小问题

<正>2019-5如图1所示,两个小球构成3自由度的机构,铰链O可以绕竖直轴z轴自由转动,直角弯杆与铰链铰接,可绕过O点的x轴自由转动,小球A固定在弯杆的末端,小球B由直杆约束绕O′A轴自由转动。铰链的质量和尺寸均忽略不计,各杆均为轻杆,直杆和直角弯杆两段的长度均为a,两小球质量均为m。     

《小问题》2019-5解答

正问题:如图1所示,两个小球构成3自由度的机构,铰链O可以绕竖直轴z轴自由转动,直角弯杆与铰链铰接,可绕过O点的x轴自由转动,小球A固定在弯杆的末端,小球B由直杆约束绕O′A轴自由转动。铰链的质量和尺寸均忽略不计,各杆均为轻杆,直杆和直角弯杆两段的长度均为a,两小球质量均为m。(1)在图1所示位置,小球A的坐标为(0, a,-a),小球B的坐标为(a, a,-a),求系统由静止释放时,施     

线振动硅微机械陀螺结构误差参数分离和辨识

推导了线振动微机械陀螺的三自由度误差力学方程,并详细分析了陀螺耦合误差的产生机理。分析结果表明,各种结构误差是导致陀螺耦合误差信号的主要原因。在此基础上,利用振动和模态理论给出了陀螺结构误差参数的分离和辨识的试验方法和结果。试验结果表明,同相耦合分量和正交耦合分量是微机械陀螺的两种主要误差信号,造成正交耦合的主要原因是驱动轴和检测轴之间的刚度耦合以及驱动轴和检测轴各自的刚度不对称,造成同相耦合的主要原因是驱动轴和检测轴之间的阻尼耦合以及检测轴刚度不对称和驱动力不对称。结构误差参数的分离和辨识试验方法将为下一步的陀螺结构优化、微加工工艺改进以及耦合误差抑制提供基础。     

圆钢管K型弯管锥头节点轴向刚度曲线参数化分析

K型弯管锥头节点核心区由节点管、空心切头锥两部分组成。本文采用ANSYS参数化分析了节点管外径及其壁厚、弦管外径及其壁厚、腹管外径及其壁厚、腹管轴线与节点管轴线夹角?、屋面坡度i、弦管轴力与其屈服荷载的比值σz/fy对节点轴向刚度的影响。分析表明:减小弦管1与节点管外径之比、增加腹管的壁厚会降低节点的轴向刚度,屋面坡度对节点轴向刚度的影响不大,腹管受拉的节点轴向刚度优于腹管受压的节点轴向刚度;弦管承受轴拉力的节点轴向刚度优于弦管承受轴压力的。引入两个量纲归一化参数,即节点轴向刚度因子η和节点轴力因子ω,根据有限元计算的η-ω曲线,通过多元线性回归拟合了η-ω曲线的计算公式,该计算公式为钢管结构的分析及设计提供了节点刚度计算模型。     

基于因子克里金分析方法的航空重力梯度降噪

针对航空重力梯度测量数据降噪处理中,传统低通滤波器存在需要选择最优滤波参数和对原始数据网格化的问题,提出应用地质统计学中的克里金分析方法进行重力梯度测量数据降噪。首先对重力梯度这一区域化变量进行结构分析,确定其变异函数是否具有各向同性的性质。接着采用加权最小二乘法对各向同性的变异函数套合拟合,分解出不同参数的变异函数。最后利用因子克里金方程组将不同参数的变异函数转换成不同尺度的因子,从而实现重力梯度的多尺度分析,进而达到降噪的目的。模拟数据试验表明,因子克里金降噪法非常适用于地质特征明显区域的梯度场降噪,相对于传统的低通滤波器,重力梯度各分量精度平均提升了36%,而垂直梯度分量尤为显著达到了42%。降噪后的实测航空重力梯度也呈现出明显的地质走向特征。     

反作用轮扰动特性测量及研究

反作用轮微振动是影响卫星姿态控制精度的重要因素.测量反作用轮扰动的目的是掌握其扰动规律,进而采取相应的控制方法和隔离技术.考虑到反作用轮的扰动与安装条件有关,使用"刚性六分量测试平台"和"柔性六分量测试平台"两种方法进行反作用轮扰动特性测量,并从三个方面对两种方法得到的结果进行比较.比较结果表明,不同测试条件下得到的谐波数是相同的;安装结构刚度降低会降低反作用轮的固有频率;柔性安装条件的减振作用会降低扰动峰值.试验结果可以为探讨卫星结构动态特性对扰动力的影响提供经验和指导.     

