Calculating Jacobian coefficients of primitive constraints with respect to Euler parameters

It is a fundamental problem to calculate Jacobian coefficients of constraint equations in assembly constraint solving because most approaches to solving an assembly constraint system will finally resort to a numerical iterative method that requires the first-order derivatives of the constraint equations. The most-used method of deriving the Jacobian coefficients is to use virtual rotation which is originally presented to derive the equations of motion of constrained mechanical systems. However, when Euler parameters are adopted as the state variables to represent the transformation matrix, using the virtual rotation will yield erroneous formulae of Jacobian coefficients. The reason is that Euler parameters are incompatible with virtual rotation. In this paper, correct formulae of Jacobian coefficients of geometric constraints with respect to Euler parameters are presented in both Cartesian coordinates and relative generalized coordinates. Experimental results show that our proposed formulae make Newton–Raphson iterative method converge faster and more stable.     

基于矢量环装配模型的二维公差分析

在公差分析中,大多数都要求提供描述装配响应函数与零件尺寸设计变量之间关系的函数。然而,复杂的二维公差分析中,这种函数关系通常难于得到。本文提出的基于矢量环装配公差模型,不须提供这些函数关系,而是通过矢量运算得到计算封闭环公差所需的灵敏度系数,进而有效地解决二维尺寸链的公差分析问题。最后给出一个工程应用实例,说明该方法的有效性。     

End-Face Seal Deflection Effects—The Problems of Two-Component Stationary or Rotating Assemblies

Component deformations have a significant effect on performance of high-pressure, end-face seals. Deflection analysis is necessary for prediction, control and understanding, but is often complicated by existing arrangements of support for seal faces. The common commercial design for both a stationary and a rotating seal face is the two-component assembly.

A method for treating the effects of changes of pressure, general temperature and steady frictional heating is presented. Deflection sensitivities of a two-component assembly are expressed as ldquo;influence coefficients,” evaluated by finite element analysis of multiple load cases. The importance of radial Coulomb friction due to differential shrinkage at the interface of n two-component assembly is highlighted. Such friction gives rise to undesirable performance hysteresis.

Once ldquo;influence coefficients” for a particular end-face seal have been evaluated by the method outlined in this report, the effect of various shape and material changes can be investigated as part of the design process. In this way, the potential response of a seal to various disturbances may either be minimized at the design stage, or be tailored to meet special requirements.

An example calculation of history-dependent face deflection of a high-performance nuclear seal is given. The dependence of seal friction and leakage on this deflection is discussed; i.e. the proportionality of friction to seal face divergence and of leakage to convergence cubed.     

Concurrent tolerance charting for component and assembly using “modified tree” approach

The interaction between components in an assembly plays a major role in the performance and reliability of the assembly. However, in conventional design, the dimensions and tolerances of components are usually assigned intuitively to satisfy design constraints. Tolerance analysis is then performed to determine the critical tolerance accumulation that results from the assembly. The tolerances are then modified so that the interaction requirements are satisfied. This approach relies on the experience of the designers and the results may not be an optimum.This paper presents a direct method to determine the working dimensions and tolerances of components that allows control of the assembly interaction. The model is easy to construct and it provides a clear picture of the entire process and assembly links. Using the model, a set of linear equations is formulated directly based on the design constraints and interaction requirements. With appropriate constraints derived in terms of the process capabilities, the desired working dimensions and tolerances can be determined using LINDO, software for solving the linear programming problem. This approach allows the working dimensions and tolerances of all components in an assembly to be determined concurrently.     

A probabilistic approach to variation propagation control for straight build in mechanical assembly

Random component variations have a significant influence on the quality of assembled products, and variation propagation control is one of the procedures used to improve product quality in the manufacturing assembly process. This paper considers straight-build assemblies composed of axi-symmetric components and proposes a novel variation propagation control method in which individual components are re-orientated on a stage-by-stage basis to optimise the table-axis error for the final component in the assembly. Mathematical modelling methods are developed to predict the statistical variations present in the complete assembly. Three straight-build assembly strategies are considered: (a) direct build, (b) best build and (c) worst build assembly. Analytical expressions are determined for the probability density function of the table-axis error for the final component in the assembly, and comparisons are made against Monte Carlo simulations for the purposes of validation. The results show that the proposed variation propagation control method offers good accuracy and efficiency, compared to the Monte Carlo simulations. The probability density functions are used to calculate the probability that the eccentricity will exceed a particular value and are useful for industrial applications and academic research in tolerance assignment and assembly process design. The proposed method is used to analyse the influence of different component tolerances on the build quality of an example originating in aero-engine sub-assembly.     

