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

Abstract

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.

Look-ahead-window-based interval adaptive feedrate scheduling for long five-axis spline toolpaths under axial drive constraints

“…In addition, the proposed method is also compared with the recent published regional constant five-axis feedrate scheduling method by Ma et al 22 Employing similar axial drive constraints provided in Table 2, the feedrate profile for the S-shape toolpath scheduled by Ma's method is obtained, and it is compared with the feedrate scheduled by the proposed method in Figure 8. As shown in Figure 8, comparing with the regional constant feedrate the proposed interval adaptive feedrate varies more frequently, but more time-optimality can be obtained within the drive limitations.…”

A Novel Local Smoothing Method for Five-Axis Machining With Time-Synchronization Feedrate Scheduling

“…The relative velocity between the tool tip and the workpiece should be strictly controlled in the machining process, since it directly affects the finished surface quality [1]. Therefore, the corners of the tool position are blended and the feedrate profile of the smoothing toolpath is planned in the WCS to guarantee the objective velocity of the tool tip.…”

“…ϕ is the corner angle. The length of the transition segments, B 0 p P 2 and B 1 p P 2 , is denoted as l p . The lengths of the smoothing curve, B 0 p Q and QB 1 p , are denoted as l 0 Bp and l 1 Bp , respectively.…”

“…Five-axis machine tools are widely adopted to machine free-form parts due to the graceful advantages in the cutting efficiency and machining reachability. The parametric curves, such as polynomial splines, B-spline, Bézier or NURBS, are ideal approaches to describe the toolpaths of the free-form parts, which have been experimentally proven to be superior to achieve smooth motion and perfect surface finish [1]. However, most of CNC systems are hard to follow the parametric splines directly, since some bottlenecks still exits, including the poor interpretation ability from CAD to NC [2],…”

Real-Time NURBS Interpolation under Multiple Constraints

“…Jia et al [ 8 ] proposed a NURBS interpolator under kinetic characteristics and contour error constraints, in which the feedrate remained constant in most areas and only changed smoothly in areas with large curvature, but the production efficiency was degraded when utilizing a constant low feedrate without making full use of the motion performance in this method. Ma et al [ 9 ] also considered, from the perspective of axis restriction, maintaining constant feedrate in the sensitive area and smooth transition in the non-sensitive area. Liu et al [ 10 ] used a linear mathematical model to explore the relationship between feedrate and geometric constraints.…”