During aircraft maintenance; an attach nut was lost and subsequently found jammed in the elevator trim mechanism resulting in an air turn-back.

Narrative

Technician replaced the defective carburetor heat control cable with a new FAA approved cable. During removal of the old carburetor heat control cable the attach nut attaching the cable housing to the instrument panel was lost and eventually became lodged in the elevator trim control wheel sprocket and chain. During the next training flight; the pilot/student attempted to apply nose up and nose down trim and it was discovered that the trim wheel was jammed. The flight crew further moved the trim wheel to the point where the trim 'just gave' and 'slipped' and the aircraft was forced into a stuck extreme nose down trim configuration. The flight crew performed an air turn back and performed a successful landing. Upon further inspection the cable attach nut was found lodged between the sprocket and chain. The sprocket and chain were inspected for damage and system rigging checks were performed with no defects noted. We believe the cause of this incident was human error by the inaction of the technician to retrieve the missing nut. Despite previously loosening the nut and installing a new cable with a new nut; the technician either forgot to find the missing nut or did not hear it fall in the trim components.