Cutting chatter is extremely harmful to the machining process, and it is of great significance to eliminate chatter through analyzing the stability of the machining process. In this work, the stability of the milling process with multiple delays is investigated. Considering the regeneration effect, the dynamics of the milling process with variable pitch cutter is modeled as periodic coefficients delayed differential equations (DDEs) with multiple delays. An adaptive variable-step numerical integration method (AVSNIM) considering the effect of the helix angle is developed firstly, which can discretize the cutting period accurately, thereby improving the calculation accuracy of the stability limit of the milling process. The accuracy and efficiency of the AVSNIM are verified through a benchmark milling model. Subsequently, a novel spindle speed-dependent discretization algorithm is proposed, which is combined with the AVSNIM to further reduce the calculation time of the stability lobes diagram (SLD). The simulation experiment results demonstrate that the proposed algorithm can effectively reduce the calculation time.

Complex ceramic core is the critical part for manufacturing hollow turbine blade in the investment casting process. The complex geometry, small inner structures and high-precision requirements of ceramic cores make them difficult to fabricate, and the shape and dimensional accuracy of ceramic cores are very low in factory practice. To understand the deformation characteristics of ceramic cores, a noisy points recognition algorithm, an extraction method of measuring cross-section contour points and a B-spline iterative fitting algorithm using dominant points of chord deviation are proposed. First, the cross-section contour points were provided through registration, slicing and intersection methods. Second, the noisy points were deleted by convex noisy points and concave noisy points recognition algorithms. Third, the cross-section contour curve of the ceramic core was fitted through B-spline iterative fitting method with chord deviation dominant points. The curves fitted with chord deviation points and curves fitted with local maximum curvature points were compared with simulating data and scanning data, respectively, and the results show that B-spline fitting curve needs fewer chord deviation points than local maximum curvature points, 24.4% fewer in simulation validation and 12.5% fewer in experimental validation. In the end, the bending deformation, torsion deformation and shrinkage deformation errors of ceramic core are established by fitting contour curves of serial cross sections of the ceramic core.