# Profit-Driven Methodology for Servo Press Motion Selection under Material Variability
## 1 Introduction  
In the last 15 years, industry has begun adopting servo presses as a replacement for conventional presses in metal forming. Servo presses enable the press motion profile to be designed for improved forming results. Of particular interest for this work, new high strength steels with applications for vehicle lightweighting can be successfully formed with servo motion [1]. However, high strength steels are known to have a relatively wide variability in material properties [2]. This variability can lead to inconsistent results from a designed servo motion profile.  
Since good parts can be sold for profit and defective parts induce a loss, it is important, when planning for profits, to consider the uncertainty of what kind of parts will be produced. This paper proposes a Bayesian statistical tool in helping manufacturers estimate returns in the face of uncertainty.  
A typical metal forming manufacturing process begins with a roll of sheet metal arriving at the manufacturer. The metal is rolled out through a press, where the metal is stamped into a specified shape. Although servo presses allow for variations in press motion, a simple manufacturing approach is to let the press run one pre-configured motion. After the part comes out of the press, it can be examined for defects. If the part is found to have no defects, it is good to be assembled for a final product and provides value. Defective parts are scrapped and induce a loss (Figure 1). Here, a part is considered defective if a forming expert identifies cracking, necking, or wrinkling during a visual inspection. The proposed Smart Forming Algorithm fits into the process after the metal blank or coil arrives but before it is stamped (Figure 2). As the metal is rolled into the press, sensors can detect material properties of the metal and relay that information to a software application running the Smart Forming Algorithm. The Smart Forming Algorithm then produces probability distributions of producing a good part for several press motions. Employing these probabilities in expected utility can provide recommendations to the operator as to which press motion is expected to produce the greatest number of good parts.  
Returning to the simple approach of using one pre-configured press setting, one strategy of making a profit is to choose the press setting that produces the greatest number of good parts based on previously collected data. However, this approach could be improved, as press motions can yield different results even when the material properties are different.  
Figure 1: Example of parts manufactured by metal forming. Note that the defective part has both a crack as well as wrinkling, though either would be sufficient to classify the part as defective.  
Figure 2: Process diagram of metal forming with the Smart Forming Algorithm. The process diagram without the Smart Forming Algorithm would jump directly from “Roll out metal” to “Choose motion”.  
of the input sheet metal are similar. Although, ideally, suppliers would produce sheet metal with consistent material properties, the reality is that material properties vary across batches, even from the same supplier.  
The proposed Smart Forming Algorithm is a framework for taking both press motion and material property variability into account when predicting the probability that the part produced will be good. Applying the theory of expected utility to the Smart Forming Algorithm can then provide profit estimates. The manufacturer can use these estimates to make an informed decision in its strategy to make a profit. The proof-of-concept work presented here suggests that manufacturers can expect to achieve substantial cost savings as smart forming approaches are generalized for wider application.