The discontinuity of linear tool path(or G01 blocks) brings about unnecessary feedrate deceleration and fluctuation during machining. To improve the continuity, the linear tool path is usually smoothed by the local tr...The discontinuity of linear tool path(or G01 blocks) brings about unnecessary feedrate deceleration and fluctuation during machining. To improve the continuity, the linear tool path is usually smoothed by the local transition method or the global fitting method. For micro-line tool path, the transition method will significantly decrease the machining efficiency and introduce feedrate fluctuation. The global fitting method cannot be directly used in the NC interpolation because the indispensable chord error checking and iterative fitting processes are computation-intensive. This paper presents a general, fast and robust B-spline fitting scheme under chord error constraint for high speed interpolation of micro-line tool path. The proposed fitting method guarantees the chord error by utilizing the strong convex hull property of B-spline curves. The knot vector and control points are initially generated by a progressive iterative approximation method and locally refined to conform to the chord error constraint by using an analytical method. The analytical approximation and refining methods avoid solving a linear system of equations that is necessary in the standard B-spline fitting method. The feasibility and efficiency of the proposed scheme has been verified via simulations and experiments. Compared with the traditional fitting method, the proposed scheme can strictly constrain the chord error and can significantly decrease the computational load. Compared with the transition scheme, the proposed scheme can significantly increase the machining efficiency for the same micro-line tool path under the same chord error tolerance.展开更多
A T-mesh is basically a rectangular grid that allows T-junctions. Recently, Deng etal introduced splines over T-meshes, which are generalizations of T-splines invented by Sederberg etal, and proposed a dimension formu...A T-mesh is basically a rectangular grid that allows T-junctions. Recently, Deng etal introduced splines over T-meshes, which are generalizations of T-splines invented by Sederberg etal, and proposed a dimension formula based on the B-net method. In this paper, we derive an equivalent dimension formula in a different form with the smoothing cofactor method.展开更多
The Hengduan Mountains Region(HMR) is essential for the future ecological protection, clean energy production,Sichuan-Xizang and Yunnan-Xizang railways, and other major infrastructure projects in China. The distributi...The Hengduan Mountains Region(HMR) is essential for the future ecological protection, clean energy production,Sichuan-Xizang and Yunnan-Xizang railways, and other major infrastructure projects in China. The distributions of climate and vegetation exhibit significant regional differentiation and vertical zonality due to the rugged longitudinal ranges and gorges and the complex disaster-prone environments in HMR. Therefore, it is urgent to develop the climate-vegetation regionalization in HMR to effectively satisfy the national requirements such as agricultural production and ecological protection, mountain disaster risk prevention, and major project construction. We here develop a new scheme of climate-vegetation regionalization with the latest demarcation outcome of HMR, the ground observation from 122 meteorological stations in HMR and its surrounding areas during 1990–2019, and the high-precision remote sensing data of land cover types. The new scheme first constructs the regionalization index system, fully considering the extraordinarily complicated geomorphic pattern of mountains and valleys, the scarcity of meteorological observations, and the remarkable differentiation of climate and vegetation in HMR. The system consists of three primary regionalization indices(i.e., days with daily average temperature steady above 10°C, aridity index, and main vegetation types, dividing the temperature zones, moisture regions, and vegetation subregions, respectively) and three auxiliary indices of the accumulated temperature above 10°C, and the temperatures in January and July. Then, the HMR is divided into five temperature zones, 20 moisture regions, and 55 vegetation subregions. Compared with previous regionalization schemes, the new scheme optimizes the climate spatial interpolation model of thin plate smoothing spline suitable for the unique terrain in HMR. Moreover, the disputed division index threshold between different climatic zones(regions) is scientifically clarified using geographical detectors. Specificall展开更多
Smooth transitions between two adjacent five-axis toolpaths can reduce feedrate fluctuation,improving machining quality and efficiency.Hybrid robots’flexibility to adjust the orientation is advantageous in five-axis ...Smooth transitions between two adjacent five-axis toolpaths can reduce feedrate fluctuation,improving machining quality and efficiency.Hybrid robots’flexibility to adjust the orientation is advantageous in five-axis machining,but their kinematic issues raise challenges for toolpath smoothing.This paper proposes a G3continuous toolpath smoothing method for a hybrid robot.B-splines in the machine coordinate system(MCS)are inserted at corners to synchronize five-axis transitions.The transition errors of the tool position and orientation paths are estimated with the golden section method.These approximation errors are constrained by adaptively modifying the B-splines,i.e.,adding anchor points and optimizing the control points.A bisection search method is proposed for these geometric modifications,guaranteeing the user-defined error tolerance limit.Compared to the method based on the workpiece coordinate system(WCS),the proposed framework generates a smoother trajectory under the same error tolerance limit.Simulations and experiments are provided to validate the effectiveness.展开更多
The T-meshes are local modification of rectangular meshes which allow T-junctions. The splines over T-meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a ...The T-meshes are local modification of rectangular meshes which allow T-junctions. The splines over T-meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a basic problem for the theories and applications of splines. However, the problem of determining the dimension of a spline space is difficult since it heavily depends on the geometric properties of the partition. In many cases, the dimension is unstable. In this paper, we study the instability in the dimensions of spline spaces over T-meshes by using the smoothing cofactor-conformality method. The modified dimension formulas of spline spaces over T-meshes with T-cycles are also presented. Moreover, some examples are given to illustrate the instability in the dimensions of the spline spaces over some special meshes.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.51475302,U1537209)the Shanghai Municipal Scienceand Technology Commission(Grant No.17XD1422500)
文摘The discontinuity of linear tool path(or G01 blocks) brings about unnecessary feedrate deceleration and fluctuation during machining. To improve the continuity, the linear tool path is usually smoothed by the local transition method or the global fitting method. For micro-line tool path, the transition method will significantly decrease the machining efficiency and introduce feedrate fluctuation. The global fitting method cannot be directly used in the NC interpolation because the indispensable chord error checking and iterative fitting processes are computation-intensive. This paper presents a general, fast and robust B-spline fitting scheme under chord error constraint for high speed interpolation of micro-line tool path. The proposed fitting method guarantees the chord error by utilizing the strong convex hull property of B-spline curves. The knot vector and control points are initially generated by a progressive iterative approximation method and locally refined to conform to the chord error constraint by using an analytical method. The analytical approximation and refining methods avoid solving a linear system of equations that is necessary in the standard B-spline fitting method. The feasibility and efficiency of the proposed scheme has been verified via simulations and experiments. Compared with the traditional fitting method, the proposed scheme can strictly constrain the chord error and can significantly decrease the computational load. Compared with the transition scheme, the proposed scheme can significantly increase the machining efficiency for the same micro-line tool path under the same chord error tolerance.
