Electromagnet Experiment

Write-up: The electromagnet is a very versatile exercise for experimental design, process capability studies, and Gage R&R studies. The kit includes actual designed experiments with results from previous experiments.

Raw Materials: magnet wire (Radio Shack 278-1345B; it has 3 diameters), cores (railroad ties), batteries (D cells…1.5 volts…need at least two), battery holder (Radio Shack 270-396A will hold up to 4 batteries), alligator clips (2 or more), gauss meter (Alphalab DC Magnetometer). Sand paper (fine). Masking tape. Wire cutter.

Directions: Several factors can be studied.

Possible Factors / Levels
Magnet wire gage / 30,26, 22
Number of D cells / 1,2,3,4
Number of turns / 40 to 80
Core size (optional variable) / Smaller, bigger
Distance from solenoid / As you choose

Caution: For some combinations the wires can get hot.

Suggestions on conducting trials: Cut the wire length for the runs greatest number of turns first. Use this same wire length for all (fewer and more turns).

The magnet wire is coated with non-conductive materials. After winding the coils, use the sand paper to remove the non-conductive material at the end of the wires so as to obtain a good connection. Wrap all coils to the same diameter. Try not to overlap the windings.

The magnet field varies with distance and direction. One approach is to measure the field strength at the same distance and direction from the coil for each run. Alternatively, you could also treat distance and angle as factors (either control or noise).

The gauss meter probe will likely be very sensitive to angle and position. Before gathering the experimental data, have your measurement people practice taking readings while attempting to minimize variability. You will want to consider fixtures (tape) to position the probe and samples exactly the same from run-to-run.

The batteries can display significant current drain during the experiment. One-way to lesson the impact of this bias on the estimate of variable effects would be to randomize the run order of the trials. If the results are not run in a random order, a time ordered plot of the residuals would demonstrate any impact on the results.

If you run the trials with a steel core: Initially the steel core will not be magnetized. As soon as current is run thru the wire it acquires some magnetic properties. Cycle your circuit several times until the magnetic field at the measurement location stabilizes before conducting the trials (this varies a great deal with material type for the core)

The basic theory:

Field strength is proportional to: (number of turns in magnet wire)(permittivity of the core)(current flowing thru wire) and inversely proportional to the length of the coil.

Resistance in wire equals: (volume resistivity of material) (length)/(cross sectional area)

A typical designed experiment for the electromagnet is as follows:

(Note: no core was used in this experiment)

Factor / Low / High
Wire / Green / Gold
Voltage / 1.5 / 3.0
Dist. To Coil / 0 / 1
Number of turns / 10 / 20

A 16 run full-factorial design was conducted (random order) with 3 replicates. The only response measured was field strength.

Analysis of the data was as follows:

DOE Wisdom Analysis of Variance
Dependent Variable: / field str
Number Runs(N): / 48
Multiple R: / 0.984948
Squared Multiple R: / 0.970123
Adjusted Squared Multiple R: / 0.957447
Standard Error of Estimate: / 2.14336
Variable / Coefficient / Std Error / 95% CI / Tolerance / T / P(2 Tail)
Constant / 10.0833 / 0.309368 / ± 0.629414 / 32.593 / 0
wire(A) / 2.09125 / 0.309368 / ± 0.629414 / 1 / 6.76 / 0
voltage(B) / 1.89792 / 0.309368 / ± 0.629414 / 1 / 6.135 / 0
dist(C) / -9.1 / 0.309368 / ± 0.629414 / 1 / -29.415 / 0
turns(D) / 0.6925 / 0.309368 / ± 0.629414 / 1 / 2.238 / 0.032
AB / -0.37 / 0.309368 / ± 0.629414 / 1 / -1.196 / 0.24
AC / -2.15042 / 0.309368 / ± 0.629414 / 1 / -6.951 / 0
AD / 1.18458 / 0.309368 / ± 0.629414 / 1 / 3.829 / 0.001
BC / -1.72708 / 0.309368 / ± 0.629414 / 1 / -5.583 / 0
BD / -0.335417 / 0.309368 / ± 0.629414 / 1 / -1.084 / 0.286
CD / -0.4325 / 0.309368 / ± 0.629414 / 1 / -1.398 / 0.171
ABC / 0.346667 / 0.309368 / ± 0.629414 / 1 / 1.121 / 0.271
ABD / 0.405833 / 0.309368 / ± 0.629414 / 1 / 1.312 / 0.199
ACD / -1.21542 / 0.309368 / ± 0.629414 / 1 / -3.929 / 0
BCD / 0.28125 / 0.309368 / ± 0.629414 / 1 / 0.909 / 0.37

Discussion questions: Is the effect associated with wire diameter (color, gold is greater diameter) for real or is it due to decreased resistivity, hence greater current flow thru the greater diameter wire. What is the impact of current drain on the experimental results? Of course, we could avoid both of the above concerns by making use of a constant current supply.

Confirmation trial: Wrap a coil for the team using the 22-gage wire (gold). Do not tell them how many windings there are. Have them hook up the circuit with any voltage of their choice and ready the field strength. From this reading, they can estimate the number of turns. The winning team is the one that comes closest to the actual number of windings.

Experiment #2:

In order to assess non-linearity, we conducted the following DOE (I did these as an electromagnet, with all solenoids wrapped on the same core)

Number of Turns / Volts / Gauss
20 / 1.5 / 17
20 / 3 / 21
20 / 4.5 / 25
20 / 6 / 27
30 / 1.5 / 23
30 / 3 / 29
30 / 4.5 / 33
30 / 6 / 35
40 / 1.5 / 27
40 / 3 / 34
40 / 4.5 / 39
40 / 6 / 43

Some graphical analysis was as follows:

DOE Wisdom Analysis of Variance
Dependent Variable: / gauss
Number Runs(N): / 12
Multiple R: / 0.999093
Squared Multiple R: / 0.998187
Adjusted Squared Multiple R: / 0.996676
Standard Error of Estimate: / 0.439381
Variable / Coefficient / Std Error / 95% CI / Tolerance / T / P(2 Tail)
Constant / 30.9375 / 0.270927 / ± 0.662942 / 114.191 / 0
turns(A) / 6.625 / 0.155345 / ± 0.380119 / 1 / 42.647 / 0
volts(B) / 6.35 / 0.170171 / ± 0.416400 / 1 / 37.315 / 0
AB / 1.425 / 0.208417 / ± 0.509983 / 1 / 6.837 / 0
turns**2 / -0.875 / 0.269065 / ± 0.658386 / 1 / -3.252 / 0.017
volts**2 / -1.6875 / 0.285386 / ± 0.698323 / 1 / -5.913 / 0.001

Options to try:

1.  Gage R&R study of gauss meter (will look pretty ugly unless you have really worked on measurement variability)

2.  Designed experiment with three (or more) levels

3.  Short-term process capability study of one coil configuration so as to study stability and variability