A modeling method for predicting the precision loss of the preload double-nut ball screw induced by raceway wear based on fractal theory

Precision double-nut ball screws are key functional parts in machine tools. The positioning accuracy of a ball screw can directly affect the machining accuracy of a machine tools. During actual use, the preload degradation and the large axial clearance of the double-nut ball screw are caused by the contact wear, which directly affects the transmission positioning accuracy. The contact wear is focused on the ball and the rough raceway surface of the ball screw. Therefore, a novel method is proposed in this paper to characterize the rough spherical morphology of raceways for ball screws based on fractal theory, and the fractal parameters of the screw and nut raceways are identified. A fractal contact model of the asperity on the raceway surface is established. By introducing contact parameters to modify the contact area, an area distribution function suitable for the coordinated contact is obtained. A mathematical model for calculating the normal contact load of the ball screw in three states is established by considering the friction factor. A precision loss model of the ball screw is established based on the full ball load distribution model and the multiscale contact load model, and the proposed model is verified by experiments. The surface contact coefficient of the inner and outer raceways is discussed. The influence of raceway fractal parameters on the wear rate is analyzed, and coupling research on precision loss and preload degradation for the ball screw is carried out. The initial wear rate under different axial load is discussed, and the change trend of wear rate with time is analyzed. The precision loss model of the preload double-nut ball screw based on fractal theory provides a new theoretical basis for accurately predicting the precision degradation and provides method support for establishing the wear life prediction of a ball screw.