In CNC machining center,highspeed motorized spindle is used,the motorized spindle heating leads to obvious thermal extension of the spindle working end,seriously affecting the machining accuracy.Taking the permanent magnet synchronous motorized spindle used in CNC precision engraving machine as the research object,the characteristic temperature and thermal error data of motorized spindle under different rotating speed and working modeswere tested by setting up the thermal characteristic experiment platform,and the prediction model of axial thermal error of motorized spindle based on natural exponential function was established.The experimental verification of the compensation results of the model under different working conditions shows that the prediction model is simple,high precision,low modeling cost,and can be quickly applied to the actual processing environment.