This article is one of five papers on modeling and simulation (part two) to be presented exclusively on the web as part of the September 1999 JOM-e—the electronic supplement to JOM. The first part of this topic supplemented the August issue. The coverage was developed by Steven LeClair of the Materials Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base.
	The following article appears as part of JOM-e, 51 (9) (1999), http://www.tms.org/pubs/journals/JOM/9909/Medina/Medina-9909.html JOM is a publication of The Minerals, Metals & Materials Society

Incorporating Hybrid Models into a Framework for Designing Multistage Materials Processes

TABLE OF CONTENTS
INTRODUCTION A SYSTEMS APPROACH TO MATERIALS PROCESS DESIGN DEMONSTRATION ACKNOWLEDGEMENT References

INTRODUCTION

A large portion of the cost of a system or component is decided early in the design process. The design framework presented will address affordability and sustainability of military and commercial systems by allowing the designer to consider alternative materials and processes and to estimate the influence of design decisions on cost at early design stages. The initial focus of the project is the preliminary and intermediate design of process sequences used in producing turbine-engine components. The proposed design framework is based on an object-oriented, geometry-intensive environment–the Adaptive Modeling Language (AML^TM)²–and will support different types of models (analytical or numerical) and different mathematical optimization algorithms. Customizable visualization capabilities; web accessibility; and distributed, collaborative design are all planned features of the system.

Figure 1. Alternative processing sequences for manufacturing a sample turbine disk. 1–cast ingot, 2–upset, 3–machine preform, 4–blocker forge, 5–rough machine, 6–finish machine, 7–extrude, 8–close die forge.

The fundamental difference between this and other simulation-based design tools is the concept that when design is the objective it is beneficial for the underlying modeling methodology to be formulated taking into account the design function directly. Basic mathematical analysis enhanced with empirical knowledge can be used to create hybrid models that include known design drivers at a level appropriate for preliminary and intermediate design. Optimization algorithms can then be used to vary the parameters of these models to solve appropriately formulated design problems that address materials, process, equipment, and cost by means of suitable combinations of objectives and constraints. A motivation for the use of hybrid models that combine experimentally determined rules with simplified analytical physics models is the fact that sophisticated models used for analysis or simulation are not necessarily appropriate for design. These sophisticated models may not be very robust and may tend to provide large amounts of information that make it difficult to determine the dominant mechanisms that govern the interactions among material behavior, process physics, and equipment responses. However, there are cases in which high-fidelity models are necessary for simulating particular material or process phenomena that affect quality and cost. The integration system will provide mechanisms for incorporating finite-element solvers as one of the modeling alternatives.

While the first applications of the design system are in the design of metal-forming and related processes, the methodology and software framework can be used for other types of processes. The process for manufacturing a disk component similar to those used in aircraft turbine engines is considered here for the purpose of illustrating the nature of the manufacturing design problem. Figure 1 shows various alternative methods for manufacturing a sample turbine engine disk. Heat-treatment stages are not shown in this simplified schematic. Each operation involves the evaluation of several material, process, and geometry variables, and, therefore, the space of feasible solutions is very large.

A SYSTEMS APPROACH TO MATERIALS PROCESS DESIGN

Previous U.S. Air Force research efforts have explored the use of discrete-event models and optimization techniques for designing metalforming operations.³ Given a sequence of operations described by simplified, analytical models, this framework can determine the set of parameters for each operation that will minimize a given optimality criterion expressed in terms of cost and properties.⁴ A common difficulty with such an optimization approach is that the user may not have an appropriate method for observing and analyzing the changes that the optimization algorithm performs during the solution iterations or for evaluating intermediate and final designs.

Figure 2. Object-oriented representation of a sequence of operations and an optimization-based design system.

A process design technique for the control of microstructure development during hot metal deformation processes is described in Reference 5. That work uses state-space models to describe material behavior during hot forming. Processing maps are used for identifying favorable ranges of strain rate and temperature for hot deformation.⁶ Different trajectories of strain rate and temperature will cause a material to experience different microstructure-development mechanisms and, in turn, achieve different qualities or develop different defects. An optimal-control algorithm is used to obtain strain-rate trajectories that achieve the desired microstructure without violating workability⁶ or equipment limitations. Suitable process and equipment parameter settings are then obtained by using a second optimization algorithm.

