A Precision-Positioning Method for a High-Acceleration Low-Load Mechanism Based on Optimal Spatial and Temporal Distribution of Inertial Energy

High-speed and precision positioning are fundamental requirements for high-acceleration low-load mechanisms in integrated circuit （IC） packaging equipment. In this paper, we derive the transient nonlinear dynamicresponse equations of high-acceleration mechanisms, which reveal that stiffness, frequency, damping, and driving frequency are the primary factors. Therefore, we propose a new structural optimization and velocity-planning method for the precision positioning of a high-acceleration mechanism based on optimal spatial and temporal distribution of inertial energy. For structural optimization, we first reviewed the commonly flexible multibody dynamic optimization using equivalent static loads method （ESLM）, and then we selected the modified ESLM for optimal spatial distribution of inertial energy; hence, not only the stiffness but also the inertia and frequency of the real modal shapes are considered. For velocity planning, we developed a new velocity-planning method based on nonlinear dynamic-response optimization with varying motion conditions. Our method was verified on a high-acceleration die bonder. The amplitude of residual vibration could be decreased by more than 20% via structural optimization and the positioning time could be reduced by more than 40% via asymmetric variable velocity planning. This method provides an effective theoretical support for the precision positioning of high-acceleration low-load mechanisms.

Fragment spatial distribution of prismatic casing under internal explosive loading

Non-cylindrical casings filled with explosives have undergone rapid development in warhead design and explosion control.The fragment spatial distribution of prismatic casings is more complex than that of traditional cylindrical casings.In this study,numerical and experimental investigations into the fragment spatial distribution of a prismatic casing were conducted.A new numerical method,which adds the Lagrangian marker points to the Eulerian grid,was proposed to track the multi-material interfaces and material dynamic fractures.Physical quantity mappings between the Lagrangian marker points and Eulerian grid were achieved by their topological relationship.Thereafter,the fragment spatial distributions of the prismatic casing with different fragment sizes,fragment shapes,and casing geometries were obtained using the numerical method.Moreover,fragment spatial distribution experiments were conducted on the prismatic casing with different fragment sizes and shapes,and the experimental data were compared with the numerical results.The effects of the fragment and casing geometry on the fragment spatial distributions were determined by analyzing the numerical results and experimental data.Finally,a formula including the casing geometry parameters was fitted to predict the fragment spatial distribution of the prismatic casing under internal explosive loading.

Nonlinear Analysis of Axial-load and Stress Distribution for Threaded Connection

Analytical method for the distributions of axial-load and stress is based on elastic assumption, but the threaded connections are often in plastic deformation stage in practice. Meanwhile the strain in the threaded connection is difficult to measure. So it is necessary to study the reliable numerical method. At present neither the convergence analysis of the computational results nor the elastic-plastic analysis in the loading-unloading process are studied. In this paper, von Mises plasticity and kinematic hardening model is used to describe the material response. A new convergence criterion for nonlinear finite element analysis of the loading-unloading process is proposed. An axisymmetric finite element model according to the proposed convergence criterion is developed and used to analyze the distributions of axial-load and stress. It can be conclude that the stress distribution analysis is more dependent on the mesh density than the axial-load distribution analysis. The stress distribution result indicates that with increasing of applied load, the engaged threads close to the nut-bearing surface become plastic firstly. The axial-load distribution result reveals that the load percentage carried by single thread depends on the position of thread and load intensity. When the load is relatively small, the applied load is mainly carried by the engaged threads near the nut-bearing surface, when the load is larger, the differences of percentages for all threads become small. The proposed convergence analyzing procedure is applicable for other nonlinear analyses. The obtained distributions of axial-load and stress can be a reference of engineering application.

Theoretical calculation and experimental study on the load distribution coefficient (LDC) of three-ring gear reducer

In this paper, primary manufacturing and assembling errors of three-ring gear reducer （TRGR） are analyzed. TRGR is a new transmission type whose eccentric phase difference between middle ring plate and side ring plates is 120°, Its mass of middle ring plate is equal to that of side ring plate or 180°, and its inass of middle ring plate is twice of that of side ring plate, which affects load distribution between ring plates. The primary manufacturing and assembling errors include eccentric error of eccentric sheath E111, internal gear plate E1 and output external gear E11. A new theoretical method is presented in this paper, which converts load on ring plates into the dedendum bending stress of ring plate to calculate load distribution coefficient （ LDC ）, by means of gap element method （GEM）, one of finite element method （FEM）. The theoretical calculation and experimental study, which measures ring plate dedendum bending stress by means of sticking strain gauges on the dedendum of middle ring plate internal gear and side ring plate internal gears, are presented. The theoretical calculation and comparison with experiment result of LDC are implemented an two kinds of three-ring gear reducers whose eccentric phase difference between eccentric sheaths is 120° and 180°respectively. The research indicates that the result of theoretical calculation is consistent with that of experimental study. That is to say, the theoretical calculation method is feasible.

