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

Abstract

This paper presents an analytical continuous smoothing method for the five-axis toolpath by simultaneously scheduling the tool position and tool orientation trajectories. In order to ensure the high-order continuous, the peak-controlled jerk and arclength-parameterized property, a novel curve ''airthoid'' is proposed for the first time. The biairthoid is involved to smooth the corners of the tool position in the workpiece coordinate system (WCS) and the corners of the tool orientation in the machine coordinate system (MCS), the geometries of which are analytically determined by the user-defined deviation errors. A time synchronization strategy is proposed to extend the duration of the predetermined cubic acceleration profile to a specified time. With the kinematic constraints of the tool position and the tool orientation, the transitional and rotational trajectories are analytically synchronized by sharing the same motion time. To comply with the constraints of the linear feed drives, an optimization strategy is conducted by adjusting the kinematics of the tool position. By doing so, the approximation errors of the tool position and tool orientation in the WCS are strictly satisfied. The analytical arclength expression of the smoothing curves is more suitable for the on-line interpolation. Due to the arclength-parametrized transition curve, the feedrate fluctuation is eliminated. With the proposed time synchronization strategy, the physical limits of the feed drives are all respected. Moreover, the high-order continuous airthoid makes the motion more smoothing-going. Simulations and experiments verify the effectiveness of the proposed algorithm.

Proposal of a Machining Test to Evaluate Dynamic Synchronization Error of Rotary and Linear Axes With Reversal of Rotation Direction

“…In the proposed tool path smoothing method, the tool path is firstly smoothed in the WCS along the feed direction, and then the command trajectory of each axis is obtained by solving the inverse kinematics calculation based on the filtered trajectory in the WCS. As reviewed in Section 1, some researchers [18][19][20][21][22] adopted essentially the same scheme. The entire process of the proposed tool path smoothing method is shown in Fig.…”

“…Sencer [18] converted the feedrate along the tool path in a cubic B-spline form in the WCS, and generated the tool path profile based on the spline expression of the feedrate considering the physical constraints of drives. Huang [19] proposed a novel curve "airthoid" to smooth the five-axis tool path in the WCS. Hu [20] smoothed the transition corners of the TCP in the WCS by G3 continuous PH lines.…”

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

“…Although B-spline and Bezier spline can smooth the toolpath, their arc lengths have no analytical solutions with spline parameters, which make it difficult to calculate the next parameter in the fine interpolation. To overcome this problem, the clothoid spline based methods [24][25][26][27][28][29] and Pythagorean-hodograph (PH) spline based methods [5,[30][31][32][33][34][35][36] have been developed. Shahzadeh et al [26] usesd biclothoid fillets as transition curves to smooth the corners and ensure the 𝐺 2 continuity of the toolpath.…”

“…𝐺 3 continuity. Huang et al [28] proposed a novel curve ''airthoid'' based on clothoid spline, then the biairthoid was involved to smooth the corners of the tool position in the WCS and the corners of the tool orientation in the MCS. In [29], a novel smoothing method based on a pair of clothoid splines was proposed to realize the integral planning of the geometrical curve and the feedrate profile, which can achieve the adaptive contour accuracy.…”

Joint Trajectory Prediction of Multi-Linkage Robot Based on Graph Convolutional Network

“…It was proved that the performance of the cubic NURBS curve was better than cubic polynomial spline and cubic B-spline. A new curve named "airthoid" was put forward [11]. The feedrate fluctuation was eliminated by an arclengthparametrized transition curve, and the motion was smoother.…”