Influence of elastic compliance of links on the dynamics and accuracy of a manipulating robot with rotational and translational joints

We pose problems of dynamic and kinematic control of spatial motions for multilink manipulating robot with elastic links and with rotational and translational joints. These problems are reduced to solving a system of ordinary and partial differential equations of hybrid type in the independent variables. We use a numerical integration algorithm for such systems which was developed earlier for manipulating robots with elastic links of anthropomorphic type. We discuss the difficulties arising in mathematical simulation of manipulating robots with simultaneously rotational and translational joints and with elastic links. To perform a comparative analysis and estimate the positional accuracy for the center of mass of the weight transported by the manipulator, we pose problems of dynamic and kinematic control of spatial motions of a manipulating robots with rigid links and with rotational and translational joints. The resolving equations obtained in this case are based on the Lagrange formalism of the second kind. By way of example, we present the solution of dynamic control problems for elastic and rigid two-link manipulators with one translational and two rotational joints.     

Numerical simulation of the hydrodynamic interaction between a sedimenting particle and a neutrally buoyant particle

A new method for the simulation of the translational and rotational motions of a system containing a sedimenting particle interacting with a neutrally buoyant particle has been developed. The method is based on coupling the quasi-static Stokes equations for the fluid with the rigid body equations of motion for the particles. The Stokes equations are solved at each time step with the boundary element method. The stresses are then integrated over the surface of each particle to determine the resultant forces and moments. These forces and moments are inserted into the rigid body equations of motion to determine the translational and rotational motions of the particles. Unlike many other simulation techniques, no restrictions are placed on the shape of the particles. Superparametric boundary elements are employed to achieve accurate geometric representations of the particles. The simulation method is able to predict the local fluid velocity, resolve the forces and moments exerted on the particles, and track the particle trajectories and orientations.     

粗糙颗粒动理学及稠密气固两相流动的数值模拟

考虑颗粒碰撞过程中摩擦作用,给出了粗糙颗粒碰撞动力学.引入颗粒相拟总温来表征颗粒平动和转动脉动能量的特征.基于气体分子运动论,建立颗粒碰撞中平动和旋转共同作用的粗糙颗粒动理学,给出了颗粒相压力和黏度等输运参数计算模型.运用基于颗粒动理学的欧拉-欧拉气固两相流模型,数值模拟了流化床内气体颗粒两相流动特性,分析了颗粒旋转流动对颗粒碰撞能量交换和耗散的影响.模拟得到的流化床内径向颗粒浓度和提升管内颗粒轴向速度与他人实验结果相吻合.模拟结果表明随着颗粒浓度的增加,颗粒相压力和能量耗散逐渐增加,而颗粒拟总温先增加后下降.随着颗粒粗糙度系数的增加,床内平均颗粒相拟总温和能量耗散增加,表明颗粒旋转产生的摩擦将导致颗粒旋转脉动能量的改变,影响床内气体-颗粒两相宏观流动特性.      

竖直流道宽度对气泡运动行为影响的数值模拟

用数值方法模拟了竖直通道宽度对气泡在液体中的非定常运动、变形以及传热特性的影响。在这个模拟中,界面跟踪采用了VOF方法,并采用PL IC进行界面重构。主流场计算采用有限容积方法将控制方程离散,其中扩散项采用中心差分格式,对流项采用一阶迎风格式。用成熟的S IM PLE算法求解N-S方程的速度与压力的耦合问题。引入CSF模型处理运动界面的表面张力。利用所编制的程序计算了竖直流道中的单个气泡的形状、运动特性以及气泡内外流场与传热特性,并对竖直通道宽度在不同情况下,对气泡的形状、运动特性以及传热特性进行了进一步的研究。得到了一系列有价值的结果,并与实验结果比较。表明数值模拟结果与实验结果吻合的较好。     

Gas–liquid mass transfer in the gas–liquid–solid mini fluidized beds

The gas–liquid–solid mini fluidized bed (GLSMFB) combines the advantages of fluidized bed and micro-reactor, and meets the requirements for safety and efficiency of green development of process industry. However, there are few studies on its flow performance and no studies on its mass and heat transfer performance. In this paper, the characteristics of gas–liquid mass transfer in a GLSMFB were studied in order to provide basic guidance for the study of GLSMFB reaction performance and application. Using CO₂ absorption by NaOH as the model process, the gas–liquid mass transfer performance of GLSMFB was investigated. The results show that the liquid volumetric mass transfer coefficient and the gas–liquid interfacial area both increase with the increase of the superficial gas velocity within the experimental parameter range under the same given superficial liquid velocity. At the same ratio of superficial gas to liquid velocity, the liquid volumetric mass transfer coefficient increases with the increase of the superficial liquid velocity. Fluidized solid particles strengthen the liquid mass transfer process, and the liquid volumetric mass transfer coefficient is about 13% higher than that of gas–liquid mini bubble column.     

