Eccentricity Error Detection in Axial Flux Resolvers

Document Type : Original Article

Author

Assistant Professor, Imam Hossein University, Tehran, Iran

Abstract

Mechanical errors are one of the most common errors related to electric machines. Among them, eccentricities have the major share of mechanical errors. Resolvers, as an electric machine, can be affected by eccentricities or the electric motor connected to it. The existence of eccentricities in the resolvers, which can be caused by the rotation of the machine at critical speed, incorrect installation of the rotor and stator, core turning defects, and wear and corrosion of the bearings, leads to an increase in the position estimation error. The position estimation error will eventually increase the torque fluctuations, reduce the efficiency, lose the ideal control of the electric motor, and disrupt the automation process. Therefore, providing indicators to detect the occurrence of eccentricity in the resolver can be a preventive solution. Based on this, in this article, focusing on the inclined eccentricity, the equations describing air gap reluctance, magnetic flux density, and mutual inductance will be presented using the modified winding function method. By using the relationships describing the output voltage, the harmonic spectrum of the output voltage in the static and dynamic eccentricities will be compared with the healthy mode, and an index will be provided to identify static and dynamic mechanical error.

Highlights

[1]     P. Naderi, A. Ramezannezhad and L. Vandevelde, "A Novel Linear Resolver Proposal and Its Performance Analysis Under Healthy and Asymmetry Air-Gap Fault," in IEEE Transactions on Instrumentation and Measurement, vol. 71, pp. 1-9, 2022, Art no. 9504109, doi: 10.1109/TIM.2022.3155747.

[2]     R. Faryadras, F. Tootoonchian, “The Proposal of a 2-DOF Resolver for Linear Motion,” in Scientific Journal of Applied Electromagnetics, vol. 10, no. 1, pp. 81-90, March 2022, dor: 20.1001.1.26455153.1401.10.1.8.2.

[3]     A. Ramezannezhad, P. Naderi and L. Vandevelde, "A Novel Method for Accuracy Improvement of Variable Reluctance Linear Resolvers," in IEEE Sensors Journal, vol. 22, no. 19, pp. 18409-18417, 1 Oct.1, 2022, doi: 10.1109/JSEN.2022.3199807.

[4]     N. Lini Mathew, A. Sharma, “Various Indices for Diagnosis of Air-gap Eccentricity Fault in Induction Motor-A Review,” 3rd International Conference on Communication Systems (ICCS-2017), doi: 10.1088/1757-899X/331/1/012032.

[5]     G. Genta, “Dynamic of Rotating Systems,” Mechanical Engineering Series, Springer, 2005.

[6]     J.S. Rao, “Rotor Dynamics,” 3rd ed., New Age, 2004.

[7]     J.S. Rao, “Vibratory Condition Monitoring of Machines,” CRC Press, 2000.

[8]     U. Werner, “Mathematical analysis of rotor shaft displacements in asynchronous machines; a critical speed or just a rotation of the orbit axis?” ZAMM - Journal of Applied Mathematics and Mechanics, vol. 89, no.7, pp.514–535, 2009, doi: 10.1002/zamm.200900237.

[9]     S.J. Yang, “Low-Noise Electrical Motors (Monographs in Electrical and Electronic Engineering),” Oxford University Press, pp. 37, 1981.

[10]  A. Sinervo, “Effects of slotting and unipolar flux on magnetic pull in a two-pole induction motor with an extra four-pole stator winding,” Ph.D. Thesis, 2013.

[11]  Masaki, K., et al. "Magnetic field analysis of a resolver with a skewed and eccentric rotor." In Sensors and Actuators A: Physical 81.1 (2000): 297-300, doi: 10.1016/S0924-4247(99)00179-X.

[12]  Tootoonchian, F., K. Abbaszadeh, and M. Ardebili. "A new technique for analysis of static eccentricity in axial flux resolver."in Measurement Science Review 12.1 (2012): 14-20, doi: 10.2478/v10048-012-0004-y.