文摘A T-mesh is basically a rectangular grid that allows T-junctions. Recently, Deng etal introduced splines over T-meshes, which are generalizations of T-splines invented by Sederberg etal, and proposed a dimension formula based on the B-net method. In this paper, we derive an equivalent dimension formula in a different form with the smoothing cofactor method.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDA23090302)the Second Tibetan Plateau Scientific Expedition and Research Program(STEP)(Grant No.2019QZKK0903)。
文摘The Hengduan Mountains Region(HMR) is essential for the future ecological protection, clean energy production,Sichuan-Xizang and Yunnan-Xizang railways, and other major infrastructure projects in China. The distributions of climate and vegetation exhibit significant regional differentiation and vertical zonality due to the rugged longitudinal ranges and gorges and the complex disaster-prone environments in HMR. Therefore, it is urgent to develop the climate-vegetation regionalization in HMR to effectively satisfy the national requirements such as agricultural production and ecological protection, mountain disaster risk prevention, and major project construction. We here develop a new scheme of climate-vegetation regionalization with the latest demarcation outcome of HMR, the ground observation from 122 meteorological stations in HMR and its surrounding areas during 1990–2019, and the high-precision remote sensing data of land cover types. The new scheme first constructs the regionalization index system, fully considering the extraordinarily complicated geomorphic pattern of mountains and valleys, the scarcity of meteorological observations, and the remarkable differentiation of climate and vegetation in HMR. The system consists of three primary regionalization indices(i.e., days with daily average temperature steady above 10°C, aridity index, and main vegetation types, dividing the temperature zones, moisture regions, and vegetation subregions, respectively) and three auxiliary indices of the accumulated temperature above 10°C, and the temperatures in January and July. Then, the HMR is divided into five temperature zones, 20 moisture regions, and 55 vegetation subregions. Compared with previous regionalization schemes, the new scheme optimizes the climate spatial interpolation model of thin plate smoothing spline suitable for the unique terrain in HMR. Moreover, the disputed division index threshold between different climatic zones(regions) is scientifically clarified using geographical detectors. Specificall
基金supported by the National Natural Science Foundation of China(Grant Nos.51935010 and 52275501)。
文摘Smooth transitions between two adjacent five-axis toolpaths can reduce feedrate fluctuation,improving machining quality and efficiency.Hybrid robots’flexibility to adjust the orientation is advantageous in five-axis machining,but their kinematic issues raise challenges for toolpath smoothing.This paper proposes a G3continuous toolpath smoothing method for a hybrid robot.B-splines in the machine coordinate system(MCS)are inserted at corners to synchronize five-axis transitions.The transition errors of the tool position and orientation paths are estimated with the golden section method.These approximation errors are constrained by adaptively modifying the B-splines,i.e.,adding anchor points and optimizing the control points.A bisection search method is proposed for these geometric modifications,guaranteeing the user-defined error tolerance limit.Compared to the method based on the workpiece coordinate system(WCS),the proposed framework generates a smoother trajectory under the same error tolerance limit.Simulations and experiments are provided to validate the effectiveness.
基金Acknowledgments. This work is partly supported by the National Natural Science Foundation of China （Nos. 11290143, Ul135003, 11471066, 11271060, 11301052）, Fundamental Research of Civil Aircraft （No. MJ-F-2012-04）, and the Fundamental Research Funds for the Central Universities （Nos. DUT13LK07, DUT13LK45, DUT14YQ111）.
文摘The T-meshes are local modification of rectangular meshes which allow T-junctions. The splines over T-meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a basic problem for the theories and applications of splines. However, the problem of determining the dimension of a spline space is difficult since it heavily depends on the geometric properties of the partition. In many cases, the dimension is unstable. In this paper, we study the instability in the dimensions of spline spaces over T-meshes by using the smoothing cofactor-conformality method. The modified dimension formulas of spline spaces over T-meshes with T-cycles are also presented. Moreover, some examples are given to illustrate the instability in the dimensions of the spline spaces over some special meshes.
