(2.1) The Bose electromagnetic fatigue testing machine in room 114 Upson-I applies load and displacements to a test specimen via the application of a variable magnetic field to permanent magnets aligned along the top load shaft. A simplified model of the internal structure is shown in the attachment. The specimen is held by the top and bottom load shafts. The copper electric coil is held in place via epoxy (thermoset) adhesive connections with the surrounding machine structure (not shown). The motion of the metallic permanent magnets through the magnetic field and the flow of current through the electric coil cause energy to be dissipated as heat.
Based on your knowledge of the potential effects of heat on the magnetic, electrical and mechanical properties of materials, summarize potential problems that could arise in this system (e.g. potential sources of error in the test results or potential mechanisms of failure in the machine itself) if the heat is not properly dissipated.
(2.2) The National Electrical Code specifies, among other things, values for the minimum allowable cross-sectional area of conductors for a given voltage and maximum allowable total length of circuits depending on the diameter of conductor used. Based on your knowledge of the motion of charge carriers, the origins of electrical resistivity, and the typical micro-structure of metallic conductors,
(a) explain why there is a minimum allowable cross-sectional area for a given applied voltage, and
(b) why there is a maximum allowable total length of electrical circuit for a given conductor diameter.
Would you expect these limits to be the same for copper and aluminum wires?
What about two copper wires with different grain sizes, work hardening histories or levels of impurities? Explain.
(2.1) Looking and thinking about the setup I can see that
1) The coil will induce a magnetic field that either opposes or attracts the field produced by the permanent magnets.
2) If an AC current is supplied to the coil at a frequency of f Hz, the magnetic field in the coil will oscillate at a frequency of f Hz and the top shaft will vibrate at this frequency due to the interaction of the coil and the fixed magnetic field.
3) Linear stress and strain is applied to the specimen to fatigue it by the vibrating top shaft, the magnitude of this stress (related to the strain) is proportional to the amplitude of the AC current applied to the coil.
4) Energy lost from the coil due to heating will increase the temperature of the coil and surroundings.
5) As the temperature in the coil increases, its resistance increases (by the Resistance & Temperature relationship for conductors [Reference: http://www.allaboutcircuits.com/vol_1/chpt_12/6.html]) and the maximum current amplitude flowing in the coil decreases by a proportional amount.
6) The maximum alternating magnetic field in the coil will thus decrease by a proportional amount.
7) The resulting stress and strain applied to the specimen will be in error by a similar amount, eg. less stress and strain will be applied to the specimen under test than the operator thinks.
8) The fatigue related measurements will be underestimated by a certain degree thus leading to false results. This will ultimately mean that a specimen that is specified to fail at a certain stress applied over a certain time will in practice fail some time before that in a practical situation. Leading to all sorts of dangerous consequences.
9) In order to ...
A solution to answer questions about the electrical characteristics of the Bose electromagnetic machine and analysis of some souces of error when using such a machine, errors resulting from heating and other effects