Theoretical and experimental research towards labyrinth sealing mechanism of liquid nitrogen in the cryogenic spindle

Labyrinth seal works as an inter-stage seal in the cryogenic spindle which is provided with the through-tool cooling feature of liquid nitrogen. The thermoelastic deformation of seal teeth and cryogenic cavitation inevitably take place in labyrinth sealing for liquid nitrogen which really matters the cryogenic sealing. It is highly essential to discuss how these factors impact the sealing effectiveness at the theoretical level. This study aims to theoretically model the cryogenic labyrinth seal in the spindle. New leakage equations concerning both deformation and cavitation are presented for a quantitative calculation, in which their effects on sealing capacity are revealed. Confirmations of the calculation results with experimental data are performed to better recognize the phenomena arising in sealing process in the spindle. The results indicate that the equations heavily rely on seal structural parameters and fluid physical variables. The structural parameters can be altered by the deformation especially the increase of tooth clearance leads to a leakage rise. The physical variables are changed by the cavitation, particularly the formation of vapor phase decreases the leakage. However, the cavitation has a greater impact on the leakage than the deformation when below the critical supercooling. Low inlet pressure, low supercooling and seal material with low thermal expansion coefficient can promote the improvement of sealing capability. This work suggests series of relatively complete theoretical models for the cryogenic labyrinth seal.