A smooth curve evolution approach to the feedrate planning on five-axis toolpath with geometric and kinematic constraints

• A smooth curve evolution based federate planning method is proposed.
• Feedrate fluctuations are prevented while keeping the entire profile smoothness.
• Conditions and strategies against violation of constraints in planning are given.
• The proposed method has been validated by simulations and experimental results.

Feedrate planning with geometric and kinematic constraints is crucial for sculptured surface machining. Due to the non-linear relationship between the Cartesian space and the joint space, the feedrate planning method for a given five-axis toolpath is very limited compared with that in three-axis machining. To achieve the exact control of the chord error and the kinematic characteristics of cutter and machine tool, this paper presents a new feedrate planning method for five-axis parametric path using a smooth curve evolution strategy. The constraints in feedrate planning are first classified as two types of neighbor-independent (NI) constraints and neighbor-dependent (ND) constraints. Then for constraint violated region, the detailed formulas of determining the update feedrates of violated sampling points are given using a decoupled manner. As a result, NI and ND constraints are satisfied respectively with one step and multi-step smooth curve evolution technique, which can smoothly deform the target feedrate profile to the desired update positions. Simulations and experiments are performed on the given tool path to validate the effectiveness of the proposed feed planning method. The results show that the proposed method is robust and effective in the exact control of constraints in the feedrate planning on complex five-axis toolpath.