Optimization in product development - An efficient approach to integrate single CAE Technologies up to the entire design chain

Figure 1: Stress analysis of a crank shaft

Overview
In today’s industrial production plants, state-of-the-art software systems are used to analyze different loading conditions in order to determine the performance and durability of a product. Similarly, production companies use simulation for manufacturing processes, such as casting and welding. Optimization techniques are widely regarded and applied as the next logical step to perfect competencies in simulation for modern product development. Possible applications of optimization techniques range from local problems with single applications up to the mapping and optimization of a large range of parameters of an entire product development process. Hence optimization can provide significant time and resources savings, opportunities that are illustrated in this article.

Introduction
Since the introduction of the computer, nearly all areas of life have changed rapidly. This applies also, and in particular, to the working environment and all professional activities of engineers. For example, engineering drawings are no longer made on a drawing board using 2D techniques; 3D models are created instead on the screen.

Figure 2: CFD simulations for a turbine blade

Thus necessary adjustments to the product are realized quickly, for example the weight or the moment of inertia of complex geometries can be determined – all in an automated way.
Advances in computational mechanics, such as the FEA Finite-Element Method, have also made their way into modern production facilities a long time ago. Again, clear advantages of simulation are shortened product development cycles, improved assessments of product quality and, importantly, savings in experimental time and equipment.

Today’s status of simulation in product development covers a number of standard analyses, including:

• Strength and durability/fatigue analyses of mechanical and/or thermally stressed devices in most diverse loading conditions (Figure 1),
  
• Computation of characteristic measures in CFD problems as shown in Figure 2,
  
• Crash Simulations in the area of Safety Engineering and
  
• Vibration and dynamic analyses of complex multi-body models.

Considering its industrial infrastructure, the area of manufacturing process simulation could be regarded as a separate domain of computation. The attention here is not purely focused on the product, as also the required tools for the processes have to be taken into account. Those simulation methods comprise among others:

• Simulation of casting processes including filling and solidification processes, the resulting impacts on the material microstructure and the corresponding local mechanical properties as well as the residual stresses (Figure 3a),
  
• Simulation of forging processes with forming simulations performed continuously or in several steps, including material and stress-strain analyses of the device and the forging dies (Figure 3b),
  
• Injection-Molding Simulation of plastic-based devices including filling and solidification processes as well as joint formation,
  
• Simulation of machining processes including chip-forming analysis, thermo-mechanical analysis of the material removal rate of the workpiece and the tools as well as of surface properties.

Figure 3 (a) Solidification stage of a casting simulation and (b) forging simulation of a crank shaft

If we consider the structural trends in manufacturing and R&D industries as an example - the ever-growing global competition, shorter development cycles and increasing demands on product quality to name a few - it is evident that further efforts are necessary to reduce costs and improve product quality. This is particularly important for companies whose operations are based in technologically advanced countries, such as Germany. Here, the CAE application “Optimization” is a well-known common practice and among the primary goals of technical developments.

Optimization
Optimization is defined as the mathematical process for finding optimal parameters of mostly complex systems with regard to a single or multi-objective functions. It is important to understand the advantages of optimization which are explained hereafter with the help of some examples:

• Target functions depend on individual problems and, in reality, often conflict with each other. Therefore, the ultimate objective of optimization is to find a solution which represents the best compromise among the different objective functions.
  
• Due to its mathematical background and its independency from respective applications, optimization is often regarded as a complex and independent field of action. Thereby, commercial tools, such as modeFRONTIER, are readily available for use since a long time. Such tools allow to setup, perform and automate optimization analyses in an easy way.
  
• The optimization level (and, hence, potential savings) depends to some degree on the development status of a company. On the one hand, it is possible to perform optimization on a relatively low level for the parameters of a single product. On the other hand, optimization can be considered as a tool of process integration and automation, hence, to enable the mapping and simulation of the complete process and design chain.

Figure 4: Parameter Optimization of a bycicle frame

Optimization of a bicycle frame
Figure 4 illustrates an optimization of a bicycle frame with relatively traditional optimization objectives in structural mechanics: The goal here is to minimize the stresses caused by different loading conditions; at the same time, the weight of the frame should be minimized. Moreover, requirements regarding limits for maximum stresses (tensile strength and fatigue resistance) have to be observed.

In this example, the available geometric optimization variables are some lengths, the thicknesses of the tubes and their radial dimensions. In fact, with modeFRONTIER the present problem can be described in a single run and by integrating a single FEA application, as shown in Figure 5. Here, after an automatic analysis of the problem structure, modeFRONTIER recommends to run the optimization with a certain algorithm - in the present case a Multi-Objective Genetic Algorithm MOGA-II, with an appropriately generated DOE.

Figure 5: (a) The modeFRONTIER Workflow which integrates a FEA application for a strength calculation of a bicycle frame. (b) The results of the optimization run presented in a Bubble Chart with the highlighted Pareto Frontier.

