To obtain the analytical expressions for a ball screw's axial and torsional stiffnesses and guarantee their high precision,a new method was proposed to calculate the ball screw's stiffnesses.Using the theoretical derivation,the finite element method analysis and the fitting of a modified density function with lognormal distribution,the analytical expressions of stiffnesses considering different parameters were provided.Comparing the data obtained by the expressions with the finite element method results,it is shown that the expressions proposed are of much better generality and accuracy.