Considering the Rigidity

To increase the positioning accuracy of feed screws in NC machine tools or precision machines, or to reduce the displacement caused by the cutting force, it is necessary to design the rigidity of the components in a well-balanced manner.

Axial Rigidity of the Feed Screw System

When the axial rigidity of a feed screw system is K, the elastic displacement in the axial direction can be obtained using equation (36) below.

The axial rigidity (K) of the feed screw system is obtained using equation (37) below.

Axial rigidity of the screw shaft

The axial rigidity of a screw shaft varies depending on the method for mounting the shaft.

For Fixed-Supported or Fixed-Free Configuration

Fig. 16 shows an axial rigidity diagram for the screw shaft.

For Fixed-Fixed Configuration

Fig. 17 shows an axial rigidity diagram of the screw shaft in this configuration.

Axial Rigidity of the Nut

The axial rigidity of the nut varies widely with preloads.

Without Preload

The theoretical axial rigidity with an axial load accounting for 30% of the basic dynamic load rating (Ca) applied is indicated in the dimensional tables of the corresponding model number. This value does not include the rigidity of the components related to the nut-mounting bracket. In general, set the rigidity at roughly 80% of the value in the table.
The rigidity when the applied axial load is not 30% of the basic dynamic load rating (Ca) is calculated using equation (40) below.

With Preload

The theoretical axial rigidity with a preload accounting for 10% of the basic dynamic load rating (Ca) applied is indicated in the dimensional tables of the corresponding model number.This value does not include the rigidity of the components related to the nut-mounting bracket. In general, set the rigidity at roughly 80% of the value in the table.
The rigidity when the applied preload is not 10% of the basic dynamic load rating (Ca) is calculated using equation (41) below.

Axial Rigidity of the Support Bearing

The rigidity of the ball screw support bearing varies depending on the support bearing used.
The calculation of the rigidity with a representative angular contact ball bearing is shown in equation (42) below.

For details of a specific support bearing, contact its manufacturer.

Axial Rigidity of the Nut Bracket and the Support Bearing Bracket

Take this factor into consideration when designing your machine. Set the rigidity as high as possible.