Generation of assembly models from kinematic constraints

In this paper, we propose a new joint-based assembly modeling method. In joint-based assembly modeling, the assembly constraints are specified on the components, but not on the geometric elements of the components. The proposed method generates assembly models from kinematic joint constraints by applying three procedures (1) to extract all feasible JMFs (Joint Mating Feature) for each mating component using information on joint constraints, (2) to derive mating alternatives for each pair of mating components after reducing the number of JMFs using the pruning criteria, and (3) to generate an assembly model by choosing the intended one from the mating alternatives for each pair of mating components and solving the JMF constraints. Since the joint constraints are expressed in terms of the relations between components rather than relations between geometric elements, the proposed method is more intuitive and natural for assembly modeling and supports modeling activities effectively by minimizing user interactions. By using joint mating constraints for assembly modeling, moreover, the kinematic behaviors of assemblies determined in the conceptual design stage can be directly applied and consistently maintained up to the detailed design stage. In the proposed method, it is also not necessary to re-input the mating constraints even when the component topology is changed.     

基于 AUTOCAD 的面向机械装配图的关键技术及其应用

提出了基于ＡＵＴＯＣＡＤ生成装配图的技术关键及解决方案；设计了零件的统一表示模式；引入了一种新的轮廓自动识别算法，将内外轮廓识别统一起来。采用线段端点分类及交点排序的策略，快速可靠地解决需要消除的部分。最后给出一个稳定可靠的任意多边形裁剪算法。上述方法已成功地应用于机械工程装配图。     

面向可装配性评价的零件插装方向自动提取方法

零件插装方向是影响产品可装配性的主要特征之一,其自动化提取对于提高可装配性评价的效率具有重要意义。本文提出了一种面向机器人装配的可装配性评价的零件插装方向自动化提取方法,根据给定的产品装配序列及计算机辅助设计信息,运用几何推理技术判断产品零件间的装配关系,建立产品装配关系模型,并基于自由度分析导出零件插装方向。     

飞机装配高精度测量控制网精度分析与构建准则

为满足飞机装配大尺寸、高精度、测量点分散的测量要求,提出了飞机装配高精度测量控制网的构建方法。该方法利用激光跟踪仪在飞机装配车间地面上布设长期保存的公共基准点,由公共基准点构成飞机装配测量控制网,建立飞机装配全局坐标系。结合近似坐标系变换和最小二乘原理,推导测量控制网的7参数误差计算式。综合利用二范数和不等式变换,研究布设误差与测量控制网精度的关系,推导布设误差传递系数。借助法方程和正定矩阵性质,证明了测量点数与测量控制网精度的关系。最后利用蒙特卡洛仿真实验给出了飞机装配高精度测量控制网的布设准则。     

基于勒让德多项式各项系数拟合的柱面镜面形检测研究

超薄玻璃热成形技术是目前国际上研制X射线掠入射天文成像望远镜的重要技术之一,超薄玻璃圆柱面镜片面形的高精度检测是实现超薄玻璃热成形的关键。围绕我国高能X射线掠入射天文望远镜研制对高面形精度的超薄玻璃柱面镜的需求,采用勒让德多项式对柱面镜面形的测量数据进行拟合,利用勒让德多项式各项系数与特定的几何像差的对应性,通过拟合勒让德多项式各项的系数,获得了待测柱面镜面形的特定几何像差,为全面评价柱面镜面形质量提供了参考。     

