Sensitivity analysis of the equal angle divider mechanism kinematics with the synthesis of the joint gap tolerances

Tolerance analysis of mechanical components and assemblies is a key element in the industry for improving product quality and reducing overall cost. This paper is an attempt to propose a methodology to formulate and compute the kinematic assembly variations with respect to the critical dimensions (joint clearances) by calculating the homogeneous matrix of loops with considering the transforming and rotation matrix, the tolerance sensitivities, the geometrical responses to assembly variations, and the tolerance sensitivity of mechanism for clearance in the joints in different motion phases. The analysis is performed by the systematic methodology which is extended for kinematic sensitivity and positional error analysis with published results.     

The Kinematics and the Full Minimal Dynamic Model of a 6-DOF Parallel Robot Manipulator

In this paper we present a particular architecture of parallel robots which has six-degrees-of-freedom (6-DOF) with only three limbs. The particular properties of the geometric and kinematic models with respect to that of a classical parallel robot are presented. We show that inverse problems have an analytical solution. However, to solve the direct problems, an efficient numerical procedure which needs to inverse only a 3 × 3 passive Jacobian matrix is proposed. In a second step, dynamic equations are derived using the Lagrangian formalism where the joint variables are passive and active joint coordinates. Based on the geometrical properties of the robot, the equations of motion are derived in terms of only nine coordinates related by three kinematic constraints instead of 18 joint coordinates. The computational cost of the dynamic model obtained is reduced by using a minimum set of base inertial parameters.     

基于动力松弛法的松弛索杆体系找形分析

索杆张力结构施工成形分析需要解决一个松弛态索杆系统的平衡形态求解问题,该问题可归结为一个给定构件原长的受荷索杆机构系统的找形问题。文中利用动力松弛法进行该类松弛索杆体系的找形分析。由于不建立刚度矩阵,避免了体系几何不稳定性所引起的刚度矩阵奇异问题。该方法采用悬链线索单元模型,可以考虑索大垂度效应。文中还推导了反映索原长和内力之间关系的悬链线索单元协调方程。通过一个正交松弛索网算例分析,考察了该找形方法的计算精度和收敛性。最后还模拟了一个索穹顶的施工成形过程,表明了该找形方法用于索杆张力结构施工成形分析的有效性。     

爆破开挖扰动下锚固节理岩质边坡位移突变特征与能量机理

针对白鹤滩水电站左岸坝基河谷底部边坡岩体爆破开挖,采用现场岩体位移监测、锚索轴力监测及数值模拟的手段,研究了爆破开挖扰动下锚固节理岩质边坡的位移突变特征及其能量机理。研究结果表明:对于深切河谷底部高地应力边坡岩体爆破开挖,爆炸荷载挤压及地应力作用下,岩体所积聚的应变能快速释放,导致了节理岩质边坡的位移突变,突变位移包括节理张开位移和岩体回弹位移两部分;地应力水平越高、岩体弹性模量越低,总的突变位移量越大;预应力锚索主要通过抑制节理张开位移来控制边坡岩体的位移突变,锚索预应力等级越高,其吸能和释能速率越高,对节理岩体位移突变的控制效果越好,当锚索的预应力等级高到一定程度后,节理岩体的突变位移不再随锚索预应力等级的升高而显著减小。     

Particle flow mechanism into cable shovel dippers

Electric cable (or rope) shovels are critical equipment in the surface mining industry. An improved understanding of the factors which affect the flow of broken material into the dipper during loading can help to evaluate the performance of the excavator, define the criteria for equipment selection and develop ways to mitigate equipment damage caused by broken particles. In this paper, the mechanism of granular material flow was investigated through a series of laboratory tests by moving 1:32 and 1:20 (cube root scale) models of a 44 m³ dipper through a test bin filled with angular crushed limestone. It was found that neither dipper angle nor hoist speed has significant influence on the general flow pattern. It was also found that the general flow mechanism is independent on the size of the dipper. Quantitatively, it was determined that hoist speed and pitch angle affect the productivity of the machine with lower pitch angle resulting in higher payload, and faster hoist speed results in shorter dig time. While both lower pitch angle and faster hoist speeds also produce a higher rate of energy consumption, overall both contribute to improved machine productivity.     

