This paper discusses ontology mapping between two taxonomies of functions of artifacts for the engineering knowledge management. The mapping is of two ways and has been manually established with deep semantic analysis based on a reference ontology of function for bridging the ontological gaps between the taxonomies. We report on the successful results thanks to such deep analysis not at the lexical level but at the ontological level. Using the mapping knowledge, we developed a semantic search system which can provide engineers with interoperable access to technical documents by searching for functional metadata based on either of functional taxonomies.