A novel approach is proposed for correcting command points and compressing discrete axis commands into a C2 continuous curve.The relationship between values of rotation angles and tool posture errors is firstly analyz...A novel approach is proposed for correcting command points and compressing discrete axis commands into a C2 continuous curve.The relationship between values of rotation angles and tool posture errors is firstly analyzed.A segmentation method based on values of rotation angles and lengths of adjacent points is then used to subdivide these command points into accuracy regions and smoothness regions.Since tool center points generated by CAD/CAM system are usually lying in the space that is apart from the desired curve within a tolerance distance,and the corresponding tool orientation vector may change a lot while the trajectory length of the tool center point is quite small,directly machining with such points will lead to problems of coarse working shape and long machining time.A correction method for command points is implemented so that good processing effectiveness can be achieved.Also,the quintic spline is used for compressing discrete command points into a C2 continuous smooth curve.The machining experiment is finally conducted to demonstrate the effectiveness of the proposed algorithm.展开更多
For a spherical four-bar linkage,the maximum number of the spherical RR dyad（R：revolute joint）of five-orientation motion generation can be at most 6.However,complete real solution of this problem has seldom been st...For a spherical four-bar linkage,the maximum number of the spherical RR dyad（R：revolute joint）of five-orientation motion generation can be at most 6.However,complete real solution of this problem has seldom been studied.In order to obtain six real RR dyads,based on Strum＇s theorem,the relationships between the design parameters are derived from a 6th-degree univariate polynomial equation that is deduced from the constraint equations of the spherical RR dyad by using Dixon resultant method.Moreover,the Grashof condition and the circuit defect condition are taken into account.Given the relationships between the design parameters and the aforementioned two conditions,two objective functions are constructed and optimized by the adaptive genetic algorithm（AGA）.Two examples with six real spherical RR dyads are obtained by optimization,and the results verify the feasibility of the proposed method.The paper provides a method to synthesize the complete real solution of the five-orientation motion generation,which is also applicable to the problem that deduces to a univariate polynomial equation and requires the generation of as many as real roots.展开更多
When milling part surfaces with a ball-end tool in 5-axis CNC machining,maintaining a constant cutting speed by keeping a fixed inclination angle between the tool axis and surface normal is crucial to ensure safe oper...When milling part surfaces with a ball-end tool in 5-axis CNC machining,maintaining a constant cutting speed by keeping a fixed inclination angle between the tool axis and surface normal is crucial to ensure safe operation and achieve high quality of the machined surface.Under this constraint,the variation of tool orientation is expected to be“smoothest possible”to reduce the angular speed of the rotary axes for the efficient and robust machining.To address this issue,the spatial tractrix which is the extension of classic tractrix is presented to establish the geometry model of the tool orientation kinematics in the part coordinate system.The proposed model describes the relations between the tilt angle and the variation of ball-end tool orientation.Two spatial tractrix-based methods,synchronizing tractrix-based method and equilibrating tractrix-based method,are developed to minimize the variation of tool orientation by controlling the variation of tilt angle.These methods are used to plan the tool orientation on a part surface modeled by a bicubic spline surface.The performance evaluation carried by intense simulations demonstrates the equilibrating tractrix-based method provide the best results in most cases compared with the existing differential geometry-based methods such as the tractrix-based method and parallel transport method.The synchronizing tractrix-based method works well in some special cases.展开更多
The key proposition of this hypothesis is logic behind the order of movements of Hua Tuo’s qigong Wu Qin Xi(Five animal frolics).To date,there were many discussions about connection of the movements of Wu Qin Xi with...The key proposition of this hypothesis is logic behind the order of movements of Hua Tuo’s qigong Wu Qin Xi(Five animal frolics).To date,there were many discussions about connection of the movements of Wu Qin Xi with existing TCM theories and why Hua Tuo made it in that particular way.Some experts are saying that there is no connection but if all stories of Hua Tuo’s abilities and knowledge were half-truth,he wouldn’t let even the order of movements of qigong that he created be just a random order.Hypothesis is exploring different views on Taiji movement direction,Wu Xing and connection between animals in Wu Qin Xi,Lo Shu square and Sun wheel and proposing possible solution to the question“Why Hua Tuo made such order of animals in Wu Qin Xi?”by analyzing and and cross referencing the common ground between theories and bridging the gap the we were left without any written explanation from the master itself.Further progress and confirmation of this hypothesis requires deeper research and cooperation between Qigong expert historians.展开更多
Well-designed tool orientation is crucial for the quality execution of five-axis machining with flat-end tools.Tool orientation can be specified in terms of tool inclination and tool tilt angles.For a given surface pa...Well-designed tool orientation is crucial for the quality execution of five-axis machining with flat-end tools.Tool orientation can be specified in terms of tool inclination and tool tilt angles.For a given surface path,these aspects need to be specified for each cutter contact point along the path,because poor tool orientation choice can cause large axial acceleration of the machine tool,leading to inferior quality of the machined surface.The rotation-minimizing frame aims to reduce unnecessary frame rotation during movement.This concept has been adopted to develop tool orientation methods that allow variation in the inclination angle,the tilt angle,and both the inclination and tilt angles.The intention is to reduce unnecessary rotation of the tool frame as the tool follows a specified path.Evaluation was conducted in the context of five-axis flat-end tool machining.Based on these methods,tool orientation was planned along surface paths of a torus,sphere,and dome.Changes in tool orientation were always smooth.From the perspective of reducing tool orientation changes and axial acceleration,it was demonstrated that simultaneous variation of the inclination and tilt angles based on rotation minimization provided the best results.展开更多
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 ...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.展开更多
基金supported by the National Key Basic Research and Development Projects under Grant No.2011CB302400
文摘A novel approach is proposed for correcting command points and compressing discrete axis commands into a C2 continuous curve.The relationship between values of rotation angles and tool posture errors is firstly analyzed.A segmentation method based on values of rotation angles and lengths of adjacent points is then used to subdivide these command points into accuracy regions and smoothness regions.Since tool center points generated by CAD/CAM system are usually lying in the space that is apart from the desired curve within a tolerance distance,and the corresponding tool orientation vector may change a lot while the trajectory length of the tool center point is quite small,directly machining with such points will lead to problems of coarse working shape and long machining time.A correction method for command points is implemented so that good processing effectiveness can be achieved.Also,the quintic spline is used for compressing discrete command points into a C2 continuous smooth curve.The machining experiment is finally conducted to demonstrate the effectiveness of the proposed algorithm.
