Your post did not indicate that this occurs in one or multiple fans. I assume that only one fan has these symptoms.
Unless this fan is in a critical operation, trouble shooting efforts will probably be limited since with such a small fan, replacement of components may be cheaper than extensive testing. Thus--low cost/no costs tests first.
I would also check to see that no fans are rotating backward during start-up, and, if dampers are present, they are closed for start-up. Make sure that static pressure characteristics cannot cause the motor to overload.
Observe the contactors during startup to ensure that chatter is not occuring. Check that all connections, particularly overload connections are tight so that there is no chance that the motor is single phasing. A visual inspection of the motor peckerhead terminations should be made.
Next, conduct vibration or ultrasonic testing on the fan bearings and motor to determine whether a bearing or other mechanical condition were causing this condition.
If desired, a disturbance analyzer can be used to confirm voltage condition seen by the motor during start-up. This will confirm proper contactor operation. Simultaneous current monitoring can indicate whether the motor loading during start-up is consistent with the motor rating and design.
If the fans and motors pass these preliminary tests, I would suspect an electrical fault in the motor.
Both rotor or stator faults could produce behavior of the sort described here. Since this is a small motor, the simplest approach at this point to trouble shooting may be to simply replace the motor, rather than pay for additional testing to deterime the condition of the motor rotor and stator.
