A novel feed rate scheduling method based on Sigmoid function with chord error and kinematics constraints

TL;DR

This paper introduces a new feed rate scheduling method for high-speed CNC machining that uses a Sigmoid function, considering geometric and kinematic errors to generate smooth, efficient, and time-optimized feed rate profiles.

Contribution

The paper proposes a novel Sigmoid-based feed rate scheduling approach that incorporates error constraints and kinematic limitations for improved machining performance.

Findings

The proposed method produces more concise feed rate profiles than polynomial methods.

It achieves higher efficiency compared to trigonometric profiles.

Simulation results validate the method's feasibility and effectiveness.

Abstract

In high speed CNC (Compute Numerical Control) machining, the feed rate scheduling has played an important role to ensure machining quality and machining efficiency. In this paper, a novel feed rate scheduling method is proposed for generating smooth feed rate profile conveniently with the consideration of both geometric error and kinematic error. First, a relationship between feed rate value and chord error is applied to determine the feed rate curve. Then, breaking points, which can split whole curve into several blocks, can be found out using proposed two step screening method. For every block, a feed rate profile based on the Sigmoid function is generated. With the consideration of kinematic limitation and machining efficiency, a time-optimal feed rate adjustment algorithm is proposed to further adjust feed rate value at breaking points. After planning feed rate profile for each block, all blocks feed rate profile will be connected smoothly. The resulting feed rate profile is more concise compared with the polynomial profile and more efficient compared with the trigonometric profile. Finally, simulations with two free-form NURBS curves are conducted and comparison with the sine-curve method are carried out to verify the feasibility and applicability of the proposed method.