基金Supported by National Natural Science Foundation of China(Grant Nos.51375059,61105103)National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA040203)Beijing Municipal Natural Science Foundation of China(Grant No.4132032)
文摘For a spherical four-bar linkage,the maximum number of the spherical RR dyad（R：revolute joint）of five-orientation motion generation can be at most 6.However,complete real solution of this problem has seldom been studied.In order to obtain six real RR dyads,based on Strum＇s theorem,the relationships between the design parameters are derived from a 6th-degree univariate polynomial equation that is deduced from the constraint equations of the spherical RR dyad by using Dixon resultant method.Moreover,the Grashof condition and the circuit defect condition are taken into account.Given the relationships between the design parameters and the aforementioned two conditions,two objective functions are constructed and optimized by the adaptive genetic algorithm（AGA）.Two examples with six real spherical RR dyads are obtained by optimization,and the results verify the feasibility of the proposed method.The paper provides a method to synthesize the complete real solution of the five-orientation motion generation,which is also applicable to the problem that deduces to a univariate polynomial equation and requires the generation of as many as real roots.
基金supported by National Natural Science Foundation of China(No.51975231)。
文摘When milling part surfaces with a ball-end tool in 5-axis CNC machining,maintaining a constant cutting speed by keeping a fixed inclination angle between the tool axis and surface normal is crucial to ensure safe operation and achieve high quality of the machined surface.Under this constraint,the variation of tool orientation is expected to be“smoothest possible”to reduce the angular speed of the rotary axes for the efficient and robust machining.To address this issue,the spatial tractrix which is the extension of classic tractrix is presented to establish the geometry model of the tool orientation kinematics in the part coordinate system.The proposed model describes the relations between the tilt angle and the variation of ball-end tool orientation.Two spatial tractrix-based methods,synchronizing tractrix-based method and equilibrating tractrix-based method,are developed to minimize the variation of tool orientation by controlling the variation of tilt angle.These methods are used to plan the tool orientation on a part surface modeled by a bicubic spline surface.The performance evaluation carried by intense simulations demonstrates the equilibrating tractrix-based method provide the best results in most cases compared with the existing differential geometry-based methods such as the tractrix-based method and parallel transport method.The synchronizing tractrix-based method works well in some special cases.
文摘The key proposition of this hypothesis is logic behind the order of movements of Hua Tuo’s qigong Wu Qin Xi(Five animal frolics).To date,there were many discussions about connection of the movements of Wu Qin Xi with existing TCM theories and why Hua Tuo made it in that particular way.Some experts are saying that there is no connection but if all stories of Hua Tuo’s abilities and knowledge were half-truth,he wouldn’t let even the order of movements of qigong that he created be just a random order.Hypothesis is exploring different views on Taiji movement direction,Wu Xing and connection between animals in Wu Qin Xi,Lo Shu square and Sun wheel and proposing possible solution to the question“Why Hua Tuo made such order of animals in Wu Qin Xi?”by analyzing and and cross referencing the common ground between theories and bridging the gap the we were left without any written explanation from the master itself.Further progress and confirmation of this hypothesis requires deeper research and cooperation between Qigong expert historians.
文摘Well-designed tool orientation is crucial for the quality execution of five-axis machining with flat-end tools.Tool orientation can be specified in terms of tool inclination and tool tilt angles.For a given surface path,these aspects need to be specified for each cutter contact point along the path,because poor tool orientation choice can cause large axial acceleration of the machine tool,leading to inferior quality of the machined surface.The rotation-minimizing frame aims to reduce unnecessary frame rotation during movement.This concept has been adopted to develop tool orientation methods that allow variation in the inclination angle,the tilt angle,and both the inclination and tilt angles.The intention is to reduce unnecessary rotation of the tool frame as the tool follows a specified path.Evaluation was conducted in the context of five-axis flat-end tool machining.Based on these methods,tool orientation was planned along surface paths of a torus,sphere,and dome.Changes in tool orientation were always smooth.From the perspective of reducing tool orientation changes and axial acceleration,it was demonstrated that simultaneous variation of the inclination and tilt angles based on rotation minimization provided the best results.
基金supported by the National Basic Research Program of China ("973" Program)(Grant No.2005CB724103)the National Natural Science Foundation of China (Grant No.50805093) the Science & Technology Commission of Shanghai Municipality (Grant No.07JC14028)
文摘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.
