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

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Abstract

Interpolators play a core and important role in CNC systems, and the scheduling of feedrate is a main task of CNC interpolators. It is routine to schedule the feedrate of linear/circular toolpaths because of their regular geometry; however, the feedrate scheduling of spline toolpaths remains challenging due to the freely and unpredictable geometric shape. Most of the existing methods require looking ahead or pre-processing to acquire sufficient toolpath information for generating drive-bounded smooth feedrate profile, which limits the integral machining efficiency. This paper presents a FIR (finite impulse response) filtering-based interpolation algorithm for spline toolpath, thus realizing the fully real-time capability without using time-consuming optimization such as looking ahead or pre-processing. The presented method merely utilizes the curvature radius information of the current interpolation point on the spline toolpath, and the scheduled feedrate can be generated within one step. Furthermore, the global tangential smoothness of the feedrate profile is guaranteed by directly applying convolution with a chain of two cascaded FIR filters. However, the FIR filtering induces interpolation error which plays as a negative cost during the one-step feedrate scheduling. To solve this issue, the principle of the filtering induced error is analyzed, so that it is computed by feed parameters and curvature radius, and the maximum error is added as an extra constraint beyond the commonly considered axial kinematic constraints. Effectiveness of the presented approach is demonstrated by both numerical illustration and experimental tests.

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Funding

This research is supported by the National Nature Science Foundation of China (52005121), the China Postdoctoral Science Foundation (2020M681076), the Postdoctoral Science Foundation of Heilongjiang Province (LBH-Z20048), and the Fundamental Research Funds for the Central Universities (3072020CF0701).

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Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin, 150001, China

    De-Ning Song, Yu-Guang Zhong, Jian-Jun Yao & Chao Zhou

  2. Key Laboratory for Precision and Non-traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China

    Jian-Wei Ma

  3. Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, Hefei, 230031, China

    Dan Xiao

Authors
  1. De-Ning Song
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  2. Jian-Wei Ma
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  3. Yu-Guang Zhong
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  4. Dan Xiao
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  5. Jian-Jun Yao
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  6. Chao Zhou
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Contributions

Methodology, investigation, verification tests, writing—original draft: De-Ning Song; investigation, writing—reviewing, supervision: Jian-Wei Ma, Yu-Guang Zhong, Jian-Jun Yao; experimental setup hardware: Dan Xiao; writing—reviewing and format editing: Chao Zhou.

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Correspondence to De-Ning Song.

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Song, DN., Ma, JW., Zhong, YG. et al. A fully real-time spline interpolation algorithm with axial jerk constraint based on FIR filtering. Int J Adv Manuf Technol 113, 1873–1886 (2021). https://doi.org/10.1007/s00170-021-06738-8

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  • DOI: https://doi.org/10.1007/s00170-021-06738-8

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