There is Something Missing from Engineering Optimization
This post was co-authored by Ansley Barnard, ESTECO and Amanda Bligh, aPriori
In more and more cases, optimization is being used to solve engineering problems. This includes examples of topology/topography optimization, parametric optimization and simultaneous analysis of multiple performance criteria—stress, strain, vibration, and heat transfer, for example. The solutions to these optimizations are often dramatically different, sometimes counterintuitive, but always exciting. In the end, though, these exciting solutions need to be manufactured. And if manufacturing cost isn’t included as a criteria, is your solution really the best it can be?
Adding Manufacturing Cost to Your Optimization
In the fictional case study that follows, we will demonstrate an automotive team leveraging ESTECO’s modeFRONTIER software to coordinate a parametric optimization that includes all the performance requirements plus manufacturing cost with aPriori. The goal is to improve the cost of a sub-assembly, while maintaining all the needed performance requirements. But most importantly, we will demonstrate how to do it FAST!
The Problem, The Assembly & The Team
Let’s take a look at the story of our fictional supplier, Acme Automotive. Acme supplies suspension assemblies to major OEMs. Acme is responsible for all the elements shown in Image 1, including the upper control arm (UCA), lower control arm (LCA) and front anti roll bar.
Image 1: The overall assembly
The OEM is looking for a 5% cost reduction on the full assembly. A cross-functional team at Acme includes Patty the program manager, Sean the engineer, and Beth the simulation analyst. The team is looking at how they can best save money on key assemblies to meet the OEM cost reduction target while maintaining the functional requirements. They’ll be doing this using aPriori run by modeFRONTIER to optimize for best results. Follow along with the team’s strategy below:
Step 1: Identify The Target Assembly & Part
Based on the latest information from the OEM, Patty knows she needs to save 5% overall in the suspension assembly. She starts by opening aPriori’s Cost Insight Reporting and reviewing the assembly in question. By reviewing the top-level subassemblies (see Image 2), she can see very quickly that most of the cost is in the Front Anti Roll Bar, Lower Control Arms (LCA), and the Upper Control Arm (UCA) assemblies. The roll bar assembly is frozen due to requirements from a subcontractor, so that is out of consideration. The shape of the LCA is heavily constrained based on the surrounding parts. Since another team is responsible for these packaging restrictions, this assembly is currently not eligible for re-design.
Image 2: Comparison of major sub-assembly costs within the overall assembly
Patty remembers that Sean, her team’s engineer, talking about some ideas for decreasing costs in the UCA assembly (Image 3) by using optimization and asks him to review the assembly.
Image 3: Upper Control Arm (UCA) assembly
Image 4: Costs in aPriori of parts in the UCA Assembly.
Sean opens the target assembly in aPriori Professional, as shown in Image 4, and notices that one part, the main UCA stamping, at $7.66 of the total $12.39 for the assembly. This makes it an obvious candidate for cost reduction.
Image 5: Cost of the Main UCA part in aPriori, showing material cost as dominant.
Looking closer at the part scenario in aPriori, as shown in Image 5, the dominant cost is clearly the material, at $5.17 of the $7.66. Sean has worked with the simulation team before optimizing a design for multiple variables and thinks this part may be a good candidate for such an analysis. For the UCA, he has a selection of performance criteria, plus the cost reduction the OEM is asking them to find. He schedules a meeting with Beth in the simulation group to discuss setting up this problem as a multi-objective optimization.
Step 2: Set-Up the Problem
Beth, from Acme’s simulation group, walks through the problem setup with Sean. To support the analysis, Beth needs to collect a selection of inputs, including a CAD model of the part, the performance requirements and the previously cost aPriori scenario. She and Sean set the scope of the problem to focus on how redesigning the part can save costs using the same material type and production volume. This problem is parametric: by changing certain input parameters the cost to manufacture the part will change. Through this analysis, Beth and Sean are trying to identify the best input parameters resulting in the lowest cost design.
