IV. PRODUCT APPLICATIONS OF PHYSICAL MODELING AND DOE

Product Application I: Nerf™ Missile storm ™ (Norrell 1995)

http://www.youtube.com/watch?v=ze1qV6TDuTM

http://www.youtube.com/watch?v=_wm3tLB7dkk

In this application, we consider the redesign of a Nerf'^TM Missile storm ^TM product. This product is a children's toy that shoots soft projectiles with human actuation. Three primary customer needs are to minimize pull force, to increase projectile range, and to increase accuracy. Figure 18.18 shows a photograph of the current product. Preliminary Experimentation: Preliminary experiments allow the determination of various product component properties. Several items must be investigated within the Missile storm™. First, for the barrel rotation spring, the spring constant, k, must be determined. Figure 18.19 shows the input force as a function of spring displacement.

Concurrent with these spring tests is the measurement of the maximum force encountered during a pull action on the blue handle, or launch base rotation. Ten different pull readings are taken using a spring-based fishing scale. The average value of the readings is approximately 19.6 N. Given the coarse value of the spring scale, an accuracy of approximately ±2 N is assumed. It is quite apparent that something aside from spring force is dominating the maximum force needed to withdraw the blue handle.

The last preliminary test completed on the original product considers accuracy of the device. A base point is needed to develop an appropriate target value. The test consists of several launches over a range of distances, attempting to hit a 7.5 X 7.5-cm-square target. The results are shown in Figure 18.20.

The middle data points are the averages for the four shots performed at the given range. The upper and lower points represent the maximum and minimum distance from the target respectively and are included to provide an indication of the Missile storm ™ scatter. The plot shows that accuracy falls off nonlinearly with distance. A log transform of the data would give a reasonable means of predicting the current accuracy capability. Instead, though, we focus on means to redesign the product.

Morphology: As a step in the product development process, a morphological matrix (Chapter 10), shown in Table 18.14, is created to tabulate the solution principles used by the original Missile storm ™ to solve some of the crucial functions. During preliminary analysis, some alternative solution principles are generated and presented here.

Adaptive Redesign: By considering the missiles of the Missile storm ^TM, we realize an immediate improvement in the product. Of the four missiles received with the toy, none of them had fins placed in the same location about the circumference of the missile body. More consistent and accurate flight will be achieved with tighter control over fin placement. In addition to fin placement, tighter control needs to be exacted over placement of missile mounting holes (i.e., the holes the launch tubes are slipped into). On all of the four missiles, the missile-mounting hole is off center. Additionally, the four stock Missile storm ^TM missiles do not have the same cavity length, the length of space in the missile past the launch tube tip. Values of cavity length, without modification, range from 0 to 3 cm.

In Table 18.14, several different solution principles are presented to stabilize the missile during flight. Offering the most promise are a combination of solution principles, joining precise location of fins, angling of fins, and an increase of angular momentum. Whereas fin location and an increase in angular momentum fall under the domain of parametric design, the angling of fins will add some entirely new functionality to the missile. Not only should angled fins increase the accuracy and stabilize the missile, it will cause the missile to spin! At first, this change simply seems to be a means to an end, until we remember we are considering a toy during this redesign effort. One primary purpose of a toy is to entertain and a spinning missile flying through the air will increase children's enjoyment of the Missile storm ^TM.

Parametric Design: As mentioned above, there are two areas for parametric redesign of the Missile storm ™ missile, precise location of fins and an increase in angular momentum. There are two principal ways of increasing angular momentum: Increase rotational speed or move mass from the center of the rotating body to the outer edges. Adding mass to the missile raises several more issues including where to place the mass. The other concern is the fact that the mass of the missile and its minimization relates to a safety customer need of minimizing the projectile mass. Therefore, efforts are directed at increasing the angular spin rate of the missile, a goal obtainable with canted, or angled, fins. These canted fins will be used to increase the accuracy and precision of the missile.

In conjunction with increasing the angular momentum, let's consider the device creating the energy transfer from blue piston handle to missile. A high-level model predicts that an increase in missile cavity length should result in a greater launch velocity. Additionally, the model predicts that decreasing friction between the missile and the launch tube should result in greater launch velocity and subsequently larger flight distance. However, as the old saying goes, "The proof is in the pudding:' so experiments must be designed and performed to validate the model.

Physical Modeling and Experimentation: Due to the inherently complex nature of analytically modeling a spinning missile, experimentation is undertaken to determine the effects of changes to the standard, stock Nerf^TM missile. Three factors are chosen for variation throughout the experiment (Table 18.15).

The goals of the tests are to examine the effects of the above factors on the accuracy of the Missilestorm ™ as well as the maximum distance achievable. Before the tests begin, planning and construction must be undertaken.

Environmental effects, such as wind, are minimized by performing all tests in one day, inside a building hallway. Weight differences between the stock missiles and the modified missiles are another possible source of noise in these experiments. A digital scale calibrated to +/ -0.005 g is used, and the results are shown in Table 18.16.

As can be shown from the first two entries in the table, there is a significant amount of variation among stock missiles. In addition, the modified missiles are approximately the same mass as the unmodified ones. Lastly, the mass of the plugs added to the missiles does not significantly increase the total mass.

One very important and likely source of noise is contamination between tests, in particular where graphite is concerned. The graphite is difficult to remove. To block out this effect and force it into the higher order terms, the experimental trials are ran in a random blocked order. The tests are ran with a conscious effort put toward delaying the addition of graphite to the system until all other tests are complete.

Experimental results:

Given the three control (design) factors, each at two levels, a full 2³-factorial experiment is to be run, with one replicate (for each particular test). The tests and the trial order are given in Table 18.17. Data for the experiments is collected in one day, and the trials were run in a random order for each of the measured responses, as shown by the "Run #" columns. The results of the experiments are shown in the table.

The first step in analysis of the physical tests is to perform an ANOVA on the data. A template for this analysis is shown in Table 18.18. As an example analysis for the NerF product, the results for the 3-m accuracy tests are included in the table.

Based on a 95% confidence test, we obtain a reduced regression model of:

Keeping in mind that the reduced model indicates distance from the intended target, we want to minimize y. To this end, we choose d₁ +, in this instance, curved fins, which gives an output of 0.16 m. This result makes sense, since curved fins increase the rotational inertia of the missiles, thereby increasing the accuracy. The trials also indicated, however, that the rotation did not adversely affect throwing distance. Similar results occurred from the distance and 20' accuracy tests.

Date: 2016-01-14; view: 858