ШВИДКОДІЮЧІ МІКРОДВИГУНИ ПОСТІЙНОГО СТРУМУ: АНАЛІТИЧНА МЕТОДИКА ВИБОРУ МАГНІТНИХ НАВАНТАЖЕНЬ І КОНСТРУКЦІЇ ЯКОРЯ ЗА КРИТЕРІЄМ ЕЛЕКТРОМЕХАНІЧНОЇ СТАЛОЇ ЧАСУ

Михайло Коваленко; Віктор Гребєнніков; Андрій Стулішенко; Євген Ігнатюк

doi:10.20535/1813-5420.3.2026.369073

Vol. · Issue 3 · 2026 Oct 12, 2026 TECHNOLOGIES AND EQUIPMENT IN ENERGY

HIGH-RESPONSE DC MICROMOTORS: AN ANALYTICAL METHODOLOGY FOR SELECTING MAGNETIC LOADINGS AND ARMATURE ARCHITECTURE BY THE ELECTROMECHANICAL TIME-CONSTANT CRITERION

Mykhailo Kovalenko Corresponding National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute», Ukraine

Viktor Grebennikov Institute of Electrodynamics of the National Academy of Sciences of Ukraine, Ukraine

Andrii Stulishenko National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute», Ukraine

Yevhen Ihnatiuk National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute», Ukraine

Pages83-88 PublishedOct 12, 2026 LicenseOpen Access

PDF (Ukrainian)

VOL · ISS 3 · 2026 85 View issue

Abstract

The purpose of the study is to construct a closed, dimensionally consistent SI analytical methodology for estimating and minimizing the electromechanical time constant of DC servo micromotors at the preliminary design stage, which directly sets the speed-loop bandwidth of the drive. The implementation technique is based on the analytical derivation of the relations linking the time constant with the magnetic loadings, the slot-zone geometry, and the rotor architecture; every derived expression is verified symbolically and numerically, and all examples are reproducible.

The results are as follows. A size-invariant expression for the time constant has been derived which links it only to the rotor material density, the copper resistivity, the magnetic loading, and a dimensionless copper-utilization factor of the armature cross-section; it is shown that, for geometrically similar machines, the time constant does not depend on the armature diameter, so a substantial improvement in the response can be achieved only by changing the rotor architecture or the materials. A closed-form expression has been obtained for the optimum air-gap magnetic loading under simultaneous tooth- and yoke-saturation constraints; for typical electrical steels the optimum is about 0.58 T and the minimum of the time constant is shallow, which leaves room for thermal and manufacturing trade-offs. Exact inertia ratios have been derived for cup-type and disc armatures: for typical parameters a cup armature reduces the rotor inertia five- to ten-fold, and a disc armature by up to two orders of magnitude at the same diameter.

The conclusions state that a conventional laminated armature attains 12–23 ms depending on the slot fill and the thermal state, whereas a cup-type armature practically reaches 4–8 ms, the ultimate dynamics being set by the commutation current limits; the methodology provides the designer with explicit dependences of the response on the controllable parameters of the machine.

Keywords

#DC micromotor #electromechanical time constant #dynamic response #magnetic loading #cup-type armature #disc armature #moment of inertia

References

S. J. Chapman, Electric Machinery Fundamentals, 5th ed. New York: McGraw-Hill, 2011.
J.-X. Shen and J. F. Gieras, Modern Permanent Magnet Electric Machines. Boca Raton: CRC Press, 2023, doi: 10.1201/9781003103073.
D. C. Hanselman, Brushless Permanent Magnet Motor Design, 2nd ed. Lebanon, NH: Magna Physics Publishing, 2006.
R. Krishnan, Permanent Magnet Synchronous and Brushless DC Motor Drives. Boca Raton: CRC Press, 2010.
A. Di Gerlando, G. Foglia, M. Iacchetti, and R. Perini, "Design criteria and operation analysis of a high speed brushless PM micro-motor," in Proc. XIX Int. Conf. Electrical Machines (ICEM), Rome, Italy, 2010, doi: 10.1109/ICELMACH.2010.5608301.
S. G. Min, "Analytical design and optimization of axial flux permanent magnet machines with slotless structure," IEEE Trans. Transp. Electrific., vol. 8, no. 2, 2022, doi: 10.1109/TTE.2021.3124258.
C. Chu and Y. Huang, "Analysis and verification of the method of improving inductance by magnetic endcaps in slotless permanent magnet motor," Machines, vol. 10, no. 4, Art. 274, 2022, doi: 10.3390/machines10040274.
H. Zhu, S. Shen, and X. Wang, "Multiobjective optimization design of outer rotor coreless bearingless permanent magnet synchronous motor," IEEE J. Emerg. Sel. Topics Power Electron., vol. 9, no. 5, pp. 5489–5498, 2021, doi: 10.1109/JESTPE.2021.3072773.
Z. Zhang and H. Zhu, "Decoupling control on outer rotor coreless bearingless permanent magnet synchronous motor using LS-SVM generalized inverse," Prog. Electromagn. Res. M, vol. 111, pp. 65–76, 2022, doi: 10.2528/PIERM22032601.
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W. Zhang, H. Zhang, J. Mu, and S. Wang, "Design of a single-sided, coreless, flat-type linear voice coil motor," Actuators, vol. 12, no. 2, Art. 77, 2023, doi: 10.3390/act12020077.
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Chao K.-H., Huang K.-H., Guo Y.-H. Design of a brushless DC motor drive system controller integrating the zebra optimization algorithm and sliding mode theory. Electronics. 2025. Vol. 14, No. 17. Art. 3353. DOI: https://doi.org/10.3390/electronics14173353.
Chao K.-H., Lin Z.-N. Design of a robust controller for speed sensorless brushless DC motor drive. Electronics. 2026. Vol. 15, No. 14. Art. 3126. DOI: https://doi.org/10.3390/electronics15143126.
Kovalenko, M., Burlakov, A., & Kovalenko, I. (2025). Modeliuvannia kharakterystyk dvyhuna postiinoho strumu pryvodu palyvnoi systemy avtomobilia. Visnyk NTU «KhPI». Seriia: Problemy udoskonaliuvannia elektrychnykh mashyn I aparativ. Teoriia I praktyka, (1 (13), 37–43. https://doi.org/10.20998/2079-3944.2025.1.08.
M.A. Kovalenko, O.L. Tymoshchuk, O.O. Samoilenko Development of an device for small power direct current motors testing with electromagnetic excitation. Enerhetyka: ekonomika, tekhnolohii, ekolohiia. 2019. – № 3 – s 87-93.