[13]  B. Ebrahimi, “Eccentricity error detection in three-phase permanent magnet synchronous motor,”Ph.D. Thesis, 2011 (In Persian).

[14]  S. Nandi, H. A. Toliyat and X. Li, "Condition Monitoring and Fault Diagnosis of Electrical Motors—A Review," in IEEE Transactions on Energy Conversion, vol. 20, no. 4, pp. 719-729, Dec. 2005, doi: 10.1109/TEC.2005.847955.

[15]  J. R. Cameron, W. T. Thomson and A. B. Dow, "Vibration and current monitoring for detecting airgap eccentricity in large induction motors," in IEE Proceedings B - Electric Power Applications, vol. 133, no. 3, pp. 155-163, May 1986, doi: 10.1049/ip-b.1986.0022.

[16]  P. Jover Rodríguez, A. Belahcen, A. Arkkio, , A. Laiho, and J. Antonino-Daviu, “Air-gap force distribution and vibration pattern of induction motors under dynamic eccentricity,” Electrical Engineering, vol. 90, no. 3, pp. 209–218, Feb. 2008, doi: 10.1007/s00202-007-0066-2. 

[17]  E. Rosenberg, “Magnetic pull in electric machines,”in Transactions of the American Institute of Electrical Engineers, vol. XXXVII, no. 2, pp. 1425–1469, July 1918, doi: 10.1109/T-AIEE.1918.4765578.

[18]  A. Gray and J. G. Pertsch, "Critical Review of the Bibliography on Unbalanced Magnetic Pull in Dynamo-Electric Machines," in Transactions of the American Institute of Electrical Engineers, vol. XXXVII, no. 2, pp. 1417-1424, July 1918, doi: 10.1109/T-AIEE.1918.476557.

[19]  D. Dorrell, “Calculation of unbalanced magnetic pull in cage induction machines,” Ph.D. Thesis, University of Cambridge, UK., 1993.

[20]  H. Lasjerdi, “Electrical and eccentricity error detection in wound rotor resolvers,” M.Sc. Thesis, 2019 (In Persian).

[21]  D.Harlin, “Oscillation Behaviour in Asynchronous motors as a Result of Unbalances,” Ph.D thesis, 1965.

[22]  A.R. Randell, “Performance of Electrical Machines Using a Generalised Theory and Including air-gap Flux Harmonics,” Ph.D thesis, 1965.

