Dual-Bézier path smoothing and interpolation for five-axis linear tool path in workpiece coordinate system

Abstract

The tool path composed of consecutive short linear segments (G01 blocks) is still the widespread tool path representation form in five-axis machining. The inherent shortcoming of linear tool path is first-order discontinuity at the corner, which is the bottleneck to achieve high-speed and high-accuracy machining. In this article, a dual-Bézier path smoothing algorithm for five-axis linear tool path in workpiece coordinate system is proposed. There are three steps involved in our method. First, the corner error distribution model is introduced to assign the given tolerance to the smoothing approximation error constraint and the chord error constraint to ensure the interpolation trajectory error within the given tolerance. Second, segment junctions of the linear tool path in workpiece coordinate system are smoothed by double G 2 continuous cubic Bézier curves. One cubic Bézier curve is used to round the corner of the tool tip point path, and the other Bézier curve is used to round the corner of the tool axis point path. This algorithm takes the conditions of approximation error constraint, the parameterized synchronization constraint, and continuous curvature constraint into consideration. Hence, the tangency and curvature continuities are both guaranteed in the new path. Third, an adaptive feedrate scheduling method is introduced to interpolate the new path. Simulation and experiment are performed to verify the effectiveness of the proposed method in five-axis tool path smoothing, speed smoothing, and trajectory accuracy controlling.

Rolling ball method applied to 3½½-axis machining for tool orientation and positioning and path planning

“…Be´zier path smoothing could also be employed. 20 Working with parametric surfaces allows for easy replication to other surfaces. The machining experiments were conducted on a Deckel Maho 80 P Hi-dyn 5-axis machining center.…”

“…Safka et al 18 and Van Tuong and Pokorn 19 also partitioned free-form surfaces into convex, concave, and saddle regions based on the Gaussian curvature and the mean curvature. Other more recent 5-axis machining path smoothing techniques such as Be´zier smoothing 20 and local jerk smoothing 21 are not compatible with 3½½ machining.…”

Asymmetrical pythagorean-hodograph spline-based C4 continuous local corner smoothing method with jerk continuous feedrate scheduling along linear toolpath

“…In [16], a two-step strategy was proposed to generate 𝐺 2 continuous toolpath, where the curvature energy of the cubic Bezier curve was minimized first, then the optimal transition length was determined by minimizing the sum of two curvature extremes. Jin et al [17] proposed a transition method for five-axies machining in workpiece coordinate system (WCS), which utilized a dual-Bezier splines as transition curves. Bi et al [18] developed a 𝐺 2 continuous transition method with a cubic Bezier curve, the approximation error at the segment junction can be accurately guaranteed and the curvature extreme was analytically computed and optimized.…”

An Analytical Decoupled Corner Smoothing Method for Five-Axis Linear Tool Paths

“…Beudaert et al [19] utilized two cubic B-splines to blend the corner of tool tip position and a reference point on tool axis, meanwhile, a third spline was constructed to optimize the orientation connection with tool tip position. Jin et al [20] proposed a dual-Bézier based method, and Shi et al [21] blended corner with a pair of PH curves. Different from the coupled methods [19]- [21], Tulsyan et al [22] proposed a decoupled method, which uses a quintic B-spline to blend tool tip position and a near-unit B-spline for tool orientation respectively.…”