Using statistically designed experiments to improve investment casting quality

Although it’s been practiced for centuries, investment casting is still regarded by many as part science, part art, and part black magic. This is due in large part to the unpredictable behavior of precious metals in the molten state. Much of the data available about lost-wax casting is based on trial-and-error experimentation, not scientific procedure.

In today’s competitive business environment, unless you get lucky with trial-and-error experimentation and hit an answer, you could find yourself out of business quickly. Instead, it would be ideal to find a scientific yet relatively simple way to problem solve your casting issues without very expensive hardware, software, or rocket science.

Fortunately, methods that fit the bill have been around for a long time, and they’ve been used in many other industries with great success. One of these methods is statistically designed experiments, also called Design of Experiments (DOE). This fairly simple tool can be used to quickly zero in on important parameters for casting, while weeding out the trivial ones. It prevents time wasted working with variables that you may think are important, but in reality don’t affect your results. More important, this method allows you to see how different factors may interact with each other to influence results, which is very difficult to determine through observation alone.

Background on DOE
The classical view of experimentation is to change one factor at a time, run the experiment, observe the results, and move on to the next factor. This approach has several drawbacks: It takes much longer and uses up more resources; the optimum combination of all variables may never be revealed; and the interaction between factors may never be revealed.

Unlike classical experimentation, statistically designed experiments can provide the following benefits:

• Many factors can be examined simultaneously.

• Some input factors that cannot be controlled, which are called noise factors, can influence the output; however, other input factors can then be controlled to reduce the effect of the “noise.”

• In-depth statistical knowledge is not necessary to perform these tests and reap their benefits.

• Relatively few experiments can look at a large number of factors and separate the trivial from the important.

• In most cases, quality and reliability can be improved without increasing costs.

Although experimental design was developed in England and the U.S. many years ago, it was aimed at statisticians, not engineers. The latter were not exposed to it until a Japanese engineer named Gen’ichi Taguchi took the method and adapted it for use by Japan’s engineering community. In the 1980s, as Japan was fast becoming a world economic leader, Americans noticed the Japanese using a powerful new experimental tool: the Taguchi method. Today this method is used in many industries to shorten product development lifecycles while at the same time producing higher quality, lower cost products. In the jewelry manufacturing industry, it can be applied to casting in order to determine the proper parameters needed to produce good, consistent castings. It also enables manufacturers to assess what factors are important in ultimately determining how to produce high quality castings.

Setting Up an Experiment
In the sample experiment presented in this article, my objective was to examine what factors would influence the filling of a fine piece when casting platinum on my centrifugal caster—a Galloni automatic induction, double-broken-arm machine. The fine piece that I cast was a 10 square by 10 square grid made of 0.05 mm diameter wax wire (figure 1). It was gated along one edge with a main gate in the middle.

After establishing an objective, the first step of any DOE is to determine what factors you want to examine. To assess influences on fill, I felt the obvious choices were oven temperature and metal temperature because they are two of the most important factors in casting. Since I can control acceleration and final velocity on my casting machine, I chose them as the other two factors, leaving me with four factors to examine.

Typically, to keep the experiment from getting out of hand, I look at two levels for each of those factors, a high level and a low level. It is useful to pick levels that are within the realm of your machine and process capability. For a four-factor, two-level experiment, you will need to run 16 experiments. This is typically referred to as a 2 by 4 factorial.

Once you’ve determined what factors you want to examine, you must set the matrix (figure 2). The pluses represent the higher level and the minuses represent the lower level. As you can see, there is a pattern to the pluses and minuses to ensure that every combination of factors is covered at every level.

This matrix will provide the main factors. If you want to explore the interaction between two factors, you can expand this matrix (figure 3).

There are two additional columns in figure 3. Column five examines the interaction between velocity and acceleration, while column six examines the interaction between metal temperature and oven temperature. A result that shows a strong interaction indicates that you can’t consider one factor without considering the influence of the other. If there is no interaction, the factors are independent of each other.

To set up the additional columns, use basic math to multiply the pluses and minuses in the columns of interest. A plus multiplied by a plus equals a plus, as in run number four for velocity x acceleration. A minus multiplied by a minus equals a plus, as in run number one for velocity x acceleration. A plus multiplied by a minus equals a minus, as in run number two for velocity x acceleration. Once again, you can see a pattern developing.

Plotting the Numbers
When the high and low levels are plotted in the matrix, you need to fill in the actual numbers. Since my Galloni casting machine provides a velocity choice of 200 to 500 rpm, I make these levels my plus and minus.

