Thermo-energetic modelling of machine tool spindles with active cooling based on macro models

Enabling high precision milling requires sophisticated thermal conditioning of spindle units in order to minimise thermal elongations and deformations of the spindle shaft and surrounding machine structures due to temperature gradients. In the design and implementation of new spindle units, a model based approach can be of substantial use to predict the thermo-energetic behaviour of the system. In this work, the fundamental set of governing equations required to describe the thermo-energetic effects on machine tool spindle units are derived and discussed. On two exemplary cases, the application of the model is demonstrated. Using empirical data obtained from a spindle test bench, the performance of the macro models and their implementations are quantified.