In automated aircraft assembly, multifunctional end effectors and one-shot drilling, reaming, and countersinking processes are commonly used for riveting holes in stacked structures. The pressure foot integrated into the end effector monitors and compensates for workpiece deformation effects on countersinking accuracy. However, due to structural constraints of the pressing unit and application-specific limitations, the pressure foot cannot adaptively conform to the workpiece surface contour, leading to systematic compensation errors. To understand the mechanisms behind countersinking errors and compensation errors during automated drilling of stacked structures, this study designs a frame-type stacked specimen that accurately reflects the deformation characteristics of aircraft structures during countersinking.

Finite element simulations and machining experiments were conducted to quantitatively analyze how typical aircraft structural parameters (e.g., geometric features) and hole location parameters influence deformation, countersinking errors, and depth compensation errors.

Countersinking errors manifest as depth, normal vector, and apex angle errors. In the frame-type stacked setup, the lower layer influences the upper layer's deformation through its support effect, while the ribs increase frame's stiffness and reduce localized deformation of the upper layer. Even when normal vector detection and adjustment are performed before drilling to ensure the pressure foot and tool are perpendicular to the stack, the axial drilling force causes stack deformation. Since the pressure foot is rigidly attached to the pressing unit and cannot adapt to workpiece deformation, a relative deviation occurs between the tool's feed direction and the actual normal vector at the drilling point. Although the displacement sensor in the pressing unit can monitor the pressure foot's displacement and compensate for stack deformation online, the pressing position of the pressure foot does not align with the center of the countersinking hole. This mismatch leads to different local deformations at these two points, which is the fundamental cause of the systematic error in the pressure foot-based compensation method. The size of this systematic error increases as the structural rigidity at the drilling location decreases. Under a constant axial drilling force, the deformation behavior depends on the structural geometric parameters of the frame-type stack and the hole position. Specifically, when the hole is farther from the intermediate rib, the lower layer mainly undergoes bending deformation of the frame's top surface, and the deformation characteristics to the right of the vertical rib significantly impact countersinking errors. The frame height and structural layout to the left of the vertical rib primarily influence the overall torsional deformation of the stack; increasing the frame height improves stiffness and reduce torsion under axial load. While structural parameters have limited effect on normal vector and apex angle errors, they greatly influence depth and compensation errors. Notably, the compensation error remains stable within a certain range of structural parameters.

Finite element simulations enable a quantitative analysis of the systematic deformation compensation error via the pressure foot and help identify structural parameter thresholds where the compensation error stays stable. This regular pattern makes it possible to eliminate systematic errors using a feedforward strategy. In engineering practice, zone-specific compensation values for countersinking depth can be defined in advanced, ensuring accurate and efficient depth control in frame-type stacked structures.