In this paper, the extremal problem, min, of two convex bodies K and L in ?n is considered. For K to be in extremal position in terms of a decomposition of the identity, give necessary conditions together with the opt...In this paper, the extremal problem, min, of two convex bodies K and L in ?n is considered. For K to be in extremal position in terms of a decomposition of the identity, give necessary conditions together with the optimization theorem of John. Besides, we also consider the weaker optimization problem: min. As an application, we give the geometric distance between the unit ball B2n and a centrally symmetric convex body K.展开更多
特高压直流GIL运行可靠性取决于内绝缘设计的可靠性。此外,导电元件直流电流密度的取值、弹簧触头的定位设计、GIL各元件中的绝缘件与金具连接处的楔形气隙的处理以及母线中支撑件的结构设计细节,都会对产品运行可靠性产生重大影响,不...特高压直流GIL运行可靠性取决于内绝缘设计的可靠性。此外,导电元件直流电流密度的取值、弹簧触头的定位设计、GIL各元件中的绝缘件与金具连接处的楔形气隙的处理以及母线中支撑件的结构设计细节,都会对产品运行可靠性产生重大影响,不能忽视。对于运行环境十分严酷的UHV DC GIL为保证内绝缘工作可靠性和减少气体维护工作量,文中还提出了高气密性结构设计。为适应-50℃低温运行要求,产品选用了液化温度很低的N_(2)/SF_(6)混合气体,对两种气体的配比,压力特性和绝缘特性进行了讨论与计算。还有产品的局放、气体密度及微水含量的监视系统的可靠性设计,都会对产品运行可靠性产生直接影响。文中对上述问题的研究成果作了介绍,可供高压直流产品设计使用。对其中未解的新技术如基于冷镜露点测试原理、微机电技术制作的智能气体湿度和密度监测装置、高压直流复合绝缘套管伞面局放起始场强提出了研究方案。文中提出的诸多GIL运行可靠性设计要点,对于其他超/特高压直流气体绝缘电器可参考选用。展开更多
A precise aperture measuring system of small deep holes with capacitance sensors is presented. Based on the working principle of non-contact capacitance sensors, influence of the edge effect of gauge head is studied, ...A precise aperture measuring system of small deep holes with capacitance sensors is presented. Based on the working principle of non-contact capacitance sensors, influence of the edge effect of gauge head is studied, and one capacitance sensor for measuring the aperture of the small blind holes or through holes is introduced. The system is composed of one positioning device, one aperture measuring capacitance sensor, one measuring circuit, and software. This system employs visual CCD and two-dimensional micro-adjusting mechanism to realize the precise positioning. By LabView software this system is controlled to run automatically, to carry out calibration and automatic data collection, and to make data import into the database directly. Experiments proved that the diameter measurement range of the system can be 1.8 mm—7 mm, the resolution can be up to 5 nm—10 nm, the repeatability measurement standard deviation can be 0.05 μm—0.1 μm, and the measurement uncertainty can achieve 0.15 μm—0.3 μm. So the measuring system can realize the nanometer-level measurement.展开更多
Based on the mathematical model describing the third-order approximation of the cutter envelope surface according to one given cutter location(CL),a tool positioning strategy is proposed for efficiently machining free...Based on the mathematical model describing the third-order approximation of the cutter envelope surface according to one given cutter location(CL),a tool positioning strategy is proposed for efficiently machining free-form surfaces with non-ball-end cutters.The optimal CL is obtained by adjusting the inclination and tilt angles of the cutter until its envelope surface and the design surface have the third-order contact at the cutter contact(CC)point,which results in a wide machining strip.The strategy can handle the constraints of machine joint angle limits,global collision avoidance and tool path smoothness in a nature way,and can be applied to general rotary cutters and complex surfaces.Numerical examples demonstrate that the third-order point contact approach can improve the machining strip width greatly as compared with the recently reported second-order one.展开更多
The planetary roller screw mechanism(PRSM)is a novel precision transmission mechanism that realizes the conversion between linear and rotary motions.The contact characteristics of helical surfaces directly determine P...The planetary roller screw mechanism(PRSM)is a novel precision transmission mechanism that realizes the conversion between linear and rotary motions.The contact characteristics of helical surfaces directly determine PRSM’s performance in load-carrying capacity and transmission accuracy.Therefore,studying the contact characteristics of PRSM forms the fundamental basis for enhancing its transmission performance.In this study,a three-dimensional parametric analysis method of contact characteristics is proposed based on the PRSM meshing principle and PyVista(a high-level API to the Visualization Toolkit).The proposed method considers the influence of machining errors among various thread teeth.The effects of key machining errors on contact positions and axial clearance,as well as their sensitivities,are analyzed.With excellent solution accuracy,this method exhibits higher calculation efficiency and stronger robustness than the analytical and numerical meshing models.The influence of nominal diameter and pitch errors of the screw,roller,and nut on the axial clearance follows a linear relationship,whereas flank angle errors have negligible effects on the axial clearance.The corresponding influence coefficients for these three machining errors on the axial clearance are 0.623,0.341,and 0.036.The variations in contact positions caused by individual errors are axisymmetric.Flank angle errors and roller diameter errors result in linear displacements of the contact points,whereas pitch errors cause the contact points to move along the arc of the roller diameter.Based on the proposed threedimensional parametric contact characteristics analysis method,the Fuzzy C-Means clustering algorithm considering error sensitivity is utilized to establish a component grouping technique in the selective assembly of critical PRSM components,ensuring the rational and consistent clearances based on the given component’s machining errors.This study provides effective guidance for analyzing contact characteristics and grouping in selective assembly for PRSM components.It also presents the proposed method’s potential applicability to similar calculation problems for contact positions and clearances in other transmission systems.展开更多
文摘In this paper, the extremal problem, min, of two convex bodies K and L in ?n is considered. For K to be in extremal position in terms of a decomposition of the identity, give necessary conditions together with the optimization theorem of John. Besides, we also consider the weaker optimization problem: min. As an application, we give the geometric distance between the unit ball B2n and a centrally symmetric convex body K.
