Nonlinear Characterisation of Wind Turbine Gearbox Vibration Dynamics Driven by Inhomogeneous Helical Gear Wear Khaldoon F. Brethee, Ghalib R. Ibrahim, Al-Hussein Albarbar Vibration, 2026 Helical gear transmissions in wind turbine gearboxes operate under high torque, variable speed, and complex rolling–sliding contact conditions, where friction-induced wear evolves in a spatially non-uniform manner. However, most existing dynamic models assume uniform or mild wear and therefore fail to capture the nonlinear coupling between localised tooth surface degradation, gear mesh dynamics, and vibration response. In this work, a nonlinear dynamic model of a helical gear pair is formulated by incorporating time-varying mesh stiffness, elasto-hydrodynamic lubrication (EHL)-based friction forces, and wear-dependent contact geometry. The governing equations of motion are derived to explicitly account for the influence of inhomogeneous tooth wear on the contact load distribution and frictional excitation during meshing. Wear evolution is represented as a spatially varying modification of tooth surface topology, enabling the progressive coupling between wear depth, mesh stiffness perturbations, and dynamic transmission error. The model is employed to analyse the effects of non-uniform wear on system stability, vibration spectra, and dynamic response under wind turbine operating conditions. Numerical results reveal that uneven wear introduces nonlinear modulation of gear mesh forces and generates characteristic sidebands and amplitude variations in the vibration signal that are absent in conventional mild-wear formulations. These wear-induced dynamic features provide mathematically traceable indicators for the onset and progression of uneven tooth degradation. The proposed framework establishes a physics-based link between wear evolution and measurable vibration responses, providing a rigorous foundation for advanced vibration-based diagnostics and model-driven condition monitoring of wind turbine gearboxes.
Free vibration characteristics and localization of single and multiple cracks within beam structure Ahmed Ismail Namah, Khaldoon Fadhel Brethee World Journal of Engineering, 2025 Purpose This study aims to analyse the impact of cracks on the free vibration characteristics of various structural beams; hence, a novel damage index is implemented for accurate crack localization. A modified normalized curvature damage factor (MNCDF) has been proposed based on the curvature data of the damaged beam, without relying on the healthy beam, thereby enhancing the reliability of damage detection. Design/methodology/approach The analysis was conducted on Euler–Bernoulli beams subjected to three different boundary conditions: simply supported, clamped–clamped and cantilever beams. The cracked beams are modelled by using the continuous method with a rotational spring at the crack region. The beam is divided into uniform sub-segments, and each segment is connected by rotational springs to account for the localized flexibility of the crack formation. The stiffness of these springs is derived from the principles of fracture mechanics, where continuity and compatibility conditions were applied at the crack location to ensure accurate dynamic behaviour was performed and the vibration characteristics can be extracted accordingly. The MNCDF technique relies on the data of the extracted mode shape curvature for each mode, where a good validation was demonstrated via different frequency modes by using a simplified computational approach. Findings The results showed that the presence of cracks leads to noticeable changes in the vibration behaviour of the structural beam, which become more significant as the number of cracks increases. The MNCDF method has demonstrated high efficiency to identify the sharp variations in the mode shape curvature near the crack locations, which confirms its effectiveness in detecting both single and double cracks, and independently for each vibration mode, which can be considered an advanced step in the field of structural health monitoring. Research limitations/implications The results confirm the validity of the MNCDF with the related papers, to accurately reveal single and double crack locations within beam structure. The validation process has demonstrated that the proposed damage index can accurately identify the crack location across different frequency modes by using a simplified computational approach. Originality/value This research presents a refined damage index that leverages vibration data of the damaged beams without needing to know the modes of the healthy beam. The proposed MNCDF can accurately reveal single and double crack locations within different beam structures based upon any frequency mode. It offers a significant advancement in early-stage structural damage detection and contributes to extend service life of engineering structures.
A novel index for vibration-based damage detection technique in laminated composite plates under forced vibrations: experimental study Khaldoon F. Brethee, Ahmed N. Uwayed, Arz Y. Alden Qwam Structural Health Monitoring, 2023 In this study, vibration modal analysis has been used to experimentally investigate the detection of fiber breakage (FB) and delamination in laminated composite plates. The modal analysis was performed on two arrangement styles of carbon fiber reinforced polymer (CFRP) laminated plates under forced vibrations. The main contribution in this study is that a new index named Improved Curvature Damage Factor (ICDF) was introduced to detect and localize damages in composite structures. It is a developed version of an earlier index based on the change in mode shape curvature (MSC) of dynamic response. To include the effect of more than one mode shape Cumulative Improved Damage Factor (CICDF) was proposed. The ICDF index was validated with a number of earlier studies that investigated the damage detection in different structures in order to approve the efficiency of this index. A scanning laser vibrometer was also used to experimentally examine the modal-based and forced responses for intact and damaged plates. Various experimental tests were used to verify the advantages of the proposed methodology and its use in structural health monitoring. In addition, the analysis of experimental results showed that the mutation caused by FB is almost double that of the value of delamination peaking.
