大柔性Stewart平台的刚度研究

大型射电望远镜舱索系统通过六根索长的协调变化驱动馈源舱作跟踪射电源的六自由度运动,其工作特点类似于Stewart平台,因此被看作大柔性Stewart平台。基于大型射电望远镜舱索系统50m缩比模型,首先分析了悬索的垂跨比与悬索张力、系统基频之间的关系;其次,研究了大柔性Stewart平台零位时的竖向刚度;最后,对舱体在不同位姿处的扭转刚度进行分析。研究工作为变结构悬索系统的振动分析与运动控制奠定了基础。     

弹性杆-刚性体系统动力学分析的广义逆矩阵方法

将多刚体系统的广义逆矩阵方法推广到含弹性杆与刚性体的混合系统的动力学分析中,建立了以节点坐标表示的基于全局惯性坐标系的刚体-柔性体混合系统动力学方程.首先以两端节点坐标为变量推导了弹性杆的动力学方程,以刚性体节点坐标为变量推导了刚性体节点速度约束方程和刚性体动力学方程,最后得到弹性杆与刚性体混合系统的动力学方程和速度约束方程.本方法在同一个惯性坐标系对刚柔多体系统进行描述,具有方法简洁、便于计算建模的特点.论文最后给出两个数值算例,检验了方法的有效性.     

考虑附加质量的中心刚体-柔性梁系统的动力学特性研究

对有附加质量的中心刚体-柔性梁系统的动力学特性进行了研究。柔性梁为等截面的Euler Bernoulli梁,针对柔性梁变形场使用假设模态法进行了离散,并运用第二类拉格朗日方程推导出系统的动力学方程后,采用Matlab编制了动力学仿真软件。首先讨论了附加质量对系统的固有频率与振型的影响,其次讨论了在大范围运动已知和未知的条件下,不同位置附加质量的中心刚体-柔性梁系统的刚柔耦合动力学特性,对带有附加质量的中心刚体-柔性梁系统的中心刚体转角、梁末端位移响应以及中心刚体角速度的仿真结果进行了分析。结果表明:附加质量从柔性梁固定端向自由端移动时,柔性梁前五阶固有频率近似地呈现周期性变化;附加质量所处位置的不同,对于系统的刚柔耦合动力学响应以及系统振型的影响十分明显。     

简单柔性机械臂的构造性塑动力学方法

本文提出了适于简单柔性机械臂的一种基于谱分析的构造性逆动力学方法。数值模拟和实验结果表明，这种方法提供的开环输入力矩，不仅可以实现机械臂特定的刚体转动，而且可以有效地减弱柔性对机械臂精确定位的影响。     

提高多体系统离散时间传递矩阵法计算精度的研究

深入探讨多体系统离散时间传递矩阵法对平面、空间刚体-光滑铰多体系统运动响应的研究。提出提高该方法计算精度和计算稳定性的方法，导出相应的多端刚体传递矩阵。设计了角坐标的迭代循环，该变量不必采用近似形式，因而提高了计算精度和计算稳定性。其它方法有：1)增加泰勒展开式的高阶项；2)合理选择将速度、加速度表示为位移的线性函数的方法(本文简称线性化方法)；3)合理确定迭代循环的初值等。对4种多体系统进行了计算机仿真研究，表明本文提出的方法有效。     

简单柔性机械臂的构造性逆动力学方法

本文提出了适于简单柔性机械臂的一种基于谱分析的构造性逆动力学方法。数值模拟和实验结果表明，这种方法提供的开环输入力矩，不仅可以实现机械臂特定的刚体转动，而且可以有效地减弱柔性对机械臂精确定位的影响。     

平面刚架弹塑性大位移分析的多刚体离散元法

本文基于多刚体－弹簧系统模型，给出了求解平面刚架结构弹塑性、大位移极限承载力分析的多刚体离散元法。文中首先推导了多刚体离散元法在总体坐标下的切线刚度阵，建立多刚体离散元法的增量平衡方程；而后推导了多刚体离散元的弹塑性弹簧系数矩阵，建立了多刚体离散元内力屈服面塑性铰法的增量求解格式，成功地进行了平面钢框架的弹塑性、大位移极限承载力分析。计算结果与其他数值方法或实验结果吻合良好，显示了多刚体离散元方法进行结构极限承载力分析这一复杂问题的优越性     

