Frontiers of Mechanical Engineering in China, 2007
Models for surface modeling of free-form surface and massive data points are becoming an importan... more Models for surface modeling of free-form surface and massive data points are becoming an important feature in commercial computer aided design/computer-aided manufacturing software. However, there are many problems to be solved in this area, especially for closed free-form surface modeling. This article presents an effective method for cloud data closed surface modeling from asynchronous profile modeling measurement. It includes three steps: first, the cloud data are preprocessed for smoothing; second, a helical line is segmented to form triangle meshes; and third, Bezier surface patches are created over a triangle mesh and trimmed to shape on an entire surface. In the end, an illustrative example of shoe last surface modeling is given to show the availability of this method.
International Journal of Advanced Manufacturing Technology, 2006
Aiming at the special requirements of a shoe last high-speed machining process and the large data... more Aiming at the special requirements of a shoe last high-speed machining process and the large dataset which could be gained by the reverse engineering technique, this paper analyzes the conventional tool-offset methods and presents a B-spline tool-offset model. A simple vector-analyzed algorithm to smooth the tool-offset curve in which there are local strange points is proposed, and then the second tool-offsetting, which obtains the fine data of the machining tool’s center points, is directly processed. To reduce the error from tool offsetting of the C2 continuity curve, this paper gains a smoother curve after processing via the edge points joint algorithm, which effectively solved the overcut or undercut problems in the high-speed machining of the spline curve.
To achieve the goal of high-speed and highly accurate machining, this paper proposes a real-time ... more To achieve the goal of high-speed and highly accurate machining, this paper proposes a real-time control algorithm based on Taylor’s expansion for implementing variable feed rate non-uniform rational B-spline (NURBS) curve. To efficiently compute the NURBS curve and its derivatives in real-time, some effective methods are proposed. In contrast to the existing linear and circular interpolators, the proposed interpolator can maintain small contour errors and feedrate fluctuations. It also can shorten the size of machining code effectively compared with the linear and circular interpolators. At the same time, the NURBS-format milling codes adapting the dual NURBS Curve interpolation algorithm for 5 axis high-speed machining are adopted in this study. Besides, an effective algorithm is adopted to minimize the kinematics error by means of the shortest path scheme.
To achieve high-speed and high-accuracy machining, look-ahead scheme and parametric interpolator ... more To achieve high-speed and high-accuracy machining, look-ahead scheme and parametric interpolator have shown significant effect on interpolating micro-line blocks. On the one hand, look-ahead schemes have been integrated in many computer numerical control (CNC) systems to alleviate the frequent start/stop motion and achieve a higher feedrate. However, the unsmooth speed at the segment junctions cannot be avoided entirely due to the discontinuous nature of the linearized-segmented contour. On the other hand, parametric interpolator has been proposed to overcome the shortcomings of the linear/circular interpolator. But, it is difficult to fit the blocks into parametric curves on-line. In this paper, a local cubic B-spline fitting algorithm with real-time look-ahead scheme is proposed for consecutive micro-line blocks interpolation. First, the consecutive micro-line blocks, which satisfy the bi-chord error constraint, are fitted into a C1 continuous cubic B-spline curve. Second, machining dynamics and tool path contour constrains are taken into consideration. Third, an optimal look-ahead scheme is proposed to generate the optimal feedrate profile. Simulation and experiment are performed in real-time environment to verify the effectiveness of the proposed method. Compared with the conventional interpolation algorithm, the proposed algorithm reduces the machining time by 70%.