Nonlinear dynamics of imperfectly-supported pipes conveying fluid

In this paper, the nonlinear dynamics of a pipe imperfectly supported at the upstream end and free at the other and conveying fluid is investigated. The imperfect support is modelled via cubic translational and rotational springs. The equation of motion is obtained via Hamilton’s principle for an open system, and the Galerkin method is used for discretizing the resulting partial differential equation. The dynamics of a system with either strong rotational or strong translational stiffness is examined in details. Numerical results show that similarly to a cantilevered pipe, the system undergoes a supercritical Hopf bifurcation leading to period-1 limit cycle oscillations. The Hopf bifurcation may, however, occur at a much lower flow velocity compared to the perfect system. At higher flow velocities, quasi-periodic and chaotic-like motions may be observed. The amplitude of transverse displacement is generally much higher than that for a cantilevered pipe, mainly due to large-amplitude rigid-body motion. In addition, effects of the mass ratio, internal dissipation, hardening- or softening-type nonlinearity, as well as concentrated- or distributed-type nonlinearity on the dynamics of the system are examined.     

Droplet spindown in a high-temperature gas environment

The spindown and heating of a spherical droplet in an initially undisturbed infinite fluid is investigated by means of a numerical model based on finite-difference discretization techniques. The nonevaporating droplet enters the hot gas while rotating about a diameter and has no translational motion with respect to the suspending medium. Special attention is given to the transient secondary (nonrotational) motion developed as a result of shear interaction between the two phases. The results indicate that for droplet sizes and rotation frequencies representative of droplet combustion applications; i.e., Reynolds ∼ O(0.1), the secondary motion in both phases remains weak and heat transport is conduction-dominated. On the other hand, the secondary motion is strengthened with increased values of the rotational Reynolds number. The characteristic time for droplet spindown is found to be proportional to the square of the droplet radius. The results also show that the rotational deceleration time is of the same order of magnitude with the translational response time of the droplet. Finally, the thermocapillary stress effects on fluid dynamics and heat transfer are investigated in this flow configuration.     

Flow and heat transfer in a rotating enclosure with axial throughflow

An analysis is made of the fluid flow and heat transfer processes in a circular cylindrical enclosure rotating about its own axis. A coolant is passed through the enclosure, entering and leaving through centrally located apertures in the end walls. This configuration is intended as a model of rotating enclosures in devices such as gas turbines and air compressors. The Navier-Stokes and energy equations were solved by a finite-difference formulation which can accommodate either steady or transient conditions. Buoyancy forces associated with the rotational body forces were included in some cases. All solutions were performed for laminar flow. For the parameter ranges investigated it was found that rotation inhibited the recirculating motion within the enclosure and thereby decreased the heat transfer relative to that for the stationary enclosure. Buoyancy further reduced the heat transfer owing to the break up of residual circulatory motions in the outer portion of the enclosure. Still stronger buoyancy brought about a slight increase in the heat transfer. The coolant flow was confined to a corridor adjacent to the axis of the enclosure, and there was no mixing between the coolant and the fluid in the enclosure proper.     

Wave regimes of ascending flow of a thin layer of a viscous liquid in contact with a gas

The flow of a liquid in thin layers is one of the hydrodynamic problems of chemistry and heat engineering. The large surface area of films and their small thickness make it possible to accelerate thermal, diffusive, and chemical processes at the gas-liquid boundary.Theoretical studies of liquid flow in a vertical descending thin layer are presented in [1–4]. In this paper we study ascending wave flows of a liquid in a thin vertical layer in contact with a gas, i.e., flows in the direction opposite the action of the force due to gravity, with account for the action of the gas on the liquid surface. Such motions are encountered when oil is extracted from strata that are saturated with gas. At some distance from the stratum the oil and gas separate: the gas travels at high velocity inside the pipe, occupying a considerable portion of the pipe, and the liquid is displaced toward the pipe walls, forming a thin film. In certain cases a wave-like interface develops between the oil and gas that travels with a velocity greater than that of the liquid but less than the average gas velocity. Similar phenomena are observed in high velocity mass exchangers.We examine the effect of the gas for both laminar and turbulent flow.Studies that neglect the effect of the gas flow on the liquid show that for waves on the film surface whose lengths are considerably longer than the average thickness of the layer, the liquid motion in the film is described by boundary layer equations in which account is taken of the mass force, i.e., the force due to gravity. With some approximation, we can assume that in accounting for the effect of the gas on the liquid the liquid flow is described by these same equations.     

