Interpolation of parametric CNC machining path under confined jounce

Aiming at reducing the computer numerically controlled (CNC) machining vibration and increasing machining quality, an interpolation method for parametric tool paths with confined jounce, jerk, acceleration, and speed is proposed. An acceleration/deceleration profile with confined jounce, jerk, acceleration, and speed is proposed, and it is shown that this profile is time optimal to change the speed from one value to another under the given constraints. For a given parametric tool path, the velocity function is obtained by first computing the critical points of the tool path where the radius of curvature reaches extremal values, then determining the feasible maximal speeds at the critical points, and finally using the jounce confined acceleration/deceleration profile to connect the speeds at the adjacent critical points. A vibration experiment is conducted, which shows that vibration of the CNC machine decreases significantly for motions under confined jounce than that under confined acceleration and jerk. Simulation for two real CNC models are given to show the feasibility of the method.