• Journal of the Korean Society for Precision Engineering
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• v.16 no.4 s.97
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• pp.129-137
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• 1999

A parametric curve interpolator has been proposed for machining curves instead of a linear interpolator in which curves are approximated by a set of line segment. The parametric curve interpolator is superior to linear interpolator in machining time and contour error and generate exact position commands directly from curve equations. In this paper, a new toolpath generation method is proposed based on the parametric curve interpolator. This method retains all the benefits of parametric curve interpolator and can bound the scallop height within a specified value. By interpolating curves and surfaces directly from the mathematical equations, the amount of data from CAD/CAM system to CNC controller can be significantly reduced. The proposed method was implemented on a CNC controller and was confirmed to give a better result than the other existing method.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.5 no.4
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• pp.47-52
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• 1996

The interpolator is very important in CNC machines. This study proposed a parametric curve interpolator(PCI) which can be used for machining any sculptured surface represented in a parametric form and generates commands for tool motion between CAD data points according to given accuracy demands. The proposed interpolator is superior to the existing linear interpolator in accuracy, feed rate and acceleration continuity. Moreover in comparison to the recently developed cubic spline interpolator, the PCI has the capability of handling higher order parametric curves and also ensures precise tracking in the velocity domain. Results from real time simulations and experiments on open architecture CNC machines equipped with the proposed interpolator are presented to show its practical capagility. It is believed that the combination of the proposed interpolator and the open architecture machine controller further advances the area of command generation which is an important aspect of CAD/CAM.

• International Journal of Precision Engineering and Manufacturing
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• v.9 no.2
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• pp.84-92
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• 2008

Free-form shapes which were once considered as an aesthetic feature are now an important functional requirement. CNC industries are looking for a compact solution for reproducing free-form shapes as conventional interpolation models are inadequate, The parametric curve interpolator developed in the last decade has clearly emerged as favorite among its contemporaries in recent years, At present intense research has been done on parametric curve interpolators and interesting developments are reported. Out of the various parametric representations for curves and surfaces, NURBS has been standardized and widely used in free-form shape design. This paper presents a review of various methods of parametric interpolation for NURBS and discusses the salient features, problems and solutions. Recent approaches on variable feedrate interpolation, parameter compensation are also reviewed and research trends are addressed finally.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.341-344
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• 1997

The higher precision in manufacturing field is demanded, the more accurate servo controller is needed. To achieve the high precision, Koren proposed the cross-coupled control (CCC) method. The objective of the CCC is reducing the contour error rather than decreasing the individual axial error. The performance of CCC depends on the contour error model. In this paper we propose a new contour error model which utilizes contour error vector based on parametric curve interpolator. The experimental results show that the new CCC is more accurate than the variable-gain CCC during free-form curve motion.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.6
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• pp.152-157
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• 2000

In the control of CNC machine tools, it is significant for precise machining to reduce the contour error. The object of servo-control is reduction of contour error and tracking error. In past studies, there were two approaches to control a servo-system. One was to eliminate axial tracking errors, and the other was to control contour errors. The Cross-coupled controller(CCC) was introduced fro ma veiwpoint of contour error model. Recently, for machining part with free form surfaces, we propose a new contour error model based on curve interpolator. It is presented here that performance of CCC using proposed model is enhanced. Therefore, we can make more precise parts with the curve interpolator and the new contour error model.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.2
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• pp.1-8
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• 2003

Conventionally used linear or circular interpolator is undesirable for the precision machining of 3D free-form surface as the following reason: the transmission errors due to the huge number of data, discontinuity of segmentation, unsmooth motion speed. To this regard, modern CNC machine tools are designed with the function of machining arbitrary parametric curves. However, these systems don't consider the adaptive federate, which dominates the quality of the machining process. This paper proposes a NURBS interpolator for the constant material removal rate. That is accomplished by the variable federate using curvature of curve. The curvature-compensated feederate system has important Potential applications in ensuring part accuracy and protecting cutting tool. The simulated result show it can be applicable to the real machining.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2001.04a
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• pp.405-410
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• 2001

In this paper, a new parametric curve interpolator is proposed based on a 3D(3-dimensional) NURBS curve. A free curve is generally divided into small linear segments or circular arcs in CNC machining. The method has caused to a command error, the limitation of machining speed, and the irregular machining surface. The proposed real-time 3D NURBS interpolator continuously generates a linear segment within the range of allowable acceleration/deceleration in the motion controller. Therefore, the algorithm calculates the curvature and the remained distance of a command curve for the smoothing machining. It is expected to attaining high speed and high precision machining in CNC Machine Tool.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.12
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• pp.60-66
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• 2004

Increasing demands on precision machining of 3D free-form surface have necessitated the tool to move smoothly with varying feedrate. To this regard, parametric interpolators such as NURBS (Non-Uniform Rational B-Spline) interpolator have been introduced in CNC machining system. Such interpolators reduce the data burden in NC code, increase data transfer rate into NC controller, and finally give smooth motion while machining. In this research, a new concept to control cutting load in NURBS Interpolator was tried based on the curvature of curve. This is to protect cutting tool, and to have good machinability. For proof of the system, cutting force and surface topography were evaluated. From the experimental results. the interpolator is good enough for machining a free-form surface.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.4
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• pp.64-71
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• 2004

The growing need for higher precision and productivity in manufacturing industry has lead to an increased interest in computer numerical control (CNC) systems. It is well known fact that the cross-coupling controller (CCC) is an effective method for contouring applications. In this paper, a multi-axis contour error controller (CEC) based on a contour error vector using parametric curve interpolator is introduced. The contour error vector is a vector from the actual tool position to the nearest point on the desired path. The contour error vector is the closest error model to the contour error. The simulation results show that the CEC is more accurate than the conventional CCC for a biaxial motion system. In addition, the experimental results on 3-axis motion system show that the CEC is simply applied to 3-axis motions and contouring accuracy is significantly improved.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.895-898
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• 2003

The higher precision is demanded in modem manufacturing and it requires the more accurate servo controller. Cross-coupling control (CCC) has been developed to improve contouring motion. In this paper we introduce a new nonlinear CCC that is based on contour-error-vector using a parametric curve interpolator. A vector from the actual tool position to the nearest point on the desire path is directly adopted. The contour-error-vector is determined by constructing a tangential vector of nearest point on desired curve and determining the vector perpendicular to this tangential vector from the actual tool position. Moreover, the vector CCC can apply directly and easily to free-form curves include convex and concave form. The experimental results on a three-axis CNC machine center show that the present approach significantly improves motion accuracy in multi-axis motion