Jul 052018

Decision Based Design Framework to Identify the variables needed for Austenite Grain Size After Hot Rod Rolling


In our laboratory, we are interested in a model based realization of complex system and the complex system we are looking at is a steel manufacturing process chain. Our industrial partners are Tata Consulting Services in India. Their goal is to be able to produce a gear that can be used in cars and other machines. Producing a gear consists of numerous intermediate stages starting from producing steel. The process that we are interested in is the hot rolling with the end goal of producing a rod, which can be further modified to produce a gear. Further processes that come after rolling have already been studied.

We look at the hot rod rolling problem in a top down approach i.e. identifying the goal first and then work backwards to find the factors and variables required to reach these goals. We have made some assumptions about the strain rate and the interpass time involved to provide a focus to this study. Relating to those are certain conflicting goals we have to achieve. Using a decision based construct, compromise Decision Support Problem (cDSP), we can explore the solution space and identify the most satisficing initial variable values that will provide the microstructure we require for the rod.


There are uncountable steel products in the market today. A steel manufacturing company has multiple intermediate stages where different semi-products like sheets or rods are produced. These go under further processing to produce other complex products, for example a gear. Manufacturing engineers are looking at how to reduce the time and cost needed to produce these semi-products and to maximize the profit.

In this research, we analyze the production process of a rod. TATA Steels, our industrial partners, produce rod through the hot rolling process, which will be described in the next section. We know that the steel is in the austenite phase after it is rolled. Knowing this final austenite grain size, our research is focused on identifying the initial variables and their quantitative values required to reach this end goal. In this top-down approach, we will use a decision based design framework, where compromise decision based problem (cDSP) construct will be the core. The advantage of using cDSP is that it provides us with multiple solutions that then a human designer can use to satisfy multiple goals at the same time. It is a flexible design that lets you decide on a weightage for conflicting goals. We believe that the fundamental role of a human designer is to make decisions. By using the decision based design framework applied in this research, we can equip the decision maker with the best tools needed to find the final austenite grain size after hot rod rolling. The cDSP has not been executed and is in way forward.


Hot rod rolling is a complex manufacturing system where various parameters need to be precisely controlled to achieve a specified microstructure at the end [1]. In the figure 1, which is a modified figure from reference [2], process along with the system is displayed.

Figure 1 – presenting the hot rod rolling process, variables affecting the Final Austenite Grain size and an inverse design method – modified from reference [2]

Rolling is a multistage metal working process that can happen either at room temperature (cold rolling) or at elevated temperatures (hot rolling). During rolling, an initial billet is fed in which goes through plastic deformation to eventually produce a rod after multiple rolling stages.

When steel is made from iron ore, it has a certain microstructure. When it is casted into a solid billet, it loses the initial microstructure. One method to gain the initial microstructure back is through recrystallization[1]. Therefore, we are interested in hot rolling process because it happens at the recrystallization temperature.

[1] Recrystallization is a process in which, within a certain temperature range, new equiaxed and strain-free grains are formed, replacing the older grains. The temperature required for recrystallization ranges approximately between 0.3 and 0.5Tm, where Tm is the melting point of the metal on the absolute scale. [3]

Figure 2 – An FEM of hot rod rolling

During hot rolling, large rollers of weight much higher than the billet (figure 2 [4]), roll the billet to eventually produce a circular rod. When the rod is being rolled, the microstructural grains go through recrystallization, which is followed by grain growth. These processes help produce new equiaxed grains in the rolled rod. Accurate control of these two phenomena help us predict the final austenite grain size. From our literature search, we identified five initial variables – interpass time, which is the time taken to move the rod from one rolling unit to the next, initial austenite grain size before rolling, strain, strain rate and temperature at the point of contact.

Problem statement – Given a target austenite grain size, which depends on these 5 variables, how can a designer come up with the best combination of influencing factors to achieve the microstructure identified using simulation model.

Also, the two advantages of using hot rolling process to produce rods are that it:

  • provides the opportunity for production of new grains from previously damaged ones
  • provides enough control variables to produce various kinds of rods

In the industry, designers evaluate these variables in a complete trial and error process. We want to change this by having an associated simulation models that will help the decision makers in finding the satisficing solution.


Figure 3 – Decision Based Design Method modified from Reference [4]

As aforementioned, we want to equip human designers with tools so that they are in the best situation to make decisions. The decision based design framework (Figure 3) [4] facilitates the solution space exploration to find robust solutions.

The application of DBD method starts with finding the boundary around the end goal. Keeping that in mind, we must identify the requirements that lead us to the final product. This was covered in the previous section already. Knowing these variables, through a thorough literature search, we must identify the theoretical and empirical models available (Section 4). If we fail to find these models, we will have to rely on simulation programs to develop the surrogate and response surface models for the defined problem.

