Feedrate interpolation with axis jerk constraints on 5-axis NURBS and G1 tool path

Abstract

A key role of the CNC is to perform the feedrate interpolation which consists in generating the setpoints sent to each axis of a machine tool based on a NC program. In high speed machining, the feedrate is limited by the velocity, acceleration and jerk of each axis of the machine tool. The algorithm presented in this paper aims to obtain an optimized feedrate profile which makes best use of the kinematical characteristics of the machine. This minimum time feedrate profile is computed by intersecting all the constraints due to the drives in an iterative algorithm. It is worth noting that both tangential jerk and axis jerk are taken into consideration. The proposed VPOp (Velocity Profile Optimization) method is universal and can be applied to any articulated mechanical structure as it is demonstrated in the examples. Moreover the algorithm has been implemented for various formats: linear interpolation (G1) and NURBS interpolation in 3 and 5-axis. The effectiveness of the algorithm is demonstrated thanks to a comparison with an industrial CNC and can be freely tested using the VPOp software which is available on the internet http://webserv.lurpa.ens-cachan.fr/geo3d/premium/vpop.

Direct trajectory interpolation on the surface using an open CNC

“…This section will show how the DTIS method can merge, in a unique scheme, tool path computation and feedrate interpolation. The feedrate interpolation is based on the VPOp algorithm (Velocity Profile Optimization) previously developed [2].…”

“…Kinematical solicitations are evaluated exactly since tool positionings are previously evaluated using the CAD model and the inverse kinematical transformation of the machine tool are known. One can find more details on the equations of kinematical characteristics in [2]. If constraints are satisfied, the current tool positioning is validated and the algorithm goes to next iteration.…”

“…Experimental validations of surface interpolation are carried out on 3-axis machines in [25,5,19], but the physical constraints of high speed machining are not considered, especially the physical limitations on velocity, acceleration and jerk of the axes which limit the actual feedrate [2]. Recently, a 5-axis surface machining controller has been proposed by Liang and Li in [16].…”

NURBS curve interpolation algorithm based on tool radius compensation method

“…During parametric curve fitting process, the first step is the modification of geometry pattern (Beudaert, Lavernhe, and Tournier 2013) by substituting the corresponding continuous short blocks (CSBs) to parametric curves. The parametric curves need to be bounded according to custom tolerance parameters (Beudaert, Lavernhe, and Tournier 2012). Furthermore, the acceleration/deceleration (ACC/DEC) feedrate-planning module can look-ahead multiple blocks and predict the curvature changes of the trajectory to be machined to achieve the adaptive control of feed velocity, acceleration and jerk (Tsai, Nien, and Yau 2010).…”

A Corner Rounding and Trajectory Generation Algorithm for Five-axis Linear Toolpath

“…对于五轴加工，目前仍处在探索的阶段。目前五轴 刀路光顺方法主要有两种：拟合光顺，转接光顺。 拟合光顺采用高阶样条曲线来对离散小线段进行 逼近或者插值拟合 [4][5][6][7] 。拟合光顺算法难以控制拟 合精度，且计算量比较大，很难在实时计算环境中 使用 [8][9] 。 转接光顺的思路是在小线段连接点用圆弧或高 阶连续的样条曲线过渡。文献 [10][11] …”