基于正则化等效源模型的航空重力梯度测量信息降噪方法

航空重力梯度测量能获取重力梯度的多个分量,在保证各梯度分量内部固有约束条件下降低测量噪声,是一个巨大的挑战。为提高航空重力梯度测量精度,提出一种基于正则化等效源模型的测量降噪方法。根据矩形棱柱体与重力梯度之间的关系构建了等效源线性方程组,针对该方程组可能存在病态性的问题,引入截断奇异值TSVD和Tikhonov正则化的方法,对等效源模型进行正则化改造。模拟试验表明,正则化方法能够有效抑制病态系数矩阵小奇异值放大噪声对未知参数的污染,提高反演的精度和稳定性,其中基于L曲线确定正则化参数的截断奇异值TSVD法精度较高。实测数据表明,利用正则化等效源滤波转换的垂直梯度与利用傅里叶变换转换的结果吻合。可见,正则化等效源是重力场滤波和分量转换的有效工具。     

旋转加速度计重力梯度仪加速度计标度因数实时反馈调整方法

旋转加速度计重力梯度仪在实际工作过程中,由于平台稳定性、旋转机构控制精度、敏感器安装误差、加速度计标度因数匹配性以及其他噪声源的存在,对高精度重力梯度测量构成严峻挑战。在诸多影响因素中,加速度计标度因数的不一致性对测量精度影响最大。本文提出一种旋转加速度计重力梯度仪加速度计标度因数实时反馈调整方法,旨在提高获取重力梯度信号的能力。该方法首先对相对两只加速度计的和输出信号以及重力梯度仪总输出信号分别进行带通滤波,然后对滤波器输出信号中含有加速度计标度因数不平衡信息信号进行幅值解调,对三组解调结果分别进行平滑处理,采用模糊PID控制算法实时反馈调整加速度计内部的电磁线圈力矩,达到调整加速度计标度因数的目的。实验测试分析表明,采用模糊PID反馈调整算法可以快速实现四只加速度计标度因数一致,相对两只加速度计标度因数调整量级可以达到10?7,两对加速度计标度因数的调整量级可以达到10?5,提高了获取重力梯度信息的能力。     

柔性套管约束下轴心受压杆件的屈曲分析

针对柔性套管约束杆件,研究了轴压杆件与约束杆件点、线接触时的约束屈曲．在小挠度变形假设下,根据轴压杆件与约束杆件满足变形协调条件的二阶平衡微分方程,推导了轴压杆件挠度、轴向位移、接触反力的计算公式,并且由轴向压力唯一确定了线接触的长度．算例分析表明：当约束杆件刚度较小时,轴压杆件弯曲产生的轴向位移较大；当约束杆件刚度较大时,轴压杆件弯曲产生的轴向位移较小,该轴向位移与文献中的大挠度解吻合很好,从而得出小挠度变形假设是合理的．     

并联机器人刚度与静力学研究现状与进展

并联机器人的刚度与静力学分析, 对于机构力学性能研究具有重要的理论价值和意义. 本文围绕杆支撑、绳牵引和钢带传动 3 种结构形式, 详细阐述了国内外并联机构刚度和静力学分析的研究现状. 着重从有限元、解析模型和性能分析 3 方面分析了杆支撑并联机构的刚度研究进展. 讨论了有关绳牵引并联机构中绳拉力、动载荷频率、绳牵引预紧力与刚度、静力学之间关系的研究成果. 根据钢带并联机器人结构的特殊性, 对钢带并联机构的刚度与静力学分析中可能遇到的失稳与振动问题进行了探讨. 最后, 对并联机器人技术发展情况进行总结与展望, 指出随着刚度分析与静力学分析的不断深入, 并联机器人的力学理论将会日趋成熟和完善, 为并联机器人机构优化设计提供更深入、系统的理论依据.      