文摘特高压直流GIL运行可靠性取决于内绝缘设计的可靠性。此外,导电元件直流电流密度的取值、弹簧触头的定位设计、GIL各元件中的绝缘件与金具连接处的楔形气隙的处理以及母线中支撑件的结构设计细节,都会对产品运行可靠性产生重大影响,不能忽视。对于运行环境十分严酷的UHV DC GIL为保证内绝缘工作可靠性和减少气体维护工作量,文中还提出了高气密性结构设计。为适应-50℃低温运行要求,产品选用了液化温度很低的N_(2)/SF_(6)混合气体,对两种气体的配比,压力特性和绝缘特性进行了讨论与计算。还有产品的局放、气体密度及微水含量的监视系统的可靠性设计,都会对产品运行可靠性产生直接影响。文中对上述问题的研究成果作了介绍,可供高压直流产品设计使用。对其中未解的新技术如基于冷镜露点测试原理、微机电技术制作的智能气体湿度和密度监测装置、高压直流复合绝缘套管伞面局放起始场强提出了研究方案。文中提出的诸多GIL运行可靠性设计要点,对于其他超/特高压直流气体绝缘电器可参考选用。
文摘A precise aperture measuring system of small deep holes with capacitance sensors is presented. Based on the working principle of non-contact capacitance sensors, influence of the edge effect of gauge head is studied, and one capacitance sensor for measuring the aperture of the small blind holes or through holes is introduced. The system is composed of one positioning device, one aperture measuring capacitance sensor, one measuring circuit, and software. This system employs visual CCD and two-dimensional micro-adjusting mechanism to realize the precise positioning. By LabView software this system is controlled to run automatically, to carry out calibration and automatic data collection, and to make data import into the database directly. Experiments proved that the diameter measurement range of the system can be 1.8 mm—7 mm, the resolution can be up to 5 nm—10 nm, the repeatability measurement standard deviation can be 0.05 μm—0.1 μm, and the measurement uncertainty can achieve 0.15 μm—0.3 μm. So the measuring system can realize the nanometer-level measurement.
基金supported by the National Natural Science Foundation of China(Grant Nos.50835004,50775147)the National Basic Research Program of China("973"Program)(Grant No.2005CB724103)the Science&Technology Commission of Shanghai Municipality(Grant No.07JC14028)
文摘Based on the mathematical model describing the third-order approximation of the cutter envelope surface according to one given cutter location(CL),a tool positioning strategy is proposed for efficiently machining free-form surfaces with non-ball-end cutters.The optimal CL is obtained by adjusting the inclination and tilt angles of the cutter until its envelope surface and the design surface have the third-order contact at the cutter contact(CC)point,which results in a wide machining strip.The strategy can handle the constraints of machine joint angle limits,global collision avoidance and tool path smoothness in a nature way,and can be applied to general rotary cutters and complex surfaces.Numerical examples demonstrate that the third-order point contact approach can improve the machining strip width greatly as compared with the recently reported second-order one.
基金supported by the National Key R&D Program of China(Grant No.2023YFB3406404).
文摘The planetary roller screw mechanism(PRSM)is a novel precision transmission mechanism that realizes the conversion between linear and rotary motions.The contact characteristics of helical surfaces directly determine PRSM’s performance in load-carrying capacity and transmission accuracy.Therefore,studying the contact characteristics of PRSM forms the fundamental basis for enhancing its transmission performance.In this study,a three-dimensional parametric analysis method of contact characteristics is proposed based on the PRSM meshing principle and PyVista(a high-level API to the Visualization Toolkit).The proposed method considers the influence of machining errors among various thread teeth.The effects of key machining errors on contact positions and axial clearance,as well as their sensitivities,are analyzed.With excellent solution accuracy,this method exhibits higher calculation efficiency and stronger robustness than the analytical and numerical meshing models.The influence of nominal diameter and pitch errors of the screw,roller,and nut on the axial clearance follows a linear relationship,whereas flank angle errors have negligible effects on the axial clearance.The corresponding influence coefficients for these three machining errors on the axial clearance are 0.623,0.341,and 0.036.The variations in contact positions caused by individual errors are axisymmetric.Flank angle errors and roller diameter errors result in linear displacements of the contact points,whereas pitch errors cause the contact points to move along the arc of the roller diameter.Based on the proposed threedimensional parametric contact characteristics analysis method,the Fuzzy C-Means clustering algorithm considering error sensitivity is utilized to establish a component grouping technique in the selective assembly of critical PRSM components,ensuring the rational and consistent clearances based on the given component’s machining errors.This study provides effective guidance for analyzing contact characteristics and grouping in selective assembly for PRSM components.It also presents the proposed method’s potential applicability to similar calculation problems for contact positions and clearances in other transmission systems.