Flexible bridge decks suspended by cable nets. A constrained form finding approach

The initial geometry of structures made of cables is steered by the cable tensioning forces. In a cable net the geometrical shape and the internal force distribution cannot be dealt as separate issues: the set of geometries defines also the feasible sets of the internal forces. During the last decades, many different approaches have been proposed to deal with the form finding of cable structures. The most efficient one is the so called Force Density Method (FDM), proposed by Schek, which allows to conforming cable nets for structural applications without requiring any further assumption, neither on the geometry, nor on the material properties. An Extension of the Force Density Method, the EFDM, makes it possible to set conditions in terms of fixed nodal reactions or, in other words, to fix the position of a certain number of nodes and, at the same time, to impose the intensity of the reaction forces. Through such an extension the EFDM enables us to deal with form finding problems of cable nets subjected to given constraints and in particular to treat mixed structures, made of cables and struts. In this paper we consider cable nets interacting with members having flexural behaviour. For a given cable assembly and for a given loading condition, aim of this work is to find that particular pretensioning system which replaces both the static and the kinematic functions of the inner reactions of a flexural elastic continuous beam. It is, for instance, the case of the bridge decks suspended by cables, shaped in various forms. The specialization of the EFDM to this type of problem is presented and a progressive set of examples shows the efficiency and the versatility of this approach in contributing to the design of new creative forms.     

Modeling 3D revolute joint with clearance and contact stiffness

The clearances in the kinematic joints are due to deformations, wear, and manufacturing errors; the accurate modeling of these effects in multibody analysis is a complex issue but in many practical applications, it is mandatory to take into them into account in order to understand the actual behavior of mechanical systems. In this paper, the authors present a general computer-aided model of a 3D revolute joint with clearance suitable for implementation in multibody dynamic solvers. While a perfect revolute joint imposes kinematic constraints, the proposed revolute joint with clearance leads to a force constraint. The revolute joint has been modeled by introducing a nonlinear equivalent force system, which takes into account the contact elastic deformations. The model depends on the structural and geometrical properties of materials in contact that have been investigated using finite element models. The purpose is to give a general approach to study the influence of actual joints on kinematic, dynamic, and structural behavior of mechanisms. The proposed model has been applied in dynamic simulations of a spatial slider-crank mechanism.     

可变体系的几何稳定平衡状态及受力分析

索和撑杆组成的张拉集成体系，膜结构及悬索体系，一般都要施加预应力使其成为能承受荷载的几何不变体系，整体受力表现为几何非线性。本文将其受力状态分解为两部分，一是几何稳定平衡状态，二是弹性稳定平衡状态。文中提出几何稳定平衡状态的分析计算方法，证明增量迭代法的收敛性。结果表明，所提出的方法收敛快，精度高。     

在轨组装空间结构面向主动控制的动力学建模

在轨组装是未来超大型空间结构最有发展潜力的构建方式之一, 组装过程中空间结构尺寸逐渐增长、动力学特性也随之改变, 给结构主动控制任务带来了新的挑战. 针对这一问题, 提出一种在轨组装空间结构面向主动控制的动力学建模方法. 首先, 建立不同类别组装模块的基础模型库, 以用于后续直接调用; 然后, 定义模块的邻接关系矩阵以描述在轨组装过程中空间结构的变化, 并根据在轨组装任务特点, 设计了面向分布式控制的智能组件结构形式; 在有限元建模方法的基础上提出"节点自由度加载"方法, 利用模块的基础模型库与邻接关系矩阵, 分别建立智能组件和空间结构整体的动力学模型, 该模型可随组装的进行同步自适应更新; 最后, 以在轨组装桁架结构为例, 给出组装碰撞冲击下动力学建模与分布式主动控制数值仿真. 结果表明, 在轨组装过程中桁架结构整体的动力学特性有明显的变化, 主动控制非常必要; 基于提出的建模方法, 可高效地建立构型多样的在轨组装空间结构动力学模型; 智能组件的动力学模型在组装过程中可进一步根据邻接关系矩阵限定更新范围, 适用于在轨组装过程中的分布式主动控制系统设计.      

Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I: Theoretical formulation and model validation

This paper is first of the two papers dealing with analytical investigation of resonant multi-modal dynamics due to 2:1 internal resonances in the finite-amplitude free vibrations of horizontal/inclined cables. Part I deals with theoretical formulation and validation of the general cable model. Approximate nonlinear partial differential equations of 3-D coupled motion of small sagged cables – which account for both spatio-temporal variation of nonlinear dynamic tension and system asymmetry due to inclined sagged configurations – are presented. A multi-dimensional Galerkin expansion of the solution of nonplanar/planar motion is performed, yielding a complete set of system quadratic/cubic coefficients. With the aim of parametrically studying the behavior of horizontal/inclined cables in Part II [25], a second-order asymptotic analysis under planar 2:1 resonance is accomplished by the method of multiple scales. On accounting for higher-order effects of quadratic/cubic nonlinearities, approximate closed-form solutions of nonlinear amplitudes, frequencies and dynamic configurations of resonant nonlinear normal modes reveal the dependence of cable response on resonant/nonresonant modal contributions. Depending on simplifying kinematic modeling and assigned system parameters, approximate horizontal/inclined cable models are thoroughly validated by numerically evaluating statics and non-planar/planar linear/non-linear dynamics against those of the exact model. Moreover, the modal coupling role and contribution of system longitudinal dynamics are discussed for horizontal cables, showing some meaningful effects due to kinematic condensation.     