International Journal of Advanced Manufacturing Technology, 2010
With recent advances in high-speed and high-accuracy machining, the NURBS interpolator has shown ... more With recent advances in high-speed and high-accuracy machining, the NURBS interpolator has shown significant effect on dealing with the free-form curves and surfaces. The existing study aims at developing the adaptive interpolator which confines the chord error, the tangent acceleration, and jerk. However, the excessive axis acceleration is still unavoidable at the sharp corners and will deteriorate the contour accuracy. In this paper, a real-time adaptive NURBS interpolator considering the acc/dec capacity for each individual axis is developed to confine both the chord error and the axis acceleration. The maximum feasible feed and tangent acceleration range are deduced, respecting the given axis acc/dec limit. A two-stage feed determination scheme is applied to calculate the adaptive feed rate for each sampling period. A look-ahead window is utilized to improve the calculation performance for real-time application. Simulations and experiments are performed to verify the resulting feed rate, acc/dec profiles, and the real-time performance of the proposed interpolator.
International Journal of Advanced Manufacturing Technology, 2009
In free-form surface machining, it is essential to optimize the feedrate in order to improve the ... more In free-form surface machining, it is essential to optimize the feedrate in order to improve the machining efficiency. Conservative constant feedrate values have been mostly used up to now since there was a lack of physical models and optimization tools for the machining processes. The overall goal of this research is the integration of geometric and mechanistic milling models for force prediction and feedrate scheduling in five-axis CNC free-form surface machining. For each tool move, the geometric model calculates the cut geometry, and a mechanistic model is used along with a maximum allowable cutting force to determine a desired feedrate. The results are written into the part NC program with optimized feedrates. When the integrated modeling approach based feedrate scheduling strategy introduced in this paper was used, it was shown that the machining time can be decreased significantly along the tool path.
International Journal of Advanced Manufacturing Technology, 2009
To alleviate the feed fluctuation and to maintain a smooth feed in conventional five-axis machini... more To alleviate the feed fluctuation and to maintain a smooth feed in conventional five-axis machining, an optimal feed interpolation algorithm (look-ahead) is proposed. However, the problem arises where the segment usually cannot be interpolated exactly in an integer period because of the nonzero joint feed at the junction. To overcome this problem, and to achieve faster machining speed and higher quality parts, this paper presents an optimal feed interpolation algorithm for high-speed, five-axis machining having the function of “look-ahead”, i.e., variable-period linear interpolation algorithm. In real applications, the proposed algorithm results in: (1) constant speed; (2) high machining accuracy. Moreover, in this paper, an efficient method for acceleration and deceleration control is presented to achieve the highest-quality feed profiles and to shorten machining times. The precision and speed of machining is improved greatly. Experimental results verify the effectiveness of the proposed method.
International Journal of Advanced Manufacturing Technology, 2010
Flank milling with a taper cutter is widely used in industry. The analytical representation of th... more Flank milling with a taper cutter is widely used in industry. The analytical representation of the envelope surface generated by a conical cutter undergoing rational motion is derived by bringing together the theories of line geometry and kinematics. Based on the projective duality between a point and a plane in line geometry, a cone surface is represented as two pieces of rational quadratic Bézier developable surfaces in terms of the plane coordinates instead of the traditional point coordinates. It provides a way to describe and calculate the envelope surface exactly by analyzing the trajectory of a plane undergoing a two-parameter rational motion. The rotation around the axis of the cone is adopted to ensure that the characteristic curve is located on the same piece of rational quadratic Bézier developable surface of the cone. The degenerate cases that the characteristic curve does not exist are also discussed. Examples are provided, in which the envelope surfaces of a conical cutter undergoing rational Bézier and B-spline motions are computed. The results can be applied to tool-path planning and error analysis for five-axis flank milling machining.
A new algorithm is proposed to generate compact dual NURBS tool paths with equal distance (DNTPED... more A new algorithm is proposed to generate compact dual NURBS tool paths with equal distance (DNTPED) for 5-axis NC machining. The DNTPED has significant advantages over conventional linear tool path in the NC machining of free-form surface since it reduces the tangency discontinuities along the tool path. The discontinuities, the inherent character of the linear interpolation, are the important sources of practical feed-speed fluctuation of the machine tool. The new algorithm is proposed to generate DNTPED based on the theories of rational motion. Here the rational rigid movement of a cutter is represented by a B-spline curve in dual quaternion space. DNTPED is obtained directly from the B-spline dual quaternion curve with the help of the blossom form of the B-spline curve. Comparing with the existing method, the DNTPED consists of less data and each NURBS can be treated as one curve, not as a collection of bézier segments.
