Features of Applying the Force Displacement Theory to the Contact Stiffness Calculation for the Spindle Angular Contact Ball Bearing Support

Abstract

Contact stiffness is an important parameter for describing the interaction of plenty precise engineering solutions, for example, for machine-tool manufacture, the most important element of the carrier system is the spindle assembly supports, largely determining the accuracy of machining parts on the machine. The article considers an example of a system approach to describing the variable stiffness of a high-precision spindle bearing, combining an analytical approach to calculating the variable quasi-static stiffness of an angular contact ball bearing and a methodological approach that takes into account the contact normal and tangential force displacements of the upper bearing ring while considering the friction force for tangential interactions. The proposed system approach to calculating the stiffness of a ball bearing support is based on fairly simple models, in particular, the apparatus proposed by Professor P.M. Chernyanskiy, describing the phenomena of changing the spindle supports stiffness. These changes were experimentally obtained and weren’t described in earlier works. It is shown that the experimental stiffness consists of elastic and contact components, depending on the friction forces, therefore, the concept of apparent stiffness is introduced for data that are not taken into account in the processes under study. The effect of the axial displacement of the spindle is explained on the basis of contact interactions in the support of the spindle unit. The resulting analytical system model was tested on well-known bearing supports and the obtained stiffness solutions were compared with validated experimental data from open sources