AI-accelerated gear stress analysis
- Alvaro Filho
- Oct 15
- 6 min read
Challenge: achieve fast and accurate virtual prototyping
The optimal multi-attribute design of transmissions remains a critical challenge for drivetrain engineers, gaining even greater significance in the era of electric vehicles. Today’s automotive industry demands powertrains that excel in multiple aspects: minimizing noise and vibrations, maximizing power density and efficiency, while ensuring unprecedented durability performance. For this purpose, transmission engineers need to design innovative transmissions that meet the multi-attribute performance criteria. Computer-Aided Engineering (CAE) allows engineers in industry to virtually prototype and optimize their next product optimization. Simulations are essential to accurately predict and optimize component behavior and the system-level transmission performance throughout the development cycle.
Powerful physics-based models and simulation capabilities are available, which accurately model real-life products, perform predictive simulations and optimize the product’s performance for statics, dynamics, aerodynamics, acoustics, durability, etc. These physics-based models, for example Finite Element (FE) models, are successfully adopted in industrial development workflows. For high-fidelity simulations (e.g. detailed FE contact simulations), the model fidelity must increase to allow accurate predictions, which unfortunately also increases the model’s computation time and cost.
In CAE, Artificial Intelligence (AI) and Machine Learning (ML) technologies are revolutionizing physics simulations. Among the advancements, surrogate modeling for physics simulations experiences rapid growth thanks to advanced AI techniques and architectures. Surrogate models, or reduced-order models (ROMs), provide efficient alternatives to computationally expensive high-fidelity simulations (such as detailed FE contact simulations). These AI/ML-based surrogate models, capable of providing fast and accurate predictions while maintaining high fidelity, unlock the potential for extensive and automated design space exploration, enabling engineers to efficiently evaluate thousands of design variants in a fraction of the time required by traditional simulation methods.
Gears, as critical components in transmission systems, particularly benefit from such advanced simulation approaches, as their design requires careful consideration of deformation, contact and bending stresses, and durability. This blog post introduces a novel gear design analysis method3 that combines the strengths of FE and AI/ML models to achieve efficient and accurate gear stress prediction, demonstrating how this technology can be practically implemented in industrial workflows.
Solution: combine powerful high-fidelity models with AI/ML
The innovative gear stress analysis method3 exploits the powerful predictive simulation capabilities of FE models to generate accurate simulation data, which is then used to train an AI/ML surrogate model. Once trained, the efficient AI/ML surrogate model can accurately predict gear stresses for unseen combinations of design parameters. This combines the strengths of FE and AI/ML into a novel AI/ML-accelerated gear stress analysis capability that provides accurate predictions quickly.
The simulation workflow for comprehensive gear analysis integrates the capabilities of Simcenter 3D and Simcenter Nastran software solutions, while Simcenter HEEDS serves the dual purpose of automating data generation for AI/ML model training and orchestrating multi-objective optimization studies that make use of the AI/ML model calculations.
Figure 1 illustrates the automated data generation workflow, in which Simcenter HEEDS orchestrates the physics-based simulation process. The workflow streamlines the creation of gear datasets, while incorporating elements from Simcenter 3D Motion Gear Design Optimization methodologies. For each design, first the macrogeometry and microgeometry of the gear pair are evaluated before the nonlinear FE analysis (NLFEA) module generates the FE model and uses Simcenter Nastran for automated FE-based gear contact.
Figure 1: Automated gear data generation workflow, involving Simcenter HEEDS as orchestrator.
This workflow adopts high-fidelity physics-based simulation models, bringing several advantages to design engineers: highly accurate predictions of real-world behavior through detailed modeling of physical phenomena (such as the nonlinear contact mechanics in gear mesh), and a deep understanding of complex interactions and phenomena that could be missed in simpler models. These detailed models provide a reliable source of training data for AI models and AI model validation.
To accelerate gear stress and durability analysis, our approach replaces the traditional NLFEA-based contact analysis by an AI/ML surrogate model, trained on NLFEA contact analysis results, to predict the altering gear blank and tooth root stress throughout the gear meshing cycle. The resulting AI/ML-based ROM offers significantly reduced computation times compared to the full order NLFEA-based simulations, enabling rapid design iterations. Embedding the AI/ML model within the standard gear design simulation workflows creates an AI/ML-accelerated process that remains highly accurate, while opening doors to multi-objective optimization studies (typically unachievable via traditional, resource intensive, FE models).
Two additional solution elements are introduced to realize the AI/ML accelerated workflows:
Simcenter Reduced Order Modeling8 that enables the creation and deployment of ROMs from simulation and test data.
