Rotary Encoder-Based Health Indicators for Early Detection of Gear Pitting in Commercial Gearboxes
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Published
Jan 13, 2026
Toby Verwimp
Rui Zhu
Hao Wen
Achilleas Achilleos
Konstantinos Gryllias
https://orcid.org/0000-0001-5981-6643
Hao Wen
Achilleas Achilleos
Konstantinos Gryllias
Abstract
This paper investigates the diagnostic capabilities of rotary encoders for condition monitoring of commercial gearboxes, focusing on early detection of gear pitting. Within a multi-sensor framework, high-resolution rotary encoder data were collected alongside accelerometer signals, both mounted on a multistage commercial gearbox subjected to gear pitting. Encoder-based health indicators were developed from the square envelope (SE) of the transmission error (TE), synchronously averaged (SA) to isolate the targeted gear component within the gearbox. By automatically capturing images of the targeted gear during an accelerated life test, these indicators were evaluated for their ability to detect the onset of gear pitting and compared against conventional vibration-based metrics. Results show that encoder-based indicators can provide earlier and more consistent detection of gear pitting. These findings highlight the potential of rotary encoders as a complementary or standalone sensing solution in advanced diagnostic frameworks for commercial gearboxes.
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Keywords
rotary encoder, transmission error, gear pitting, condition monitoring, gearbox diagnostics, fault detection
References
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Chin, Z. Y., Borghesani, P., Mao, Y., Smith, W. A., & Randall, R. B. (2022). Use of transmission error for a quantitative estimation of root-crack severity in gears. Mechanical Systems and Signal Processing, 171, 108957. doi: 10.1016/j.ymssp.2022.108957
Chin, Z. Y., Borghesani, P., Smith, W. A., Randall, R. B., & Peng, Z. (2023). Monitoring gear wear with transmission error. Wear, 523, 204803. doi:10.1016/j.wear.2023.204803
Chin, Z. Y., Smith, W. A., Borghesani, P., Randall, R. B., & Peng, Z. (2021). Absolute transmission error: A simple new tool for assessing gear wear. Mechanical Systems and Signal Processing, 146, 107070. doi: 10.1016/j.ymssp.2020.107070
Elasha, F., Ruiz-Carcel, C., Mba, D., Kiat, G., Nze, I., & Yebra, G. (2014). Pitting detection in worm gearboxes with vibration analysis. Engineering Failure Analysis, 42, 366-376. doi: 10.1016/j.engfailanal.2014.04.028
Fan, J., Guo, Y., & Yin, X. (2025). Instantaneous angular speed based fault detection for planet and cycloidal gears in rotary vector reducers. IEEE Transactions on Instrumentation and Measurement, 74, 1-10. doi: 10.1109/TIM.2025.3542103
Feki, N., Cavoret, J., Ville, F., & Velex, P. (2013). Detection of gear tooth pitting based on transmission error measurements. In M. Haddar, L. Romdhane, J. Louati, & A. B. Amara (Eds.), Proceedings of the Fifth International Conference Design and Modeling of Mechanical Systems, CMSM (p. 181-188). Berlin, Heidelberg: Springer Berlin Heidelberg. doi: 10.1007/978-3-642-37143-1
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Koch, Y., Sendlbeck, S., Otto, M., Stahl, K., & Kirchner, E. (2025). A review on the use of angle measurements in gear condition monitoring and fault detection. Mechanical Systems and Signal Processing, 225, 112254. doi: 10.1016/j.ymssp.2024.112254
Lee, S. K., Shim, J. S., & Cho, B. O. (2006). Damage detection of a gear with initial pitting using the zoomed phase map of continuous wavelet transform. Key Engineering Materials, 306-308, 223-228. doi: 10.4028/www.scientific.net/KEM.306-308.223
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Mahfoudh, J., & Remond, D. (2009). Experimental study of the transmission error for the detection of gear faults. In Proceedings of the ASME Turbo Expo 2003, collocated with the 2003 International Joint Power Generation Conference (Vol. 1, p. 345-349). Atlanta, Georgia, USA: American Society of Mechanical Engineers (ASME). doi: 10.1115/GT2003-38289
Mao, Y., Tong, J., Chin, Y., Borghesani, P., & Peng, Z. (2023). Transmission-error- and vibrationbased condition monitoring of gear wear with contaminated lubricant. Wear, 523, 204760. doi: 10.1016/j.wear.2023.204760
Miao, Y., Wang, J., Zhang, B., & Li, H. (2022). Practical framework of gini index in the application of machinery fault feature extraction. Mechanical Systems and Signal Processing, 165, 108333. doi: 10.1016/j.ymssp.2021.108333
Palermo, A., Britte, L., Janssens, K., Mundo, D., & Desmet, W. (2018). The measurement of gear transmission error as an NVH indicator: Theoretical discussion and industrial application via low-cost digital encoders to an all-electric vehicle gearbox. Mechanical Systems and Signal Processing, 110, 368-389. doi:10.1016/j.ymssp.2018.03.005
Randall, R. B., Chin, Z. Y., Smith, W. A., & Borghesani, P. (2019). Measurement and use of transmission error for diagnostics of gears. In Surveillance, Vishno and AVE conferences. INSA-Lyon, Universite de Lyon, Lyon, France.
