Clamping deformation of thin circular workpiece with complex boundary in vacuum fixture system

With the increasing requirements on the parallelism and flatness of thin-walled flat parts, vacuum fixtures have been widely used in precision manufacturing. While several research studies focus on using the finite element method to predict the clamping deformation in the vacuum clamping system, it is very time-consuming and often unable to obtain the convergent solution with complex boundary conditions. In this paper, based on Kirchhoff plate theory, a new method was proposed to solve the clamping deformation of the thin circular workpiece with various complex boundary conditions subjected to vacuum negative pressure. The improved Rayleigh–Ritz method was applied to solve the spatial partial derivatives. The admissible function was composed of polynomial and trigonometric functions, which explained the unconstrained state of the workpiece. Furthermore, Courant’s penalty method was used to handle the constraint conditions. Simulations and experiments were conducted to verify the convergence, feasibility, accuracy, and applicability of the proposed method. The results showed that the proposed method is well-suited for arbitrary boundary conditions with vacuum fixture system, and its convergence was good compared to the finite element method. Finally, the influence factors of clamping deformation were discussed comprehensively and were optimized to reduce the clamping deformation. The proposed method can quickly calculate the clamping deformation of the thin circular workpiece under different vacuum clamping conditions, which provides the guidance for fixture design and the selection of clamping parameters for researchers in the processing field.