Thermal error of a hydrostatic spindle

This paper proposes a thermo-mechanical error model of a hydrostatic spindle for a high precision machine tool. By predicting the variation of motion error induced by thermal effects on a machine worktable during machining, this model allows deeper insights into the underlying mechanisms that result in evolutions of the spindle accuracy. The heat power generated in the spindle elements and the coefficients of convection heat transfer over its outer surface have been evaluated. Then, the distribution of temperature and deformation of the spindle have been simulated by a finite element coupled thermo-elastic model, from which the influence on notably spindle stiffness variation was deduced. Experimental measurement of the thrust plate axial displacement under thermal expansion is in close agreement with the computed axial thermal expansion.