A Study on Load Distribution along Contact Lines of Cylindrical Involute Gears

The mathematical model of current methods for determining load distribution along contact lines of the instantaneously engaged teeth of gears has a defect that its numerical solution is not unique. In order to overcome this defect, a new method based on three-dimensional finite element compliance matrix method improved by smoothing method is presented. Calculated examples of helical gears show that the new method can calculate tooth load distribution accurately and agree well with the results of experiments.

UNIQUENESS OF SOLUTION OF FIELD POINT OF SINGULAR SOURCE OUTSIDE-REGION-DISTRIBUTION METHOD

The uniqueness of solution of field point, inside a convex region due to singular source(s) with kernel function decreasing with distance increasing, outside-region-distribution(s) such that the boundary condition expressed by the response of the source(s) is satisfied, is proved by using the condition of kernel function decreasing with distance increasing anal an integral inequality. Examples of part of these singular sources such as Kelvin's point force, Point-Ring-Couple (PRC) etc. are given. The proof of uniqueness of solution of field point in a twisted shaft of revolution due to PRC distribution is given as an example of application.

Effect of heterogeneity on mechanical and micro-seismic behaviors of sandstone subjected to multi-level cyclic loading: A discrete element method investigation

In numerical simulation of the mechanical responses and acoustic emission(AE)characteristics of rocks under cyclic loading,the impacts of compositional heterogeneities of mineral grains have barely been considered.This will lead to a poor reproduction of rock’s behaviors in terms of stress-strain relationship and micro-seismic characteristics in numerical simulation.This work aims to analyze and reveal the impact of parameter heterogeneity on the rock’s fatigue and micro-seismic properties based on PFC3D.Two distribution patterns(uniform and Weibull distributions),are implemented to assign four critical parameters(i.e.tensile strength,cohesion,parallel bond stiffness and linear stiffness)for 32 sets of numerical schemes.The results show that the models with high heterogeneity of tensile strength and cohesion can better reproduce the stress-strain relationship as well as the patterns of cumulative AE counts and energy magnitude.The evolution of the proportion of three-level AE events in the laboratory test is consistent with the numerical results when the highly heterogeneous tensile strength and cohesion are distributed.The numerical results can provide practical guidance to the PFC-based modeling of rock heterogeneity when exposed to multi-level cyclic loading and AE monitoring.

Loaded multi-tooth contact analysis and calculation for contact stress of face-gear drive with spur involute pinion

The analytical method based on "Hertz theory on normal contact of elastic solids" and the numerical method based on finite element method (FEM) calculating the contact stress of face-gear drive with spur involute pinion were introduced, and their relative errors are below 10%, except edge contact, which turns out that these two methods can compute contact stress of face-gear drive correctly and effectively. An agreement of the localized bearing contact stress is gotten for these two methods, making sure that the calculation results of FEM are reliable. The loaded meshing simulations of multi-tooth FEM model were developed, and the determination of the transmission error and the maximal load distribution factor of face-gear drive under torques were given. A formula for the maximal load distribution factor was proposed. By introducing the maximal load distribution factor in multi-tooth contact zone, a method for calculating the maximal contact stress in multi-tooth contact can be given. Compared to FEM, the results of these formulae are proved to be reliable, and the relative errors are below 10%.

Estimating Design Loads with Environmental Contour Approach Using Copulas for an Offshore Jacket Platform

Jacket-type offshore platforms are widely used for oil, gas field, and energy development in shallow water. The design of a jacket structure is highly dependent on target environmental variables. This study focuses on a strategy to estimate design loads for offshore jacket structures based on an environmental contour approach. In addition to the popular conditional distribution model, various classes of bivariate copulas are adopted to construct joint distributions of environmental variables. Analytical formulations of environmental contours based on various models are presented and discussed in this study. The design loads are examined by dynamic response analysis of jacket platform. Results suggest that the conditional model is not recommended for use in estimating design loads in sampling locations due to poor fitting results. Independent copula produces conservative design loads and the extreme response obtained using the conditional model are smaller than those determined by copulas. The suitability of a model for contour construction varies with the origin of wave data. This study provides a reference for the design load estimation of jacket structures and offers an alternative procedure to determine the design criteria for offshore structures.

