Analytical modeling for thermal errors of motorized spindle unit

Modeling method investigation about spindle thermal errors is significant for spindle thermal optimization in design phase. To accurately analyze the thermal errors of motorized spindle unit, this paper assumes approximately that 1) spindle linear thermal error on axial direction is ascribed to shaft thermal elongation for its heat transfer from bearings, and 2) spindle linear thermal errors on radial directions and angular thermal errors are attributed to thermal variations of bearing relative ring displacements. Based on prerequisites, an analytical modeling method is developed to analyze these spindle thermal errors. Firstly, thermal-mechanical models of rotating ring geometry and interference assembled rotating ring geometries are established, for thermal variation modeling of relative ring displacements of short cylindrical roller bearing and angular contact ball bearing. Secondly, these thermal variation models are associated with heat-fluid-solid coupling FE (finite element) simulation technique, to model spindle linear thermal errors on radial/axial directions and angular thermal errors by the analytical simulation method. Consequently, verification experiments clarify that the presented method is accurate for spindle thermal errors modeling, and can be effectively applied into the design and development phases of motorized spindle units.