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Step 5: Analyze, Verify, and Test ResultsWe now wish to analyze the experimental results to create an empirical model of the solar car product. To analyze the data, we calculate the mean for each experimental configuration, in addition to the standard deviation. We also calculate the experimental error sT, here ±0.10 sec. If a multiple of the standard deviation (e.g., 3s) is greater than the response coefficient, then the controlled change of design variables cannot be distinguished from experimental error. Therefore, a factor is significant if its response coefficient is larger than 0.30 sec. In our case, we calculate a simple regression model of the empirical data and determine the significance of the terms in the model by considering the standard deviation. The regression model (bilinear) is:
where y-bar is the average response for all trials, and the beta terms are the sensitivity coefficients of the main and interaction (coupled) effects of the control factors. The response diagram is then given by Figure 18.15.
This result implies that as we increase the power from its" + 1" state to its "-1" state (two units of change), the time will decrease by 1.34/2 sec. Likewise, for car weight:
In turn, this result implies that as we increase the weight of the car, the time will increase, but not as much as the power effect! When comparing the main effects to the experimental noise, both effects are significant, since they are greater than three times the average standard deviation of the trials. The interaction between the power input and the design weight of the car may now be calculated. This interaction effect is given by: This result is close to the experimental noise; however, the interaction shows that weight and power are coupled. This means that the speed of the car does not change independently with weight and power. As we increase weight, the power will also increase and compensate for the weight increase, thus causing a decrease in coupled time.
Step 6: Evaluate the Results (Conclusions) A number of conclusions may be extracted from the experimental results and empirical model. First, a 20-30% performance increase can be achieved by increasing power or decreasing weight (assuming that a new, more powerful motor would add double the weight, which is very conservative). Second, weight and power interact, implying that we need to be concerned about which motor torque-speed curve we are on for efficiency. Third, because weight and power interact, we can actually achieve better speed than predicted by the main effects of power and weight. To understand this interaction further, let's consider the two-way diagram for the experiments (Figure 18.16). This diagram confirms the results of the regression models. Because the slopes of the weight design variable for its low state versus its high state are not parallel, an interaction exists between weight and power. This interaction implies that we must carefully choose a motor for the solar car. Based on these findings, we conclude that we can obtain significantly increased speeds, even if we add a larger motor. Applying this conclusion, Figure 18.17 shows a possible evolved concept for the solar car product. The new solar car's feel and its aesthetics have been evolved to a modern race car concept; the motor is larger, the solar panel is larger, weight is reduced in the body panels, and multiple gears have been added to adjust torque speed characteristics. The empirical tests lead to the motor, solar panel, and weight modifications. Date: 2016-01-14; view: 581
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Consider the "planes" of the control factors in Figure 18.15, as they vary from a "+ 1" state to a "- 1" state. What insights do we have by inspection? For example, the weight affects the car speed less than the change in power source (for the ranges chosen). Next we calculate the model coefficients. For the main effects (average of the high state minus avg. of low state):