Design and analysis of a novel 6-DOF redundant actuated parallel robot with compliant hinges for high precision positioning

This paper presents the design and modeling of a new 6-DOF 8-PSS/SPS compliant dual redundant parallel robot with wide-range flexure hinges. This robot can achieve either high accurate positioning or rough positioning as well as a 6-DOF active vibration isolation and excitation to the payload placed on the moving platform. Adopting a kind of wide-range flexure hinge, we establish the kinematics model of the macro parallel mechanism system via the stiffness model and Newton–Raphson method, then we build up the dynamics model using Kane’s method for the micro-motion system. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for a novel compliant dual redundant parallel mechanism in order to achieve the feature of larger workspace, higher motion precision and better dynamic characteristics. The results will be helpful in modifying the structure of the prototype platform to enhance its high kinematics and dynamics properties.     

超导量子干涉仪及其在超导陀螺中的应用

介绍了约瑟夫逊结原理及其制作方法，在此基础上对超导量子干涉仪测量磁场的基本原理作了阐述，同时就其在超导陀螺仪中的实际应用方面作了实例说明。结果表明这种仪器测量弱磁场的精度很高，技术也已成熟。     

旋转式重力梯度测量系统试验及数据处理

旋转式重力梯度测量系统采用旋转调制方式求取重力梯度信息。首先,从旋转加速度计的基本原理出发,给出了重力梯度测量系统的主要工作模式;其次,构建了旋转加速度计重力梯度测量系统组成和主要功能模块,提出了采用引力产生装置开展实验室引力梯度测量的试验方案;最后,给出了旋转加速度计重力梯度测量系统的静态梯度试验验证基本条件、试验设备,并开展了重力梯度测量试验。试验结果表明,旋转式重力梯度测量系统在实验室条件下完成引力梯度试验,该系统可以检测优于200 Eu(1 Eu=10~(-9)/s~2)的引力梯度,该系统开展的试验验证为动态重力梯度仪的研制奠定了基础。     

Three-dimensional temporally resolved measurements of turbulence–flame interactions using orthogonal-plane cinema-stereoscopic PIV

A new orthogonal-plane cinema-stereoscopic particle image velocimetry (OPCS-PIV) diagnostic has been used to measure the dynamics of three-dimensional turbulence–flame interactions. The diagnostic employed two orthogonal PIV planes, with one aligned perpendicular and one aligned parallel to the streamwise flow direction. In the plane normal to the flow, temporally resolved slices of the nine-component velocity gradient tensor were determined using Taylor’s hypothesis. Volumetric reconstruction of the 3D turbulence was performed using these slices. The PIV plane parallel to the streamwise flow direction was then used to measure the evolution of the turbulence; the path and strength of 3D turbulent structures as they interacted with the flame were determined from their image in this second plane. Structures of both vorticity and strain-rate magnitude were extracted from the flow. The geometry of these structures agreed well with predictions from direct numerical simulations. The interaction of turbulent structures with the flame also was observed. In three dimensions, these interactions had complex geometries that could not be reflected in either planar measurements or simple flame–vortex configurations.     

Some general properties of Eshelby’s tensor fields in transport phenomena and anti-plane elasticity

