To solve the problem of grinding complex shaped workpieces

a small volume and high speed air spindle with small elastic grinding tool was designed. The theoretical removal function model of the spindle was established and verified by experiments. The results show that the removal functions obtained by simulation and experiments are highly consistent and close to Gaussian-like shape

which belongs to the ideal removal function. On this basis

the spindle with the elastic resin grinding tool was used for grinding experiments

and the influence of the main process parameters on the surface quality of the workpiece was explored. The surface roughness of the workpiece after grinding decreases from 3.588μm to 0.401μm

which proves that the air spindle can be used for high-precision grinding

and provides theoretical basis for high-speed grinding of complex shaped workpiece.