Modeling and Compensation of Multitilt Geometric Errors in a Four-Axis Aero-Engine Blade Measurement System

The geometric accuracy of aero-engine blades is critical to engine performance and operational safety, imposing stringent requirements on blade profile measurement precision. This article presents a 3-D blade measurement system based on a four-axis platform equipped with a spectral confocal sensor. To model system-induced geometric deviations, a multitilt geometric error model (MT-GEM) is established to jointly account for guide-rail inclination errors, sensor installation errors, and rotary-axis deviations. The MT-GEM is solved in a two-stage manner: initial estimates of the guide-rail inclination parameters are first obtained via ellipsoid fitting combined with linear least-squares estimation, based on which the initial kinematic parameters of the rotary table, including the rotation axis and center, are derived. Subsequently, a joint nonlinear optimization is performed to refine all MT-GEM parameters. To enable efficient calibration with minimal artifacts, a three-parameter constrained sphere pair model (TPCSPM) is introduced, allowing system calibration using only a pair of standard spheres. Experimental results demonstrate that the proposed framework achieves robust and accurate parameter estimation and significantly reduces measurement deviations. After calibration, the radius error of a standard sphere is reduced to 0.018 mm, validating the effectiveness of the proposed method for high-precision, noncontact blade inspection.