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Prediction of Residual Stresses in Heat-Treated Gears Using Finite Element-Based Artificial Neural Networks

Determination of the residual stresses resulting from heat treatment processes, such as case hardening, is crucial for the structural integrity assessment of gear units. Experimental methods like deep hole drilling (DHD) are costly, time-consuming, and destructive, while non-destructive methods such as ultrasonic testing offer limited depth resolution. Advances in finite element methods (FEM) provide a promising alternative that does not damage the component. However, each FE computation can take over ten hours, depending on the complexity of the heat treatment and component geometry. By applying a data-driven machine learning approach, one can reduce the computation time from hours to a few seconds.

In this work, heat treatment for various double helical gears is designed…

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Determination of the residual stresses resulting from heat treatment processes, such as case hardening, is crucial for the structural integrity assessment of gear units. Experimental methods like deep hole drilling (DHD) are costly, time-consuming, and destructive, while non-destructive methods such as ultrasonic testing offer limited depth resolution. Advances in finite element methods (FEM) provide a promising alternative that does not damage the component. However, each FE computation can take over ten hours, depending on the complexity of the heat treatment and component geometry. By applying a data-driven machine learning approach, one can reduce the computation time from hours to a few seconds.

In this work, heat treatment for various double helical gears is designed and simulated using a commercial FE program. These results are then validated against available data from deep-hole drilling (DHD) experiments. The heat treatment design involves carburizing, hardening, and two tempering cycles, with carburizing and tempering times adjusted based on gear dimensions and case hardening depth (CHD). The FE-based residual stresses are used to train and validate an artificial neural network (ANN) regression model to predict stresses at arbitrary locations for different gear dimensions with their respective heat treatments. Applying the ANN model in fracture assessment significantly decreases evaluation time while maintaining accuracy comparable to FE simulations as well as ensuring safe and reliable operations even at higher pitch line velocities.

Reference
BR-2025-486

Title
Prediction of Residual Stresses in Heat-Treated Gears Using Finite Element-Based Artificial Neural Networks
Author(s)
B. Mushtaq, H.R. Bayat, A. Vötterl
DOI
10.48447/BR-2025-486
Event
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
Year of publication
2025
Publication type
conference paper (PDF)
Language
German
Keywords
Machine Learning,Gear,Heat Treatment,Residual Stress,Finite Element Analysis

