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Experimental identification of shaft misalignment in a turbo-generator system

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Abstract

Precise and authentic estimation of the dynamic features of rotating machines and prevention of failure requires accurate experimental characterisation of their critical components, for example, bearings and couplings. These are difficult to model theoretically, and they often suffer from uncertain parameters in their model. Especially, when there is a misalignment in the rotor system, dynamic characterisation of bearings and couplings changes drastically. In the present study, multiple fault parameters (MFPs) of critical components of turbo-generator, that is, bearing and coupling together with residual unbalances (RUs), are evaluated experimentally using model-based methodology. A test rig was developed and used for experimentation in which different levels of misalignment was introduced. After estimating the MFPs, then the accuracy was checked through an impact test on the rotor test rig. The effect of different levels of misalignments on estimated parameters was studied.

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References

  1. Gnielka P 1983 Modal balancing of flexible rotors without test runs: an experimental investigation. J. Sound Vibr. 90: 157–172

    Article  Google Scholar 

  2. Morton P G 1985 Modal balancing of flexible shafts without trial weights. Proc. IMechE. Part C. Mechanical Engineering Science 199(1): 71–78

    Google Scholar 

  3. Edwards S, Lees A W and Friswell M I 1998 Fault diagnosis of rotating machinery. Shock Vib. Dig. 30: 4–13

    Article  Google Scholar 

  4. Zhou S and Shi J 2001 Active balancing and vibration control of rotating machinery: A survey. Shock Vib. Dig. 33(4) 361–371

    Article  Google Scholar 

  5. Tiwari R 2005 Conditioning of regression matrices for simultaneous estimation of the residual unbalance and bearing dynamics parameters. Mech. Syst. Signal. Process. 19: 1085–1095

    Article  Google Scholar 

  6. Jardine A K S, Lin D and Banjevic D 2006 A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mech. Syst. Signal. Process. 20: 1483–1510

    Article  Google Scholar 

  7. Lees A W, Sinha J K and Friswell M I 2009 Model-based identification of rotating machines. Mech. Syst. Signal. Process. Special Issue: Inverse Problems. 23: 1884–1893

    Google Scholar 

  8. Edwards S, Lees A W and Friswell M I 2000 Experimental identification of excitation and support parameters of a flexible rotor bearing foundation system from a single run down. J. Sound Vibr. 232: 963–992

    Article  Google Scholar 

  9. Jain J R and Kundra T K 2004 Model based online diagnosis of unbalance and transverse fatigue crack in rotor systems. Mech. Res. Commun. 31: 557–568

    Article  Google Scholar 

  10. Sudhakar G N D S and Sekhar A S 2011 Identification of unbalance in a rotor bearing system. J. Sound Vibr. 330 (10): 229–2313

    Article  Google Scholar 

  11. Zhang Z X, Zhang Q, Li X L and Qian T L 2011 The whole-beat correlation method for the identification of an unbalance response of a dual-rotor system with a slight rotating speed difference. Mech. Syst. Signal. Process. 25: 1667–1673

    Article  Google Scholar 

  12. Lees A W and Friswell M I 1997 The evaluation of rotor unbalance in flexibly mounted machines. J. Sound Vibr. 208 (5): 671–683

    Article  Google Scholar 

  13. Naucler P and Soderstrom T 2010 Unbalance estimation using linear and nonlinear regression. Automatica 46: 1752–1761

    Article  MathSciNet  MATH  Google Scholar 

  14. Gibbons C B 1976 Coupling misalignment forces, 5th Turbo Machinery Symposium. Gas Turbine Laboratories. Texas A & M University College Station Texas. 111–116

  15. Xu M and Marangoni R 1994a Vibration analysis of a motor flexible coupling rotor system subjected to misalignment and unbalance - Part 1: Theoretical model and analysis. J. Sound Vibr. 176: 663–679

    Article  MATH  Google Scholar 

  16. Xu M and Marangoni R 1994b Vibration analysis of a motor flexible coupling rotor system subjected to misalignment and unbalance - Part 2: Experimental validation. J. Sound Vibr. 176: 681–691

    Article  MATH  Google Scholar 

  17. Sekhar A S and Prabhu B S 1995 Effect of coupling misalignment on vibration of rotating machines. J. Sound Vibr. 185: 655–671

    Article  MATH  Google Scholar 

  18. Lee Y S and Lee C W 1999 Modelling and vibration analysis of misaligned rotor ball bearing systems. J. Sound Vibr. 224: 1–12

    Article  Google Scholar 

  19. Li M and Yu L 2001 Analysis of the coupled lateral torsional vibration of a rotor bearing system with a misaligned gear coupling. J. Sound Vibr. 243: 283–300