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§ 06 — Related

[1] S. J. Chapman, Electric Machinery Fundamentals, 5th ed. New York: McGraw-Hill, 2011.

[2] J.-X. Shen and J. F. Gieras, Modern Permanent Magnet Electric Machines. Boca Raton: CRC Press, 2023, doi: 10.1201/9781003103073.

[3] D. C. Hanselman, Brushless Permanent Magnet Motor Design, 2nd ed. Lebanon, NH: Magna Physics Publishing, 2006.

[4] R. Krishnan, Permanent Magnet Synchronous and Brushless DC Motor Drives. Boca Raton: CRC Press, 2010.

[5] A. Di Gerlando, G. Foglia, M. Iacchetti, and R. Perini, "Design criteria and operation analysis of a high speed brushless PM micro-motor," in Proc. XIX Int. Conf. Electrical Machines (ICEM), Rome, Italy, 2010, doi: 10.1109/ICELMACH.2010.5608301.

[6] S. G. Min, "Analytical design and optimization of axial flux permanent magnet machines with slotless structure," IEEE Trans. Transp. Electrific., vol. 8, no. 2, 2022, doi: 10.1109/TTE.2021.3124258.

[7] C. Chu and Y. Huang, "Analysis and verification of the method of improving inductance by magnetic endcaps in slotless permanent magnet motor," Machines, vol. 10, no. 4, Art. 274, 2022, doi: 10.3390/machines10040274.

[8] H. Zhu, S. Shen, and X. Wang, "Multiobjective optimization design of outer rotor coreless bearingless permanent magnet synchronous motor," IEEE J. Emerg. Sel. Topics Power Electron., vol. 9, no. 5, pp. 5489–5498, 2021, doi: 10.1109/JESTPE.2021.3072773.

[9] Z. Zhang and H. Zhu, "Decoupling control on outer rotor coreless bearingless permanent magnet synchronous motor using LS-SVM generalized inverse," Prog. Electromagn. Res. M, vol. 111, pp. 65–76, 2022, doi: 10.2528/PIERM22032601.

[10] O. Tosun and N. F. Oyman Serteller, "The design of the outer-rotor brushless DC motor and an investigation of motor axial-length-to-pole-pitch ratio," Sustainability, vol. 14, no. 19, Art. 12743, 2022, doi: 10.3390/su141912743.

[11] W. Zhang, H. Zhang, J. Mu, and S. Wang, "Design of a single-sided, coreless, flat-type linear voice coil motor," Actuators, vol. 12, no. 2, Art. 77, 2023, doi: 10.3390/act12020077.

[12] Y. Zeng et al., "Influence of interference fit and temperature on high-speed permanent magnet motor," Appl. Sci., vol. 13, no. 20, Art. 11331, 2023, doi: 10.3390/app132011331.

[13] Chumak, V., Kovalenko, M., Kovalenko, I., & Tkachuk, I. (2023). Eksperymentalne doslidzhennia universalnoho vysokoshvydkisnoho kolektornoho dvyhuna zminnoho strumu. Visnyk NTU «KhPI». Seriia: Problemy udoskonaliuvannia elektrychnykh mashyn I aparativ. Teoriia I praktyka, (1 (9), 39–44. https://doi.org/10.20998/2079-3944.2023.1.06.

[14] Chao K.-H., Huang K.-H., Guo Y.-H. Design of a brushless DC motor drive system controller integrating the zebra optimization algorithm and sliding mode theory. Electronics. 2025. Vol. 14, No. 17. Art. 3353. DOI: https://doi.org/10.3390/electronics14173353.

[15] Chao K.-H., Lin Z.-N. Design of a robust controller for speed sensorless brushless DC motor drive. Electronics. 2026. Vol. 15, No. 14. Art. 3126. DOI: https://doi.org/10.3390/electronics15143126.

[16] Kovalenko, M., Burlakov, A., & Kovalenko, I. (2025). Modeliuvannia kharakterystyk dvyhuna postiinoho strumu pryvodu palyvnoi systemy avtomobilia. Visnyk NTU «KhPI». Seriia: Problemy udoskonaliuvannia elektrychnykh mashyn I aparativ. Teoriia I praktyka, (1 (13), 37–43. https://doi.org/10.20998/2079-3944.2025.1.08.

[17] M.A. Kovalenko, O.L. Tymoshchuk, O.O. Samoilenko Development of an device for small power direct current motors testing with electromagnetic excitation. Enerhetyka: ekonomika, tekhnolohii, ekolohiia. 2019. – № 3 – s 87-93.

HIGH-RESPONSE DC MICROMOTORS: AN ANALYTICAL METHODOLOGY FOR SELECTING MAGNETIC LOADINGS AND ARMATURE ARCHITECTURE BY THE ELECTROMECHANICAL TIME-CONSTANT CRITERION

Abstract

Keywords

References

License

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