Cutting forces with respect to different cutter orientations are analyzed for five-axis NC machin... more Cutting forces with respect to different cutter orientations are analyzed for five-axis NC machining of a ball-end cutter. A measure is then defined to quantify the effects of cutter orientation variation. According to the measure, a novel model and algorithm are proposed to wholly optimize cutter orientations based on a cutter contact (CC) point mesh. The method has two advantages. One is that the cutter orientation smoothnesses along the feed direction and pick-feed direction are both wholly optimized. The other is that only the accessibility cones of mesh points are required to compute and the computation efficiency is improved. These advantages are shown by simulating the machining efficiency, the stability of feed velocities and the smoothness of cutting force. A computational example and a cutting experiment are finally given to illustrate the validity of the proposed method.
In 3+2 axis NC machining, only three linear axes are executed while 5-axis machine’s two rotation... more In 3+2 axis NC machining, only three linear axes are executed while 5-axis machine’s two rotational axes are locked. Compared with conventional 3-axis machining, the main advantage of 3+2 machining is that it allows use of a shorter cutter. The magnitude of tool deflection and the stability of cutting process strongly depend on the slenderness of the tool. However, the tool overhang length can’t be easily shortened because of collision avoidance. In this paper the accessibility cone of a milling cutter is newly defined to generate collision-free cutting orientations. The accessibility cone and safe tool length can be efficiently computed by a novel method using graphics hardware. The proper cutting orientation of 3+2 machining is then obtained by optimizing the safe and shortest tool length. The computational example and cutting experiment of sculptured surface machining confirm the validity of the approach.
Frontiers of Mechanical Engineering in China, 2007
Models for surface modeling of free-form surface and massive data points are becoming an importan... more Models for surface modeling of free-form surface and massive data points are becoming an important feature in commercial computer aided design/computer-aided manufacturing software. However, there are many problems to be solved in this area, especially for closed free-form surface modeling. This article presents an effective method for cloud data closed surface modeling from asynchronous profile modeling measurement. It includes three steps: first, the cloud data are preprocessed for smoothing; second, a helical line is segmented to form triangle meshes; and third, Bezier surface patches are created over a triangle mesh and trimmed to shape on an entire surface. In the end, an illustrative example of shoe last surface modeling is given to show the availability of this method.
International Journal of Advanced Manufacturing Technology, 2006
Aiming at the special requirements of a shoe last high-speed machining process and the large data... more Aiming at the special requirements of a shoe last high-speed machining process and the large dataset which could be gained by the reverse engineering technique, this paper analyzes the conventional tool-offset methods and presents a B-spline tool-offset model. A simple vector-analyzed algorithm to smooth the tool-offset curve in which there are local strange points is proposed, and then the second tool-offsetting, which obtains the fine data of the machining tool’s center points, is directly processed. To reduce the error from tool offsetting of the C2 continuity curve, this paper gains a smoother curve after processing via the edge points joint algorithm, which effectively solved the overcut or undercut problems in the high-speed machining of the spline curve.
To achieve the goal of high-speed and highly accurate machining, this paper proposes a real-time ... more To achieve the goal of high-speed and highly accurate machining, this paper proposes a real-time control algorithm based on Taylor’s expansion for implementing variable feed rate non-uniform rational B-spline (NURBS) curve. To efficiently compute the NURBS curve and its derivatives in real-time, some effective methods are proposed. In contrast to the existing linear and circular interpolators, the proposed interpolator can maintain small contour errors and feedrate fluctuations. It also can shorten the size of machining code effectively compared with the linear and circular interpolators. At the same time, the NURBS-format milling codes adapting the dual NURBS Curve interpolation algorithm for 5 axis high-speed machining are adopted in this study. Besides, an effective algorithm is adopted to minimize the kinematics error by means of the shortest path scheme.