    Article  Google Scholar 

  20. Al-Hussain K M and Redmond I 2002 Dynamic response of two rotors connected by rigid mechanical coupling with parallel misalignment. J. Sound Vibr. 249: 483–498

    Article  Google Scholar 

  21. Prabhakar S, Sekhar A S and Mohanty A R 2002 Crack versus coupling misalignment in a transient rotor system. J. Sound Vibr. 256: 773–786

    Article  Google Scholar 

  22. Sinha J K, Lees A W and Frishwell M I 2004 Estimating unbalance and misalignment of a flexible rotating machine from a single run down. J. Sound Vibr. 272: 967–989

    Article  Google Scholar 

  23. Pennacchi P and Vania A 2005 Diagnosis and model based identification of a coupling misalignment. Shock Vibr. 12: 293–308

    Article  Google Scholar 

  24. Lees A W 2007 Misalignment in rigidly coupled rotor. J. Sound Vibr. 305: 261–271

    Article  Google Scholar 

  25. Patel T H and Darpe A K 2009 Vibration response of misaligned rotors. J. Sound Vibr. 325: 609–628

    Article  Google Scholar 

  26. Jalan A K and Mohanty A R 2009 Model based fault diagnosis of a rotor bearing system for misalignment and unbalance under steady state condition. J. Sound Vibr. 327: 604–622

    Article  Google Scholar 

  27. Sarkar S, Nandi A, Neogy S, Dutt J K and Kundra T K 2010 Finite element analysis of misaligned rotors on oil-film bearings. Sadhana Ind. Acad. Sci. 35: 45–61

    MATH  Google Scholar 

  28. Ganesan S and Padmanabhan C 2011 Modelling of parametric excitation of a flexible coupling-rotor system due to misalignment. In: Proc. IMechE Part-C: J. Mech. Eng. Sci. 225: 2907–2918

  29. Tadeo A T, Cavalca K L and Brennan M J 2011 Dynamic characterization of a mechanical coupling for a rotating shaft. In: Proc. IMechE Part-C: J. Mech. Eng. Sci. 225: 604–616

  30. Tiwari R, Lees A W and Friswell M I 2004 Identification of dynamic bearing parameters: A review. Shock. Vib. Dig. 36: 99–124

  31. Tiwari R, Manikandan S and Dwivedy S K 2005 A review on experimental estimation of the rotor dynamic parameters of seals. Shock. Vib. Dig. 37: 261–284

    Article  Google Scholar 

  32. Sinha J K, Frishwell M I and Lees A W 2002 The identification of the unbalance and the foundation model of a flexible rotating machine from a single run down. Mech. Syst. Signal. Process. 16 (2): 255–271

    Article  Google Scholar 

  33. Bachschmid N, Pennacchi P and Vania A 2002 Identification of multiple faults in rotor systems. J. Sound Vibr. 254: 327–366

    Article  Google Scholar 

  34. Pennacchi P, Bachschmid N, Vania A, Zanetta G A and Gregori L 2006 Use of modal representation for the supporting structure in model based fault identification of large rotating machinery: Part 1 theoretical remarks. Mech. Syst. Signal. Process. 20: 662–681

    Article  Google Scholar 

  35. Ping J J and Guang M A 2009 Novel method for multi fault diagnosis of rotor system. Mech. Mach. Theory 44: 697–709

    Article  MATH  Google Scholar 

  36. Singh S K and Tiwari R 2010 Identification of a multi crack in a shaft system using transverse frequency response functions. Mech. Mach. Theory. 45: 1813–1827

    Article  MATH  Google Scholar 

  37. Yang Q W 2011 A new damage identification method based on structural flexibility disassembly. J. Vibr. Control 17 (7): 1000–1008

    Article  MATH  Google Scholar 

  38. Lal M and Tiwari R 2012 Multi-fault identification in simple rotor-bearing-coupling systems based on forced response measurements. Mech. Mach. Theory. 51: 87–109

    Article  Google Scholar 

  39. Lal M and Tiwari R 2012 Identification of multiple faults with incomplete response measurements in rotor-bearing-coupling systems. In: ASME Gas Turbine India Conference. December 1. Mumbai India (GT India 2012-9542)

  40. Lal M and Tiwari R 2014 Experimental estimation of misalignment effects in rotor-bearing-coupling systems. In: Proceedings of IFToMM 9th International Conference on Rotordynamics. September 22–25. Politecnico di Milano Milan Italy