Analysis of prestressed mechanisms

A new theory is presented for the matrix analysis of prestressed structural mechanisms made from pin-jointed bars. The response of a prestressed mechanism to any external action is decomposed into two almost separate parts, which correspond to extensional and inextensional modes. A matrix algorithm which treats these two modes separately is developed and tested. It is shown that the equilibrium requirements for the assembly, in its initial configuration as well as in deformed configurations which are obtained through infinitesimal inextensional displacements, can be fully described by a square equilibrium matrix. It is also shown that any set of extensional nodal displacements has to satisfy some equilibrium conditions as well as standard compatibility equations, and that the resulting system of linear equations defines a square kinematic matrix. Theoretical as well as experimental evidence supporting this approach is given in the paper ; two simple experiments which were of crucial importance in arriving at the equilibrium conditions on the extensional displacements are described.The interaction between the two modes of action of a prestressed mechanism is discussed, together with a rapidly converging iterative procedure to handle it. A study of the non-linear effect by which the self-stress level in a statically indeterminate assembly rapidly increases if an inextensional mode is excited, supported by further experimental results, concludes the paper. This work is relevant to the analysis of most cable systems, pneumatic domes, fabric roofs, and “Tensegrity” frameworks.     

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.     

大跨度斜拉桥非线性振动模型与理论研究进展

斜拉桥的非线性动力学问题一直都是力学、结构和桥梁领域的研究热点.随着新材料(如碳纤维增强聚合物索)和新施工工艺的发展,斜拉桥的跨越能力不断得到提高,从而在桥梁建设中更具有竞争力.然而,斜拉桥跨度的增大和新材料的应用使结构变得更轻和更柔,使结构的非线性振动问题比以往更为突出,可能危及桥梁安全.基于课题组近年来对斜拉桥非线性动力学的研究,围绕大跨度斜拉桥的非线性建模理论及动力学问题,较为详细地评述近十年来国内外的研究进展情况.主要从斜拉索非线性动力学模型、梁的非线性动力学模型、索-梁组合结构的非线性动力学模型、斜拉桥整体非线性动力学模型与理论、以及斜拉桥的非线性振动实验等几个方面对斜拉桥非线性建模方法、力学模型、数学模型、求解方法及相应研究成果进行评述和讨论.研究结果表明,斜拉桥由于多柔性索和大跨度梁的耦合问题,以及环境载荷的复杂性,导致其具有丰富的非线性动力学行为.同时由于高维非线性系统求解方法的欠缺,整体斜拉桥非线性动力学行为又相当复杂,深入研究面临很大困难.最后,基于未来斜拉桥的发展趋势和可能面临的突出问题,对斜拉桥非线性振动问题今后的发展方向进行了探讨和展望.      

A dynamic damage constitutive model for a rock mass with non-persistent joints under uniaxial compression

Most problems faced by the practicing rock mass engineering involve the evaluation of rock mass dynamic strength and deformability. As part of a rock mass, the mesoscopic flaws such as the microcracks and the macroscopic ones such as the joints both inherently affect the rock mass dynamic strength and deformational behavior. Nearly none of the existing models can handle the co-effect of these two kinds of flaws on the rock mass dynamic mechanical behavior. This study focusses on the rock mass with multi-sets of non-persistent joints and establishes a mathematical model accounting for the anisotropy in dynamic strength and deformability induced by the joints. Accordingly, an approach incorporating the existing models or methods to enable perfect simulation of the dynamic stress-strain relationship of a rock mass is proposed, in which the joint geometrical parameters such as the joint length and dip angle, the strength ones such as the joint internal friction and the deformational ones such as the joint normal and shear stiffness can all be taken into account. In order to investigate the validity of the proposed model, a series of calculation examples have been made and the results fits very well with the theoretical ones.     