Sean provides Beth with a parametric model of the main component in the Upper Control Arm assembly. Six variable parameters, as shown in Image 6, have been defined on the model. With these geometric parameters defined, each time they are updated the CAD file will be automatically rebuilt. These parameters define the outer profile of the part and are within scope for redesign. The inner surfaces are frozen to maintain installation of bushings and clearance to other parts. The values for these inputs to the CAD geometry that result in the lowest manufacturing cost are the variables Beth and Sean are trying to identify from the optimization study.
Image 6: Plan view of the main UCA component, showing the parametric dimensions
Sean identifies noise, vibration and harshness (NVH) as a critical performance area for the Upper Control Arm assembly. He typically uses a finite element analysis (FEA) tool to check vibration modes, deflections and stresses on this part. He provides a copy of his usual analysis and the current mesh (shown in Image 7) to Beth and she is able to link the FEA model to the parametric CAD geometry.
Image 7: Meshed version of the Main UCA part, ready for analysis
Sean points Beth to the previously created aPriori scenario for the part (shown in Image 5), which includes the overrides, annual volume, material type and other standard inputs to produce the current cost of the component. This ensures that the workflow Beth sets up uses all the correct cost settings.
Beth uses these three models to create the workflow (Image 8) in modeFRONTIER. modeFRONTIER is a parametric optimization platform that will use an intelligent algorithm to drive the optimization study. The modeFRONTIER workflow represents an automated version of the process she and Sean would create manually to design and analyze the part.
Image 8: Engineering workflow in modeFRONTIER, with numbers identifying the various elements
The callouts in the modeFRONTIER workflow show each step of the automated process:
- Update the part geometry parametrically through a CAD program
- Run the FE analysis for modal, harmonic and stress responses
- Execute aPriori’s command-line bulk costing capability
- Read cost information from aPriori’s output report
- Definitions of competing objectives to optimize for low cost, low weight, and high stiffness designs
- Definitions of constraints limiting the stress on the FE results to prevent selecting a poor design
This cost reduction is their main goal, or objective. They set an objective in modeFRONTIER on the cost output parameter to seek the minimum cost. Their other goals are to keep the mass low and keep the critical frequency high.
Note: They also place several constraints to limit the structural stress in the part and limit the part deformation during critical vibration modes to prevent the part entering them during normal operation. Unlike objectives, constraints are limits determining if the design is feasible or not; they are a limit rather than a goal. The constrains on this problem are gathered from the FEA execution.
The workflow can now run parametrically through the design, analysis and costing process. modeFRONTIER will make changes to the design and record the outputs, rapidly cycling through many options and building on trends it finds in the data.
Step 3: Run the Optimization
The final step Beth completes is to determine the algorithm to control the optimization. She chooses FAST, a multi-strategy algorithm in modeFRONTIER. She explains to Sean that this algorithm will use two methods to efficiently determine the optimal solution set, a genetic algorithm (GA) that seeks the best designs over time with high accuracy and a Response Surface Model (RSM) which solves an approximation of the problem, quickly guiding the GA to potential solutions. The GA uses the analogy of natural selection and reproduction to reach an optimization target. It creates generations of designs based both on its parents’ characteristics and random mutation. The RSM (Image 9) is a metamodel, a best fit approximation of the model behavior in both the FE and cost portion of the analysis.
Image 9: A Response Surface Model is a statistical or numerical model that approximates the relationship between multiple input parameters and one output parameter
With the algorithm determined, they hit the play button in modeFRONTIER. The results start to display in real time, as shown in Image 10, and the study can continue without their intervention. Time to go home for the weekend.
Image 10. Live results from modeFRONTIER shows that the optimization is on the right track
Step 4: Review Results
On Monday morning, it’s time for the team to review the results in modeFRONTIER. They create a time history chart (Image 11) showing the full path the FAST algorithm took to find a solution. As modeFRONTIER explored more designs, it searched for solutions that would lower the Fully Burdened Cost reported by aPriori, lower the mass of the part and raise the critical frequency. The genetic part of the algorithm works through designs in generations, moving slowly but consistently toward more optimal solutions that meet Sean’s stress and displacement constraints.
