In this paper, the positional error curve of point features was extended to an error curves band of line segment features. Firstly, the constitution and shape of the error curves band were analyzed. On this basis, the...In this paper, the positional error curve of point features was extended to an error curves band of line segment features. Firstly, the constitution and shape of the error curves band were analyzed. On this basis, the general boundary curve formula of that band was derived. Secondly, the visualizing error curves bands were realized through three exam- ples. Finally,area index has been examined by comparing numerical results from error curves band and error ellipes band.展开更多
Positional error of line segments is usually described by using "g-band", however, its band width is in relation to the confidence level choice. In fact, given different confidence levels, a series of concen...Positional error of line segments is usually described by using "g-band", however, its band width is in relation to the confidence level choice. In fact, given different confidence levels, a series of concentric bands can be obtained. To overcome the effect of confidence level on the error indicator, by introducing the union entropy theory, we propose an entropy error ellipse index of point, then extend it to line segment and polygon, and establish an entropy error band of line segment and an entropy error donut of polygon. The research shows that the entropy error index can be determined uniquely and is not influenced by confidence level, and that they are suitable for positional uncertainty of planar geometry features.展开更多
The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for ...The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for truncation error of bandlimited functions in the n dimensional Lebesgue space Lp(Rn) associated with multidimensional Shannon sampling representation.展开更多
为实现高效率、低成本的镍磷合金光学元件全频段误差抑制,提出了小磨头抛光中基于宏观耕犁机制和微观化学键拔除机制的宏微观协同作用去除机理。基于赫兹接触理论,通过工件表面的弹塑性形变探讨耕犁机制产生的临界值,构建了磨粒作用机...为实现高效率、低成本的镍磷合金光学元件全频段误差抑制,提出了小磨头抛光中基于宏观耕犁机制和微观化学键拔除机制的宏微观协同作用去除机理。基于赫兹接触理论,通过工件表面的弹塑性形变探讨耕犁机制产生的临界值,构建了磨粒作用机制与工艺参数之间的关联模型——小磨头抛光磨头极限压力模型,实现了对宏微观去除机制的调控,从而达成全频段误差的有效抑制。随后通过第一性原理分子动力学仿真分析,探究了抛光过程中磨粒分子团簇与镍磷合金光学元件表层分子的相互作用,直观表征了镍磷合金抛光过程中的微观化学键拔除机制,该仿真分析对镍磷合金光学元件超光滑抛光具有指导意义。基于宏微观协同作用去除机理对φ50的铝基镀镍磷合金平面反射镜进行小磨头迭代抛光实验,在有效抑制中低频误差的同时,将表面粗糙度R a从2.252 n m提升到0.502 nm,提升了77.7%,实现了镍磷合金反射镜超光滑表面全频段误差的抑制。实验结果表明,宏微观协同作用去除机理适用于镍磷合金光学元件的全频段误差抑制,对于镍磷合金光学元件超精密加工提供了借鉴意义。展开更多
基金Project Supported by the National Natural Science Foundation of China (No.49801016 and 49671063)
文摘In this paper, the positional error curve of point features was extended to an error curves band of line segment features. Firstly, the constitution and shape of the error curves band were analyzed. On this basis, the general boundary curve formula of that band was derived. Secondly, the visualizing error curves bands were realized through three exam- ples. Finally,area index has been examined by comparing numerical results from error curves band and error ellipes band.
基金ProjectsupportedbytheNationalNaturalScienceFoundationofChina (No .40 0 71 0 68) .
文摘Positional error of line segments is usually described by using "g-band", however, its band width is in relation to the confidence level choice. In fact, given different confidence levels, a series of concentric bands can be obtained. To overcome the effect of confidence level on the error indicator, by introducing the union entropy theory, we propose an entropy error ellipse index of point, then extend it to line segment and polygon, and establish an entropy error band of line segment and an entropy error donut of polygon. The research shows that the entropy error index can be determined uniquely and is not influenced by confidence level, and that they are suitable for positional uncertainty of planar geometry features.
基金Projcct supported by the Natural Science Foundation of China (Grant No. 10371009 ) of Beijing Educational Committee (No. 2002KJ112).
文摘The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for truncation error of bandlimited functions in the n dimensional Lebesgue space Lp(Rn) associated with multidimensional Shannon sampling representation.
文摘为实现高效率、低成本的镍磷合金光学元件全频段误差抑制,提出了小磨头抛光中基于宏观耕犁机制和微观化学键拔除机制的宏微观协同作用去除机理。基于赫兹接触理论,通过工件表面的弹塑性形变探讨耕犁机制产生的临界值,构建了磨粒作用机制与工艺参数之间的关联模型——小磨头抛光磨头极限压力模型,实现了对宏微观去除机制的调控,从而达成全频段误差的有效抑制。随后通过第一性原理分子动力学仿真分析,探究了抛光过程中磨粒分子团簇与镍磷合金光学元件表层分子的相互作用,直观表征了镍磷合金抛光过程中的微观化学键拔除机制,该仿真分析对镍磷合金光学元件超光滑抛光具有指导意义。基于宏微观协同作用去除机理对φ50的铝基镀镍磷合金平面反射镜进行小磨头迭代抛光实验,在有效抑制中低频误差的同时,将表面粗糙度R a从2.252 n m提升到0.502 nm,提升了77.7%,实现了镍磷合金反射镜超光滑表面全频段误差的抑制。实验结果表明,宏微观协同作用去除机理适用于镍磷合金光学元件的全频段误差抑制,对于镍磷合金光学元件超精密加工提供了借鉴意义。
