Under load working conditions deformations are produced that have an effect on the machine structure, in the bearing mountings and in the ballscrew assembly. These deformations have a value represented as axial rigidity, and determined by the rate between applied load and deformation caused.
A = Deformation caused (nm)
F = Applied load
Rtot = Assembly rigidity (n/nm)
The deformations on the nuts are minimal because of its compact size. Those on the contact ball zone are reduced with two preloaded nuts. The increase of rigidity that can be obtained increasing the normal preload is insignificant, and it can reduce the service life.
The rigidity of the screw depends on its size and on its supports. Due to its length is normally lower than the nuts, for which it is convenient to make the calculating process on this part less resistant to deformation.
Rigid assembly of the screw in one end FIXED-FREE
Rs (0) = Screw ridigity (n/nm)
Ls (0) = Length between bearinh - nut (m)
Rsm = Ridigity by meter of screw (n/nm)
Rigid assembly on both ends FIXED-FIXED
Rs (1) = Screw ridigity (n/nm)
Ls (1) = Length between bearing (m)
Ls (2) = Length between bearing - nut (m)
Rsm = Ridigity by meter of screw (N/nm)
The mirror point of ridigity is given with the nuts in the centre of the bearings:
The ridigity of the assembly screw-nut is obtained by the sum of all its values, whose inverse total is less than any other partial value.
