A Five-Axis Dual NURBS Interpolator With Constant Speed at Feedrate-Sensitive Regions Under Axial Drive Constraints

In the five-axis machining, the dual nonuniform rational B-spline (NURBS) interpolator performs better than the conventional linear interpolator in improving machining efficiency and quality. However, a successful dual NURBS interpolator faces with two aspects of issues. First, the feedrate should be reasonably scheduled according to axial drive constraints. Furthermore, the axial trajectories should be precisely and rapidly calculated according to the scheduled feedrate. To schedule the feedrate, existing methods use either overall constant speed or frequent time-varying speed. However, the former one is adverse to the motion efficiency, while the latter one is adverse to the motion stability. To deal with these issues, this study schedules feedrate-sensitive and nonsensitive regions and plans constant speed at the sensitive regions and smooth transition speed within the nonsensitive regions, thus balancing the motion stability and the efficiency. In addition, to calculate the axial trajectories, existing methods, using inverse kinematics, result in multiple solutions due to the existence of antitrigonometric functions, and this requires complicated selection of the solutions, otherwise the axial positions will be discontinuity. To deal with this issue, this study proposes a Jacobi matrix-based Adams prediction–correction numerical algorithm, which uses the incremental value of the tool pose to calculate the consecutive unique solution of the five-axis positions directly. By integrating above techniques, a systematic five-axis dual NURBS interpolator with the constant speed at feedrate-sensitive regions under axial drive constraints is presented. Experimental tests are conducted to evaluate the effectiveness of the proposed method.

Estimation and Control of the Geometric Error in a Linear Interpolator With Parabola Blending

Given a sequence of G01 codes, a linear interpolator outputs a refined sequence of G01 codes obeying the inequality constraints imposed upon the velocity, acceleration, etc., of the machining tool, and the tracking error, geometric error, etc., between the two sequences. While the output G01 sequence is usually obtained from a continuous motion by sampling along the trajectory by a constant interpolation period, a simple strategy of generating the blending curve between two concatenated line segments under the velocity and axis-wise acceleration constraints of the machining tool, is to use parabolas — trajectories of constant-acceleration motions. This paper considers the estimation and control of the geometric error in such a linear interpolator. Classical model of chord error by approximating parabolas with their contact circles leads to incorrect result on the geometric error, if the latter is taken as the superposition of (i) the error of approximation of the input G01 trajectory by parabolas, and (ii) the chord error caused by sampling along the blended C1-smooth trajectory. By computing the geometric error directly without accumulating the approximation error and the chord error, we realize correct geometric error control by establishing inequality constraints on the accelerations of the motion. This work is supported partially by 2011CB302404, NSFC 10925105, 60821002/F02.

Design of Interpolation Algorithm in the Multi-Axis Motion Control System

This paper describes an interpolation algorithm in the multi-axis motion control system, which can achieve six-axis interpolation operations, greatly improving the processing efficiency. Using modular design idea on the Quartus II platform, by DDA interpolation theory, interpolation modules are built through VHDL. And these interpolator modules are connected into schematic diagrams. By those schematic diagrams a linear interpolator, a circular interpolator and a composite interpolator are formed. The corresponding functions of those interpolators have been simulated on the Quartus II platform. The simulation shows that this interpolation algorithm is effective to complex multi-axis motion control system.