Behavior of ring footing resting on reinforced sand subjected to eccentric-inclined loading

Ring footings are suitable for the structures like tall transmission towers, chimneys, silos and oil storages.These types of structures are susceptible to horizontal loads(wind load) in addition to their dead weight.In the literature, very little or no effort has been made to study the effect of ring footing resting on reinforced sand when subjected to eccentric, inclined and/or eccentric-inclined loadings. This paper aims to study the behavior of ring footing resting on loose sand and/or compacted randomly distributed fiberreinforced sand(RDFS) when subjected to eccentric(0 B, 0.05 B and 0.1 B, where B is the outer diameter of ring footing), inclined(0°,5°,10°, 15°,-5°,-10° and-15°)and eccentric-inclined loadings by using a finite element(FE) software PLAXIS 3 D. The behavior of ring footing is studied by using a dimensionless factor called reduction factor(RF). The numerical model used in the PLAXIS 3 D has been validated by conducting model plate load tests. Moreover, an empirical expression using regression analysis has been presented which will be helpful in plotting a load-settlement curve for the ring footing.

Estimation of load and resistance factors using the thirdmoment method based on the 3P-Iognormal distribution

Load and resistance factors are generally obtained using the first order reliability method(FORM)in which the design point should be determined and derivative-based iterations used.In this article,the thirdmoment reliability index,based on the three-parameter lognormal(3P-lognormal)distribution,is investigated.A simple method based on the third-moment method for estimating load and resistance factors is then proposed,and a simple formula for the target mean resistance is also presented to avoid iterative computations.Unlike the currently used method,the proposed method can be used to determine load and resistance factors,even when the probability density functions(PDFs)of the basic random variables are not available.Moreover,the proposed method does not require the iterative computation of derivatives or any design points.Thus,the method provides a more convenient and effective way to estimate load and resistance factors in practical engineering applications.Numerical examples are presented to demonstrate the advantages of the proposed third moment method for determining load and resistance factors.

An improved probabilistic load flow in distribution networks based on clustering and Point estimate methods

Clustering approaches are one of the probabilistic load flow(PLF)methods in distribution networks that can be used to obtain output random variables,with much less computation burden and time than the Monte Carlo simulation(MCS)method.However,a challenge of the clustering methods is that the statistical characteristics of the output random variables are obtained with low accuracy.This paper presents a hybrid approach based on clustering and Point estimate methods.In the proposed approach,first,the sample points are clustered based on the𝑙-means method and the optimal agent of each cluster is determined.Then,for each member of the population of agents,the deterministic load flow calculations are performed,and the output variables are calculated.Afterward,a Point estimate-based PLF is performed and the mean and the standard deviation of the output variables are obtained.Finally,the statistical data of each output random variable are modified using the Point estimate method.The use of the proposed method makes it possible to obtain the statistical properties of output random variables such as mean,standard deviation and probabilistic functions,with high accuracy and without significantly increasing the burden of calculations.In order to confirm the consistency and efficiency of the proposed method,the 10-,33-,69-,85-,and 118-bus standard distribution networks have been simulated using coding in Python®programming language.In simulation studies,the results of the proposed method have been compared with the results obtained from the clustering method as well as the MCS method,as a criterion.

冷挤压内螺纹力学性能试验研究

螺纹连接中螺母与螺栓接触型面复杂,对于螺纹牙上的应力状态分析困难,且不同加工方式对内螺纹的失效载荷影响较大。这里建立螺纹连接的简化力学模型和有限元模型,分析了内螺纹牙表面应力分布,重点对冷挤压内螺纹的力学性能进行了试验分析,并与切削内螺纹的力学性能进行对比。结果表明:内螺纹在负载状态下,应力集中和塑性变形主要集中在螺母与螺栓的牙根和第(1~3)个螺纹的牙顶处,应力大小和变形量沿载荷反方向逐渐递减;挤压内螺纹的连接强度明显高于切削内螺纹,失效载荷比切削内螺纹提升了(18~58.6)%不等;随着内螺纹牙高率从65%增加至80%,挤压内螺纹和切削内螺纹的力学性能均增加,切削内螺纹的失效载荷提升了(28.86~55.45)%,挤压内螺纹的失效载荷提升了(22.89~41.93)%。

车辆载荷作用下桩后黏性土主动土压力分析

针对现有设计规范进行桩后主动土压力计算时未考虑车辆载荷的动力效应对支护结构影响的问题,在平面滑裂面假定的基础上,结合拟动力学分析方法,考虑车辆动载荷作用下桩后土体受惯性力的影响,推导出车辆载荷作用下主动土压力的计算式,将主动土压力分为动土压力分量和静土压力分量。分析土体容重、桩-土外摩擦角对主动土压力的影响,以及水平振动加速度系数、内摩擦角、行车速度、车桩间距对动土压力的影响,对比分析不同黏聚力情况下的主动土压力分布规律。研究结果表明:桩后动土压力呈非线性分布;在车辆载荷作用下,一个振动周期内桩后主动土压力随滑动面倾角的增大和时间的持续先增大后减小;动土压力幅值随车桩间距的增大而减小,振动周期随车速的增大而增大。