计及热应变的空间曲梁的刚-柔耦合动力学

研究带中心刚体的作大范围运动的空间曲梁的刚-柔耦合动力学.结合混合坐标法和绝对坐标法的特点,取与中心刚体大范围运动有关的变量和柔性梁各单元节点相对中心刚体连体基的位移和斜率作为广义坐标,建立了一种新的柔性梁的刚柔耦合模型.基于精确的应变和位移的关系式,根据Jourdian速度变分原理,建立了带中心刚体柔性曲梁的有限元离散的动力学方程.数值对比了空间曲梁系统和空间直梁系统的刚柔耦合动力学性质,用能量守恒规律验证了文中曲梁模型的合理性.在此基础上,在应变能中计及热应变,研究温度增高引起的曲梁的热膨胀对系统的动力学性态的影响.     

中心刚体-柔性梁系统的耦合变形影响

本文对作大范围运动的中心刚体-柔性梁系统的耦合变形的影响进行研究.给出一种新的描述柔性梁耦合变形的有限元插值方法,该方法采用笛卡尔变形坐标对横向变形和纵向变形之间的耦合项进行描述,该耦合变形项只与本单元的节点变形坐标相关.分别讨论了耦合变形项对惯性力与弹性力的贡献,分析了它们对刚-柔耦合动力学行为的影响.通过研究指出当采用笛卡尔变形坐标描述时,如果在计算弹性力的时候考虑了耦合变形影响,无论在计算惯性力时是否考虑耦合变形影响,都可以得到稳定收敛的结果.反之,如果在计算弹性力时忽略了耦合变形影响,无论在计算惯性力时是否考虑耦合变形影响,当大范围运动的速度较高时,将会得到错误的发散的结果.因此,通过忽略耦合变形对质量分布的影响,只保留耦合变形对弹性力的影响,可实现对动力学方程的简化.     

柔性体的刚-柔耦合动力学分析

对柔性梁的刚－柔耦合动力学特性进行分析，从连续介质力学理论出发，在纵向变形位移中计及了耦合变形量，用Jourdain速度变分原理导出了柔性梁的刚－柔耦合动力学方程，定量地研究了非惯性系下柔性梁的动力学性质，比较了在不同转速下零次近似模型和耦合模型的振动频率的差异。为了确定零次近似模型的适用范围，引入与转速和基点加速度有关的相关系数，提出了零次近似模型的适用判据为相关系数小于0．1。在此基础上，进一步研究在大范围运动是自由的情况下柔性梁的大范围运动和变形运动的耦合机理，计算了带平动刚体的柔性梁的大范围运动规律，揭示零次近似模型和耦合模型的刚－柔耦合动力学性质的根本差异。     

LT50m模型二级运动调整系统的动力学分析

安装在悬挂馈源舱内的Stewart平台作为馈源位姿精调机构与舱索粗调系统一起构成了大型射电望远镜(LT)馈源位姿的两级调整系统。使用索结构的悬链线解析方程以及在忽略舱体振动导致的Stewart平台惯性力的基础上,应用Newton-Euler法建立了舱索系统与Stewart平台耦合的动力学简化模型。通过对LT50m缩比模型的仿真分析,模拟了馈源舱对Stewart平台扰动的响应,并由实验进行了验证。     

Tractor cabin’s passive suspension parameters optimization via experimental and numerical methods

Reduction of transmitted vibrations of tractor cabin which is caused by road roughness is the major objective of this study; consequently operator health can be achieved. This objective is carried out via experimental measurements and finite element modeling. For this purpose the vertical acceleration of the cabin as well as the rear axle of the tractor is measured in different road conditions and forward speeds. However, it should be mentioned that tests were carried out according to the ISO 2631-1985 but no measurements were done on the driver’s seat. Then the finite element model of the cabin’s tractor is developed and the dynamic response of the cabin interior (with the measured axle acceleration as input dynamic force) is obtained. At the third step the suspension parameters are calculated by comparing the accelerations obtained from the model and measurements. Finally the suspension parameters are optimized according to ISO 2631-1985 via iterative method.     

