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Updated: Aug 5, 2026
10:09
Operation of the Collaborative Composite Manufacturing (CCM) System
Published on: October 1, 2019
High-Speed Precision Machining and Surface Roughness Determination of Freeform Curves Using Galerkin-NURBS
Usman Haladu Garba1, Taiyong Wang1, Ying Tian1
1School of Mechanical Engineering, Tianjin University, Tianjin 300354, China.
Sensors (Basel, Switzerland)
|July 28, 2026
Summary
This study introduces a novel Galerkin-NURBS framework for high-speed machining of complex shapes. It significantly reduces processing time and interpolation steps, enhancing efficiency and surface quality in precision manufacturing.
Area of Science:
- Manufacturing Engineering
- Computational Geometry
- Robotics
Background:
- High-speed machining of complex freeform geometries presents challenges in computational efficiency, kinematic constraints, and precision.
- Traditional interpolation methods struggle with geometric errors and vibrations in high-curvature regions.
Purpose of the Study:
- To develop an optimized interpolation framework for high-speed machining of complex freeform geometries.
- To improve computational efficiency, kinematic constraint satisfaction, and surface quality.
Main Methods:
- Integration of Galerkin projection for Non-Uniform Rational B-Splines (NURBS) parameterization to minimize geometric error.
- Coupling with a jerk-limited S-curve trajectory planning algorithm for C3 continuity and constraint enforcement.
- Validation through numerical simulations and five-axis CNC machining experiments with surface roughness measurements.
Main Results:
- Achieved a 32.9% reduction in processing time compared to the CQSF method.
- Reduced interpolation steps by 35.1% relative to FSRC.
- Surface roughness (Ra) values were compliant with ISO 21920-1:2021, meeting high-precision thresholds for aluminum alloy 6061.
Conclusions:
- The proposed Galerkin-NURBS framework significantly enhances machining efficiency and surface quality.
- The method maintains geometric fidelity, crucial for precision manufacturing applications.
- Sensor-guided process optimization is critical for advanced manufacturing where this framework is applicable.
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