A Numerical Analysis of the Bearing Vibration Response under Varying Outer Race Defect Positions
Received: 20 August 2025 | Revised: 17 September 2025 | Accepted: 27 September 2025 | Online: 8 December 2025
Corresponding author: Thabisang Sylvester Lekalakala
Abstract
A dynamic model of a ball bearing with an outer race spall defect was formulated to investigate the influence of the defect angular position on the vibration response. The model integrates Hertzian contact deformation, elastic energy principles, and a mathematical representation of the spall geometry within the bearing system. The governing equations of motion were derived using the Lagrangian approach and solved numerically through a fourth-order Runge–Kutta method. Defect orientations at 0°, 90°, 180°, and 270° were examined to capture the variations in system behavior. The time-domain analysis revealed periodic impact signals corresponding to the successive rolling elements striking the defect. The most severe vibratory amplitudes occurred at 270°, where the defect coincides with the zone of maximum radial load. In contrast, positions away from this load zone exhibited weaker responses due to the reduced contact forces. The envelope analysis highlighted modulation at the Ball Pass Frequency of the Outer Race (BPFO) and its higher harmonics, confirming the diagnostic significance of defect-induced excitations. The results demonstrated that defect orientation plays a crucial role in shaping vibration signatures, and accurate fault detection depends on accounting for angular position effects in the condition monitoring of rotating machinery.
Keywords:
ball-bearing, Hertzian contact, outer race spall defect, envelope analysis, time-domain analysisDownloads
References
O. Rathodkar and P. Jain, "Analysis of Effects of Increase in Defect Size on Vibration of a Ball Bearing," International Journal of Mechanical Engineering, vol. 9, no. 10, pp. 1–11, Oct. 2022. DOI: https://doi.org/10.14445/23488360/IJME-V9I10P101
C. Malla and I. Panigrahi, "Review of Condition Monitoring of Rolling Element Bearing Using Vibration Analysis and Other Techniques," Journal of Vibration Engineering & Technologies, vol. 7, pp. 407–414, 2019. DOI: https://doi.org/10.1007/s42417-019-00119-y
T. Mashiyane, D. Desai, and L. Tartibu, "Numerical simulation of the effect of angular misalignment on the dynamic behaviour of bearing," in Proceedings of the MATEC Web of Conferences, Stellenbosch, South Africa, 2022, vol. 370. DOI: https://doi.org/10.1051/matecconf/202237009003
F. Combet and X. Thomas, "Modelling and diagnosis of a crack of a bearing inner ring," France, https://hal.science/hal-04179598v1/document.
Y. Bella, A. Oulmane, and M. Mostefai, "Industrial Bearing Fault Detection Using Time-Frequency Analysis," Engineering, Technology & Applied Science Research, vol. 8, no. 4, pp. 3294–3299, Aug. 2018. DOI: https://doi.org/10.48084/etasr.2135
L. Liang, C. Liu, and F. Liu, "Bearing fault diagnosis based on singular value distribution of impulse response segment," ISA Transactions, vol. 134, pp. 511–528, Mar. 2023. DOI: https://doi.org/10.1016/j.isatra.2022.08.015
M. Wang, K. Yan, X. Zhang, and J. Hong, "Research on the Dynamic Properties of Ball Bearings Based on the Quasi-Static Method," Advances in Mechanical Design, vol. 111, pp. 281–290, 2022. DOI: https://doi.org/10.1007/978-981-16-7381-8_19
S. Chen, D. Zou, X. Chen, Y. Wang, and D. Cai, "Support Force and Load Distribution Analysis of Angular Contact Ball Bearing Considering Rotor Deformation," Tribology Online, vol. 18, no. 4, pp. 125–135, 2023. DOI: https://doi.org/10.2474/trol.18.125
J. Liu, L. Xue, L. Wang, Z. Shi, and M. Xia, "A new impact model for vibration features of a defective ball bearing," ISA Transactions, vol. 142, pp. 465–477, Nov. 2023. DOI: https://doi.org/10.1016/j.isatra.2023.08.014
D. Ruan, C. Gühmann, and J. Yan, "A new solving method for ball bearing dynamics model based on optimization with nonlinear constraints: Contact angles as iterative variables," Journal of Manufacturing Processes, vol. 106, pp. 338–346, Nov. 2023. DOI: https://doi.org/10.1016/j.jmapro.2023.09.076
Y. Wu, C. Zhang, J. Wang, and S. Xu, "Dynamic Modeling of Rolling Bearing Outer Ring Failure with Time-Varying Excitation Under Contact Deformation," in Proceedings of the UNIfied Conference of DAMAS, IncoME and TEPEN Conferences (UNIfied 2023), Huddersfield, United Kingdom, 2023, pp. 777–783. DOI: https://doi.org/10.1007/978-3-031-49413-0_59
K. More et al., "Vibrational analysis of faulty deep-groove ball bearing under radial load," Frontiers in Mechanical Engineering, vol. 11, Apr. 2025. DOI: https://doi.org/10.3389/fmech.2025.1560986
A. Rashed, A. G. E.-M. Ahmed, and M. Ali, "Condition Monitoring of Localized Outer Race Defects of Taper Roller Bearings Using Vibration Analysis," Journal of the Egyptian Society of Tribology, vol. 20, no. 1, pp. 51–62, Jan. 2023. DOI: https://doi.org/10.21608/jest.2023.284023
F. Wang, X. Ling, Z. Zhang, P. Dai, S. Yan, and L. Wang, "The Effect of Fit Clearance between Outer Race and Housing on Vibration Characteristics of a Cylindrical Roller Bearing with Localized Defects," Machines, vol. 10, no. 6, 2022, Art. No. 415. DOI: https://doi.org/10.3390/machines10060415
A. Nabhan, M. Nouby, A. Sami, and M. Mousa, "Vibration analysis of deep groove ball bearing with outer race defect using ABAQUS," Journal of Low Frequency Noise, Vibration and Active Control, vol. 35, no. 4, pp. 312–325, 2016. DOI: https://doi.org/10.1177/0263092316676414
Y. Tian, C. Yan, W. Luo, Y. Liu, and L. Wu, "Dynamic Modeling and Stability Analysis of High-Speed Angular Contact Ball Bearing," in Proceedings of TEPEN 2022, Baotou, China, 2022, pp. 818–828. DOI: https://doi.org/10.1007/978-3-031-26193-0_72
C. Zhang, Y. Wu, S. Xu, F. Qin, L. Wu, and B. Ouyang, "Dynamic modeling and analysis of rolling bearing faults under time-varying excitations considering defect deformation," Journal of Vibroengineering, vol. 26, no. 4, pp. 776–792, 2024. DOI: https://doi.org/10.21595/jve.2024.23672
A. H. A. Mattar, H. Sayed, Y. K. Younes, and H. H. El-Mongy, "Experimental Verification and Nonlinear Dynamic Response Analysis of a Rolling Element Bearing with Localized Defects," Journal of Failure Analysis and Prevention, vol. 22, pp. 1753–1770, 2022. DOI: https://doi.org/10.1007/s11668-022-01466-x
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Copyright (c) 2025 Thabisang Sylvester Lekalakala, Alfayo Anyika Alugongo, Bernard Xavier Tchomeni, Desejo Filipeson Sozinando
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