Double B-Spline Curve-Fitting and Synchronization-Integrated Feedrate Scheduling Method for Five-Axis Linear-Segment Toolpath

Abstract

The discontinuities of a five-axis linear-segment toolpath result in fluctuation in the feedrate, acceleration and jerk commands that lead to machine tool vibration and poor surface finish. For path smoothing, with the global curve-fitting method it is difficult to control fitting error and the local corner-smoothing method has large curvature extreme. For path synchronization, the parameter synchronization method cannot ensure smooth rotary motion. Aiming at these problems, this paper proposes a double B-spline curve-fitting and synchronization-integrated feedrate scheduling method. Two C2-continuous and error-bounded B-spline curves are produced to fit tool-tip position and tool orientation, respectively. The fitting error is controlled by locally refining the curve segments that exceed the fitting tolerance. The tool-tip position trajectory is firstly planned to address axial kinematic constraints in the feedrate scheduling process. Then the feedrate is deformed for the tool orientation to guarantee smooth rotary motion as well as to share the same motion time with the tool-tip position segment by segment. The feasibility and effectiveness of the proposed method have been validated by simulations and experiments on the S-shape test piece. Simulations show that the proposed curve-fitting method can generate smooth toolpath and constrain fitting error. The proposed feedrate scheduling method can guarantee smooth rotary motion and keep axial motions under kinematic limits, compared with the method that does not consider axial kinematic constraints and the parameter synchronization method. Experimental results verify that the proposed curve-fitting method can generate smooth tool path under fitting tolerance, and the proposed feedrate scheduling method can produce smooth and restricted axial motions.

Special Issue on “Machining Dynamics and Parameters Process Optimization”

“…Another source of vibration in five-axis machining is the discontinuities of the linear-segment toolpath inducing fluctuation in the programmed feed rate. Gao et al [5] proposed a double B-spline curve-fitting and synchronization-integrated feed rate scheduling method. They experimentally concluded that this method generates a smooth toolpath with an allowable fitting error.…”

B-Spline Curve Fitting of Hungry Predation Optimization on Ship Line Design

“…B-spline curve approximation has been a hot research topic in the field of computeraided geometric design in recent years. With the development of computer-aided design (CAD) and the rise of advanced manufacturing technology, B-spline is widely used in the design and manufacturing industry of free curves and surfaces [1][2][3][4][5]. In the field of shipbuilding, the design of ship lines is the basis of shipbuilding [6].…”

A New Processing Method for the Nonlinear Signals Produced by Electromagnetic Flowmeters in Conditions of Pipe Partial Filling

“…B-spline curve fitting [19][20][21][22][23] is an approach that performs a nonlinear fit of data based on a limited selection of these data. As the B-spline curve method is a simple calculation procedure with fast calculation speed and geometric invariance, it is widely used in engineering practice, such as for the geometric definition of various industrial products and nonlinear curve reconstruction.…”

“…As the B-spline curve method is a simple calculation procedure with fast calculation speed and geometric invariance, it is widely used in engineering practice, such as for the geometric definition of various industrial products and nonlinear curve reconstruction. Gao et al [20] proposed a double B-Spline curve fitting and synchronization-integrated federate scheduling method for a Five-Axis linear-segment tool path, and simulation showed that this method can generate a smooth tool path and constrain the fitting error. Xu et al [21] rebuilt the strain field of multiple elements by using the B-spline curve and inverse finite element methods to prove that the proposed algorithm can significantly improve the accuracy of reconstruction displacement.…”