Shock wave interactions with particles and liquid fuel droplets

Shock waves traveling through a multiphase flow environment are studied numerically using the Flux Corrected Transport (FCT) algorithm. Both solid particles and liquid droplets are used as the dispersed phase with their trajectories being computed using a Lagrangian tracking scheme. The phases are coupled by including source terms which account for mass transfer, momentum, and energy exchange from the dispersed phase in the governing equations of motion for the gas phase. For solid particles, droplet size effects are examined at constant mass loading. Deceleration of the shock wave is observed with effects increasing with decreasing particle size. The equilibrium velocity attained is found to agree with analytical results for an equivalent dense gas with a modified specific heat ratio. For liquid droplets, a droplet breakup model is introduced and the results show a faster attenuation rate than with the solid particle model. The inclusion of vaporization to the breakup model is seen to increase the attenuation rate but does not alter the final equilibrium velocity. When an energy release model is used in the simulations, behavior resembling a detonation is observed under certain conditions, with energy release coupling with and accelerating the shock front. Received 17 July 2000 / Accepted 20 August 2002 / Published online 4 December 2002 Correspondence to: Dr. K. Kailasanath (e-mail: kailas@lcp.nrl.navy.mil)     

Estimation of particle dynamics in 2-D fluidized beds using particle tracking velocimetry

The experimental characterization of particle dynamics in fluidized beds is of great importance in fostering an understanding of solid phase motion and its effect on particle properties in granulation processes. Commonly used techniques such as particle image velocimetry rely on the cross-correlation of illumination intensity and averaging procedures. It is not possible to obtain single particle velocities with such techniques. Moreover, the estimated velocities may not accurately represent the local particle velocities in regions with high velocity gradients. Consequently, there is a need for devices and methods that are capable of acquiring individual particle velocities. This paper describes how particle tracking velocimetry can be adapted to dense particulate flows. The approach presented in this paper couples high-speed imaging with an innovative segmentation algorithm for particle detection, and employs the Voronoi method to solve the assignment problem usually encountered in densely seeded flows. Lagrangian particle tracks are obtained as primary information, and these serve as the basis for calculating sophisticated quantities such as the solid-phase flow field, granular temperature, and solid volume fraction. We show that the consistency of individual trajectories is sufficient to recognize collision events.     

Transportation of heat through Cattaneo-Christov heat flux model in non-Newtonian fluid subject to internal resistance of particles

Thermal conduction which happens in all phases(liquid,solid,and gas) is the transportation of internal energy through minuscule collisions of particles and movement of electrons within a working body.The colliding particles comprise electrons,molecules,and atoms,and transfer disorganized microscopic potential and kinetic energy,mutually known as the internal energy.In engineering sciences,heat transfer comprises the processes of convection,thermal radiation,and sometimes mass transportation.Typi...     

Dynamics of a pipe conveying fluid flexibly restrained at the ends

The subject of this paper is the study of dynamics and stability of a pipe flexibly supported at its ends and conveying fluid. First, the equation of motion of the system is derived via the extended form of Hamilton׳s principle for open systems. In the derivation, the effect of flexible supports, modelled as linear translational and rotational springs, is appropriately considered in the equation of motion rather than in the boundary conditions. The resulting equation of motion is then discretized via the Galerkin method in which the eigenfunctions of a free-free Euler–Bernoulli beam are utilized. Thus, a general set of second-order ordinary differential equations emerges, in which, by setting the stiffness of the end-springs suitably, one can readily investigate the dynamics of various systems with either classical or non-classical boundary conditions. Several numerical analyses are initially performed, in which the eigenvalues of a simplified system (a beam) with flexible end-supports are obtained and then compared with numerical results, so as to verify the equation of motion, in its simplified form. Then, the dynamics of a pinned-free pipe conveying fluid is systematically investigated, in which it is found that a pinned-free pipe conveying fluid is generally neutrally stable until it becomes unstable via a Hopf bifurcation leading to flutter. The next part of the paper is devoted to studying the dynamics of a pinned-free pipe additionally constrained at the pinned end by a rotational spring. A wide range of dynamical behaviour is seen as the mass ratio of the system (mass of the fluid to the fluid+pipe mass) varies. It is surprising to see that for a range of rotational spring stiffness, an increase in the stiffness makes the pipe less stable. Finally, a pipe conveying fluid supported only by a translational and a rotational spring at the upstream end is considered. For this system, the critical flow velocity is determined for various values of spring constants, and several Argand diagrams along with modal shapes of the unstable modes are presented. The dynamics of this system is found to be very complex and often unpredictable (unexpected).     

