A fully real-time spline interpolation algorithm with axial jerk constraint based on FIR filtering

Song, De-Ning; Ma, Jian-wei; Zhong, Yong; Xiao, Dan; Yao, Jianjun; Zhou, Chao

doi:10.1007/s00170-021-06738-8

Cited by 8 publications

(7 citation statements)

References 26 publications

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“…The Jerk, acceleration, velocity and displacement of the 7 segments S-shaped flexible acceleration/deceleration algorithm are obtained from equations(4)(5)(6) (7), respectively.…”

Section: S-shaped Acceleration/deceleration Algorithmmentioning

confidence: 99%

“…The duration in each segment fit the relationship T1 = T3 = T5 = T7, T2 = T6. And T1-T7 can be obtained from Table 3 and formulas(4)(5)(6) (7). See Appendix A for the formula Jm*τ1*τ2+Jm*τ1*τ1=Vm.…”

Section: Build Typical Scheduling Patternsmentioning

confidence: 99%

“…The duration in each segment fit the relationship T1 = T3 = T5 = T7, T2 = T6 = 0, T4 = 0. And T1, T3, T5, T7 can be obtained from Table 4 and formulas(4)(5)(6) (7). Fig.…”

Section: Pattern B: 4 Segments S-shaped Acceleration/deceleration Sch...mentioning

confidence: 99%

“…In the field of free-form surface machining, parametric interpolation has significant advantages in reducing approximation error and improving feedrate stability compared with traditional linear and circular interpolation, which is shown in Table 1. So, it has always been the topic research by many scholars [1][2][3][4][5][6][7]. In conventional parametric interpolation methods, the STE interpolator were often used by scholars due to its advantages of high-precision and high-stability.…”

Section: Introductionmentioning

confidence: 99%

“…The duration in each segment fit the relationship T1 = T3 = T5 = T7, T2 = T6, T4 = 0. And T1, T2, T3, T5, T6, T7 can be obtained from Table5and formulas(4)(5)(6)(7). Fig.2(c) is the 6 segments S-shaped acceleration/deceleration scheduling pattern.Pattern d: 5 segments S-shaped acceleration/deceleration scheduling patternIn this pattern, the feedrate curve is a 5 segments acceleration/deceleration without enough long path L. The feedrate curve consists of only AA, CA, DA, DD, AD segment or DD, CD, AD, AA,…”

mentioning

confidence: 99%

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Innovation of NURBS feedrate direct interpolator in five-axis for CNC high-precision and high-efficiency machining

Cao

Wang

Jia

et al. 2022

Preprint

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The high-precision machining is restricted by truncation error and computational burden of second-order derivative in the second-order Taylor expansion (STE) interpolator which is usually used by scholars due to its advantages of high-precision and G3 continuity or higher. In conventional methods, the improved accuracy of interpolation parameter in the Taylor expansion interpolator will lead to a great increase in the computational burden of higher-order derivatives or compensation methods, resulting in degraded real-time performance. To tackle the bottlenecks, Non-uniform rational B-Splines (NURBS) feedrate direct interpolator (FDI) is proposed in the paper. The FDI for NURBS is divided into three parts, S-shaped acceleration/deceleration algorithm, feedrate scheduling, and the proposed FDI. In feedrate scheduling, four typical scheduling patterns are established to reduce the complexity of feedrate scheduling based on S-shaped flexible acceleration/deceleration and are used to obtained the maximum starting feedrate with feedrate constraint. The round method of feedrate duration must be adopted due to the non-integer multiple between interpolation period Ts and the generated duration time based on S-shaped acceleration/deceleration in conventional methods, while the proposed FDI completely follows the original feedrate produced by the feedrate scheduling. FDI is an equation in the continuous time domain rather than an inequality like STE, which can ensure the accuracy of interpolation parameter in theory. Furthermore, Computerized Numerical Control (CNC) system are inherently discrete-time systems, not continuous-time systems. Based on discrete features, the FDI equation is discretized to follow the precision of original feedrate duration which is the exact mapping of NURBS curve. The consistent precision greatly ensures the accuracy of the interpolation parameter in theory. Only with the original feedrate, can FDI directly obtain theoretically accurate interpolation parameter without any round and compensation method. With the proposed FDI, feedrate synchronous interpolator (FSI) method is proposed for dual-NURBS in five-axis machining. Only the tool tip interpolation parameter needs to be calculated by FDI and the interpolation parameter of tool orientation can be obtained by FSI directly with optimal tool attitude and high real-time performance. The FSI can make the tool orientation vector closer to the surface normal direction, which is more conducive to improving the cutting quality. Experiments were carried out on the machine tool to demonstrate the advantage of the proposed method in improving machining efficiency and the accuracy of interpolation parameter, simultaneously.

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“…The Jerk, acceleration, velocity and displacement of the 7 segments S-shaped flexible acceleration/deceleration algorithm are obtained from equations(4)(5)(6) (7), respectively.…”

Section: S-shaped Acceleration/deceleration Algorithmmentioning

confidence: 99%

Section: Build Typical Scheduling Patternsmentioning

confidence: 99%

“…The duration in each segment fit the relationship T1 = T3 = T5 = T7, T2 = T6 = 0, T4 = 0. And T1, T3, T5, T7 can be obtained from Table 4 and formulas(4)(5)(6) (7). Fig.…”

Section: Pattern B: 4 Segments S-shaped Acceleration/deceleration Sch...mentioning

confidence: 99%