  41. Lal M and Tiwari R 2013 Quantification of multiple fault parameters in flexible turbo–generator systems with incomplete rundown vibration data. Mech. Syst. Signal Process. 41(1): 546–563

    Article  Google Scholar 

  42. Tiwari R 2017 Rotor Systems: Analysis and Identification. Boca Raton: CRC Press, Taylor and Francis Group

    Google Scholar 

  43. Zorzi E S and Nelson H D 1977 Finite element simulation of rotor-bearing systems with internal damping. ASME: J Eng. Power 99 (1): 71–76

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Industrial Design, National Institute of Technology Rourkela, Rourkela, 769 008, India

    Mohit Lal

  2. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, 781 039, India

    Rajiv Tiwari

Authors
  1. Mohit Lal
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  2. Rajiv Tiwari
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Correspondence to Mohit Lal.

Appendices

Appendix A: Timoshenko Beam Model [43]

1.1 A.1. Translational mass matrix

$$ [M_{t} ] = [M_{t} ]_{0} + \phi [M_{t} ]_{1} + \phi^{2} [M_{t} ]_{2} $$
(A.1)
$$ [M_{t} ]_{0} = \frac{\rho Al}{{420(1 + \phi )^{2} }}\left[ {\begin{array}{*{20}c} {156} & 0 & 0 & {22l} & {54} & 0 & 0 & { - 13l} \\ {} & {156} & { - 22l} & 0 & 0 & {54} & {13l} & 0 \\ {} & {} & {4l^{2} } & 0 & 0 & { - 13l} & { - 3l^{2} } & 0 \\ {} & {} & {} & {4l^{2} } & {13l} & 0 & 0 & { - 3l^{2} } \\ {} & {} & {} & {} & {156} & 0 & 0 & { - 22l} \\ {} & {} & {} & {} & {} & {156} & {22l} & 0 \\ {} & {\text{Sym}} & {} & {} & {} & {} & {4l^{2} } & 0 \\ {} & {} & {} & {} & {} & {} & {} & {4l^{2} } \\ \end{array} } \right] $$
(A.2)
$$ [M_{t} ]_{1} = \frac{\rho Al}{{420(1 + \phi )^{2} }}\left[ {\begin{array}{*{20}c} {294} & 0 & 0 & {38.5l} & {126} & 0 & 0 & { - 31.5l} \\ {} & {294} & { - 38.5l} & 0 & 0 & {126} & {31.5l} & 0 \\ {} & {} & {7l^{2} } & 0 & 0 & { - 31.5l} & { - 7l^{2} } & 0 \\ {} & {} & {} & {7l^{2} } & {31.5l} & 0 & 0 & { - 7l^{2} } \\ {} & {} & {} & {} & {294} & 0 & 0 & { - 38.5l} \\ {} & {} & {} & {} & {} & {294} & {38.5l} & 0 \\ {} & {\text{Sym}} & {} & {} & {} & {} & {7l^{2} } & 0 \\ {} & {} & {} & {} & {} & {} & {} & {7l^{2} } \\ \end{array} } \right] $$
(A.3)
$$ [M_{t} ]_{2} = \frac{\rho Al}{{420(1 + \phi )^{2} }}\left[ {\begin{array}{*{20}c} {140} & 0 & 0 & {17.5l} & {70} & 0 & 0 & { - 17.5l} \\ {} & {140} & { - 17.5l} & 0 & 0 & {70} & {17.5l} & 0 \\ {} & {} & {3.5l^{2} } & 0 & 0 & { - 17.5l} & { - 3.5l^{2} } & 0 \\ {} & {} & {} & {3.5l^{2} } & {17.5l} & 0 & 0 & { - 3.5l^{2} } \\ {} & {} & {} & {} & {140} & 0 & 0 & { - 17.5l} \\ {} & {} & {} & {} & {} & {140} & {17.5l} & 0 \\ {} & {\text{Sym}} & {} & {} & {} & {} & {3.5l^{2} } & 0 \\ {} & {} & {} & {} & {} & {} & {} & {3.5l^{2} } \\ \end{array} } \right] $$
(A.4)

with

$$ \phi = \frac{12EI}{{k_{sc} GAl^{2} }},\quad k_{sc} = \frac{6(1 + \upsilon )}{(7 + 6\upsilon )} $$

Displacement vector \( \left\{ \eta \right\}^{s} = \left\{ {x_{i} ,y_{i} ,\varphi_{{x_{i} }} ,\varphi_{{y_{i} }} ,x_{i + 1} ,y_{i + 1} ,\varphi_{{x_{i + 1} }} ,\varphi_{{y_{i + 1} }} } \right\}^{T} \), where sub-script i is element number

