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Real-Time NURBS Interpolation under Multiple Constraints.

Mingxing Nie1, Yaping Wan1, Aijun Zhou1

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This study introduces a real-time NURBS interpolation method (RNIC) to improve machining accuracy. The novel approach addresses feed fluctuations and mechanical shocks for enhanced surface quality in complex curve machining.

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Area of Science:

  • Computer-Aided Manufacturing
  • Geometric Modeling
  • Control Systems

Background:

  • Non-Uniform Rational B-Splines (NURBS) offer advantages in code size, surface quality, and machining efficiency over traditional methods.
  • Challenges in NURBS interpolation arise from the nonlinear relationship between curve and arc length, leading to feed fluctuations and affecting surface accuracy.
  • Increasing demands for high-accuracy and efficient machining necessitate advanced interpolation techniques.

Purpose of the Study:

  • To propose a real-time NURBS interpolation method under multiple constraints (RNIC) to address challenges in high-accuracy machining.
  • To develop a method that mitigates feed fluctuations and mechanical shocks impacting surface quality.
  • To enhance the overall efficiency and accuracy of NURBS-based machining processes.

Main Methods:

  • Formulas for constrained feedrate considering geometric errors, kinematic, drive, and contour errors were derived.
  • A two-stage interpolation process was established: offline preprocessing to identify Feedrate Sensitive Areas (FSAs) and an online stage for real-time velocity smoothing.
  • A bidirectional scanning algorithm was employed in the preprocessing stage to detect FSAs and adjust feedrates at subsegment boundaries.

Main Results:

  • The offline stage effectively identifies FSAs and adjusts feedrates, creating acceleration and deceleration segments that match machining processes.
  • The online stage smooths velocity, compensating for nonlinearities inherent in NURBS curves.
  • Simulations of a "butterfly-shaped" NURBS curve using the S-shaped ACC/DEC algorithm validated the reliability and effectiveness of the RNIC method.

Conclusions:

  • The proposed real-time NURBS interpolation under multiple constraints (RNIC) effectively enhances machining accuracy and surface quality.
  • The two-stage approach (offline FSA identification and online velocity smoothing) successfully manages feed fluctuations and mechanical shocks.
  • The RNIC method offers a reliable and efficient solution for advanced NURBS-based machining applications.