The　wire　is　the　main　processing　unit　of　the　low　speed　wire-cut　electrical　discharge　machine　(WEDM-LS).　The　wire　rack　is　a　cantilever　structure.　Its　support　member-the　up　and　down　wire　racks　is　a　cantilever　structure.　The　error　of　the　up　and　down　wire　racks　is　significantly　affected　by　ambient　temperature,　and　the　change　of　the　up　and　down　wire　racks＇　relative　position　makes　the　wire＇s　position　and　orientation　change　directly,　which　reduce　the　machining　precision.　In　this　paper,　the　screw　theory　was　used　to　establish　the　WEDM-LS＇　theoretical　thermal　error　model.　The　finite　element　method　was　used　to　calculate　the　deformation　of　the　upper　and　lower　wire　racks　in　x,　y,　and　z　directions　when　the　ambient　temperature　changes,　and　drawn　the　change　of　the　wire＇s　position　and　orientation　with　MATLAB　in　the　Cartesian　coordinate　system.　An　experimental　platform　was　built　to　measure　the　wire　rack＇s　thermal　deformation　under　different　ambient　temperatures,　and　establish　a　thermal　error　model　based　on　the　M-RAN　RBF　neural　network　algorithm,　which　provides　a　basis　for　compensating　for　the　numerical　control　system.　Results　show　that　the　model　residual　error　is　less　than　1　μm,　and　it　can　well　reflect　the　distribution　and　the　variation　of　the　thermal　error.　©　2016,　Beijing　University　of　Technology.　All　right　reserved.