DOI: https://doi.org/10.32515/2664-262X.2025.12(43).1.126-132

Modernization of the Influence Coefficient Method for Determining the Dynamic Unbalance of a Rigid Two-support Rotor

Gennadiy Filimonikhin, Yuliia Sokalska, Yuliia Ostapchuk

About the Authors

Gennadiy Filimonikhin, Professor, Doctor of Technical Sciences, Head of the Department of Machine Parts and Applied Mechanics, Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, ORCID: http://orcid.org/0000-0002-2819-0569, e-mail: filimonikhin@ukr.net

Yuliia Sokalska, PhD student in Applied Mechanics, Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, ORCID: https://orcid.org/0009-0008-4043-6251, e-mail: julija_8383@ukr.net

Yuliia Ostapchuk, PhD student in Applied Mechanics, Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, ORCID: https://orcid.org/0000-0002-7826-364X, e-mail: juli.biluk97@gmail.com

Abstract

The purpose of the work is to modernize the method of influence coefficients to increase the accuracy of determining the dynamic unbalance of a rigid two-support rotor. According to the modernized method, the rotor is installed on a balancing stand and the amplitudes and phases of the oscillations of the signals recorded from two single-axis vibration sensors during rotor rotation with a constant angular velocity are determined three times. The first time the rotor is rotated without adding test masses. The second time, a test mass is attached to the rotor in the first correction plane. The third time, a test mass is attached to the rotor in the second correction plane. After that, the relative values and relative positions of the unbalanced masses are calculated using complex coefficients in exponential form. The modulus of the complex number determines how many times the unbalanced mass in a certain correction plane is greater than the corresponding test mass. The angle sets the position of the unbalanced mass on the rotor and is counted from the test mass to the unbalanced mass in the direction of rotor rotation. Unbalanced masses are placed on the rotor at the same radius as the test masses. The modernized method uses in the calculations only the signals taken from two uniaxial vibration sensors and the phase sensor. The influence coefficients are not calculated explicitly. The values and locations of the test masses are not used in the calculations. This reduces the calculation errors, in particular, those caused by asynchronous data collection from the sensors.

Keywords

rotor, unbalance, balancing stand, vibration analysis, balancing

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References

1. Darlow, M. S. (1989). Review of literature on rotor balancing. In Balancing of High-Speed Machinery (pp. 39– 52). Mechanical Engineering Series. New York, NY: Springer. https://doi.org/10.1007/978-1-4612-3656-6_3

2. Foiles, W. C., Allaire, P. E., & Gunter, E. J. (1998). Review: Rotor balancing. Shock and Vibration, 5(5–6), 325–336. https://doi.org/10.1155/1998/648518

3. Ibraheem, A., Ghazaly, N., & Abd el-Jaber, G. (2019). Review of rotor balancing techniques. American Journal of Industrial Engineering, 6(1), 19–25. Retrieved April 21, 2025, from https://www.sciepub.com/ajie/abstract/11311

4. Li, L., Cao, S., Li, J., Nie, R., & Hou, L. (2021). Review of rotor balancing methods. Machines, 9(5), 89. https://doi.org/10.3390/machines9050089

5. Everett, L. J. (1997). Optimal two-plane balance of rigid rotors. Journal of Sound and Vibration, 208(4), 656– 663. https://doi.org/10.1006/jsvi.1997.1211

6. Xu, X., & Fan, P. (2013). Rigid rotor dynamic balancing by two-plane correction with the influence coefficient method. Applied Mechanics and Materials, 365–366, 211–215. https://doi.org/10.4028/www.scientific.net/AMM.365-366.211

7. Fomenko, D. S., & Kostenko, V. L. (2019). Dynamic unbalance of metal rotating bodies of gas-compressor units of gas-compressor stations. Integrated Technologies and Energy Saving. Series: Integrated Technologies of Industry, (2), 47–56 [in Ukrainian]. https://repository.kpi.kharkov.ua/handle/KhPI-Press/43787

8. Filimonikhin, H. B., Ostapchuk, Yu. O., & Oliinychenko, L. S. (2025). Practical methods of determining mass and aerodynamic (hydrodynamic) imbalance of a blade propeller. In Proceedings of the 4th International Scientific and Technical Conference “Prospects for the Development of Mechanical Engineering and Transport” (Vinnytsia, June 3–5, 2025). Vinnytsia [in Ukrainian]. Retrieved April 21, 2025, from https://conferences.vntu.edu.ua/index.php/prmt/pmrt2025/paper/viewFile/24926/20616

9. Filimonikhin, H. B., Sokalska, Yu. O., & Ostapchuk, Yu. O. (2025). Method of four test runs for determining mass and aerodynamic imbalance of an air propeller. In Proceedings of the 4th International Scientific and Technical Conference “Prospects for the Development of Mechanical Engineering and Transport” (Vinnytsia, June 3–5, 2025). Vinnytsia [in Ukrainian]. Retrieved April 21, 2025, from https://conferences.vntu.edu.ua/index.php/prmt/pmrt2025/paper/view/25137

