Thermal-Feature System Identification for a Machine Tool Spindle

The internal temperature is an important index for the prevention and maintenance of a spindle. However, the temperature inside the spindle is undetectable directly because there is no space to embed a temperature sensor, and drilling holes will reduce its mechanical stiffness. Therefore, it is worthwhile understanding the thermal-feature of a spindle. This article presents a methodology to identify the thermal-feature model of an externally driven spindle. The methodology contains self-made hardware of the temperature sensing and wireless transmission module (TSWTM) and software for the system identification (SID); the TSWTM acquires the temperature training data, while the SID identifies the parameters of the thermal-feature model of the spindle. Then the resulting thermal-feature model is written into the firmware of the TSWTM to give it the capability of accurately calculating the internal temperature of the spindle from its surface temperature during the operation, or predicting its temperature at various speeds. The thermal-feature of the externally driven spindle is modeled by a linearly time-invariant state-space model whose parameters are identified by the SID, which integrates the command n4sid provided by the System ID Toolbox of MATLAB and the k-fold cross-validation that is common in machine learning. The present SID can effectively strike a balance between the bias and variance of the model, such that both under-fitting and over-fitting can be avoided. The resulting thermal-feature model can not only predict the temperature of the spindle rotating at various speeds but can also calculate the internal temperature of the spindle from its surface temperature. Its validation accuracy is higher than 98.5%. This article illustrates the feasibility of accurately calculating the internal temperature (undetectable directly) of the spindle from its surface temperature (detectable directly).