Renaudin, L., Bonnardot, F., Musy, O., Doray, J. B., & Remond, D. (2010). Natural roller bear- ing fault detection by angular measurement of true instantaneous angular speed. Mechanical Systems and Signal Processing, 24(7), 1998-2011. doi:
10.1016/j.ymssp.2010.05.005
Remond, D. (1998). Practical performances of high-speed measurement of gear transmission error or torsional vibrations with optical encoders. Measurement Science and Technology, 9(3), 347-353. doi: 10.1088/0957- 0233/9/3/006
Remond, D., & Mahfoudh, J. (2005). From transmission error measurements to angular sampling in rotating machines with discrete geometry. Shock and Vibration, 12(2), 149-161. doi: 10.1155/2005/205291
Sharma, V., & Parey, A. (2016). A review of gear fault diagnosis using various condition indicators. Procedia Engineering, 144, 253-263. doi: 10.1016/j.proeng.2016.05.131
Sheng, S. (2014). Gearbox typical failure modes, detection, and mitigation methods (Presentation): NREL (National Renewable Energy Laboratory) (Other No. NREL/PR-5000-60982). National Renewable Energy Lab (NREL), Golden, CO (United States).
Verwimp, T., Mousmoulis, G., Gryllias, K., & Hajnayeb, A. (2023). Cavitation detection based on instantaneous angular speed. In 19th International Conference on Condition Monitoring and Asset Management, CM 2023. The British Institute of Non-Destructive Testing. doi: 10.1784/CM2023.2E1
Wang, D. (2018). Some further thoughts about spectral kurtosis, spectral L2/L1 norm, spectral smoothness index and spectral Gini index for characterizing repetitive transients. Mechanical Systems and Signal Processing, 108, 360-368. doi: 10.1016/j.ymssp.2018.02.034
Yang, J., Pu, L., Wang, Z., Zhou, Y., & Yan, X. (2001). Fault detection in a diesel engine by analysing the instantaneous angular speed. Mechanical Systems and Signal Processing, 15(3), 549-564. doi: 10.1006/mssp.2000.1344
Zhao, M., Jia, X., Lin, J., Lei, Y., & Lee, J. (2018). Instantaneous speed jitter detection via encoder signal and its application for the diagnosis of planetary gearbox. Mechanical Systems and Signal Processing, 98, 16-31. doi: 10.1016/j.ymssp.2017.04.033
Zhao, M., & Lin, J. (2018). Health assessment of rotating machinery using a rotary encoder. IEEE Transactions on Industrial Electronics, 65(3), 2548-2556. doi: 10.1109/TIE.2017.2739689
Zhu, R., Van Maele, D., Poletto, J. C., De Baets, P., & Gryllias, K. (2024). Development and evaluation of vibration indicators for gear pitting detection. In International Conference on Noise and Vibration Engineering (ISMA 2024) and International Conference on Uncertainty in Structural Dynamics (USD 2024) (pp. 508– 521). Katholieke Universiteit Leuven, Department of Mechanical Engineering.