10. Filimonikhin, H. B., Bilyk, Yu. O., & Oliinychenko, L. S. (2021). Stand for studying ordinary and aerodynamic imbalances of an air propeller. In Proceedings of the 2nd International Scientific and Technical Conference “Prospects for the Development of Mechanical Engineering and Transport” (Vinnytsia, May 13–15, 2021) (pp. 57–59). Vinnytsia [in Ukrainian]. Retrieved April 21, 2025, from https://conferences.vntu.edu.ua/index.php/prmt/pmrt2021/paper/view/13296

11. Filimonikhin, G., Yatsun, V., Matsui, A., Olijnichenko, L., & Pukalov, V. (2022). Determining experimentally the patterns of the manifestation of the Sommerfeld effect in a ball auto-balancer. Eastern-European Journal of Enterprise Technologies, 5(7/119), 96–104. https://doi.org/10.15587/1729-4061.2022.265578

Citations

1. Darlow M. S. Review of Literature on Rotor Balancing. In: Balancing of High-Speed Machinery. Mechanical Engineering Series. Springer, New York, NY, 1989. P. 39–52. https://doi.org/10.1007/978-1-4612-3656-6_3

2. Foiles W. C., Allaire P. E., Gunter E. J. Review: Rotor Balancing. Shock and Vibration. 1998. Vol. 5, № 5–6. P. 325–336. https://doi.org/10.1155/1998/648518

3. Ibraheem A., Ghazaly N., Abd el-Jaber G. Review of Rotor Balancing Techniques. American Journal of Industrial Engineering. 2019. Vol. 6, № 1. P. 19–25. URL: https://www.sciepub.com/ajie/abstract/11311 (дата звернення: 21.04.2025).

4. Li L., Cao S., Li J., Nie R., Hou L. Review of Rotor Balancing Methods. Machines. 2021. Vol. 9, № 5: 89. https://doi.org/10.3390/machines9050089

5. Everett L. J. Optimal Two-Plane Balance of Rigid Rotors. Journal of Sound and Vibration. 1997. Vol. 208, № 4. P. 656–663. https://doi.org/10.1006/jsvi.1997.1211

6. Xu X., Fan P. Rigid Rotor Dynamic Balancing by Two-Plane Correction with the Influence Coefficient Method. Applied Mechanics and Materials. 2013. Vols. 365–366. P. 211–215. https://doi.org/10.4028/www.scientific.net/AMM.365-366.211

7. Фоменко Д. С., Костенко В. Л. Динамічна неврівноваженість металевих тіл обертання газоперекачувальних агрегатів газокомпресорної станції. Інтегровані технології та енергозбереження. Серія: Інтегровані технології пром-сті. 2019. № 2. С. 47–56. URI: https://repository.kpi.kharkov.ua/handle/KhPI-Press/43787

8. Філімоніхін Г. Б., Остапчук Ю. О., Олійніченко Л. С. Практичні способи визначення масової і аеродинамічної (гідродинамічної) незрівноважености лопатевого гвинта. Перспективи розвитку машинобудування та транспорту: тези доп. IV Міжнар. наук.-техн. конф. (Вінниця, 3–5 черв. 2025 р.). Вінниця, 2025. URL: https://conferences.vntu.edu.ua/index.php/prmt/pmrt2025/paper/viewFile/24926/20616 (дата звернення: 21.04.2025).

9. Філімоніхін Г. Б., Сокальська Ю. О., Остапчук Ю. О. Метод чотирьох пробних пусків для визначення масової і аеродинамічної незрівноваженості повітряного гвинта. Перспективи розвитку машинобудування та транспорту: тези доп. IV Міжнар. наук.-техн. конф. (Вінниця, 3–5 черв. 2025 р.). Вінниця, 2025. URL: https://conferences.vntu.edu.ua/index.php/prmt/pmrt2025/paper/view/25137 (дата звернення: 21.04.2025).

10. Філімоніхін Г. Б., Білик Ю. О., Олійніченко Л. С. Стенд для дослідження звичайної і аеродинамічної незрівноваженостей повітряного гвинта. Перспективи розвитку машинобудування та транспорту: тези доп. ІІ Міжнар. наук.-техн. конф. (Вінниця, 13–15 трав. 2021 р.). Вінниця, 2021. С. 57–59. URL: https://conferences.vntu.edu.ua/index.php/prmt/pmrt2021/paper/view/13296 (дата звернення: 21.04.2025).

11. Filimonikhin G., Yatsun V., Matsui A., Olijnichenko L., Pukalov V. Determining experimentally the patterns of the manifestation of the Sommerfeld effect in a ball auto-balancer. Eastern-European Journal of Enterprise Technologies. 2022. Vol. 5, № 7 (119). P. 96–104. https://doi.org/10.15587/1729-4061.2022.265578

Copyright (©) 2025, Gennadiy Filimonikhin, Yuliia Sokalska, Yuliia Ostapchuk