Algebraic parameterization-based spiral machining toolpath generation for C1-continuous compound surfaces

In the CAM machining of complex surfaces such as open blisk blades, unsmooth tool paths often occur at the common boundaries of compound surfaces. Conventional parameter alignment cannot guarantee C1continuity in the Euclidean parameter domain. To generate boundary-consistent spiral tool paths on compound or trimmed surfaces, a method based on Coons reparameterization is proposed for computing the control lines required to generate spiral tool paths. On the unfolded Coons compound surfaces, spiral tool paths are generated directly by connecting the start and end points, avoiding the need to compute 3D points one by one. However, this may still fail to ensure C1 continuity at surface boundaries. Therefore, a 2D compound parameter domain is reconstructed via Coons mapping, which maintains the geometric features of the part and ensures C1-continuous tool paths at common boundaries. Simulation and machining of an open blisk blade verify the effectiveness of the method, showing improved contour accuracy and an 18% reduction in surface roughness after optimization.