基于新的系统数学模型的三维形貌测量法

提出新的测量系统数学模型,将投影仪投射光场视为由相位值唯一标识的光投射面的集合所形成的空间,将摄像机成像模型视为一种由成像点图像坐标确定的成像射线形成的集合,将被测点视为所对应的投射面与成像射线的交点。以此为理论基础,采用逆向求解法建立投影仪的数学模型,避免显示标定投影仪的复杂操作过程。将离心畸变与径向畸变分解为两个独立的过程顺序求解,再使用小孔成像模型建立消除畸变后的摄像机数学模型。采用平面靶标自由移动法采集足够多的标定数据,对标定靶的尺寸与位置要求不严,并且在不要求标定数据充满整个视场空间的情况下仍可获得完整的标定结果。本标定过程对系统位置无任何严格要求,同时摆脱对精密位移装置的需求,并有效地消除摄像机与投影仪镜头畸变所产生的标定误差。     

微颗粒的三维空间跨尺度装配方法

针对微颗粒空间装配的问题,以外径为十几微米的微颗粒与外径为几百微米的柱腔装配为研究对象,开展微颗粒空间跨尺度装配方法研究。首先,针对微颗粒受到基底表面作用力影响不易被拾取与释放的问题,分析了微颗粒的受力情况,设计了真空吸附式微夹持器用于微颗粒的拾取与释放;然后,针对由于微颗粒与柱腔的尺寸跨度大,很难实现装配过程中二者空间位置实时监测的问题,设计了具有多维视觉监测功能的微装配机器人并且建立了多维视觉监测模型,实现微颗粒与柱腔装配过程的在线监测;最后,提出了基于多维视觉监测模型的微颗粒与柱腔空间半自动装配方法。实验结果证明了所提方法的有效性,并且实现了将外径为20μm的微颗粒放入外径为200μm的柱腔内的目标。该方法适用于微机电系统制造中微颗粒的三维空间装配。     

Periodic trend detection from CMM data based on the continuous wavelet transform

The main goal of this paper is to describe a method based on the continuous wavelet transform (CWT). The Shannon entropy of CWT coefficients in each scale is calculated in order to detect the characteristic trends of the CMM measurement data efficiently. This method is successfully implemented in a body-in-white (BIW) assembly for the detection of periodic trends in coordinate measure machine (CMM) data. It would contribute to main cause location in BIW quality control. The principle of the CWT and the property of the periodic trend after the CWT are explained from a mathematical viewpoint. An actual quality-control case is analyzed using the CWT method. Consistency between the results and the actual situation proves the effectiveness of this CWT method.     

基于特征的产品装配序列自动规划研究

以问题规约的求解策略,以分解法规划产生的装配序列,提出与或图表达装配体拆卸序列解空间。通过求解拆卸序列与或图的解空间得到装配体的拆卸序列,将拆卸序列反向得到装配序列。为降低装配体拓扑联接图的复杂度,对作业组件做识别,文中提出判断零件拆卸性的 ３ 个条件,大部分零件无需进行干涉检验,而由逻辑推理即可判断是否满足拆卸条件,每一成功拆卸操作对应于一个拆卸或装配序列,避免了多次试凑,有更高求解效率,可更广泛地用于装配序列求解上。     

Pro／E布局功能在虚拟样机装配中的应用

在Pro／E环境中,利用一种以布局为基础的装配方式提高复杂机械产品的装配效率。首先确定部件间的装配关系与顺序,再通过布局设定参数基准并自动完成装配。该方法可以快速完成零件的装配过程。以联合收割机中夹持输送链条的链盒为例说明了该方式的使用过程。     

基于UG的三维装配尺寸面链表组自动生成方法研究

针对目前装配尺寸链不能实现真正意义上的自动生成及在装配尺寸链中很少考虑几何要素的几何公差的问题,提出了一种基于几何要素控制点理论公差表示模型的三维装配尺寸面链表组自动生成方法。在分析装配公差建模的信息组成的基础上,建立了装配公差信息的计算机储存储数据混合图结构。以UG NX7.5为二次开发平台,提取了三维装配体内零件上尺寸公差、几何公差、装配基准以及装配目标等信息。首先,确定了封闭环;然后,根据建立装配尺寸链的最短路径的原则搜索装配公差信息图,建立了三维装配尺寸面链表;最后,根据装配顺序及设计基准将其按零件拆分为三维装配尺寸面链表组。以三正交平面作为装配基准的轴孔装配为例,对该方法进行了验证。研究结果表明,该方法能够综合考虑几何要素的尺寸和几何公差,为后续的公差分析工作打下坚实的基础。     