Keywords

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References

  1. Naderi, A. Ramezannezhad and L. Vandevelde, "A Novel Linear Resolver Proposal and Its Performance Analysis Under Healthy and Asymmetry Air-Gap Fault," in IEEE Transactions on Instrumentation and Measurement, vol. 71, pp. 1-9, 2022, Art no. 9504109, doi: 10.1109/TIM.2022.3155747.
  2. Faryadras, F. Tootoonchian, “The Proposal of a 2-DOF Resolver for Linear Motion,” in Scientific Journal of Applied Electromagnetics, vol. 10, no. 1, pp. 81-90, March 2022, dor: 20.1001.1.26455153.1401.10.1.8.2.
  3. Ramezannezhad, P. Naderi and L. Vandevelde, "A Novel Method for Accuracy Improvement of Variable Reluctance Linear Resolvers," in IEEE Sensors Journal, vol. 22, no. 19, pp. 18409-18417, 1 Oct.1, 2022, doi: 10.1109/JSEN.2022.3199807.
  4. Lini Mathew, A. Sharma, “Various Indices for Diagnosis of Air-gap Eccentricity Fault in Induction Motor-A Review,” 3rd International Conference on Communication Systems (ICCS-2017), doi: 10.1088/1757-899X/331/1/012032.
  5. Genta, “Dynamic of Rotating Systems,” Mechanical Engineering Series, Springer, 2005.
  6. S. Rao, “Rotor Dynamics,” 3rd ed., New Age, 2004.
  7. S. Rao, “Vibratory Condition Monitoring of Machines,” CRC Press, 2000.
  8. Werner, “Mathematical analysis of rotor shaft displacements in asynchronous machines; a critical speed or just a rotation of the orbit axis?” ZAMM - Journal of Applied Mathematics and Mechanics, vol. 89, no.7, pp.514–535, 2009, doi: 10.1002/zamm.200900237.
  9. J. Yang, “Low-Noise Electrical Motors (Monographs in Electrical and Electronic Engineering),” Oxford University Press, pp. 37, 1981.
  10. Sinervo, “Effects of slotting and unipolar flux on magnetic pull in a two-pole induction motor with an extra four-pole stator winding,” Ph.D. Thesis, 2013.
  11. Masaki, K., et al. "Magnetic field analysis of a resolver with a skewed and eccentric rotor." In Sensors and Actuators A: Physical 81.1 (2000): 297-300, doi: 1016/S0924-4247(99)00179-X.
  12. Tootoonchian, F., K. Abbaszadeh, and M. Ardebili. "A new technique for analysis of static eccentricity in axial flux resolver."in Measurement Science Review1 (2012): 14-20, doi: 10.2478/v10048-012-0004-y.
  13. Ebrahimi, “Eccentricity error detection in three-phase permanent magnet synchronous motor,”Ph.D. Thesis, 2011 (In Persian).
  14. Nandi, H. A. Toliyat and X. Li, "Condition Monitoring and Fault Diagnosis of Electrical Motors—A Review," in IEEE Transactions on Energy Conversion, vol. 20, no. 4, pp. 719-729, Dec. 2005, doi: 10.1109/TEC.2005.847955.
  15. R. Cameron, W. T. Thomson and A. B. Dow, "Vibration and current monitoring for detecting airgap eccentricity in large induction motors," in IEE Proceedings B - Electric Power Applications, vol. 133, no. 3, pp. 155-163, May 1986, doi: 10.1049/ip-b.1986.0022.
  16. Jover Rodríguez, A. Belahcen, A. Arkkio, , A. Laiho, and J. Antonino-Daviu, “Air-gap force distribution and vibration pattern of induction motors under dynamic eccentricity,” Electrical Engineering, vol. 90, no. 3, pp. 209–218, Feb. 2008, doi: 10.1007/s00202-007-0066-2.
  17. Rosenberg, “Magnetic pull in electric machines,”in Transactions of the American Institute of Electrical Engineers, vol. XXXVII, no. 2, pp. 1425–1469, July 1918, doi: 10.1109/T-AIEE.1918.4765578.
  18. Gray and J. G. Pertsch, "Critical Review of the Bibliography on Unbalanced Magnetic Pull in Dynamo-Electric Machines," in Transactions of the American Institute of Electrical Engineers, vol. XXXVII, no. 2, pp. 1417-1424, July 1918, doi: 10.1109/T-AIEE.1918.476557.
  19. Dorrell, “Calculation of unbalanced magnetic pull in cage induction machines,” Ph.D. Thesis, University of Cambridge, UK., 1993.
  20. Lasjerdi, “Electrical and eccentricity error detection in wound rotor resolvers,” M.Sc. Thesis, 2019 (In Persian).
  21. Harlin, “Oscillation Behaviour in Asynchronous motors as a Result of Unbalances,” Ph.D thesis, 1965.
  22. R. Randell, “Performance of Electrical Machines Using a Generalised Theory and Including air-gap Flux Harmonics,” Ph.D thesis, 1965.
Applied Electromagnetics
Volume 11, Issue 2 - Serial Number 27
September 2023
Pages 101-118

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History

  • Receive Date: 30 June 2023
  • Revise Date: 29 September 2023
  • Accept Date: 13 October 2023
  • Publish Date: 07 November 2023

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