A multi-objective macro-geometry spur gear optimization process to improve weight, efficiency and NVH performance utilizing neural networks
Kalligeros C. Papalexis C. Kostopoulos G. Terpos K. Tzouganakis P. Kostas K. Halim D. Yang J. Spitas C. Tsolakis A. Sakaridis E. Spitas V.
July 2026Elsevier Ltd
Mechanism and Machine Theory
2026#223
In this study, a macro-geometry optimization process is developed to improve the weight, efficiency, and Noise, Vibration, and Harshness (NVH) performance of spur gears. NVH improvement is achieved through the minimization of the peak-to-peak static transmission error (STE). STE curves are calculated using a fully connected feed-forward neural network (FFNN) that achieves a mean absolute percentage error below 0.5%. Based on the FFNN, a multi-objective optimization framework using the NSGA-II algorithm is developed and applied to seven case studies. The results demonstrate that macro-geometry optimization can significantly enhance NVH performance, achieving reductions in the RMS of dynamic transmission error exceeding 35%, while simultaneously reducing power losses by more than 40%. The findings reveal a strong correlation between power loss reduction and peak-to-peak STE and confirm peak-to-peak STE as an effective surrogate objective for improving dynamic behavior. The proposed framework enables rapid and accurate NVH-driven gear design by integrating neural-network-based STE prediction with multi-objective evolutionary optimization, demonstrating that substantial NVH improvements can be achieved through macro-geometry optimization alone. In addition, general guidelines for the selection of macro-geometric parameters are proposed.
Evolutionary Optimization , Macro-geometry , Neural networks , NVH , Optimization , Transmission Error
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Laboratory of Machine Design, National Technical University of Athens, 9 Iroon Polytechniou, Zografou, 15780, Greece
Laboratory of Machine Elements and Vehicles, Department of Mechanical Engineering, University of West Attica, Egaleo, 12244, Greece
Department of Mechanical and Aerospace Engineering, Nazarbayev University, Kazakhstan
Department of Mechanical, Materials and Manufacturing Engineering, Faculty of Science and Engineering, University of Nottingham, Ningbo, China
Laboratory of Machine Design
Laboratory of Machine Elements and Vehicles
Department of Mechanical and Aerospace Engineering
Department of Mechanical
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