Materials Modeling for Better Gear Design and Performance

Modeling techniques can quickly determine the best design and required steel cleanness level based on a gear’s application and performance requirements.


Prior articles in this series have highlighted the importance of clean steels as they relate to gear design and preventing premature component failures. Discussions on the increased occurrence of sub-surface-originated fatigue failures at material imperfections, inadequacy of current industrial standards for steel cleanness measurement, choosing the right material from the start in order to prevent failures, and increased demand to develop power dense mechanical systems all highlight the need for industrially relevant tools that can quantify the effect of steel cleanness on component life performance with minimal physical testing and design iterations. As my colleague put it in the May 2017 Materials Matter column: “From the design perspective of the bearing and gear engineer, the challenge is deciding how much cleanness the application requires…”

Fortunately, advances in materials modeling software and computer hardware have brought materials modeling to the forefront of innovating the next generation of materials — even gear steels. These tools, now commonly referenced in the connected framework of integrated computational materials engineering (ICME), can be used to decrease the time and money spent designing and implementing new steel solutions. Intensive efforts and collaborations are underway between national laboratories, universities, and industry to create and apply computational tools that can connect the nano- and micro-scale characteristics of materials to the typical bulk materials specifications relating to strength, toughness, and fatigue performance. [1, 2]

In the case of designing steels for successful application to power density and light-weighting initiatives, material models become even more powerful when used in conjunction with refined measurement methods such as automated scanning electron microscopy or ultrasonic inspection for inclusion analysis. For example, a laboratory measurement tool, such as an SEM, is used to feed realistic inclusion population characteristics into a computational materials model that calculates the effect of various inclusions on fatigue performance. The results provide a quantitative measure of the impact of a particular steel cleanness on fatigue performance, thus providing critical information to gear designers on the allowable inclusion population for a given gear application.

More traditional modeling efforts focused on finite element analysis (FEA), which is a mature methodology that can provide 2D or 3D stress and strain distributions in a component, such as those shown in Figure 1 for the surface stress created when bending a gear tooth. If any material imperfections were incorporated in these calculations in the past, they were typically only simplified inclusion or void shapes due to computational limitations.

Figure 1: Traditional finite element analysis showing the surface stress on a gear tooth during bending.

Thanks to advances in custom materials modeling software, we are now able to easily incorporate the combined effects of component geometry (shape, surface finish), material strength (alloying, grain size), inclusion characteristics (type, size, location, shape, stringer interaction) and stress state (component loading conditions, residual stress from heat treat or machining). Now, even complex inclusions or microstructural heterogeneities can be captured and accounted for in finite element models using tools that can mesh 2D or 3D materials data directly or by creating synthetic microstructure features based on representative measured data. [3, 4]

The latter method was used to generate the stringer oxide inclusion shown in Figure 2a. Inclusion characteristics were distilled from laboratory measurements in order to adequately describe a random stringer geometry configuration.

Figure 2: Simulated images showing: (a) a complex stringer inclusion and the local stress state when considering; (b) just contact loading stress, and (c) contact loading stress plus residual stress from heat treatment.

The advantage for any further calculations is that this subsurface stringer inclusion shown in Figure 2a is not self-aware. The inclusion doesn’t know if it is in a gear or a bearing, or whether its home component has been carburized or through-hardened. It simply interacts with the applied stress field according to the rules of the simulation environment. The stress field shown in Figure 2b takes into account the stress induced from contact loading, while Figure 2c additionally includes a pre-existing residual stress field. The resultant, cumulative, localized stress concentration effect for single or repetitive loading cycles can then be quantified using one of many calculations or indicator parameters. [5, 6]

While the example shown is interesting, and Figure 2 is visually appealing, the true power of this method in particular comes from quickly running this calculation in a highly repetitive fashion within a structured statistical framework. This allows us to truly connect the variability in the inputs to the potential variability in the output result — fatigue performance. By taking the results from a larger scale computational design of experiments, you can now produce the previously discussed relationships between steel cleanness, torque and gear mass on fatigue performance (July 2017 Materials Matter).

The increased need for gear materials design support can be met by advanced materials models used in conjunction with appropriate measurement methods. This confluence of past (laboratory) and present (computational) approaches can answer the critical question at hand: What level of steel cleanness is needed for my gear? The potential benefit from materials modeling increases the earlier it is used in the design process, but the approach can be applied at any stage—whether a new, smaller gear that requires an equivalent load to its predecessor or an existing gear that is being asked to carry an increased load.


  1. Integrating Computational Materials Engineering (ICME): Implementing ICME in the Aerospace, Automotive, and Maritime Industries, TMS, Warrendale, PA, 2013.
  2. Modeling Across Scales: A Roadmapping Study for Connecting Materials Models and Simulations Across Length and Time Scales, TMS, Warrandale, PA, 2015.
  3. V.R. Coffman, A.C.E. Reid, S.A. Langer, G. Dogan, “OOF3D: An image-based finite element solver for materials science,” Mathematics and Computers In Simulation, Vol. 82, pp. 2951-2961, 2012.
  4. M.A. Groeber, M.A. Jackson, “DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D,” Integrating Materials and Manufacturing Innovation, Vol. 3, Issue 1, Article 5, 2014.
  5. Fundamentals of Modeling for Metals Processing, Handbook Vol. 22A , ASM International, Materials Park, OH, USA, 2009.
  6. G.J. Schmitz and U. Prahl (eds), Handbook of Software Solutions for ICME, Wiley-VCH, Weinheim, Germany, 2017.
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is manager of the Advanced Modeling group at TimkenSteel Corporation. Since 2006, he has worked on projects related to alloy development and advanced computer modeling of metallurgical processes. Learn more at