A NURBS interpolation method with minimal feedrate fluctuation for CNC machine tools

• Published in: International journal of advanced manufacturing technology Vol. 78; no. 5-8; pp. 1241 - 1250
• Main Authors: Liu, Huan, Liu, Qiang, Zhou, Shengkai, Li, Chuanjun, Yuan, Songmei
• Format: Journal Article
• Language: English
• Published: London Springer London 01.05.2015; Springer Nature B.V
• Subjects: Approximation; CAE) and Design; Computer simulation; Computer-Aided Engineering (CAD; Engineering; Industrial and Production Engineering; Interpolation; Machine tools; Mechanical Engineering; Media Management; Numerical controls; Original Article; Parameters; Quartic equations; Taylor series; Variation; Interpolation; Feedrate; CNC; Fluctuation; NURBS
• ISSN: 0268-3768; 1433-3015
• DOI: 10.1007/s00170-014-6753-z

To reduce the feedrate fluctuation in non-uniform rational B-spline (NURBS) interpolation caused by approximation errors of interpolation methods, a new NURBS interpolation method with minimal feedrate fluctuation for CNC machine tools is proposed to obtain the sampling curve parameter by solving a quartic equation with respect to the curve parameter increment according to the scheduled feedrate using Ferrari’s formulas and Shengjin’s formulas. Firstly, the second-order Taylor expansion is applied on the numerator and denominator in the NURBS representation separately with unknown curve parameter increment. Then, a quartic equation with respect to the curve parameter increment is formed and solved by Ferrari’s formulas and Shengjin’s formulas efficiently, which can achieve minimal feedrate fluctuation in real-time interpolation. In principle, the proposed method can totally eliminate the feedrate fluctuation for second-degree NURBS curves and can reduce it to a satisfied value for other high-degree NURBS curves. Finally, numerical simulations and experiments are conducted to verify the feasibility and applicability of the proposed method.