Image 11: Example of the resulting cost for each of the iterations in modeFRONTIER
To evaluate the relationship between part mass, cost and frequency, Sean and Beth also look at a scatter chart (Image 12) with these three variables. There is a clear correlation between lower mass parts and lower cost parts, but there isn’t a clear correlation with frequency.
Image 12: Scatter plot showing cost on y-axis, frequency response on the x-axis, and mass value shown by color. Points highlighted in red are the Pareto frontier.
Since there are multiple objectives on this analysis, Beth uses modeFRONTIER (Image 12) to highlight a set of several equally good solutions in a red outline. Beth explains that this set of solutions is called the Pareto Frontier and it is populated by solutions where one objective can’t be improved without reducing the performance of another objective. To pick a final configuration from this set, Beth and Sean need to evaluate how important the objectives are in relation to each other. They know that all the designs in the Pareto Frontier will be stiff enough and strong enough since they meet the FEA constraints. They also know that the critical mode frequencies of all these designs is high enough to be accepted by the rest of the team. With those considerations in mind, they choose the lowest cost design in the Pareto Frontier at $6.86 a unit.
Step 5: Make a Recommendation
After reviewing the best results with Beth, Sean updates the aPriori costs with the new part geometry. He compares the selected direction to the original scenario for the UCA (Image 13) and sees a decrease of 10% on the cost per piece with the dominant change being in material cost, as expected. After a little more review, he finds that the nesting of the new design has improved considerably, something that would have been hard for him to do by hand, reducing the rough mass by 12% and the width of the coil by about 30mm. This is very exciting, as improvements to a part related to material cost are usually found in single-digit percentage points.
Image 13: Cost comparison report from aPriori Professional of original and the best design identified in the modeFRONTIER optimization.
In further review, Sean also found a 13% reduction to the tooling cost—a benefit he wasn’t considering but was glad to discover. To handle the OEM’s annual quantity, usually three sets of tools will be purchased. He will be sure to bring this to Patty’s attention.
Sean prints out the comparison and brings it to his meeting with Patty.
Image 14: Comparison report of overall assembly from Cost Insight Reporting
Patty reviews the comparison and looks at the overall assembly cost in aPriori’s Cost Insight Reporting (Image 14). She notes the overall decrease in the total assembly cost of 1.5% based on the assessment, from $125.16 to $123.34. With the strength of this analysis, Patty thinks she’ll be able to promote a similar analysis to the LCA and other key sheet metal parts once the packaging constraints have been fixed and the dynamic response models can be automated. In addition, the savings in the tooling cost on this one part is substantial. While tooling savings is usually accounted for separately, Patty feels she has an opportunity for gaining some good-will with the OEM with a reduced tooling estimate.
With these opportunities in mind, she feels she should be able to easily find the remaining 3.5%. A great start to the week!
In the fictional case study above, we demonstrated the power of including cost as part of engineering optimization. By using aPriori’s cost data and automating it in a simulation workflow with modeFRONTIER, the Acme Automotive team was able to:
- Quickly identify assemblies and components with the opportunity of meeting their new cost target
- Iterate through 650 design alternatives
- Find 37 Pareto design alternatives meeting performance and cost targets
- Select the best alternative from the set for moving forward
- Update the new design in aPriori
- Compare the old and new design to understand the overall savings
- Complete this entire assessment in a matter of a few days
At the end of this analysis, the team was able to identify a(n):
- Reduction in piece part cost of 10%
- Increase in material utilization due to nesting improvements of 6.6%
- Reduction in tooling cost of 13%
This investigation additionally validated the possibilities of supercharging an engineering workflow including aPriori for costing by using ESTECO’s modeFRONTIER to automate the investigation.
Is there something missing from your engineering optimization solution? If it doesn’t include manufacturing cost, we think there is.
Register for our webinar where we will demonstrate the power of including cost as part of engineering optimization. Learn more here: