The　high-speed　permanent　magnet　synchronous　motor　supported　by　the　air　foil　bearing　for　the　air　compressor　was　used　to　provide　the　high-pressure　air　and　realized　the　high-efficiency　chemical　reaction　in　the　hydrogen　fuel　cell　vehicle.　Theoretical　analysis　was　applied　to　study　the　electromagnetic　field　harmonic　between　the　armature　and　rotor.　For　the　cylindrical　permanent　magnet,　the　expressions　of　the　magnetic　flux　density　and　tooth　harmonic　were　obtained.　The　radial　and　tangential　components　of　the　armature　magnetic　flux　density　generated　by　the　three-phase　winding　were　given　by　the　analytic　expression.　The　finite　element　simulation　analysis　was　carried　out　and　the　results　were　obtained.　The　magnetization　mode　of　the　cylindrical　permanent　magnet　could　influence　the　harmonic.　With　an　increase　in　the　air　gap　width,　the　tooth　harmonic　decreased.　The　armature　magnetic　field　harmonic　of　the　single-layer,　double-layer　and　circular　winding　were　analyzed　respectively.　Based　on　the　experiment　system,　the　experiment　data　of　the　high-speed　permanent　magnet　synchronous　motor　driven　by　10　kW　at　the　speed　of　90000　rpm　were　obtained.　It　indicated　that　the　operation　was　stably　and　the　electromagnetic　performances　were　consistent　with　the　simulation　results.　©　2020　IEEE.