To achieve high-speed and high-accuracy machining, look-ahead scheme and parametric interpolator ... more To achieve high-speed and high-accuracy machining, look-ahead scheme and parametric interpolator have shown significant effect on interpolating micro-line blocks. On the one hand, look-ahead schemes have been integrated in many computer numerical control (CNC) systems to alleviate the frequent start/stop motion and achieve a higher feedrate. However, the unsmooth speed at the segment junctions cannot be avoided entirely due to the discontinuous nature of the linearized-segmented contour. On the other hand, parametric interpolator has been proposed to overcome the shortcomings of the linear/circular interpolator. But, it is difficult to fit the blocks into parametric curves on-line. In this paper, a local cubic B-spline fitting algorithm with real-time look-ahead scheme is proposed for consecutive micro-line blocks interpolation. First, the consecutive micro-line blocks, which satisfy the bi-chord error constraint, are fitted into a C1 continuous cubic B-spline curve. Second, machining dynamics and tool path contour constrains are taken into consideration. Third, an optimal look-ahead scheme is proposed to generate the optimal feedrate profile. Simulation and experiment are performed in real-time environment to verify the effectiveness of the proposed method. Compared with the conventional interpolation algorithm, the proposed algorithm reduces the machining time by 70%.
International Journal of Advanced Manufacturing Technology, 2010
With recent advances in high-speed and high-accuracy machining, the NURBS interpolator has shown ... more With recent advances in high-speed and high-accuracy machining, the NURBS interpolator has shown significant effect on dealing with the free-form curves and surfaces. The existing study aims at developing the adaptive interpolator which confines the chord error, the tangent acceleration, and jerk. However, the excessive axis acceleration is still unavoidable at the sharp corners and will deteriorate the contour accuracy. In this paper, a real-time adaptive NURBS interpolator considering the acc/dec capacity for each individual axis is developed to confine both the chord error and the axis acceleration. The maximum feasible feed and tangent acceleration range are deduced, respecting the given axis acc/dec limit. A two-stage feed determination scheme is applied to calculate the adaptive feed rate for each sampling period. A look-ahead window is utilized to improve the calculation performance for real-time application. Simulations and experiments are performed to verify the resulting feed rate, acc/dec profiles, and the real-time performance of the proposed interpolator.
International Journal of Advanced Manufacturing Technology, 2009
In free-form surface machining, it is essential to optimize the feedrate in order to improve the ... more In free-form surface machining, it is essential to optimize the feedrate in order to improve the machining efficiency. Conservative constant feedrate values have been mostly used up to now since there was a lack of physical models and optimization tools for the machining processes. The overall goal of this research is the integration of geometric and mechanistic milling models for force prediction and feedrate scheduling in five-axis CNC free-form surface machining. For each tool move, the geometric model calculates the cut geometry, and a mechanistic model is used along with a maximum allowable cutting force to determine a desired feedrate. The results are written into the part NC program with optimized feedrates. When the integrated modeling approach based feedrate scheduling strategy introduced in this paper was used, it was shown that the machining time can be decreased significantly along the tool path.
International Journal of Advanced Manufacturing Technology, 2009
To alleviate the feed fluctuation and to maintain a smooth feed in conventional five-axis machini... more To alleviate the feed fluctuation and to maintain a smooth feed in conventional five-axis machining, an optimal feed interpolation algorithm (look-ahead) is proposed. However, the problem arises where the segment usually cannot be interpolated exactly in an integer period because of the nonzero joint feed at the junction. To overcome this problem, and to achieve faster machining speed and higher quality parts, this paper presents an optimal feed interpolation algorithm for high-speed, five-axis machining having the function of “look-ahead”, i.e., variable-period linear interpolation algorithm. In real applications, the proposed algorithm results in: (1) constant speed; (2) high machining accuracy. Moreover, in this paper, an efficient method for acceleration and deceleration control is presented to achieve the highest-quality feed profiles and to shorten machining times. The precision and speed of machining is improved greatly. Experimental results verify the effectiveness of the proposed method.
