation of dynamic coefficients of fluid journal bearings with different geometries. In: Proceedings of the 20th Brazilian congress of mechanical engineering, COBEM 2009, Gramado, RS, Brazil, 15–20 November 2009. Rio de Janeiro: ABCM.

Castro

Cavalca

Nordmann

. Whirl and whip instabilities in rotor bearing system considering a non-linear force model. J Sound Vib 2008; 317: 273–293.

10.

Capone G. Analytical description of fluid-dynamic force field in cylindrical journal bearing. L’Energia Elettrica 1991; 3: 105–110. (Italian).

11.

Lee

. Complex modal testing theory for rotating machinery. Mech Syst Sig Process 1991; 5(2): 119–137.

12.

Dias MJ and Allemang RJ. Some insights into the simultaneous forward and backward whirling of rotors. In: Wicks AL (ed) Proceedings of the XIX International Modal Analysis Conference, IMAC 2001, Kissimmee, FL, United States, 5–8 February 2001, pp.1257–1263. Bethel, CT, United States: Society for Experimental Mechanics.

13.

Mesquita AL, Dias MJ and Miranda UA. A comparison between the traditional frequency response function (FRF) and the directional frequency response function (dFRF) in rotordynamic analysis. In: Proceedings of the first south-American congress on computational mechanics, Mecánica Computacional (eds Idelshon S, Sonzogni V and Cardona A), MECOM 2002, Santa Fé (Paraná), Argentina, 28–31 October 2002, vol. 21, pp.2227–2246.

14.

Kessler CL. Complex modal analysis of rotating machinery. Thesis, University of Cincinnati, Cincinnati, OH, United States, 1999.

15.

Santana PM, Cavalca KL, Okabe EP and Machado TH. Complex response of a rotor-bearing-foundation system. In: Proceedings of the 8th IFToMM international conference on rotordynamics, IFToMM 2010, Seoul, Korea, 12–15 September 2010, vol. 1, pp.1–8. Seoul: KAIST University.

16.

Chiba

Fukao

Ishikawa

, et al. Magnetic bearings and bearingless drives, 1st edn. Oxford: Newnes, 2005, p.381–381.

17.

Maslen EH. Magnetic bearings. Lecture Notes, University of Virginia, Charlottesville, VA, 2000, p.233.

18.

Aenis

Knopf

Nordmann

. Active magnetic bearings for the identification and fault diagnosis in turbomachinery. Mechatronics 2002; 12: 1011–1021.

19.

Allaire PE, Knospe CR, Williams RD, et al. High performance magnetic bearings for aero applications –final report. NASA grant no. NAG3-1334, 5 February 1997, p.37. Charlottesville, VA, United States: Mechanical, Aerospace and Nuclear Engineering, University of Viginia.

20.

Knospe

. Active magnetic bearings for machining applications. Control Eng Pract 2005; 15: 307–313.

21.

Marshall

Kasarda

MEF

Imlach

. A multipoint measurement technique for the enhancement of force measurement with active magnetic bearings. J Eng Gas Turbines Power 2003; 125: 90–94.

22.

Polajzer

. Magnetic bearings, theory and applications, 1st edn. Croatia: Sciyo, 2010, p.132–132.

23.

Schweitzer

Maslen

. Magnetic bearings –theory design and application to rotating machinery, 1st edn. Berlin: Springer-Verlag, 2009, p.535–535.

24.

Furtado RM. A magnetic actuator development for contactless excitation in rotor systems. Thesis, University of Campinas, Campinas, SP, Brazil, 2008. In Portuguese.

25.

Castro

Furtado

Cavalca

, et al. Experimental performance evaluation of magnetic actuator used in rotating machinery analysis. J Braz Soc Mech Sci Eng 2007; 29(1/93): 99–108.

26.

Furtado RM, Butzek N, Cavalca KL, et al. Design of magnetic actuator of rotating machinery analysis. In: Varoto PS and Trindade MA (eds) Proceedings of the XII international symposium on dynamic problems of mechanics, DINAME 2007, Ilhabela, SP, Brazil, 26 February–2 March 2007, pp.1–10. Rio de Janeiro: ABCM.