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F. Paysan, E. Breitbarth
10.48447/BR-2025-491
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
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57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
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Price €25.00
Online only New
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57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
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Price €25.00
Online only New
Einfluss der T-Spannung auf das Rissablenkungsverhalten in dünnwandigen AA2024-T3 Blechen unter biaxialer Ermüdungsbeanspruchung
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57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
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57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
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2025
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Online only New
Experimentelle Ermittlung von Rissablenkungswinkeln bei außerphasiger Mixed-Mode-Belastung mittels einer neuartigen Probengeometrie
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57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
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57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
conference paper (PDF)
German
Rissablenkungswinkel,experimentelle Ermittlung,neuartige Probengeometrie,außerphasige Mixed-Mode-Belastung
Price €25.00
Online only New
57. Tagung des Arbeitskreises Bruchmechanik und Bauteilsicherheit
10.48447/BR-2025-BB
Editor(s): Prof. Dr.-Ing. Andreas Ricoeur
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2025
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Prof. Dr.-Ing. Andreas Ricoeur
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57. Tagung des Arbeitskreises Bruchmechanik und Bauteilsicherheit
10.48447/BR-2025-BB
Prof. Dr.-Ing. Andreas Ricoeur
57. Tagung des Arbeitskreises Bruchmechanik und Bauteilsicherheit
2025
conference proceedings (PDF)
German
DVM, conference, event, fracture mechanics, component safety, component evaluation, material evaluation, stress analysis, test methods, applications
Price €90.00
Online only
Beschreibung von Ermüdungsrisswachstum in duktilen Materialien unter proportionalen und nicht-proportionalen Beanspruchungen
Author(s): A. Gibb, A. Tsakmakis, M. Vormwald
10.48447/BR-2025-506
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
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Beschreibung von Ermüdungsrisswachstum in duktilen Materialien unter proportionalen und nicht-proportionalen Beanspruchungen
Beschreibung von Ermüdungsrisswachstum in duktilen Materialien unter proportionalen und nicht-proportionalen Beanspruchungen
A. Gibb, A. Tsakmakis, M. Vormwald
10.48447/BR-2025-506
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
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German
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Beschreibung von Ermüdungsrisswachstum in duktilen Materialien unter proportionalen und nicht-proportionalen Beanspruchungen
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10.48447/BR-2025-506
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
conference paper (PDF)
German
Phasenfeldmodell,Anisotropie,Ermüdungsrisse,Nicht-proportional
Price €25.00
Online only New
Duktile Schädigung und Versagen unter ebener biaxialer Belastung
Author(s): S. Gerke, M. Brünig
10.48447/BR-2025-551
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
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Duktile Schädigung und Versagen unter ebener biaxialer Belastung
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S. Gerke, M. Brünig
10.48447/BR-2025-551
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
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Duktile Schädigung und Versagen unter ebener biaxialer Belastung
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10.48447/BR-2025-551
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
conference paper (PDF)
German
Duktile Schädigung und Versagen,Biaxiale Experimente,Kontinuumsschädigungsmodell,Numerische Berechnungen
Price €25.00
Online only New
Energiebasierte Analyse zur Strukturbildung bei dreidimensionalen Rissmustern
Author(s): M. Hofmann, R. Anderssohn, N. Jesch-Weigel, R. Zielke, T. Wallmersperger
10.48447/BR-2025-483
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
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10.48447/BR-2025-483
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
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1
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10.48447/BR-2025-483
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
conference paper (PDF)
German
Rissmuster,3D-Bruchmechanik,Energiemethode
Price €25.00
Online only New
Investigation of the influence of T-stress in biaxially loaded specimen on plasticity-induced crack closure in Ti6246 using digital image correlation
Author(s): A. Zaiat, C. Kontermann, A. Blug, M. Oechsner, A. Bertz, G. Laskin, F. Conrad, D. Carl
10.48447/BR-2025-535
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
conference paper (PDF)
German
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Investigation of the influence of T-stress in biaxially loaded specimen on plasticity-induced crack closure in Ti6246 using digital image correlation
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A. Zaiat, C. Kontermann, A. Blug, M. Oechsner, A. Bertz, G. Laskin, F. Conrad, D. Carl
10.48447/BR-2025-535
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
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10.48447/BR-2025-535
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
conference paper (PDF)
German
PICC,Biaxial-Testing,Cruciform Specimens,T-Stress,DIC
Price €25.00
Online only New
Integration von digitalen und experimentellen Methoden zur Analyse des Ermüdungsfortschrittshaltens in komplexen dreidimensionalen Blechbauteilen am Beispiel von L-Profilen
Author(s): F. Dömling, F. Paysan, V. Schöne, E. Breitbarth
10.48447/BR-2025-463
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
conference paper (PDF)
German
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Integration von digitalen und experimentellen Methoden zur Analyse des Ermüdungsfortschrittshaltens in komplexen dreidimensionalen Blechbauteilen am Beispiel von L-Profilen
Integration von digitalen und experimentellen Methoden zur Analyse des Ermüdungsfortschrittshaltens in komplexen dreidimensionalen Blechbauteilen am Beispiel von L-Profilen
F. Dömling, F. Paysan, V. Schöne, E. Breitbarth
10.48447/BR-2025-463
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
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Integration von digitalen und experimentellen Methoden zur Analyse des Ermüdungsfortschrittshaltens in komplexen dreidimensionalen Blechbauteilen am Beispiel von L-Profilen
F. Dömling, F. Paysan, V. Schöne, E. Breitbarth
10.48447/BR-2025-463
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
conference paper (PDF)
German
FEM,Digitale Bildkorrelation,L-Profil,Schadenstoleranz
Price €25.00
Online only New
Anwendung von repräsentativen Proben zur Bewertung der Strukturintegrität von sicherheitsrelevanten Komponenten
Author(s): M. Madia, J. Zhu, M. Schurig, J. Kruse, F. Conrad, H. Schlums, C. Kontermann, U. Zerbst
10.48447/BR-2025-536
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
conference paper (PDF)
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Anwendung von repräsentativen Proben zur Bewertung der Strukturintegrität von sicherheitsrelevanten Komponenten
Anwendung von repräsentativen Proben zur Bewertung der Strukturintegrität von sicherheitsrelevanten Komponenten
M. Madia, J. Zhu, M. Schurig, J. Kruse, F. Conrad, H. Schlums, C. Kontermann, U. Zerbst
10.48447/BR-2025-536
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
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German
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Anwendung von repräsentativen Proben zur Bewertung der Strukturintegrität von sicherheitsrelevanten Komponenten
M. Madia, J. Zhu, M. Schurig, J. Kruse, F. Conrad, H. Schlums, C. Kontermann, U. Zerbst
10.48447/BR-2025-536
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
conference paper (PDF)
German
Strukturintegrität,Bruchmechanik,Turbinenscheibe,Repräsentative Proben
Price €25.00
Online only New
Beschreibung des R- und des Temperatureinflusses sowie des Einlaufverhaltens bei experimentell bestimmten Rissfortschrittskurven mit dem Exponentialansatz
Author(s): G. Kullmer, D. Weiß, B. Schramm
10.48447/BR-2025-492
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
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Beschreibung des R- und des Temperatureinflusses sowie des Einlaufverhaltens bei experimentell bestimmten Rissfortschrittskurven mit dem Exponentialansatz
Beschreibung des R- und des Temperatureinflusses sowie des Einlaufverhaltens bei experimentell bestimmten Rissfortschrittskurven mit dem Exponentialansatz
G. Kullmer, D. Weiß, B. Schramm
10.48447/BR-2025-492
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
Publication type: conference paper (PDF)
German
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Beschreibung des R- und des Temperatureinflusses sowie des Einlaufverhaltens bei experimentell bestimmten Rissfortschrittskurven mit dem Exponentialansatz
G. Kullmer, D. Weiß, B. Schramm
10.48447/BR-2025-492
57. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit – Tagung 2025
2025
conference paper (PDF)
German
Clinchen,Rissfortschrittsgesetz,R-Abhängigkeit,Temperaturabhängigkeit,Einlaufverhalten
Price €25.00
Online only New