Mechanism, calculation method, and analytical modeling of spindle thermal characteristics considering radiation heat transfer

Neglecting the effect of thermal dissipation by radiation heat transfer (RHT) in spindle system may lead to calculation errors in the finite element model and analytical model of temperature field and thermal errors. As a result, the actual temperature field and thermal error of the spindle cannot be truly characterized and the effectiveness of the compensation of the spindle based on the analytical model will be diminished. To address this issue, this article studies the heat dissipation mechanism of RHT of spindle system and proposes a Monte Carlo-Radiation Network Method (MC-RNM) for real-time calculation of net RHT in the spindle system during the operation of the machine tool. Then, the study proposes an improved thermal network method (I-TNM) to establish an analytical model for spindle temperature field and thermal error, taking into account RHT. It was also shown that the analytical model of the spindle taking into account RHT yields better accuracy and generalization in the calculations of temperature field and thermal error. Under different operating spindle conditions, the maximum error between the calculated steady-state temperatures at the left end face and lateral surface of the spindle and the experimental values is less than 0.4ºC. Additionally, the maximum error between the calculated steady-state thermal errors and experimental values is within 2 µm. The findings enhance the theoretical research on boundary conditions in precision spindle systems, providing theoretical support and guidance to advance the research investigating thermal structure design of the spindle and thermal error compensation.