An investigation into vibration response for condition monitoring of reciprocating compressor based on modulation signal spectrum analysis International Journal of COMADEM, 2018
Leakage-Free Segmentation-Based ANN for Crack Localization and Depth Estimation in Cantilever Beams M Majeed, K Brethee, F Basim Journal of Al-Farabi for Engineering Sciences 5 (1), 51-65 , 2026 2026
Nonlinear Characterisation of Wind Turbine Gearbox Vibration Dynamics Driven by Inhomogeneous Helical Gear Wear KF Brethee, GR Ibrahim, AH Albarbar Vibration 9 (1), 20 , 2026 2026
A refined mode shape curvature-based approach for baseline-free structural damage detection A Namah, K Brethee International Journal of Dynamics and Control 13 (12), 1-16 , 2025 2025 Citations: 2
Free vibration characteristics and localization of single and multiple cracks within beam structure AI Namah, KF Brethee World Journal of Engineering , 2025 2025 Citations: 2
Vibration analysis of simply supported Timoshenko beam subjected to a moving mass MJ Awad, KF Brethee AIP Conference Proceedings 3211 (1), 040033 , 2025 2025 Citations: 1
Vibration Analysis of Timoshenko Beam Subjected to a Moving Mass and Suffering from an Open Crack KF Brethee, MJ Awad Russian Journal of Nondestructive Testing 61 (4), 490-503 , 2025 2025 Citations: 1
Free Vibration Analysis of a Honeycomb Sandwich Structure with Orthotropic KF Brethee, GR Ibrahim, MM Yassin Proceedings of the UNIfied Conference of DAMAS, IncoME and TEPEN Conferences … , 2024 2024
Vibro-acoustic analysis for remotely condition monitoring approach of wind turbine KF Brethee, GR Ibrahim, AH Albarbar, RA Mohammed AIP Conference Proceedings 3009 (1), 030036 , 2024 2024 Citations: 1
A novel index for vibration-based damage detection technique in laminated composite plates under forced vibrations: experimental study KF Brethee, AN Uwayed, AY Alden Qwam Structural Health Monitoring 22 (5), 3109-3125 , 2023 2023 Citations: 33
Free vibration analysis of a honeycomb sandwich structure with orthotropic core KF Brethee, GR Ibrahim, MM Yassin, A Albarbar international conference on the efficiency and performance engineering … , 2023 2023 Citations: 3
Improved vibration based damage detection in laminated composite plate structures under free and forced modal analysis AN Uwayed, KF Brethee, SO Muhammad European Journal of Mechanics-A/Solids 100, 105031 , 2023 2023 Citations: 24
Monitoring of bearing based on high-order spectra analysis of electric power supply signals KF Brethee, GR Ibrahim, F Gu, AD Ball Arabian Journal for Science and Engineering 48 (5), 7145-7161 , 2023 2023 Citations: 4
The Extraction of Wind Turbine Condition Related Features Using Air-Borne Acoustic A Abouhnik¹, G Ibrahim, R Deng, K Brethee, A Badawood, W Abushanab, ... Proceedings of TEPEN 2022: Efficiency and Performance Engineering Network, 124 , 2023 2023
Hoff's Investigation of The Sandwich Panel with Honeycomb Core M Yassen, K Brethee Anbar Journal of Engineering Sciences 13 (2), 63-68 , 2022 2022
Vibration Analysis for Diagnosis of Tribo-Dynamic Interaction in Journal Bearings KF Brethee, J Ma, GR Ibrahim, F Gu, AD Ball International conference on the Efficiency and Performance Engineering … , 2022 2022 Citations: 2
The extraction of wind turbine condition related features using air-borne acoustic signals A Abouhnik, G Ibrahim, R Deng, K Brethee, A Badawood, W Abushanab, ... International conference on the Efficiency and Performance Engineering … , 2022 2022 Citations: 2
Damage degradation modelling for transverse cracking in composite laminates under low-velocity impact GR Ibrahim, A Albarbar, KF Brethee Engineering Fracture Mechanics 263, 108286 , 2022 2022 Citations: 17
Numerical analysis of lubricant viscosity variations on operating condition of helical gear system KF Brethee, RA Mohammed, GR Ibrahim International Journal of Computer Aided Engineering and Technology 17 (1), 57-73 , 2022 2022 Citations: 1
monitor the gearbox conditions at certain intervals by using the short-time Fourier transform method TZ Hamad, KF Brethee, GR Ibrahim Design Engineering, 11351-11362 , 2021 2021
Free vibration analysis of clamped laminated composite plates with centeral crack KF Brethee Anbar Journal of Engineering Sciences 12 (1), 108-115 , 2021 2021 Citations: 4
MOST CITED SCHOLAR PUBLICATIONS