It’s important to note here that the setup and results of your experiment will be specific to the equipment you are using. For example, some centrifugal casting machines don’t measure velocity in rpm like mine does. In this scenario, you could count the winds of the spring, using three winds as the low level and six winds as the high level, for example. Or, consider my treatment of the acceleration factor.

My casting machine allows an acceleration of 1 as the fastest and 4 as the slowest. Although these are simply levels of acceleration, not specific measurements, I can still plug them into the matrix and use them for my calculations. (Note: In this circumstance, you must be careful when working with software, as it will be looking for the low level number to be less than the high level number. You can plug in a -4 to get around that.)

For a metal temperature, I wanted to look at two extremes. I initially chose 1,800°C (3,272°F) and 1,975°C (3,587°F); however, early trials showed that at 1,800°C (3,272°F) I couldn’t get the metal to leave the crucible, so I changed the low temperature to 1,825°C (3,317°F).

Lastly, I set the oven temperatures to 1,550°F (843°C) and 1,450°F (788°C). When casting, I usually set the oven temperature as my last factor, so I can run all the low temperature trials first, followed by the high temperature trials. Although this is not the preferred method—random testing provides more accurate results—it saves a lot of time if you are using only one burnout oven. If you have the luxury of using two ovens, this is not an issue.

When you plug all the numbers into the matrix, it will resemble the one shown in figure 4.

Additional Factors
In addition to the factors in question, you can examine potential “noise” factors. For example, does the position of the object on the button influence fill? Logic would dictate that as the mold travels in a counterclockwise motion, the metal as it leaves the crucible will want to stay behind, traveling in the opposite direction (figure 5).

You could hypothesize that pieces at the back end of the swing would see more force and fill better than pieces at the front end of the swing. You could also hypothesize that pieces at the top and bottom of the button would fill equally. If this is really true, you can treat the position of the parts as a noise factor and try to adjust other factors to minimize or eliminate this effect. This is where DOE becomes particularly powerful and leads to robust processes and design.

For my experiment, the part was located at four different 90 degree positions on the button to test whether position played a role, and if its effect could be minimized by altering the other factors. I placed grids at the 12, 3, 6, and 9 o’clock positions. I was careful to ensure that the 12 o’clock position was always located in the same location for each flask, so as not to introduce a variable. To do this, I marked the part at the 12 o’clock position and aligned it with a mark on the flask (figure 6).

Once the parts were sprued, the flasks were invested using the same batch of investment. I ensured that all parameters were kept the same for each batch, since I could not invest all the flasks with one mix cycle.

After drying, the flasks were sent through the burnout cycle following the normal production process. The flasks were cast, devested, and pickled in caustic soda to remove investment. Each tree was en-graved with the flask number after casting to preserve the order of the casts.

To obtain results, I counted how many squares were completely filled in each grid at each position. I then plugged in the results on the spreadsheet in preparation for analysis (figure 7).

Analyzing the Results
Without doing any fancy math, one conclusion I can draw from the results is that I can get complete fill in all positions at the higher metal temperature (1,975°C), regardless of the levels of the other factors. This is an obvious effect. What is difficult to figure out is the possible subtle effects of the other factors. This is where the math enters, which is rather straightforward.

To find out the influence of a factor, take the results from all the low level runs of that factor, add them together, and subtract that number from the sum of the results from all the high level runs of that factor. Then take that result and divide it by the number of runs at the high level, in this case eight.

For example, take the influence of the velocity factor at the 12 o’clock position. The calculation is:

(86+97+100+100+64+88+100+100)-(76+28+100+100+71+59+100+100) /8 = 12.625

This result shows me that running the experiment at the higher velocity level (500 rpm) increased my fill rate by 12.6 percent. This could be a substantially significant influence.

You can run these formulas for all factors at all positions. Doing so will give you the results shown in figure 8. Here are some of my conclusions for the three remaining factors:

Metal temperature. What you can see from the results, which confirm my earlier observations of the raw data, is that metal temperature has the highest influence on fill. You can also see that the influence at the 12 and 6 o’clock positions is almost the same, and that the influence is highest at the 3 o’clock position, which is on the back end of the swing. So while metal temperature had the greatest influence, the amount of that influence was driven by flask position.

