Gray box-thermal grid evaluation for a spindle cooling unit based on axial-radial heat transfer separation with its structural impact

Purpose A full and accurate heat model, especially the thermal resistance network with a high engineering application value to describe the cooling channel impact on spindle temperature is still absent so far. For a precise role description on a cooling unit in spindle heating, this paper aims to integrate the gray-box modeling theory to develop a novel semi-empirical thermal resistance network model of a spindle cooling system with its structural constraint influence. Design/methodology/approach The structural characteristics and thermal exchange of a cooling passage were first analyzed. A gray-box description for the heat dissipation of a spindle coolant unit was subsequently implemented, and meanwhile the thermal resistance theory was introduced to perform the specific modeling tasks. In this process, the thermal equivalent resistance of a rectangular spiral channel was derived based on the formula constructed by Dittus and Boelter, and accordingly the axial and radial heat dissipation resistances of a cooling unit also were formulated separately with the influence of the coolant channel itself and its external structural constraints. The thermal network of a motorized spindle was next planned to verify our work, in which the proposed thermal resistances based on gray-box and axial-radial heat transfer separation for the spiral coolant channel were employed, the spindle segmentation factor considering the structural constraint effect was referred for modeling simplification, and furthermore the multi-node model of bearings was also revised to correct the double counting on the heat exchanged by oil-air. Finally the above-proposed work was validated by experiments. The temperature prediction based on the latest model, in addition, was added and contrasted with this newly designed grid for further verification. Findings The validation result indicates that the thermal forecasting is more accurate as the developed gray-box thermal resistance model of a cooling system is applied to assess spindle heating. Clearly, this paper provides a more proper model on the thermal assessment of a spindle cooling unit. Research limitations/implications This work is very suitable for the thermal prediction on the helical coolant unit with a rectangular/circular cross-section, especially the rectangular/circular cross-section spiral cooling system of a spindle. Originality/value Considering the structural characteristics of a coolant unit, this paper introduced the gray box and thermal grid for the first time to describe the heat transfer of a spindle coolant system, and accordingly proposed an efficient and precise semi-empirical gray box-thermal network model with axial-radial heat transfer separation to evaluate its thermal dissipation.