Accessible regions of tool orientations in multi-axis milling of blisks with a ball-end mill

Noninterference tool orientations are hard to be determined in multi-axis milling of blisks, because the integrated structure of blisks introduces more geometrical constraints. To address this problem, an original approach without interference detection is proposed to solve accessible regions of tool orientations in milling of blisks. Based on the visibility of checking surfaces, only critical points on surface profiles are searched and processed to construct the accessible regions. In this approach, the start point of each profile is sought on boundaries of the main surface with a constant step length. From this point, a new critical point is first searched along a specified direction and then adjusted iteratively until it locates on a profile. When all critical points on profiles are searched like this, the searched points on each checking surface are reordered to form one or more than one closed curve to present the accessible region related to this checking surface. These curves are then mapped onto a unit sphere and divided into nonintersecting segments. After that, a concise approach is proposed to combine accessible regions of all checking surfaces into simply connected regions. This algorithm is finally verified with two kinds of blisks and compared with a referenced method. The results show that the proposed method can efficiently solve accessible regions in multi-axis milling of blisks with an expected accuracy.