Oven temperature. If you look at the oven temperature influence, you can see that the numbers are low, and negative in the case of the 12 and 3 o’clock positions. The only number of any significance is at the 9 o’clock position. This could be indicating that this position is the last to fill, and with the higher oven temperature, the metal is still molten enough to do some filling after the other positions are filled.

Acceleration. The acceleration influence is very interesting, as it seems to show little influence at the 3 and 9 o’clock positions, but a negative influence at the 12 o’clock position, meaning a higher acceleration produces less fill at that position. The spread between the 12 and 6 o’clock positions is almost 17 percent. To explain this, you might theorize that the metal is not really leaving the crucible at a true horizontal, but has a downward motion to it. Increasing the acceleration increases the downward angle of the metal stream (or the mold is actually lifting off the cradle from the kick), causing more filling at the 6 o’clock position. Another theory is that just the opposite is occurring: The stream is riding high, hitting the upper edge of the opening and causing less fill at the 12 o’clock position.

You could theorize about what is happening, but the important thing to remember is that something is occurring that could be influencing your fill characteristics—something that you wouldn’t be able to see without this experimenting tool.

Graphing Your Results
You can also graph your results, as visuals tend to show influencing factors more clearly. This is where statistical software, such as Minitab, can be very useful. Minitab creates a factorial grid for you. You start by inputing your factors and levels. After the experiment, you input your results and the software calculates all the graphs showing the influences. Figures 9 and 10 show my results graphed by this software.

As you can see, the graphs show the influences very clearly. On the Main Effects Plot (figure 9), a horizontal line indicates no influence from the factor at the tested levels. This can be seen in the graph for oven temperature. The steeper the plotted line, the greater the influence of that factor, as is the case with metal temperature.

For the Interaction Plot (figure 10), crisscrossing lines indicate that the two factors influence each other. If the lines run parallel to each other, or don’t cross between the two levels, then they don’t influence each other.

If you look at oven temperature versus metal temperature, you see no interaction: I achieved 100 percent fill at the 1,975°C metal temperature, regardless of whether the oven was at 1,450°F or 1,550°F. If you look at oven temperature versus acceleration, on the other hand, you see that at the higher acceleration (1), increasing oven temperature increased fill. However, at the lower acceleration (4), increasing oven temperature actually decreased fill, a phenomena that is difficult to explain and would benefit from replication of the experiment.

One thing that you don’t want to do is extrapolate past the levels examined in the experiment, which would result in false conclusions. These results are only valid for these levels.

For the final graph (figure 11), I added the results of all the positions to get a total amount of fill for each run. This was then plotted to see if anything changed.

When compared with the Main Effects Plot for the 12 o’clock position, you can see two changes. There is now a slight influence from oven temperature, though not much, and a reverse influence from acceleration. (You could theorize that increasing the acceleration has a diminishing effect at some point due to the creation of excess turbulence, which impedes filling.) You can also compare the total to the other three positions to see what changes are evident.

Conclusions
The power of using statistically designed experiments is that from one set of experiments you can gather a wealth of data that otherwise would be difficult to collect and analyze. For example, this experiment showed me that oven temperature is not as critical as one might think in filling a fine piece. If this is the case, there are several advantages to staying at the lower oven temperature: less wear and tear on the equipment and materials, better cast surface due to reduced reaction with investment, easier investment re-moval, and shorter process time. These factors combined would result in a higher quality piece at lower cost. This type of data allows jewelry manufacturers to make informed decisions regarding our casting processes. Its usefulness has been proven in many industries—and now it’s time to utilize it in ours. In today’s global environment, it is a proven tool for staying competitive.

Metallurgist Tino Volpe is the technical manager for Tiffany & Co. in Cumberland, Rhode Island.

Experimenting Tips
The following tips will help you set up an experiment that will yield quantitative data and scientific results:

Think about what factors you want to study. In the experiment presented in this article, I examined how system temperatures and centrifugal forces influence fill, but there are many other factors that you could consider in a casting DOE. Tree design, mold permeability, and straight arm casting versus broken arm casting are interesting potential factors.

Measure results quantitatively. Qualitative or subjective results such as “looks good” won’t fit the formulas very well. You could have results such as the number of pieces rejected or accepted, but if the judge is human, your data could be tainted.

All subjectivity can be avoided if you set up the experiment to produce measurable results. In this case, I used a 10 square by 10 square grid to measure fill because it is easy to count how many squares filled, which can be represented as a percentage.

Watch your constants. It's essential that all factors other than those you are studying are kept constant throughout the experimental run, so as not to influence the results.