降落伞膜索非线性有限元模拟

用膜单元和索单元模拟降落伞织物绳索系统,基于完全拉格朗日格式的非线性有限元方法编程计算降落伞的结构动力学特性。采用增量与迭代混合方法改善非线性计算的收敛特性并结合HHT隐式时间推进方法减小整体迭代计算量。使用修正应力应变张量导数的方法模拟膜单元单向应力状态并针对膜单元和索单元分别进行了非线性有限元计算验证。最后针对C-9型降落伞建立三维有限元模型,根据设定流速对伞衣施加均匀压强载荷,将模拟展开的结果与使用相同模型、不同方法商业软件的文献进行对比,显示了隐式非线性有限元方法模拟降落伞膜索系统大变形动力学的能力。     

浅埋小净距隧道爆破损伤探测及数值模拟分析

为了研究爆破荷载对浅埋小净距隧道围岩造成的损伤影响,以济南顺河快速路南延工程浅埋暗挖段为工程背景,通过LSDYNA软件将建立的各向异性动态损伤本构用于隧道爆破的损伤数值模拟,研究炮孔周围的损伤范围;并基于声波测试原理,对浅埋小净距隧道围岩的损伤进行了现场探测。结果表明:在数值模拟中,单个炮孔爆破形成的最大损伤影响半径为0.58 m,最大损伤影响深度为1.88 m,根据岩体的损伤破坏阈值,岩体的破坏水平范围可达0.14 m,破坏深度为1.70 m;根据现场探测,中夹岩受双线隧道交替爆破开挖其损伤程度较围岩其他部位要高,爆破开挖对隧道围岩造成的损伤范围在0.50 m左右,与模拟结果相接近,验证了各向异性动态损伤本构的准确性。研究成果对浅埋小净距隧道的爆破开挖和损伤控制具有一定指导作用。     

形状记忆合金作动器的设计及优化

采用Ｂｒｉｓｉｏｎ［１］等提出的ＳＭＡ材料的本构关系，分析了形状记忆合金作动器在三种热交换方式（自然冷却、强制冷却和采用半导体热泵技术）下的动力特性，同时研究了ＳＭＡ丝在恒载和载荷变化时对完成正逆相变所用时间的影响，并简单讨论了影响作动器响应的几个因素和改进方法     

A multi-body optimization framework with a knee kinematic model including articular contacts and ligaments

Multi-body optimization is one of the methods proposed to reduce the errors due to soft-tissue artifact in gait analysis based on skin markers. This method uses a multi-body kinematic model driven by the marker trajectories. The kinematic models developed so far for the knee joint include a lower pair (such as a hinge or a spherical joint) or more anatomical and physiological representations including articular contacts and the main ligaments. This latter method allows a better representation of the joint constraints of a subject, potentially improving the kinematic and the subsequent static and dynamic analyses, but model definition and mathematical implementation can be more complicated. This study presents a mathematical framework to implement a kinematic model of the knee featuring articular contacts and ligaments in the multi-body optimization. Two penalty-based methods (minimized and prescribed ligament length variations) consider deformable ligaments and are compared to a further method (zero ligament length variation) featuring isometric ligaments. The multi-body optimization is performed on one gait cycle for five asymptomatic male subjects by means of a lower limb model including the foot, shank, thigh and pelvis. The mean knee kinematics, ligament lengthening and contact point positions are compared over the three methods. The results are also consistent with results from the literature obtained by bone pins or biplanar fluoroscopy. Finally, a sensitivity analysis is performed to evaluate how the joint kinematics is affected by the weights used in the penalty-based methods. The approach is purely kinematic, since the penalty-based framework does not require the solution of the joint static or dynamic analyses and makes it possible to consider ligament deformations without the definition of ligament stiffness that generally cannot be identified through in vivo measurements. Nevertheless, as far as a knee kinematic model is concerned, particularly in musculoskeletal modeling, this approach appears to be a good compromise between standard non-physiological kinematic models and complex deformable dynamic models.     

RESPONSE CHARACTERISTICS OF WIND EXCITED CABLES WITH ARTIFICIAL RIVULET

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Dynamic analysis of suspended cables carrying moving oscillators

An efficient procedure for analyzing in-plane vibrations of flat-sag suspended cables carrying an array of moving oscillators with arbitrarily varying velocities is presented. The cable is modelled as a mono-dimensional elastic continuum, fully accounting for geometrical nonlinearities. By eliminating the horizontal displacement component through a standard condensation procedure, the nonlinear integro-differential equation governing vertical cable vibrations is derived. Due to the dynamic interaction at the contact points with the moving oscillators, such equation is coupled to the set of ordinary differential equations ruling the response of the travelling sub-systems. An improved series representation of vertical cable displacement is proposed, which allows to overcome the inability of the traditional Galerkin method to reproduce the kinks and abrupt changes of cable configuration at the interface with the moving sub-systems. Following the philosophy of the well-known “mode-acceleration” method, the convergence of the series expansion of cable response in terms of appropriate basis functions is improved through the introduction of the so-called “quasi-static” solution. Numerical results demonstrate that, despite the basis functions are continuous, the improved series enables to capture with very few terms the abrupt changes of cable profile at the contact points between the cable and the moving oscillators.