Consider an infinite thermally conductive medium characterized by Fourier’s law, in which a subdomain, called an inclusion, is subjected to a prescribed uniform heat flux-free temperature gradient. The second-order tensor field relating the gradient of the resulting temperature field over the medium to the uniform heat flux-free temperature gradient is referred to as Eshelby’s tensor field for conduction. The present work aims at deriving the general properties of Eshelby’s tensor field for conduction. It is found that: (i) the trace of Eshelby’s tensor field is equal to the characteristic function of the inclusion, independently of the latter’s shape; (ii) the isotropic part of Eshelby’s tensor field over the inclusion of arbitrary shape is identical to Eshelby’s tensor field over a 2D circular or 3D spherical inclusion; (iii) when the medium is made of an isotropic material and when the inclusion has some specific rotational symmetries, the value of the Eshelby’s tensor field evaluated at the inclusion gravity center and the symmetric average of Eshelby’s tensor fields are both equal to Eshelby’s tensor field for a 2D circular or 3D spherical inclusion. These results are then extended, with the help of a linear transformation, to the general case where the medium consists of an anisotropic conductive material. The method elaborated and results obtained by the present work are directly transposable to the physically analogous transport phenomena of electric conduction, dielectrics, magnetism, diffusion and flow in porous media and to the mathematically identical phenomenon of anti-plane elasticity.     

Corrigendum: incompatible deformation field and Riemann curvature tensor

The "Corollary 1" formulation in SUN, B. H. Incompatible deformation field and Riemann curvature tensor. Applied Mathematics and Mechanics (English Edition),38(3), 311-332 (2017) is corrected. It can be stated as follows:The symmetric part of the deformation gradient has no contribution to the trace of the displacement density tensor.     

Development of a Lap Joint Fretting Apparatus

An experimental apparatus designed specifically for fretting experiments on mechanical lap joints is presented. A piezoactuator is used to impose fretting motion, and a tri-axial load cell is used to measure tangential force as well as possible misalignment forces. A laser nanosensor is employed to measure the relative motion between the joint halves. No post-processing and filtering of the data is needed to obtain the fretting response using this apparatus. Instead, raw data obtained from experiments with monolithic and 1-bolt aluminum and steel joints under various loading conditions suggest that noise, misalignment, stiffness and damping associated with the apparatus are minimal, and thus the fretting behavior of the mechanical lap joints is accurately captured. Analyses of typical fretting loops obtained by the proposed apparatus suggest that normal preload and maximum tangential displacement influence the critical joint parameters of stiffness and damping. Aluminum joints show a more compliant behavior with more energy dissipation compared to steel joints.     

Compatibility conditions and equations of motion in the linear micropolar theory of elasticity

An analog of Cesàro’s formula and several compatibility conditions are given for the three-dimensional and two-dimensional linear micropolar theory of elasticity in the form different from that used in the literature. A number of formulas are obtained to determine the antisymmetric part of the strain (stress) tensor in terms of the symmetric part of the strain tensor and the symmetric part of the bending-torsion (stress and couple-stress) tensor and to determine the antisymmetric part of the bending-torsion (couple-stress) tensor in terms of the symmetric part of the bending-torsion (couplestress) tensor. Some integro-differential equations of motion expressed in terms of the symmetric parts of the stress and couple-stress tensors are proposed for the micropolar theory of elasticity.     

静电加速度计悬浮质量块质心偏移量在轨标定

高精度静电加速度计已广泛地应用于航天任务中,用于测量作用于航天器的非引力加速度。如果静电加速度计悬浮质量块的质心与航天器的质心安装有偏差时,重力梯度力、姿态耦合产生的干扰加速度,静电加速度计控制系统引入的干扰加速度等干扰力会夹杂在测量数据中。针对这一问题,研究了航天器小质量特性变化情况下,当静电加速度计处于动态设计良好并进入稳态后,利用静电加速度计、陀螺仪和磁强计作为敏感元件,基于非线性卡尔曼滤波理论的静电加速度计悬浮质量块质心偏移量的在轨标定。仿真结果表明,该方案的精度J向可以达到0．1mm,Y和Z向能达到0．04mm。     

Three-dimensional static and dynamic stiffness analyses of the cable driven parallel robot with non-negligible cable mass and elasticity

This study investigates the three-dimensional static and dynamic stiffness analyses of the cable driven parallel robot by considering cable mass, elasticity, and mass of end-effector. According to these models, optimization of cable tensions and cable lengths using fminimax solver is performed to determine the static stiffness. Static and dynamic stiffness of the cables are obtained with simulations. Results show that analyses in three-dimension are very important to measure the actual performance of the cable driven parallel robot. This demonstrates potential for general applicability and motion of the cable driven parallel robot.