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ME 350: Design for Manufacturability Turning and Design of Experiments Example ***IMPORTANT: When following this DOE example for your assignment, make sure that your design matrices are consistent with the ones used for the G-Code program. Design of Experiments Technique The example problem below is designed to walk you through the DOE analysis. If you follow it carefully, the analysis for your lab assignment should be straightforward. Example Problem A company which flat rolls steel is having problems with one of its rolling mills. The resulting rolled steel has been exhibiting an unacceptably high number of edge cracks. The variables that affect this process are the draft (the initial thickness minus the final thickness of the steel), the roll velocity, and the coefficient of friction. The engineers, however, do not know how each of these variables affects the number of defects. In order to better understand the process the engineers decide to utilize DOE. For this process, it was decided that a 2 3 factorial design would be performed. This means that the three important variables will be examined on two levels each - a low level (-1) and a high level (+1). The high and low levels should be chosen to create a range, which encompasses the operating conditions of interest. Table 3 shows the three variables and their low and high-level values. Variable Variable Description Low (-1) High (+1) x1 Draft (mm) 6 12 x2 Roll velocity (ft/s) 8 12 x3 Coefficient of friction 0.2 0.3 Table 3: Variable Levels A complete factorial design contains 2 3 = 8 unique test conditions, so eight experiments will need to be conducted to collect all of the necessary data. Table 4 shows the eight possible test conditions and the resulting number of defects for each condition. If we were to examine a problem with 4 variables, we would have to set up an experiment with 2 4 = 16 unique test conditions. Remember that we are trying to find the effect of each term and the effect of the interaction of terms on the end result we are measuring (defects in this case). Test Draft x1 Roll velocity x2 Coeff. friction x3 Defects d 1 -1 -1 -1 5 2 +1 -1 -1 18 3 -1 +1 -1 6 4 +1 +1 -1 16 5 -1 -1 +1 13 6 +1 -1 +1 33 7 -1 +1 +1 16

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ME 350: Design for Manufacturability Turning and Design of Experiments Example 8 +1 +1 +1 34 Table 4: Design Matrix The information in the design matrix can be represented geometrically as shown in Figure 1. Each corner of the cube represents one of the eight test conditions. The number of defects, which were observed for each condition, is shown at each corner in bold. By using this cube as a tool for examining the data, it can be discovered how each of the variables affect the number of defects. For example, by looking at the cube, it can be seen that there are four opportunities to explore how the number of defects changes when the coefficient of friction (x3) is changed, and the other variables are held constant.
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