Antolick, L. J., Branning, J. S., Wade, D. R., & Dempsey, P. J. (2010). Evaluation of gear condition indicator performance on rotorcraft fleet. In AHS 66th Annual Forum and Technology Display: Rising to New Heights in Vertical Lift Technology. Phoenix, AZ, United States. Bechhoefer, E., & Butterworth, B. (2019). A comprehensive analysis of the performance of gear fault detection algorithms. In Proceedings of the Annual Conference of the PHM Society 2019 (Vol. 11). Prognostics and Health Management Society. doi: 10.36001/phmconf.2019.v11i1.823
Bourdon, A., Chesne, S., Andre, H., & Remond, D. (2019). Reconstruction of angular speed variations in the angular domain to diagnose and quantify taper roller bearing outer race fault. Mechanical Systems and Signal Processing, 120, 1-15. doi: 10.1016/j.ymssp.2018.09.040
Chin, Z. Y., Borghesani, P., Mao, Y., Smith, W. A., & Randall, R. B. (2022). Use of transmission error for a quantitative estimation of root-crack severity in gears. Mechanical Systems and Signal Processing, 171, 108957. doi: 10.1016/j.ymssp.2022.108957
Chin, Z. Y., Borghesani, P., Smith, W. A., Randall, R. B., & Peng, Z. (2023). Monitoring gear wear with transmission error. Wear, 523, 204803. doi:10.1016/j.wear.2023.204803
Chin, Z. Y., Smith, W. A., Borghesani, P., Randall, R. B., & Peng, Z. (2021). Absolute transmission error: A simple new tool for assessing gear wear. Mechanical Systems and Signal Processing, 146, 107070. doi: 10.1016/j.ymssp.2020.107070
Elasha, F., Ruiz-Carcel, C., Mba, D., Kiat, G., Nze, I., & Yebra, G. (2014). Pitting detection in worm gearboxes with vibration analysis. Engineering Failure Analysis, 42, 366-376. doi: 10.1016/j.engfailanal.2014.04.028
Fan, J., Guo, Y., & Yin, X. (2025). Instantaneous angular speed based fault detection for planet and cycloidal gears in rotary vector reducers. IEEE Transactions on Instrumentation and Measurement, 74, 1-10. doi: 10.1109/TIM.2025.3542103
Feki, N., Cavoret, J., Ville, F., & Velex, P. (2013). Detection of gear tooth pitting based on transmission error measurements. In M. Haddar, L. Romdhane, J. Louati, & A. B. Amara (Eds.), Proceedings of the Fifth International Conference Design and Modeling of Mechanical Systems, CMSM (p. 181-188). Berlin, Heidelberg: Springer Berlin Heidelberg. doi: 10.1007/978-3-642-37143-1
Hanna, J., Hatch, C., Kalb, M., Weiss, A., & Luo, H. (2012). Detection of wind turbine gear tooth defects using sideband energy ratio™. China Wind Power, 32. Harris, S. L. (1958). Dynamic loads on the teeth of spur gears. Proceedings of the Institution of Mechanical Engineers, 172(1), 87-112. doi: 10.1243/PIME-PROC1958-172-017-02
Koch, Y., Sendlbeck, S., Otto, M., Stahl, K., & Kirchner, E. (2025). A review on the use of angle measurements in gear condition monitoring and fault detection. Mechanical Systems and Signal Processing, 225, 112254. doi: 10.1016/j.ymssp.2024.112254
Lee, S. K., Shim, J. S., & Cho, B. O. (2006). Damage detection of a gear with initial pitting using the zoomed phase map of continuous wavelet transform. Key Engineering Materials, 306-308, 223-228. doi: 10.4028/www.scientific.net/KEM.306-308.223
Li, Y., Gu, F., Harris, G., Ball, A., Bennett, N., & Travis, K. (2005). The measurement of instantaneous angular speed. Mechanical Systems and Signal Processing, 19(4), 786-805. doi: 10.1016/j.ymssp.2004.04.003
Liang, L., Liu, F., Kong, X., Li, M., & Xu, G. (2019). Application of instantaneous rotational speed to detect gearbox faults based on double encoders. Chinese Journal of Mechanical Engineering, 32(9). doi: 10.1186/s10033-019-0324-z
Liu, H., Lin, J., Jiao, J., Zhang, B., Liu, Z., & Lu, X. (2023). A differential diagnosis approach of localized planet gear fault using overall transmission error. Measurement, 222, 113647. doi: 10.1016/j.measurement.2023.113647