27.

Furtado RM, Silveira ZC, Cavalca KL, et al. Study of magnetic actuator parameters influence in the magnetic force. In: Merlet JP and Dahan M (eds) Proceedings of the 12th IFToMM world congress – machine and mechanisms, IFToMM 2007, Bensancon, France, 17–21 June 2007, vol. 1, pp.1–6. Besancon: IFToMM.

28.

Furtado RM, Cavalca KL and Mendes RU. Development of a magnetic actuator for modal analysis application in rotating systems. In: Proceedings of the V national congress of mechanical engineering, CONEM 2008, Salvador, BA, Brazil, 25–28 August 2008. Rio de Janeiro: ABCM (Portuguese).

29.

Mendes RU. Development of a magnetic actuation system to rotating system excitation. Dissertation, University of Campinas, Campinas, SP, Brazil, 2011. In Portuguese.

30.

Mendes RU, Cavalca KL, Perini EA, et al. Model of a magnetic actuator as an external excitation source on rotating machinery. In: Proceedings of the 21st Brazilian congress of mechanical engineering, COBEM 2011, Natal, RN, Brazil, 24–28 October 2011. Rio de Janeiro: ABCM.

31.

Mendes RU, Castro HF, Cavalca KL, et al. Magnetic actuator modelling for rotating machinery analysis. In: Náprstek J, Horáček J, Okrouhlík M, Marvalová B, Verhulst F and Sawicki JT (eds) Proceedings of the 10th International Conference on Vibration Problems, ICOVP 2011, Prague, Czech Republic, 5–8 September 2011, Proceedings in Physics, vol. 139, pp.537–542. New York: Springer.

32.

Weiming

Novak

. Dynamic behaviour of turbine-generator-foundation systems. Earthquake Eng Struct Dyn 1995; 24(3): 339–360.

33.

Machado TH. Evaluation of hydrodynamic bearings with geometric discontinuities. Dissertation, University of Campinas, Campinas, SP, Brazil, 2011. In Portuguese.

34.

Greenhill LM and Cornejo GA. Critical speeds resulting from unbalance excitation of backward whirl modes. In: Proceedings of the 1995 ASME design engineering technical conferences, DETC 1995, Boston, MA, 15–20 September 1995, DE vol. 84(2), vol. 3, part b, pp.991–1000. New York, United States: American Society of Mechanical Engineers.

35.

Richardson MH. Is it a mode shape, or an operating deflection shape? Sound and Vibration Magazine, March 1997, 30th Anniversary Issue, p.1–11.

36.

Muszynska

. Whirl and whip –rotor/bearing stability problems. J Sound Vib 1986; 110(3): 443–462.

37.

Muszynska A and Bently DE. Fluid-generated instabilities of rotors. Orbit, April 1989, p.6–14.

38.

Perini EA. Rotor vibration reduction using magnetic actuators and the feedforward control system. Dissertation, São Paulo State University, Ilha Solteira, SP, Brazil, 2009. In Portuguese.

39.

Halliday

Resnick

Walker

. Fundamentals of physics 3. 7th edn. New York, United States: John Wiley & Sons, 2007, p.379–379.

40.

Sen

. Principles of electric machines and power electronics, 2nd edn. New York, United States: John Wiley & Sons, 1997, p.615–615.

41.

Marszolek M. Implementierung von hallsensoren in einen magnetaktor zur kraftmessung –studienarbeit. Fachgebiet Mechatronik im Maschinenbau, Darmstadt University of Technology, Germany, 2006. In German.

42.

Goldman P and Muszynska A. Application of full spectrum to rotating machinery diagnostics. Orbit, 1999, First Quarter, p.17–21.

43.

Muszynska

. Rotordynamics, Boca Raton, FL: Taylor and Francis Group, 2005, p.1054–1054.

44.

Laws B. When you use spectrum, don’t use it halfway. Orbit, June 1998, p.23–26.

45.

Southwick D. Using full spectrum plots –part I. Orbit, December 1993, p.19–21.

46.

Southwick D. Using full spectrum plots –part II. Orbit, June 1994, p.11–15.