Implicit feedrate planning method for high-efficient parametric CNC interpolation with multi-constraints

Spline-based parametric interpolation has been widely applied in CNC systems. However, conventional feedrate planning which focuses on scheduling the tool tip feedrate profile, presents several challenges. These include difficulties in managing 5-axis trajectories with fixed tool tips due to zero feedrate, and a complex interpolation process that requires calculating the arc-length increment ds and parameter increment du, which may lead to feedrate fluctuations. To overcome these challenges, this paper proposes a novel implicit feedrate planning method that directly establishes the relationship between the trajectory parameter u and machining time t, with the feedrate implicitly represented in the u−t profile. This allows the CNC to compute the parameter increment du based on a time step dt, without the calculation of arc-length and significantly simplifying the interpolation process, thus enhancing efficiency. Moreover, a new characteristic of B-spline, the Local Modification Scheme of the First Derivative, is introduced, which enables iterative adjustments to the u−t curve to achieve near time-optimal feedrate while adhering to multiple constraints. Simulation and experimental results demonstrate that the proposed method achieves a superior balance between computational efficiency and machining time compared to other iterative-based or dynamic look-ahead feedrate planning methods. Moreover, it improves interpolation efficiency by approximately 45 % compared to explicit feedrate planning methods.