1.2 A.2. Rotational mass matrix

$$ [M_{r} ] = [M_{r} ]_{0} + \phi [M_{r} ]_{1} + \phi^{2} [M_{r} ]_{2} $$
(A.5)
$$ [M_{r} ]_{0} = \frac{\rho Al}{{(1 + \phi )^{2} }}\left[ {\begin{array}{*{20}c} {6/5l} & 0 & 0 & {1/10} & { - 6/5l} & 0 & 0 & {1/10} \\ {} & {6/5l} & { - 1/10} & 0 & 0 & { - 6/5l} & { - 1/10} & 0 \\ {} & {} & {2l/15} & 0 & 0 & {1/10} & { - l/30} & 0 \\ {} & {} & {} & {2l/15} & { - 1/10} & 0 & 0 & { - l/30} \\ {} & {} & {} & {} & {6/5l} & 0 & 0 & { - 1/10} \\ {} & {} & {} & {} & {} & {6/5l} & {1/10} & 0 \\ {} & {\text{Sym}} & {} & {} & {} & {} & {2l/15} & 0 \\ {} & {} & {} & {} & {} & {} & {} & {2l/15} \\ \end{array} } \right] $$
(A.6)
$$ [M_{r} ]_{1} = \frac{\rho Al}{{(1 + \phi )^{2} }}\left[ {\begin{array}{*{20}c} 0 & 0 & 0 & { - 1/2} & 0 & 0 & 0 & { - 1/2} \\ {} & 0 & {1/2} & 0 & 0 & 0 & {1/2} & 0 \\ {} & {} & {l/6} & 0 & 0 & { - 1/2} & { - l/6} & 0 \\ {} & {} & {} & {l/6} & {1/2} & 0 & 0 & { - l/6} \\ {} & {} & {} & {} & 0 & 0 & 0 & {1/2} \\ {} & {} & {} & {} & {} & 0 & { - 1/2} & 0 \\ {} & {\text{Sym}} & {} & {} & {} & {} & {l/6} & 0 \\ {} & {} & {} & {} & {} & {} & {} & {l/6} \\ \end{array} } \right] $$
(A.7)
$$ [M_{r} ]_{2} = \frac{\rho Al}{{(1 + \phi )^{2} }}\left[ {\begin{array}{*{20}c} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ {} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ {} & {} & {l/3} & 0 & 0 & 0 & {l/6} & 0 \\ {} & {} & {} & {l/3} & 0 & 0 & 0 & {l/6} \\ {} & {} & {} & {} & 0 & 0 & 0 & 0 \\ {} & {} & {} & {} & {} & 0 & 0 & 0 \\ {} & {\text{Sym}} & {} & {} & {} & {} & {l/3} & 0 \\ {} & {} & {} & {} & {} & {} & {} & {l/3} \\ \end{array} } \right] $$
(A.8)

1.3 A.3. Stiffness matrix

$$ \left[ K \right] = \left[ K \right]_{0} + \phi \left[ K \right]_{1} $$
(A.9)
$$ \left[ K \right]_{0} = \frac{EI}{{(1 + \phi )l^{3} }}\left[ {\begin{array}{*{20}c} {12} & 0 & 0 & {6l} & { - 12} & 0 & 0 & {6l} \\ {} & {12} & { - 6l} & 0 & 0 & { - 12} & {6l} & 0 \\ {} & {} & {4l^{2} } & 0 & 0 & {6l} & {2l^{2} } & 0 \\ {} & {} & {} & {4l^{2} } & { - 6l} & 0 & 0 & {2l^{2} } \\ {} & {} & {} & {} & {12} & 0 & 0 & { - 6l} \\ {} & {} & {} & {} & {} & {12} & {6l} & 0 \\ {} & {\text{Sym}} & {} & {} & {} & {} & {4l^{2} } & 0 \\ {} & {} & {} & {} & {} & {} & {} & {4l^{2} } \\ \end{array} } \right] $$
(A.10)
$$ \left[ K \right]_{1} = \frac{EI}{{(1 + \phi )l^{3} }}\left[ {\begin{array}{*{20}c} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ {} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ {} & {} & {l^{2} } & 0 & 0 & 0 & { - l^{2} } & 0 \\ {} & {} & {} & {l^{2} } & 0 & 0 & 0 & { - l^{2} } \\ {} & {} & {} & {} & 0 & 0 & 0 & 0 \\ {} & {} & {} & {} & {} & 0 & 0 & 0 \\ {} & {\text{Sym}} & {} & {} & {} & {} & {l^{2} } & 0 \\ {} & {} & {} & {} & {} & {} & {} & {l^{2} } \\ \end{array} } \right] $$
(A.11)

