The Entek diagnostic wall chart that I have indicates that a loose connection on a motor supply lead will produce 1/3 line frequency sidebands around the 2Xline frequency vibration peak. In my experience I have never nailed one of these.
Petri - I agree with you 100%. I have seen that wall chart and I have never been able to come up with any thoeretical explanation whatsoever for why a loose connection would cause F_Line/3 sidebands or any real-world example of that pattern (never seen anything at these frequencies even on a log scale). Personally I believe that a loose connection will have no detectable vibration effect whatsoever until it becomes very severe (severe enough to change the voltage to the motor), at which point twice line frequency vibration may show up due to the voltage imbalance.