Study on a probabilistic algorithm for the forming and 3D characterization of special-shaped surfaces under profile grinding

Profile grinding is the most crucial method for the ultra-precision machining of special-shaped surfaces. However, profile grinding produces a unique machining profile, and many random factors in the machining process lead to complex surface characteristics. In this study, the structural and probabilistic characteristics of the profile grinding of a special-shaped surface were analyzed, and a probabilistic algorithm for the forming and 3D characterization of special-shaped surfaces under profile grinding was developed. The forming process of a GH738 blade tenon tooth surface was considered as an example to demonstrate the algorithm. The comparison results showed that the simulation results had similar surface characteristics to the measurement results, and the relative error range of the 3D roughness parameter was 0.21%–19.76%, indicating an accurate prediction and characterization of the complex special-shaped surface under the action of multiple factors.