Stiffness

Besides the pure geometric accuracy the precision in position is mainly influenced by the stiffness (rigidness) of a ballscrew drive. Steinmeyer describes the stiffness accotding to the manner of DIN / ISO standards and uses the same stipulations: We use the following stipulations:

For single nuts without preload there are different values for R_nu than for the preloaded version. Generally stiffnesses for preloaded nuts are higher than for non-preloaded ones.

As an approximate estimation, twice the stiffness of a non-preloaded nut can be obtained by preloading the nut.
The values listed here apply only to deflections of the nut. For total stiffness of the drive, the stiffnesses of the shaft under load and the stiffness of the thrust bearing must be taken into account. The total stiffness (R_t) is calculated as follows:

R_nu,ar: Reduced stiffness of nut [N/µm]
R_s : Stiffness of screw [N/µm]
R_b : Axial stiffness of thrust bearing [N/µm]

The stiffness of the shaft is determined by the Young´s modulus of the material, the screw cross section and the length.

When using the fixed-free mounting method, the stiffness of the shaft is:

In case of fixed-fixed mounting method it is:

A : Screw cross-section [mm2]
E : Youngs modulus [210.000 N/mm2]