In　order　to　solve　the　problem　of　precision　optimization　design　of　CNC　machine　tools,　the　spatial　motion　error　model　of　CNC　internal　cylindrical　compound　grinder　is　established　based　on　the　theory　of　multi-body　system　based　on　the　analysis　of　the　structural　parameters　and　motion　form　of　the　grinder.　Based　on　the　space　motion　error　model　is　established,　using　the　theory　of　interval　mathematics,　defines　the　interval　expansion　factor,　study　the　grinder　involved　36　geometric　error　of　space　motion　error　sensitivity　of　the　interval,　the　interval　sensitivity　analysis　results　are　represented　as　vectors　form,　get　along　with　the　change　of　the　grinder　movement　axis,　the　effect　of　various　geometric　error　on　space　motion　error.　The　maximum　values　of　each　error　sensitivity　index　in　the　whole　region　are　defined,　and　the　normalized　results　of　the　sensitivity　analysis　of　the　maximum　interval　in　the　whole　region　are　obtained.　Finally,　the　three　coordinate　measuring　machine　is　used　to　carry　out　two　different　compensation　strategies　on　the　grinding　machine,　and　the　roundness　errors　of　the　three　heights　of　the　two　shaft　parts　are　measured　respectively,　which　verified　the　correctness　of　the　sensitivity　analysis　method　proposed,　and　laid　a　foundation　for　the　subsequent　precision　optimization　design.　©　2022　Editorial　Office　of　Chinese　Journal　of　Mechanical　Engineering.　All　rights　reserved.