Gear Optimization
Gear Optimization
Multi-objective optimization of gear tooth profiles to improve weight, efficiency, dynamic behavior, and wear performance, focusing on both involute macro-geometry and free-form non-involute profiles. Key results include more than 40% reduction in power losses and 35% reduction in vibration RMS for optimized involute gears. For free-form gears, reductions of up to 55% in average wear depth and 70% in maximum wear depth have been achieved.
Impact
Gear optimization has a major industrial impact, as gears are essential components in nearly all power transmission systems, including vehicles, wind turbines, aerospace systems, robotics, and industrial machinery.
Its importance is further amplified by the rapid growth of electrification. The global EV market is expected to grow from approximately $13 billion to more than $25 billion by 2030, while the industrial gearbox market is projected to approach $40 billion. EV gearboxes impose particularly strict requirements for high efficiency and low noise, as drivetrain losses and transmission noise significantly affect vehicle performance and comfort. For example, reducing gearbox losses in a passenger vehicle by only 1 kW can save up to 4 kW of fuel energy equivalent. At the same time, gearbox noise must remain below 30-35 dB(A).
In wind turbines, a 50% reduction in gearbox losses in a modern 5 MW turbine can decrease total power losses by approximately 200 kW per turbine. Gearbox reliability is also a major challenge: around 1,200 gearbox failures occur annually in wind turbines worldwide, with repairs often requiring several days to two months.
MD-Lab’s Research
Our research focuses on two main directions:
- Macro-geometry optimization of involute gears
- Free-form optimization of non-involute gears
Involute Gears
We investigate multi-objective macro-geometry optimization of gear transmissions to simultaneously improve weight, efficiency, and NVH (Noise, Vibration, and Harshness) performance. Design variables include:
- Number of teeth
- Module
- Face width
- Profile shift coefficients
- Pressure angle
- Secondary geometric parameters such as addendum and dedendum coefficients, backlash, and rack tip radius
Our methodology uses the Static Transmission Error (STE) as the primary indicator of vibration and noise excitation. Although STE is computationally cheaper than full dynamic simulations, its evaluation still requires demanding numerical models.
To overcome this limitation, we developed Feed Forward Neural Network (FFNN) surrogate models capable of predicting STE curves with high accuracy. The computational time was reduced from approximately 3 seconds per evaluation using physics-based reduced-order models to only 0.001 seconds per evaluation. The generated dataset covered the full design space while maintaining a mean absolute percentage error of only 0.395%.
For optimization, we mainly employ evolutionary multi-objective algorithms, particularly NSGA-II. Current results include:
- More than 40% reduction in power losses
- More than 35% reduction in RMS dynamic transmission error
- More than 70% reduction in vibration amplitude
The optimal trade-off between efficiency, NVH performance, and weight is generally achieved by increasing the number of teeth, reducing the module and face width, and increasing the profile shift coefficients.
Publications
- Kalligeros, C., Papalexis, C., Kostopoulos, G., Terpos, K., Tzouganakis, P., Kostas, K., Halim, D., Yang, J., Spitas, C., Tsolakis, A., Sakaridis, E., & Spitas, V. (2026). A multi-objective macro-geometry spur gear optimization process to improve weight, efficiency and NVH performance utilizing neural networks. Mechanism and Machine Theory, 223, 106422. https://doi.org/10.1016/j.mechmachtheory.2026.106422
- Sakaridis, E., Kalligeros, C., Papalexis, C., Kostopoulos, G., & Spitas, V. (2023). Symmetry preserving neural network models for spur gear static transmission error curves. Mechanism and Machine Theory, 187, 105369. https://doi.org/10.1016/j.mechmachtheory.2023.105369
Non-Involute Gears
Although involute gears dominate modern gear transmissions, significant research has focused on alternative non-involute profiles to address known limitations of involute geometries, such as suboptimal pitting resistance, lubrication characteristics, and convex-to-convex contact conditions. Most existing approaches investigate predefined profiles, including cycloidal, circular-arc, and parabolic geometries, to improve specific performance metrics.
At MD-Lab, we follow a different approach. Instead of optimizing predefined geometries, we treat the tooth profile itself as a design variable and directly optimize its shape to maximize performance. The tooth flank is represented as a parametric curve, such as a B-spline, while the control points are optimized to improve metrics including efficiency and wear resistance.
This free-form optimization methodology has already achieved:
- Up to 55% reduction in average wear depth
- Up to 70% reduction in maximum wear depth
We have also developed new analytical methods and geometric constraints to ensure proper meshing conditions, eliminate geometric discontinuities, and maintain acceptable contact ratios.
Publications
- Kalligeros, C., Papalexis, C., Georgiou, D., Kryfos, D., Vakouftsis, C., Terpos, K., Goudas, K., Balis, P., Kontaris, T., Kaisarlis, G., Tsolakis, A., Zalimidis, P., Sapidis, N., Provatidis, C., & Spitas, V. (2023). Improving the wear resistance of 3D printed spur gears through a free-form tooth flank optimization process. MATEC Web of Conferences, 387. https://doi.org/10.1051/matecconf/202338701002
- Kalligeros, C., Koronaios, P., Tzouganakis, P., Papalexis, C., Tsolakis, A., & Spitas, V. (2022). Development of a free-form tooth flank optimization method to improve pitting resistance of spur gears. MATEC Web of Conferences, 366, 01003. https://doi.org/10.1051/matecconf/202236601003