Helical gear wear monitoring: Modelling and experimental validation KF Brethee, D Zhen, F Gu, AD Ball Mechanism and Machine Theory 117, 210-229 , 2017 2017 Citations: 98
A novel index for vibration-based damage detection technique in laminated composite plates under forced vibrations: experimental study KF Brethee, AN Uwayed, AY Alden Qwam Structural Health Monitoring 22 (5), 3109-3125 , 2023 2023 Citations: 33
Frictional effects on the dynamic responses of gear systems and the diagnostics of tooth breakages KF Brethee, F Gu, AD Ball Systems Science & Control Engineering 4 (1), 270-284 , 2016 2016 Citations: 32
The detection of lubricating oil viscosity changes in gearbox transmission systems driven by sensorless variable speed drives using electrical supply parameters S Abusaad, K Brethee, M Assaeh, R Zhang, F Gu, AD Ball Journal of Physics: Conference Series 628 (1), 012078 , 2015 2015 Citations: 25
Free vibration analysis of a symmetric and anti-symmetric laminated composite plate with a cutout at the center KF Brethee Al-Qadisiya Journal for Engineering Sciences 2 (2) , 2009 2009 Citations: 25
Improved vibration based damage detection in laminated composite plate structures under free and forced modal analysis AN Uwayed, KF Brethee, SO Muhammad European Journal of Mechanics-A/Solids 100, 105031 , 2023 2023 Citations: 24
Damage degradation modelling for transverse cracking in composite laminates under low-velocity impact GR Ibrahim, A Albarbar, KF Brethee Engineering Fracture Mechanics 263, 108286 , 2022 2022 Citations: 17
Monitoring gearbox using a wireless temperature node powered by thermal energy harvesting module B Elforjani, Y Xu, K Brethee, Z Wu, F Gu, A Ball 2017 23rd International Conference on Automation and Computing (ICAC), 1-6 , 2017 2017 Citations: 15
Progressive failure mechanism of laminated composites under fatigue loading GR Ibrahim, A Albarbar, KF Brethee Journal of Composite Materials 55 (1), 137-144 , 2021 2021 Citations: 14
An Investigation into Vibration Response for Condition Monitoring of Reciprocating Compressor based on Modulation Signal Spectrum Analysis. U Haba, K Brethee, O Hassin, AD Ball International Journal of COMADEM 21 (3) , 2018 2018 Citations: 14
An investigation of electrical motor parameters in a sensorless variable speed drive for machine fault diagnosis N Hamad, KF Brethee, F Gu, AD Ball 2016 22nd international conference on automation and computing (ICAC), 329-335 , 2016 2016 Citations: 14
Condition Monitoring of Lubricant Starvation Based on Gearbox Vibration Signatures. KF Brethee, F Gu, AD Ball International Journal of COMADEM 20 (3) , 2017 2017 Citations: 8
Analysis of frictional effects on the dynamic response of gear systems and the implications for diagnostics KF Brethee, J Gao, F Gu, AD Ball 2015 21st International Conference on Automation and Computing (ICAC), 1-9 , 2015 2015 Citations: 8
Diagnosis of induced gear wear in two-stage helical gearbox based on vibration analysis KF Brethee, GR Ibrahim, RA Mohammed, AH Albarbar 2020 13th International Conference on Developments in eSystems Engineering … , 2020 2020 Citations: 7
Modelling and simulation of a two stage reciprocating compressor for condition monitoring based on motor current signature analysis U Haba, K Brethee, S Alabied, D Mondal, F Gu, A Ball Condition Monitoring and Diagnostic Engineering Management 2 , 2018 2018 Citations: 5
Monitoring of bearing based on high-order spectra analysis of electric power supply signals KF Brethee, GR Ibrahim, F Gu, AD Ball Arabian Journal for Science and Engineering 48 (5), 7145-7161 , 2023 2023 Citations: 4
Free vibration analysis of clamped laminated composite plates with centeral crack KF Brethee Anbar Journal of Engineering Sciences 12 (1), 108-115 , 2021 2021 Citations: 4
Free vibration analysis of a honeycomb sandwich structure with orthotropic core KF Brethee, GR Ibrahim, MM Yassin, A Albarbar international conference on the efficiency and performance engineering … , 2023 2023 Citations: 3
Investigating the Effect of Water Contamination on Gearbox Lubrication based upon Motor Control Data from a Sensorless Drive S Abusaad, A Benghozzi, KF Brethee, F Gu, A Ball 3rd International Workshop and Congress on eMaintenance , 2014 2014 Citations: 3
A refined mode shape curvature-based approach for baseline-free structural damage detection A Namah, K Brethee International Journal of Dynamics and Control 13 (12), 1-16 , 2025 2025 Citations: 2