矿用自动液压锚杆钻机可靠性分配研究

针对自动液压锚杆钻机可靠性数据缺乏、结构复杂、工作环境恶劣的问题,优选了代数分配法作为其可靠性分配方法。通过结构功能分析,将钻机划分为8个组元并建立了可靠性分析模型。依据MT/T 688-1997《煤矿用锚杆钻机通用技术条件》计算了钻机故障率。运用代数分配法完成了钻机可靠性分配,研究结果表明控制系统等4个组元为薄弱环节。从提升关键部件可靠性和钻机加载试验两方面提出了钻机可靠性提升建议,对于自动液压锚杆钻机研发具有参考价值。

分配特殊群桩空间作用效应的双向m法

群桩到单桩的作用分配是桩基计算的关键问题,针对规范中的单向m法只适用于平面作用的局限性,从单桩刚度、群桩刚度、受力平衡方程3个层面进行公式推导,建立了变形协调的群桩刚度矩阵和空间受力平衡方程,形成了适用于空间作用的双向m法,并以对称等长直桩、双向斜桩、不对称桩为计算实例,对比分析了单向m法和双向m法的计算结果。结果表明:单向m法计算对称等长直桩时,结果准确,计算双向斜桩时,单桩的弯矩和剪力波动较大,最大值偏小20%左右,计算不对称桩时,单桩外力之和与总外力不闭合,可信度低;而双向m法的理论解可覆盖这些桩基类型,结果更接近有限元数值解。研究成果为特殊桩基提供了一种快速且简便的计算方法,扩展了公路和铁路桥梁桩基设计规范的适用范围。

热载荷下星载天线逆有限元变形重构方法

为实现星载天线结构在服役过程中的实时变形监测,针对真实分布式热载荷下的星载天线板结构,研究了基于应变监测的逆有限元变形重构方法.首先,针对星载天线板结构提出了一种基于四节点四边形逆向壳单元的变形监测方法,通过建立基于位移梯度的单元划分方法,对逆有限元单元划分进行优化,采用最小二乘误差函数构造结构应变与位移的矩阵关系.其次,建立天线板热试验系统,获取典型热载荷下的结构温度分布.然后,建立典型实验温差状态下的复合材料星载天线板结构有限元模型,获取结构表面应变和位移.最后,在典型热载荷下,验证所提变形重构方法的有效性.结果表明,变形重构的位移误差不超过0.5 mm,说明逆有限元法能够在典型热载荷下准确重构天线板变形.

集体球类项目的训练负荷强度分布:区别与规律

寻找集体球类项目训练负荷强度分布(training intensity distribution,TID)在专项特征和使用条件下的项间差异与共性规律,为训练负荷的制定提供理论依据。在Pub Med、Web of Science、中国知网数据库进行系统文献检索并提取TID数据及相关影响变量;采用广义混合模型比较运动员、运动项目、统计方法和训练阶段4个维度对TID的影响;采用偏最小二乘法将纳入项目在上述4个维度上进行聚类分析。共纳入24篇相关文献;运动项目、训练阶段、统计方法3个维度对TID产生影响;依据VO _(2max)和MCV将7个运动项目分为3类。与整体性统计方法相比,过程性统计方法在Zone1的比例更大;与全年训练相比,比赛前期和比赛期的训练负荷在Zone2和Zone3的负荷比例更大;与低VO _(2max)和MCV项目相比,高VO _(2max)和MCV项目在Zone2和Zone3的比例更大。

考虑主轴疲劳载荷的虚拟同步双馈风电场有功功率分布式优化方法

为降低风电场内各台基于虚拟同步发电机控制策略的双馈风电机组在响应电网功率指令值变化时所承受的主轴疲劳载荷,提出一种基于改进惩罚系数的交替方向乘子法的考虑主轴疲劳载荷的有功功率分布式优化方法。在推导可量化表征机组有功功率指令值与其主轴力矩之间关系的离散化模型基础上,以各台机组的主轴力矩波动总和最小作为目标函数,并根据机组运行状态设定目标函数的约束条件。为分担风电场中央控制器的计算压力,基于改进惩罚系数的交替方向乘子法将目标函数拆解为主函数(中央控制器)和多个子函数(本地控制器)的分布式优化结构,各本地控制器通过在线优化各台机组有功功率指令值以实现主轴疲劳载荷的降低。最后,仿真结果验证了所提优化方法的优越性。