A new approach to generating arc length parameterized NURBS tool paths for efficient three-axis machining of smooth, accurate sculptured surfaces

Chen, Zezhong C.; Khan, Maqsood Ahmed

doi:10.1007/s00170-013-5411-1

Cited by 13 publications

(2 citation statements)

References 21 publications

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“…In recent years, with much deeper research on the parametric curves, such as Bezier, B-Spline and non-uniform rational basis spline (NURBS), the tool path of parametric curves has been widely used to describe smooth trajectories and realize tangential continuities [7] to [9]. Thus, there are two kinds of ways available in the literature to smooth the linear tool path by utilizing these smooth parametric curves: global smoothing and local smoothing [10], as shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Local Corner Smoothing Transition Algorithm Based on Double Cubic NURBS for Five-axis Linear Tool Path

Zhang

Yan

2016

SV-JME

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A five-axis tool path is often composed of a linear path that has a tangential discontinuity so that the tangential velocity will be abrupt or be equal to zero at the corner of the adjacent segments. Therefore, it greatly affects the machining efficiency and quality. Thus, a corner smoothing transition algorithm based on double cubic NURBS, which is curvature-continuous and satisfies the given accuracy constraint, is proposed to smooth the local corner at the adjacent five-axis linear path. On the basis of the smoothing transition model, the parametric synchronization between the smoothed double NURBS trajectories and the remaining two linear segments are respectively constructed to realize the smoothing variation along the tool tip translational trajectory and tool axis rotational trajectory. The simulation and examples show that the proposed transition algorithm can satisfy the error constraints, reduce the feedrate fluctuation, and improve the machining quality. Keywords: five-axis machining, corner transition, double NURBS curves, tool path Highlights • A corner smoothing transition algorithm based on double cubic NURBS is proposed to smooth the five-axis linear tool path. • The proposed algorithm is curvature-continuous and satisfies the given accuracy constraint. • The approximation error has an analytical relationship with the transition length of the smoothed curve. • The synchronization method can guarantee tool-tip translation and tool axis rotation with continuous and smooth variation. • The proposed method has been validated with simulations and experimental results.

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Section: Introductionmentioning

confidence: 99%

Local Corner Smoothing Transition Algorithm Based on Double Cubic NURBS for Five-axis Linear Tool Path

Zhang

Yan

2016

SV-JME

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“…20 established the nonlinear relationship between the arc length and path parameter by a parameter correction B-spline. Chen and Khan 21,22 proposed a new approach to generate arc length parameterized NURBS tool paths with high accuracy.…”

Section: Introductionmentioning

confidence: 99%

A parametric interpolation method with minimal feedrate fluctuation by nonuniform rational basis spline

Zhang

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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Because the relation between the arc length s and curve parameter u cannot be represented by explicit function for most of the curves, it is difficult to consider the accuracy, robustness, and computational efficiency for most of the parametric interpolation, especially when the curves are complex or extremes. Therefore, an off-line fitting interpolation method by using nonuniform rational basis spline is presented in this paper. As nonuniform rational basis spline has many geometry implementation tools and numerous good properties as compared to the polynomial, the required fitting accuracy can be obtained more easily than with polynomial. After the de Boor method is applied, the computational load of nonuniform rational basis spline is decreased as compared to the Taylor approximation and the higher order polynomial fitting method. In order to obtain the proper s-u fitting nonuniform rational basis spline and reduce the computational load of the fitting process, the sampled s-u data points are divided according to the properties of nonuniform rational basis spline, and in each segment, the knot vectors, control points, and weights are calculated by the iterative-optimization method. Then the s-u nonuniform rational basis spline can be applied in real-time interpolation, and the accuracy, robustness, and computational efficiency are demonstrated by simulations and experiments.

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Direct trajectory interpolation on the surface using an open CNC

Beudaert

Lavernhe

Tournier

2014

Int J Adv Manuf Technol

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Free-form surfaces are used for many industrial applications from aeronautical parts, to molds or biomedical implants. In the common machining process, CAM software generates approximated tool paths because of the limitation induced by the input tool path format of the industrial CNC. Then, during the tool path interpolation, marks on finished surfaces can appear induced by non smooth feedrate planning. Managing the geometry of the tool path as well as the kinematical parameters of the machine tool are two key factors for quality and productivity improvements. The aim of this paper is to present a unified method to compute the trajectory directly on the surface to be machined avoiding CAM approximations and producing a smoother trajectory. This paper proposes an interpolation of the trajectory based on the free form surface mathematical model while considering the kinematical limitations of a high speed milling machine (velocity, acceleration and jerk). The amelioration of the data exchange between CAD/CAM and CNC opens new ways to optimize the manufacturing process. The Direct Trajectory Interpolation on the Surface (DTIS) method allows to obtain both a higher productivity and a better surface quality. Machining experiments carried out with an Open CNC on a 5-axis high speed milling machine show the benefits of the proposed method compared to the classical strategies available with an industrial CNC.

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A new approach to generating arc length parameterized NURBS tool paths for efficient three-axis machining of smooth, accurate sculptured surfaces

Cited by 13 publications

References 21 publications

Local Corner Smoothing Transition Algorithm Based on Double Cubic NURBS for Five-axis Linear Tool Path

Local Corner Smoothing Transition Algorithm Based on Double Cubic NURBS for Five-axis Linear Tool Path

A parametric interpolation method with minimal feedrate fluctuation by nonuniform rational basis spline

Direct trajectory interpolation on the surface using an open CNC

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