Mahfoudh, J., & Remond, D. (2009). Experimental study of the transmission error for the detection of gear faults. In Proceedings of the ASME Turbo Expo 2003, collocated with the 2003 International Joint Power Generation Conference (Vol. 1, p. 345-349). Atlanta, Georgia, USA: American Society of Mechanical Engineers (ASME). doi: 10.1115/GT2003-38289
Mao, Y., Tong, J., Chin, Y., Borghesani, P., & Peng, Z. (2023). Transmission-error- and vibrationbased condition monitoring of gear wear with contaminated lubricant. Wear, 523, 204760. doi: 10.1016/j.wear.2023.204760
Miao, Y., Wang, J., Zhang, B., & Li, H. (2022). Practical framework of gini index in the application of machinery fault feature extraction. Mechanical Systems and Signal Processing, 165, 108333. doi: 10.1016/j.ymssp.2021.108333
Palermo, A., Britte, L., Janssens, K., Mundo, D., & Desmet, W. (2018). The measurement of gear transmission error as an NVH indicator: Theoretical discussion and industrial application via low-cost digital encoders to an all-electric vehicle gearbox. Mechanical Systems and Signal Processing, 110, 368-389. doi:10.1016/j.ymssp.2018.03.005
Randall, R. B., Chin, Z. Y., Smith, W. A., & Borghesani, P. (2019). Measurement and use of transmission error for diagnostics of gears. In Surveillance, Vishno and AVE conferences. INSA-Lyon, Universite de Lyon, Lyon, France.
Renaudin, L., Bonnardot, F., Musy, O., Doray, J. B., & Remond, D. (2010). Natural roller bear- ing fault detection by angular measurement of true instantaneous angular speed. Mechanical Systems and Signal Processing, 24(7), 1998-2011. doi:
10.1016/j.ymssp.2010.05.005
Remond, D. (1998). Practical performances of high-speed measurement of gear transmission error or torsional vibrations with optical encoders. Measurement Science and Technology, 9(3), 347-353. doi: 10.1088/0957- 0233/9/3/006
Remond, D., & Mahfoudh, J. (2005). From transmission error measurements to angular sampling in rotating machines with discrete geometry. Shock and Vibration, 12(2), 149-161. doi: 10.1155/2005/205291
Sharma, V., & Parey, A. (2016). A review of gear fault diagnosis using various condition indicators. Procedia Engineering, 144, 253-263. doi: 10.1016/j.proeng.2016.05.131
Sheng, S. (2014). Gearbox typical failure modes, detection, and mitigation methods (Presentation): NREL (National Renewable Energy Laboratory) (Other No. NREL/PR-5000-60982). National Renewable Energy Lab (NREL), Golden, CO (United States).
Verwimp, T., Mousmoulis, G., Gryllias, K., & Hajnayeb, A. (2023). Cavitation detection based on instantaneous angular speed. In 19th International Conference on Condition Monitoring and Asset Management, CM 2023. The British Institute of Non-Destructive Testing. doi: 10.1784/CM2023.2E1
Wang, D. (2018). Some further thoughts about spectral kurtosis, spectral L2/L1 norm, spectral smoothness index and spectral Gini index for characterizing repetitive transients. Mechanical Systems and Signal Processing, 108, 360-368. doi: 10.1016/j.ymssp.2018.02.034
Yang, J., Pu, L., Wang, Z., Zhou, Y., & Yan, X. (2001). Fault detection in a diesel engine by analysing the instantaneous angular speed. Mechanical Systems and Signal Processing, 15(3), 549-564. doi: 10.1006/mssp.2000.1344
Zhao, M., Jia, X., Lin, J., Lei, Y., & Lee, J. (2018). Instantaneous speed jitter detection via encoder signal and its application for the diagnosis of planetary gearbox. Mechanical Systems and Signal Processing, 98, 16-31. doi: 10.1016/j.ymssp.2017.04.033
Zhao, M., & Lin, J. (2018). Health assessment of rotating machinery using a rotary encoder. IEEE Transactions on Industrial Electronics, 65(3), 2548-2556. doi: 10.1109/TIE.2017.2739689
Zhu, R., Van Maele, D., Poletto, J. C., De Baets, P., & Gryllias, K. (2024). Development and evaluation of vibration indicators for gear pitting detection. In International Conference on Noise and Vibration Engineering (ISMA 2024) and International Conference on Uncertainty in Structural Dynamics (USD 2024) (pp. 508– 521). Katholieke Universiteit Leuven, Department of Mechanical Engineering.
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