An upcoming Simcenter AI technology for 3D surrogate modelling that leverages operator learning techniques.
Results: realize fast and accurate gear stress analysis
A solution workflow has been introduced, aimed at combining the power of high-fidelity models with AI/ML models to achieve AI/ML-accelerated gear stress analysis. This section introduces a gear use case to verify the workflow vs. the objective to achieve efficient yet accurate gear stress analysis.
The gear design use case is described in detail below and has four design parameters:
the normal pressure angle, in range [18°-22°],
the addendum coefficient of the Pinion, in range [1.00-1.30],
the addendum coefficient of the Wheel, in range [1.00-1.30], and
the profile shift coefficient of the Pinion, in range [0.35-0.70].
Using Simcenter HEEDS and Simcenter Nastran, 81 gear designs were created, varying the four design parameters through a level 3 full factorial DOE. The data set is split randomly into 64 designs as training set and 17 designs as test set.
A transformer-based operator learning AI/ML model is trained to predict gear surface stresses, given the surface geometry and contact forces as model inputs. In this first study, we chose to have the AI/ML model learn the full 3D signed von Mises stress field, which captures both compressive and tensile behavior. The signed von Mises stress is created via postprocessing of the full 3D tensor at each node, which is stored in the NLFEA-based contact results. The model focuses on surface nodes where failures typically initiate (tooth root and contact regions), optimizing computational efficiency while maintaining accuracy for critical stress predictions3. Three approaches are evaluated for the gear design use case:
FE Reference: NLFEA-based contact simulations (Reference),
ML with FE Forces: AI/ML predictions using NLFEA contact forces,
ML with Motion Forces: AI/ML prediction using Simcenter 3D Motion contact forces.
Multibody-based gear contact forces (computed via Simcenter 3D Motion) are used in this study as they provide a computationally efficient alternative to expensive nonlinear finite element analyses, while still maintaining sufficient accuracy in predicting contact force distributions – an aspect that will be crucial for future design optimization workflows.
Figure 2 presents an analysis of the full stress field using the three approaches. The stress field predicted by the AI/ML surrogate model with FE-based contact forces as input (Fig. 2b), shows to be near-identical to that of the reference FE-based results (Fig. 2a), while the stress field predicted by the AI/ML surrogate model with Motion-based contact forces as input (Fig. 2c) shows only minor deviations from the reference results. These findings are confirmed by Figure 3, which presents the results for the tooth root stress during five mesh cycles for a point located along the middle of the face width and in the middle of the tooth root arc.
Figure 2: Von Mises (signed) stress fields, computed from a) NLFEA-based contact simulations, b) ML model with FE-based forces (input), c) ML model with Motion-based forces (input), for a pinion gear example case.
Figure 3: Comparison of tooth root stress for a point (middle flank, middle root arc) over the course of 5 mesh cycles (created based on the stress of 5 teeth during 1 mesh cycle) for a pinion gear example case Figure 3.
Though data generation and AI/ML model training require an initial time investment, these are one-time offline processes. The resulting trained model enables rapid predictions, ideal for efficient design space exploration and optimization.
The AI/ML model that was used in this study requires about 0.1 seconds to compute the full stress field for one point in the mesh cycle, while one NLFEA contact simulation requires on average about 5 minutes. Knowing that a full mesh cycle requires about 20 to 30 angular configurations per gear pair and that an industrial transmission has multiple gear pairs for which hundreds of variants are explored, the inclusion of the AI/ML surrogate models can truly accelerate gear design optimization.
Conclusion and outlook
This study demonstrates the successful integration of AI/ML surrogate models into gear design workflows, achieving both speed and accuracy in stress prediction. The AI/ML approach delivers results that closely match traditional nonlinear finite element analyses while being multiple orders of magnitude faster. This dramatic speed improvement, combined with maintained accuracy, opens new possibilities for comprehensive design space exploration and optimization of transmission systems.
The developed workflow, supported by Simcenter tools, and validated through practical case studies, effectively demonstrates the industrial viability of AI/ML-accelerated gear and transmission design.
References
D. Park, A. Rezayat and Y. Gwen, “Gear design optimization for multi-mesh and multi-power flow transmissions under a broad torque range incorporated with multibody simulations”, in VDI International Conference on Gears 2022, Munich, Germany, 2022.
M. Vivet, J. Melvin, S. Donders, “Advancing bevel gear contact simulation towards quiet transmissions”, Simcenter Blog, August 19, 2024.
M. Vivet, D. Park, A. Scheuer, “AI/ML-accelerated gear durability analysis within gear design optimization”, in VDI International Conference on Gears 2025, Garching near Munich, Germany, September 10-12, 2025.
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