By　studying　the　edge-workpiece　engagement　(EWE),　and　taking　two　inclination　(lead　and　tilt)　angles　into　account,　the　time-varying　cutting　areas　and　boundaries　are　determined,　the　instantaneous　numerical　chip　thickness　(NCT)　within　different　EWEs　at　each　point　of　the　edge　curve　during　the　milling　process　of　the　ball　end　milling　tool　is　solved,　and　the　milling　force　and　stability　are　calculated.　The　milling　force　and　SLD　of　the　model　in　this　paper　(NCT-EWE　model)　and　the　model　in　the　literature　(Altintas　and　Otzurk　model)　are　compared.　It　is　verified　that　the　algorithm　adopted　in　this　paper　has　higher　accuracy,　and　the　algorithm　is　simple　and　fast.　In　addition,　it　is　found　that　increasing　the　lead　and　tilt　angles　can　reduce　the　milling　force　and　improve　the　stability,　and　the　free　vibration　in　the　stable　region　decreases　gradually,　while　in　the　non-stable　region,　it　increases.　The　algorithm　in　this　paper　has　certain　theoretical　and　application　value　for　five-axis　milling.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　London　Ltd.,　part　of　Springer　Nature　2024.