International Journal of Advanced Manufacturing Technology, 2010
Flank milling with a taper cutter is widely used in industry. The analytical representation of th... more Flank milling with a taper cutter is widely used in industry. The analytical representation of the envelope surface generated by a conical cutter undergoing rational motion is derived by bringing together the theories of line geometry and kinematics. Based on the projective duality between a point and a plane in line geometry, a cone surface is represented as two pieces of rational quadratic Bézier developable surfaces in terms of the plane coordinates instead of the traditional point coordinates. It provides a way to describe and calculate the envelope surface exactly by analyzing the trajectory of a plane undergoing a two-parameter rational motion. The rotation around the axis of the cone is adopted to ensure that the characteristic curve is located on the same piece of rational quadratic Bézier developable surface of the cone. The degenerate cases that the characteristic curve does not exist are also discussed. Examples are provided, in which the envelope surfaces of a conical cutter undergoing rational Bézier and B-spline motions are computed. The results can be applied to tool-path planning and error analysis for five-axis flank milling machining.
A new algorithm is proposed to generate compact dual NURBS tool paths with equal distance (DNTPED... more A new algorithm is proposed to generate compact dual NURBS tool paths with equal distance (DNTPED) for 5-axis NC machining. The DNTPED has significant advantages over conventional linear tool path in the NC machining of free-form surface since it reduces the tangency discontinuities along the tool path. The discontinuities, the inherent character of the linear interpolation, are the important sources of practical feed-speed fluctuation of the machine tool. The new algorithm is proposed to generate DNTPED based on the theories of rational motion. Here the rational rigid movement of a cutter is represented by a B-spline curve in dual quaternion space. DNTPED is obtained directly from the B-spline dual quaternion curve with the help of the blossom form of the B-spline curve. Comparing with the existing method, the DNTPED consists of less data and each NURBS can be treated as one curve, not as a collection of bézier segments.
Cutting forces with respect to different cutter orientations are analyzed for five-axis NC machin... more Cutting forces with respect to different cutter orientations are analyzed for five-axis NC machining of a ball-end cutter. A measure is then defined to quantify the effects of cutter orientation variation. According to the measure, a novel model and algorithm are proposed to wholly optimize cutter orientations based on a cutter contact (CC) point mesh. The method has two advantages. One is that the cutter orientation smoothnesses along the feed direction and pick-feed direction are both wholly optimized. The other is that only the accessibility cones of mesh points are required to compute and the computation efficiency is improved. These advantages are shown by simulating the machining efficiency, the stability of feed velocities and the smoothness of cutting force. A computational example and a cutting experiment are finally given to illustrate the validity of the proposed method.
In 3+2 axis NC machining, only three linear axes are executed while 5-axis machine’s two rotation... more In 3+2 axis NC machining, only three linear axes are executed while 5-axis machine’s two rotational axes are locked. Compared with conventional 3-axis machining, the main advantage of 3+2 machining is that it allows use of a shorter cutter. The magnitude of tool deflection and the stability of cutting process strongly depend on the slenderness of the tool. However, the tool overhang length can’t be easily shortened because of collision avoidance. In this paper the accessibility cone of a milling cutter is newly defined to generate collision-free cutting orientations. The accessibility cone and safe tool length can be efficiently computed by a novel method using graphics hardware. The proper cutting orientation of 3+2 machining is then obtained by optimizing the safe and shortest tool length. The computational example and cutting experiment of sculptured surface machining confirm the validity of the approach.
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Papers by Yuhan Wang