We are carrying out these steps solely to formulate the compromise Decision Support Problem (cDSP) construct, which is at the core of this DBD framework. cDSP is a design tool utilized in problems with multiple conflicting goals under uncertainty. A weightage value for the different goals can be set and based on that, the cDSP generates solutions for the initial variables. These solutions can be plotted on ternary plots for visual analysis. Different ternary plots for different initials variables are superimposed to identify the points where most of the variables tested are in the desired range. The decision maker can then compromise on a certain goal and focus more on a different more important goal and choose the solution point to implement accordingly [5, 6].



We looked at various research papers available on hot rod rolling to identify the models on the grain size during recrystallization, grain size during grain growth and fraction recrystallized. Figure 4 was found in reference [9] that helped us state assumptions and narrow the problem.

There are three types of recrystallizations – static (SRX), dynamic (DRX) and meta-dynamic recrystallization (MDRX). In hot rod rolling, the MDRX always follows the DRX. Therefore, DRX is neglected in the model and only MDRX is included even though the rod goes through DRX.

Figure 4 – procedure for calculating the AGS – modified from reference [2]

From the figure 4, there are total 4 possibilities to determine the final grain size. To narrow the problem, we made an assumption that our strain is less than the critical strain and interpass time will be greater than the time needed for SRX to complete. The empirical formulas for SRX and grain growth were provided in the same paper.


As identified in the yellow boxes in the figure, a full static recrystallization needs to take place so that grain growth can follow, this means that the fraction recrystallized during SRX (XDRX) needs to be as close to the value of 1 as possible.

where t is the time duration since the static recrystallization starts and t0.5 is:

where t0 = 2.3*10-15, p = 2.5, q = 2, QRX = 230kJ/mol

We also need to identify the grain size after SRX (dSRX)

where A = 343, a = 0.5, b = 0.4 and d0 is the initial grain size

Finally, we have the model for grain size after grain growth (dMDRX)

where m = 2 and k = 4.0*107

These models have been identified from reference [7] and were selected because it was a reliable source.


These are the current models we have identified. A more in-depth literature survey is also required to determine whether these models are sufficient, and how they are connected to each other. One observation we made was that different publications had similar empirical models but with slightly different constants. I believe, Professor Singh is the appropriate person to guide us towards a comprehensive literature search to recognize the best models to be used. In case if the models are not available, then we will have to develop the response surface models (RSM).

After we have recognized the empirical models or developed response surface models, we must program these empirical models so that it can be read by the FEM that Anand had developed for hot rod rolling.

After that, we can communicate the initial variables identified in section 2 and the empirical models or RSM to the compromise Decision Support Problem to explore the solution space.


The cDSP is a mathematical construct at the core of the DBD method. The fundamental assumption here is that the models are not complete, accurate or of equal fidelity. This is why there is a distance between the aspiration space, where we would like to be, and the feasible space, where we currently are. This distance is known as the deviation and the cDSP construct reduces the deviation function to bring the solutions closer to the designer’s aspirations.

Figure 5 – deviation function in cDSP

There are four key words in the cDSP formulation – Given, Find, Satisfy and Minimize. The “Given” captures all the information available to the designer. The information regarding the system variables and deviation variables is contained in “Find.” The “Satisfy” contains the system constraints, system goals and variable bounds that determine the feasible design space and the aspiration space. Finally, “Minimize” consists of the deviation function that quantifies the deviation of the system performance.

The three goals that we have identified this semester are:

G1: Static recrystallized grain size

G2: Fraction recrystallized to a target value of 1

G3: Final austenite grain size

In cDSP, it is important to make sure that the three most important goals are conflicting. Our hypothesis in our case is that they are not. So, what we have identified is that two of these goals are sequential, i.e. only when static recrystallization finishes, grain growth starts. From Anand’s past work, we are aware of the final austenite grain size needed to continue the problem. That is one of the goals we are sure about. Also, from the assumptions we are making from figure 4, fraction recrystallized has to equal 1, otherwise partial recrystallization will take place and the assumptions we made will not hold. Therefore, G2 and G3 are obvious goals but we are unsure about G1 as one of the conflicting goals and again, a deeper literature search is required to either provide a focus on the current G1 or find a new goal.

After we have gained the relevant information to formulate the cDSP from the summer internship, we can execute the cDSP with the guidance of Anand and Professors Allen and Mistree when I come to OU in the Fall.


This semester was foundational for me to reach my goal of pursuing my further studies at MIT. In the Fall 2016, I had the same goal but I was addressing it in the wrong way. Through the guidance and mentorship of Professor Allen and Mistree, and Anand Balu, I have come to the right path that will lead me to find happiness and success. As an overview, they have helped me to not just realize my inner potential, but also helped me focus on starting to work on it.

Lessons learned:

  • I experienced that one method of learning fast is by reflection on what you have learned.

