I enjoy analytical modeling, both the simple and the complex. It
helps bring clarity to chaotic situations. Most of us have
experienced such times during high-profile failures. The number of
possible causes seems to model helps to quantify the true cause.
Agitators are mixing devices used to blend products. Most
pressured vessel designs require a mechanical shaft seal and the
shaft must run true to prevent leakage. In this case history a
high-speed agitator had a shaft that was bolted together in
sections for easy installation. On startup external vibration of
the agitator was excessive and vibration measurements indicated the
amplitude to be at shaft rotating frequency, mean
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