The optimization run takes place automatically and allows a systematic Illustration of the results as, for example, by using a Bubble Chart as shown in Figure 5 (b). Here, the optimal solutions on the Pareto Frontier are clearly visible.
In this example, the automation enabled the engineer to compute 300 designs within a few minutes time. Hence, the design time was shortened, instead of wasting time for multiple manual variations. Additionally, the performance of the bicycle frame with respect to stresses could be improved, while achieving significantly lower weight conditions, which also led to lower material costs.

Design Chain Optimization
The relatively simple optimization approach applied to the design of the bicycle frame already delivered significant savings. This approach however is based on the (mostly feasible) assumption that existing residual stresses, σ0, inside the device can be neglected. These stresses derive from upstream manufacturing processes. With regard to the bicycle frame, we could consider such stresses being related to welding, heat treatment, and quasi-static bending (straightening) processes of the frame. If available, this data could be used in a subsequent stress analysis to take into account real initial stress conditions and thus provide a far more accurate optimization. This way, we would obtain a process chain with four different applications which also can be mapped and optimized in modeFRONTIER.

As another similar example, we can take a closer look at a roller support of a paper machine, as illustrated in Figure 6. The roller support is manufactured by a casting process, the weight of the first design was 476 kg. The optimization goal here was to minimize the weight and deformation at the same time. In addition, the castability of the final form had to be guaranteed.

Figure 7: Standard Optimization (left) in comparison with an Optimization which encompasses the entire process chain: at the critical points, the analysis that considers casting simulation shows increased van Mises stress values.

In this example, the sole and initially performed optimization of the geometry (variation of 13 parameters) with respect to the most extreme load-case delivered a weight reduction from 476 kg to 360 kg, while the deformation was reduced slightly. The verification of the castability was performed using the software tool MAGMASOFT (sand casting) in a second step after optimization.
Analyzing the casting simulation, the results additionally revealed zones with non-homogeneous microstructure and hardness due to different thicknesses and local cooling rates. Also, local zones with high residual peak stresses were found, which have a decreasing effect on the fatigue life of the roller support.

These results gave reason to consider performing a largely extended optimization analysis that includes both the casting simulation and load-case analyses. In a tool such as modeFRONTIER, the complete process chain could be setup, in which results of the casting simulation are transferred as initial conditions to the subsequent FEM-based load-case simulation. Hence, all following steps are included in this kind of optimization problem:

• Casting simulation with MAGMASOFT to ensure the quality of the materials, to avoid casting defects, determination of local material properties (for example Young’s module, fatigue and yield stress limits), as well as residual stresses on the different roller support zones.
  
• Transfer of the results via MAGMAlink (residual stresses and material properties) as initial conditions to be used in ANSYS.
  
• Load case (stress-) analysis with ANSYS.

This procedure enables also the systematic optimization of the support roller geometry with respect to the load in operating conditions, but including the consideration of residual stresses and the locally changed material properties from the casting manufacturing process. The castability could, therefore, be guaranteed reliably. Additionally, statements with respect to the fatigue life of the product could be obtained and coupled to the optimization procedure as constraints.
Figure 7 shows the original (traditional) load case analysis (left) and an excerpt of such a novel design chain approach that considers the results from the casting simulation (right). It is clearly seen that the stresses in the roller support are in no way homogeneously distributed due to different pre-stress conditions and non-homogeneous mechanical material properties. Similarly, peak stresses (van Mises) can be seen to be increased in some areas from approximately 30MPa to 50MPa (166%). Maximum principle stresses (not shown) even highlight increased values from 60MPa to 228MPa (380%). Although these values are yet far away from the materials tensile and fatigue stresses, they lead to significant reductions in the fatigue life of the product.

Figure 7: Optimization of a support roller of a paper machine

Conclusions
The ever growing competitive global market place will call for more and more applications of optimization techniques in various industrial sectors. In this article, we have outlined the following key points:

• The optimization of real problems most often defines solutions which are in conflict with each other. Such Multi-Objective Optimization tasks can already be solved today with easy-to-use software, such as modeFRONTIER.
  
• It is possible to perform automatic optimization already for simple development cases by linking standard tools from arbitrary areas (e.g. CAE tools).
  
• Optimization can be extended infinitely and, hence, be regarded as a tool for process integration and automation. In this way, it is possible to setup simulations of an entire process chain and, therefore, to systematically extend the optimization capabilities from single device parameters to the parameters of the entire design chain.
  
• There is potential for large savings. They may comprise in experimental costs and reduction of development times due to the automation of computations. Thereby, savings even go hand-in-hand with ensuring product quality.

Hans-Uwe Berger, EnginSoft GmbH, Frankfurt am Main
25. Schmalkaldener Fachtagung/Conference:
Die Digitale Fabrik–Module und Referenzlösungen/Digital Plant – Modules and Solutions