Helicopter
Flight Crew Instrument; Flight Crew Commercial; Flight Crew Flight Instructor
Communication Breakdown; Situational Awareness
Conflict NMAC
Flight Crew Took Evasive Action
Human Factors; Procedure
We were conducting Instrument flight training. We had completed the approach and finished the published missed back to the VOR. We were completing the first turn back over the VOR when a [high wing aircraft] crossed our path at 2;000 feet MSL directly over the VOR. We were continually reporting our position on CTAF and after the near miss we tried unsuccessfully to contact the [high wing aircraft].At no time did [the other aircraft] make a position report. We had to pull up sharply to avoid an impacted with the [other aircraft] and we were close enough to clearly read their N number.
Helicopter crew reported experiencing a near collision with another aircraft while conducting a practice VOR approach.  Reporter maintains that the other aircraft never reported their position on CTAF.