1.4 A.4. Gyroscopic matrix

$$ \left[ G \right] = \left[ G \right]_{0} + \phi \left[ G \right]_{1} + \phi^{2} \left[ G \right]_{2} $$
(A.12)
$$ \left[ G \right]_{0} = \frac{{\rho Ar^{2} }}{{60(1 + \phi )^{2} l}}\left[ {\begin{array}{*{20}c} 0 & {36} & { - 3l} & 0 & 0 & { - 36} & { - 3l} & 0 \\ {} & 0 & 0 & { - 3l} & {36} & 0 & 0 & { - 3l} \\ {} & {} & 0 & {4l^{2} } & { - 3l} & 0 & 0 & { - l^{2} } \\ {} & {} & {} & 0 & 0 & { - 3l} & {l^{2} } & 0 \\ {} & {} & {} & {} & 0 & {36} & {3l} & 0 \\ {} & {} & {} & {} & {} & 0 & 0 & {3l} \\ {} & {\text{Skew}} & {\text{Sym}} & {} & {} & {} & 0 & {4l^{2} } \\ {} & {} & {} & {} & {} & {} & {} & 0 \\ \end{array} } \right] $$
(A.13)
$$ \left[ G \right]_{1} = \frac{{\rho Ar^{2} }}{{60(1 + \phi )^{2} l}}\left[ {\begin{array}{*{20}c} 0 & 0 & {15l} & 0 & 0 & 0 & {15l} & 0 \\ {} & 0 & 0 & {15l} & 0 & 0 & 0 & {15l} \\ {} & {} & 0 & {5l^{2} } & {15l} & 0 & 0 & { - 5l^{2} } \\ {} & {} & {} & 0 & 0 & {15l} & {5l^{2} } & 0 \\ {} & {} & {} & {} & 0 & 0 & 0 & { - 15l} \\ {} & {} & {} & {} & {} & 0 & 0 & {5l^{2} } \\ {} & {\text{Skew}} & {\text{Sym}} & {} & {} & {} & 0 & {5l^{2} } \\ {} & {} & {} & {} & {} & {} & {} & 0 \\ \end{array} } \right] $$
(A.14)
$$ \left[ G \right]_{2} = \frac{{\rho Ar^{2} }}{{60(1 + \phi )^{2} l}}\left[ {\begin{array}{*{20}c} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ {} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ {} & {} & {10l^{2} } & 0 & 0 & 0 & 0 & {5l^{2} } \\ {} & {} & {} & 0 & 0 & 0 & {5l^{2} } & 0 \\ {} & {} & {} & {} & 0 & 0 & 0 & 0 \\ {} & {} & {} & {} & {} & 0 & 0 & 0 \\ {} & {\text{Skew}} & {\text{Sym}} & {} & {} & {} & 0 & {10l^{2} } \\ {} & {} & {} & {} & {} & {} & {} & 0 \\ \end{array} } \right] $$
(A.15)

1.5 A.5. Rigid disc model

Mass matrix

$$ [M]^{d} = \left[ {\begin{array}{*{20}c} {m_{d} } & 0 & 0 & 0 \\ 0 & {m_{d} } & 0 & 0 \\ 0 & 0 & {I_{d} } & 0 \\ 0 & 0 & 0 & {I_{d} } \\ \end{array} } \right] $$
(A.16)

Gyroscopic matrix

$$ [G]^{d} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & {I_{p} } \\ 0 & 0 & { - I_{p} } & 0 \\ \end{array} } \right] $$
(A.17)

Displacement vector

$$ \left\{ \eta \right\}^{d} = \left\{ {x,y,\varphi_{x} ,\varphi_{y} } \right\}^{T} $$
(A.18)

Appendix B: Natural Frequencies for Simply Supported Rotor Systems

Closed form solution is provided to obtain natural frequency of a simply supported rotor system with massless shaft and a disc at mid-span is given as

$$ \omega_{nf} = \frac{1}{2\pi }\sqrt {\frac{k}{m}} \,{\text{Hz}} $$
(B.1)

where

$$ k = \frac{48EI}{{L^{3} }} $$
(B.2)

Material properties and rotor dimensions are taken from table 1 and natural frequencies are summarised in table B1.

Table B1 Natural frequencies with simply supported boundary conditions.
Full size table

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Lal, M., Tiwari, R. Experimental identification of shaft misalignment in a turbo-generator system. Sādhanā 43, 80 (2018). https://doi.org/10.1007/s12046-018-0859-1

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