基于杆组邻接矩阵的平面机构综合方法

为在平面机构综合中能够求解出包含R副和P副的全部运动链,给出一种基于杆组邻接矩阵的平面机构综合新方法。通过对前期研究提出的杆组邻接矩阵进行修正,构造改进的杆组邻接矩阵。基于改进的杆组邻接矩阵,求解给定杆组的所有装配方式,并同步辨识同构体,获取杆组装配关系的杆组邻接矩阵。根据提出的约束条件,采取逐级构造杆组邻接矩阵方法,求解杆组间的可行连接方式,并同步辨识同构体,从而获取全R副杆组间的连接关系的杆组邻接矩阵。将所有类型杆组代入求得的杆组连接关系矩阵,获取所有类型杆组可构成的全部机构构型,包含主动件和机架变换问题。以平面6杆机构为例,应用该方法首次求出包含R副和P副的所有机构构型为364种,验证了提出的综合方法的有效性和实用性。     

Optimal tolerance design for mechanical assembly considering thermal impact

In this paper, a cost–tolerance model based on neural network methods is proposed in order to provide product designers and process planners with an accurate basis for estimating the manufacturing cost. Tolerance allocation among the assembly components is carried out to ensure that the functionality and design quality are satisfied considering the effect of dimensional and geometric tolerance of various components of the assembly by developing a parametric computer aided design (CAD) model. In addition, deformations of various components of mechanical assembly due to inertia and temperature effects are determined and the same is integrated with tolerance design. The benefits of integrating the results of finite element simulation in the early stages of tolerance design are discussed. The proposed method is explained with an application example of motor assembly, where variations due to both dimensional and geometric tolerances are studied. The results show that the proposed methods are much effective, cost, and time saving than the ones considered in literature.     

Measuring heat transfer coefficient in convection reflow ovens

In this paper, the evaluation of a measurement method is discussed which can determine the heat transfer coefficient in convection reflow ovens. Nowadays the reflow ovens apply forced convection heating with nozzle-matrix blower system. In these ovens the heat transfer coefficients of the heater gas streams determine mainly the efficiency of heating. A method is presented which has two steps: in the first step, the heat transfer coefficient of the heater gas streams is studied above the assembly in function of height; in the second step, the heating efficiency of the nozzle-lines is compared as a distribution of the heat transfer coefficient in the oven. The heat transfer coefficients are calculated from the heat equation of the reflow oven. It is also presented with the distributions of the heat transfer coefficient that how the contamination of the nozzles affects the heating efficiency of the reflow oven.     

An experimental assembly for precise measurement of thermal accommodation coefficients

An experimental apparatus has been developed to determine thermal accommodation coefficients for a variety of gas-surface combinations. Results are obtained primarily through measurement of the pressure dependence of the conductive heat flux between parallel plates separated by a gas-filled gap. Measured heat-flux data are used in a formula based on Direct Simulation Monte Carlo (DSMC) simulations to determine the coefficients. The assembly also features a complementary capability for measuring the variation in gas density between the plates using electron-beam fluorescence. Surface materials examined include 304 stainless steel, gold, aluminum, platinum, silicon, silicon nitride, and polysilicon. Effects of gas composition, surface roughness, and surface contamination have been investigated with this system; the behavior of gas mixtures has also been explored. Without special cleaning procedures, thermal accommodation coefficients for most materials and surface finishes were determined to be near 0.95, 0.85, and 0.45 for argon, nitrogen, and helium, respectively. Surface cleaning by in situ argon-plasma treatment reduced coefficient values by up to 0.10 for helium and by ～0.05 for nitrogen and argon. Results for both single-species and gas-mixture experiments compare favorably to DSMC simulations.