Prediction of curved workpiece-fixture contact stiffness based on fractal theory

Abstract

Workpiece-fixture contact stiffness is an evaluation criterion for machining stability, and its effective prediction involves contact state analysis, surface profile analysis, and modeling of fixture and workpiece geometries, presenting a multi-source complexity. In this paper, a fractal theoretical model of contact stiffness under curved surface contact state is proposed, and the domain expansion factor and substrate deformation are considered to improve the prediction accuracy. First, based on the geometric theory and trigonometric function, the fractal theory model of microconvex body-curved surface contact is established. Then, the curved surface contact is equated to rough curved surface and smooth rigid curved surface, and analyzes the mechanical mechanism of the microconvex body-curved surface contact. Considering the influence of domain expansion factor and substrate deformation on total deformation, a fractal model of curved surface contact stiffness is obtained by force balance constraints. Then, a contact stiffness solution based on the adaptive Simpson's algorithm is proposed. Finally, the support-adsorption composite fixture is developed, and the model is verified through experiments. The results revealed that the average prediction error of the theoretical model is 11.24%. As the fractal dimension increases, the scale factor decreases, the contact stiffness gradually increases, and the fractal dimension is recommended to be limited to 1.7. Clamping force increases, intrinsic frequency and contact stiffness increase. In the case of a small initial support force, the phenomenon of increasing contact stiffness caused by the adsorption effect is more obvious, and the adsorption radius is not recommended to take a smaller value, such as 5-10mm. Support-absorption composite fixture increases contact stiffness while reducing clamping deformation.