Being with Professors Allen and Mistree, I was constantly forced to practice this. After any conversation, they expect you to reflect on the conversation and pick a take away. This exercise keeps me focused and helps in critical thinking.

  • I learned that in order to achieve any goal, a narrowed-down focus on the goal is very important to make any kind of progress.
  • Also, to solve any big problem, you have to focus on different smaller goals, achieve them and then fit them all to the big picture.

As I have been made to realize, I like to be hovering with my goals and that is my comfort zone. They constantly made me realize the importance of being on the ground and be focused.

  • I learned that by observing what my legacy is going to be, I should decide whether doing something is worth the commitment or not.
  • I learned that active listening and note taking is very important in being able to comprehend a concept.
  • I learned that for true learning to happen, a continuous analysis of the progress made is important.
  • I learned that by sharing what you know, you can enhance your ideas even more with feedback from others. – Share to gain
  • Even though technology can be used to enhance the learning, I learned that while doing an intense studying, I have to keep away from all kinds of distractions.

However, at the beginning when more information was available online, I tried to watch videos about the history of steel industry and hot rod rolling on YouTube during my free time. Even though I tried to stay away from technology, I was able to use it to my advantage.

  • Through the experience of presenting my progress report, I learned that for an effective communication from the slides, having some words is generally a good idea.

My moto since high school for PowerPoint presentation has been that it needs to be presented as a monologue with PowerPoint as an aid to instigate the idea in the audience’s mind. However, this semester I realized that to have an effective set of slides, having a sentence or two helps the audience provide context.

  • I learned that before deciding to solve a problem, a definite and precise problem statement helps in guiding the solution.
  • I realized that research is the best way to present and develop your personality and training humans by empowering them is the ultimate source of happiness (for me).


In this research, we have taken the problem from Tata Consulting Services, who are focused on producing a gear, and narrowed it down to find the initial variables a decision maker needs to achieve a certain microstructure for the rod, considering that the rod goes through static recrystallization while being hot rolled. Although this project is not finished yet, we will be working on it during the summer with Professor Amarendra Singh at Indian Institute of Technology – Kanpur and with Anand and Professors Allen and Mistree when I come back in the Fall. We will require Professor Singh’s help for acquiring the models and programming it. Because I am unaware of how long this might take, if this is done halfway through the semester, then we can carry out the same process for other possibilities pointed out in Figure 4, such as when strain rate is higher than critical strain and the interpass time is greater than time for full MDRX. When I am back in the Fall, we will work on formulating the cDSP for the problem.


I would like to thank Professor Allen and Mistree for continuous critical feedback throughout the whole semester. I am also very grateful for being able to acquaint with Anand; he has been there to help me at every moment of the whole semester. I would also like to thank the Systems Realization Laboratory for providing the family like environment to do research. I also acknowledge the Honors College for providing me this research opportunity.


[1] Nellippallil, A. B., Song, K. N., Goh, C.-H., Zagade, P., Gautham, B., Allen, J. K., and Mistree, F., 2017, “A Goal-Oriented, Sequential, Inverse Design Method for the Horizontal Integration of a Multistage Hot Rod Rolling System,” Journal of Mechanical Design, 139(3), p. 031403.

[2] Kwon, H.-C., Lee, Y., Kim, S.-Y., Woo, J.-S., and Im, Y.-T., 2003, “Numerical prediction of austenite grain size in round-oval-round bar rolling,” ISIJ international, 43(5), pp. 676-683.

[3] Kalpakjian, S., and Schmid, S., 2014, “Manufacturing Processes for Engineering Materials–5th Edition,” agenda, 12, p. 1.

[4] Nellippallil, A. B., Song, K. N., Goh, C.-H., Zagade, P., Gautham, B., Allen, J. K., and Mistree, F., “A Goal Oriented, Sequential Process Design of a Multi-Stage Hot Rod Rolling System,” Proc. ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers, pp. V02BT03A007-V002BT003A007.

[5] Mistree, F., Hughes, O. F., and Bras, B., 1993, “Compromise decision support problem and the adaptive linear programming algorithm,” Progress in Astronautics and Aeronautics, 150, pp. 251-251.

[6] BRAS, B., and MISTREE, F., 1993, “Robust design using compromise decision support problems,” Engineering Optimization, 21(3), pp. 213-239.

[7] Hodgson, P., and Gibbs, R., 1992, “A Mathematical Model to Predict the Mechanical Properties of Hot Rolled C-Mn and Microalloyed Steels,” ISIJ international, 32(12), pp. 1329-1338.



Pranav Mohan

Change and progress are two words that define my character and my ultimate goals. I have a vision to bring a global change by targeting the psychology, because that is the easiest to change. My aim is to incur a self-progressive routine for myself and then help the people around me to progress themselves. In my perspective, walking towards a defined target should be everyone’s goal while keeping in mind that things don’t go as planned but still the target should remain unchanged.

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