Numerical study of the noninertial systems: application to train coupler systems

Car coupler forces have a significant effect on the longitudinal train dynamics and stability. Because the coupler inertia is relatively small in comparison with the car inertia; the high stiffness associated with the coupler components can lead to high frequencies that adversely impact the computational efficiency of train models. The objective of this investigation is to study the effect of the coupler inertia on the train dynamics and on the computational efficiency as measured by the simulation time. To this end, two different models are developed for the car couplers; one model, called the inertial coupler model, includes the effect of the coupler inertia, while in the other model, called the noninertial model, the effect of the coupler inertia is neglected. Both inertial and noninertial coupler models used in this investigation are assumed to have the same coupler kinematic degrees of freedom that capture geometric nonlinearities and allow for the relative translation of the draft gears and end of car cushioning (EOC) devices as well as the relative rotation of the coupler shank. In both models, the coupler kinematic equations are expressed in terms of the car body and coupler coordinates. Both the inertial and noninertial models used in this study lead to a system of differential and algebraic equations that are solved simultaneously in order to determine the coordinates of the cars and couplers. In the case of the inertial model, the coupler kinematics is described using the absolute Cartesian coordinates, and the algebraic equations describe the kinematic constraints imposed on the motion of the system. In this case of the inertial model, the constraint equations are satisfied at the position, velocity, and acceleration levels. In the case of the noninertial model, the equations of motion are developed using the relative joint coordinates, thereby eliminating systematically the algebraic equations that represent the kinematic constraints. A quasistatic force analysis is used to determine a set of coupler nonlinear force algebraic equations for a given car configuration. These nonlinear force algebraic equations are solved iteratively to determine the coupler noninertial coordinates which enter into the formulation of the equations of motion of the train cars. The results obtained in this study showed that the neglect of the coupler inertia eliminates high frequency oscillations that can negatively impact the computational efficiency. The effect of these high frequencies that are attributed to the coupler inertia on the simulation time is examined using frequency and eigenvalue analyses. While the neglect of the coupler inertia leads, as demonstrated in this investigation, to a much more efficient model, the results obtained using the inertial and noninertial coupler models show good agreement, demonstrating that the coupler inertia can be neglected without having an adverse effect on the accuracy of the solution.     

Modelling and transient planar dynamics of suspended cables with moving mass

In this study, the 3D nonlinear equations of motion of the suspended cable with moving mass are obtained via the Hamilton principle, and its transient linear planar dynamics is investigated. Considering the quasi-static assumption, the condensed planar model accounting for the effect of the moving mass is derived, and it is then discretized by choosing the static deflection and sine series as shape functions. It is shown that this expansion shows good convergence features. The Newmark method is used to investigate the transient response. The effects of the inertia force, mass, sag and velocity of the moving mass on the transient dynamics of the suspended cable are systematically investigated. Finally, the horizontal tension of the suspended cable and the case of sequentially moving masses are examined.     

An analysis of horizontal plane motion of tracked vehicles

This paper presents a theoretical analysis of non-stationary motion of a tracked vehicle on level ground. A practical model that includes track slippage, inertia force and the moment of inertia was developed to analyze and predict steering dynamics and steerability on the subject examined.

The system of differential equations was programmed and numerically solved on a digital computer, where the inputs are circumferential velocities of right and left drive sprockets.

The simulations for J-turn maneuver disclose the effects of initial forward velocities on the transient responses of the track slip velocity, side slip angle, yaw rate, and acceleration of the center of gravity of a tracked vehicle.     

Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

For both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

     

Inverse dynamics analysis of a general spherical star-triangle parallel manipulator using principle of virtual work

Inverse dynamics of a general model of a spherical star-triangle (SST) parallel manipulator (Enferadi and Akbarzadeh Tootoonchi, Robotica 27:663–676, 2009) is the subject of this paper. This manipulator is of type 3-RRP, has good accuracy and relatively a large workspace which is free of singularities (Enferadi and Akbarzadeh Tootoonchi, Robotica, Revised paper, 2009). First, inverse kinematics utilizing the angle axis representation is solved. Next, velocity and acceleration analysis as well as link Jacobian matrices are obtained in invariant form. Finally, a systematic approach based on the principle of virtual work and the concept of link Jacobian matrices is presented. This method allows elimination of constraint forces and moments at the passive joints from motion equations. It is shown that the dynamics of the manipulator can be reduced to solving a system of three linear equations with three unknowns. Moreover, a computational algorithm for solving the inverse dynamics is developed. Two examples with different trajectories for the moving spherical platform are presented and motor torques are obtained. Results are verified using a commercial dynamics modeling package.     

A second strain gradient elasticity theory with second velocity gradient inertia – Part II: Dynamic behavior

This paper is the sequel of a companion Part I paper devoted to the constitutive equations and to the quasi-static behavior of a second strain gradient material model with second velocity gradient inertia. In the present Part II paper, a multi-cell homogenization procedure (developed in the Part I paper) is applied to a nonhomogeneous body modelled as a simple material cell system, in conjunction with the principle of virtual work (PVW) for inertial actions (i.e. momenta and inertia forces), which at the macro-scale level takes on the typical format as for a second velocity gradient inertia material model. The latter (macro-scale) PVW is used to determine the equilibrium equations relating the (ordinary, double and triple) generalized momenta to the inertia forces. As a consequence of the surface effects, the latter inertia forces include (ordinary) inertia body forces within the bulk material, as well as (ordinary and double) inertia surface tractions on the boundary layer and (ordinary) inertia line tractions on the edge line rod; they all depend on the acceleration in a nonstandard way, but the classical laws are recovered in the case of no higher order inertia. The classical linear and angular momentum theorems are extended to the present context of second velocity gradient inertia, showing that the extended theorems—used in conjunction with the Cauchy traction theorem—lead to the local force and moment (stress symmetry) motion equations, just like for a classical continuum. A gradient elasticity theory is proposed, whereby the dynamic evolution problem for assigned initial and boundary conditions is shown to admit a Hamilton-type variational principle; the uniqueness of the solution is also discussed. A few simple applications to wave propagation and dispersion problems are presented. The paper indicates the correct way to describe the inertia forces in the presence of higher order inertia; it extends and improves previous findings by the author [Polizzotto, C., 2012. A gradient elasticity theory for second-grade materials and higher order inertia. Int. J. Solids Struct. 49, 2121–2137]. Overall conclusions are drawn at the end of the paper.     

Dynamic Separation of Resistance Spot Welded Joints: Part I—Experiments

An analysis for an impact system is presented. The results are then used to interpret the test data from dynamic separation of resistance spot welded joints. In this Part I of the investigation emphasis is placed on the design consideration, development of a test system and verification of the design from actual test data obtained from the test system. In addition, the inertia effect of a generic dynamic system is analyzed using the principle of rigid body dynamics. It is shown that the load recorded by a load cell could include both the load experienced by the test specimen and the inertia force generated from the mass and acceleration between the specimen and the load cell, when the load cell is placed on the fixed side of the test specimen. Impact fixtures designed for spot weld strength testing are then studied for the inertia effect.     

LT50m缩比模型悬索舱体系统的风振分析

在新一代大型射电望远镜（LT）的悬索舱体系统中增加了抑制风激振动的下拉结构控制索系，并分析了50m缩比模型的风振响应。首先，由非线性静力分析确定结构初始静态参考位形和初应力；其次，针对结构特点模拟作用在悬索和馈源舱上的随机风荷。在上述研究的基础上，在时域中模拟分析下拉索系对结构风振的抑制效果，同时通过典型节点时域响应的FFT变换，给出响应自功率谱图，进一步描述了振动控制的效果。