The work presented here utilizes the above developments and enhances them with novel modeling approaches and visualization techniques to develop a commercially feasible technology for designing materials processes. This technology would be useful in design activities at metalworking and other manufacturing industries and could also facilitate manufacturing-process research and teaching in research and academic institutions. The design system will be applicable to both traditional processes, such as metalforming, and newer operations, such as reaction-based processing and spray forming. Interfaces and complete documentation will be developed to allow models for new processes and materials to be easily incorporated into the design framework.

A multistage process can be modeled by using an object-oriented approach in which the component being produced, each of the processes used for production, and each piece of equipment are modeled by objects. In the same fashion, a sequence of operations, an optimization algorithm, and an interface for user control of the design system can be modeled as software objects. Figure 2 depicts this object-oriented representation of the design framework. The objects can be distributed among several computer processes and processors. Models of complex systems can be formed by connecting submodels that can be implemented in multiple computers. Inter-networking can be used to facilitate collaborative interaction during design and integration of models from different organizations. Issues such as the choice of computer framework, visualization and multimedia capabilities, and remote access are under consideration during system-architecture development.

DEMONSTRATION

Figure 3. An illustration of the use of visualization in the simulation and optimization of material processes showing (a) disk cross sections and (b) various cost drivers. This is an animated GIF. Click on the figure to see the animation.

A small-scale, proof-of-concept system was developed to demonstrate the capabilities expected in the complete process-design system. Figure 3 shows two of the windows in that demonstration system. The simple analytical models in Reference 3 were connected to form the simulation of a metal-forming process similar to those used for manufacturing turbine-engine disks. The demonstration system was created in the Microsoft^TM COM/DCOM distributed computing framework. It uses a cost model for disk manufacturing developed at the Materials Process Design Branch of the Air Force Research Laboratory and a generalized, hill-climbing, discrete optimization algorithm developed at the Virginia Polytechnic Institute and State University. The system implements the model and optimization algorithm in one computer and can display the results on one or more computers in a Windows NT/Windows 98 network. It uses the optimization algorithm to minimize the cost of producing a disk as modeled by the cost-objective function used. Tradeoffs performed by the optimization algorithm between different elements of the objective function and the changes in the design parameters are not apparent from extensive numerical output.

The demonstration computer displays in Figure 3 show the results of each thermomechanical operation at the end of iteration 10,000 of an optimization run. Figure 3a shows the disk cross sections resulting from the blocker-forging, rough-machining, and finish-machining operations, in addition to the speed, temperature, and load for the blocker-forging process. Figure 3b shows the optimization iteration number, the total manufacturing cost, and the distribution of cost among the various cost drivers. In order to present meaningful information to the user, workpiece cross sections are drawn to scale, and results of each process have been color-coded.

The animation in Figure 3 shows that in this optimization run, the algorithm moves from an infeasible region, characterized by an impossible combination of geometries and penalized by a high cost, to a feasible region, in which better designs are subsequently found. Although very limited in scope, the demonstration system clearly shows that a visually driven tool for the design of manufacturing processes can allow a quick evaluation of alternatives and optimization of design parameters.

ACKNOWLEDGEMENT

References
1. E.A. Medina, W.G. Frazier, and J.C. Malas, "Simulation and Optimization System for Design of Multi-Stage Material Processes," Transactions of the North American Manufacturing Research Institute of the Society of Manufacturing Engineers, vol. XXVI (1998), pp. 287–292.
2. Adaptive Modeling Language, Reference Manual: AML Version 3.1.2 (Cincinnati, OH: TechnoSoft).
3. J.S. Gunasekera et al., "The Development of Process Models for Use With Global Optimization of a Manufacturing System," Proceedings of ASME International Mechanical Engineering Congress (ASME, 1996).
4. S.H. Jacobson, K.A. Sullivan, and A.W. Johnson, "Generalized Hill Climbing Algorithms for Discrete Manufacturing Process Design Problems Using Computer Simulation Models," Proceedings of the European Simulation Multiconference (1997).
5. E.A. Medina et al., "Optimization of Microstructure Development: Application to Hot Metal Extrusion," J. of Materials Engineering and Performance, 5 (6) (1996), pp. 743–752.
6. Y.V.R.K. Prasad and S. Sasidhara, Hot Working Guide—A Compendium of Processing Maps (Materials Park, OH: ASM, 1997).

Enrique A. Medina is with Austral Engineering and Software.

For more information, contact E.A. Medina, Austral Engineering and Software, P.O. Box 340646, Beavercreek, Ohio 45434; (937) 431-8500; fax (937) 431-8506; e-mail medina@australinc.com.