Resonant dynamics in a rotordynamic system with nonlinear inertial coupling and shaft anisotropy

The response of a nonlinear, damped Jeffcott rotor with anisotropic stiffness is considered in the presence of an imbalance. For sufficiently small external torque or large imbalance, resonance capture or rotordynamic stall can occur, whereby the rotational velocity of the shaft is unable to increase beyond the fundamental resonance between the rotational and translational motion. This phenomena provides a mechanism for energy transfer from the rotational to the translational mode. Using the method of averaging a reduced-order model is developed, valid near the resonance, that describes this resonant behavior. The equilibrium points of these averaged equations, which correspond to stationary solutions of the original equations and rotordynamic stall, are described as the applied torque, damping, and anisotropy vary. As the anisotropy increases, assumed to arise from increasing shaft cracks, the torque required to eliminate the possibility of stall increases. However, when the system is started with zero initial conditions, the minimum torque required to pass through the resonance is approximately constant as the anisotropy increases. The predictions from the reduced-order model are verified against numerical simulations of the original equations of motion.     

基于Takagi—Sugeno模型的半主动TLCD对偏心结构的减震控制

采用在结构水平双向设置TLCD半主动控制装置的方法，对偏心结构在多维地震作用下的振动控制问题进行了研究。首先论述了基于Takagi—Sugeno模型的模糊神经网络的基本理论。然后介绍结构-TLCD扭转耦联控制系统微分方程及其状态空间求解方法，最后在建立起半主动控制策略的基础上。利用基于Takagi—Sugeno模型的模糊神经网络，根据控制准则调整TLCD的开孔率，实现对结构的半主动控制。数值结果表明，这种方法能对结构的平动反应和扭转反应都能起到较好的减震效果。     

Numerical simulation of uranium tetrafluoride fluorination in a multistage spouted bed using the improved CFD-DEM chemical reaction model

A CFD-DEM reaction coupling model was established to simulate UF₄ fluorination process, in which heat and mass transfer, heterogeneous chemical reaction, and particle shrinkage model were considered. The gas behavior was described by the conservation laws of mass, momentum, and energy. The solid phase is modeled with the discrete element method, considering the gas–solid interphase force, contact force, heat transfer, and chemical reaction models based on the discretized surface. Each particle can be individually tracked and associated with specific physical properties. The proposed CFD-DEM reaction coupling model based on particle shrinking reaction model with discretized surface was validated by the experimental and literature results at first. Then a multistage conical spouted bed was proposed and the process of UF₄ fluoridation reaction in it was investigated. The fluidization characteristics and the concentration distribution of gaseous products in the spouted bed with an extended gas velocity range were obtained and analyzed. In addition, the effects of different parameters, such as superficial gas velocity, temperature, fluorine concentration, on fluoridation rate and the fluorine conversion rate were investigated based on the proposed CFD-DEM reaction coupling model. The results obtained in this work are beneficial for method development of the chemical reaction simulation research in particle scale using the CFD-DEM model, and useful for operation and equipment parameters design of the uranium tetrafluoride fluorinate industrial process in the future.     

Planar mobility modes of 8-bar-jointed structures with a single degree of freedom

A range of modes of mobility for spatial structures can be achieved by selecting the rotational features of the joints. Similar mechanical characteristics are observed in structures ranging from molecules to buildings. The local rotational manner in a solid with an internal spatial structure performs a key part in dictating the nature of structural deformability. In this paper, we propose a two-dimensional repetitive motion structure assembled with straight rigid bars connected by 8-bar pivot joints. By determining the rotational modes of the 8-bar joint with certain geometrical constraints, we introduce some telescopic transformations of the proposed structure producing both well-known and novel motions. In addition, we verify one of the deployable mechanisms by manufacturing it and testing activation by a single rotary operation.     

A numerical study of droplet motion/departure on condensation of mixture vapor using lattice Boltzmann method

Droplet motion/departure, which is governed by external force acceleration coefficient, droplet radius and surface wettability on solid surfaces under external forces such as gravitational force, play a significant role in characterizing condensation heat transfer, especially when high fractional non-condensable gases (NCG) present. However, due to the challenge in visualizing the vapor/steam velocity field imposed by droplet motion/departure, the detailed mechanism of droplet motion/departure on condensing surfaces has not been completely investigated experimentally. In this study, droplet motion/departures on solid surfaces under external forces and their interactions with steam flow are simulated using two dimensional (2D) multiphase lattice Boltzmann method (LBM). Large external force acceleration coefficient, droplet radius and contact angle, lead to large droplet deformation and high motion/departure velocity, which significantly shortens the droplet residual time on the solid surface. Our simulation shows that steam vortices (lateral velocity) induced by droplet motion/departure can greatly disturb the vapor flow and would be intensified by increasing external force acceleration coefficient, droplet radius, and contact angle. In addition, the location of vortex center shifts in the ascending direction with increase of these factors. The average lateral velocities induced by droplet motion/departure at various conditions are obtained. The mass transfer resistance is substantially reduced owing to the droplet motion/departure, leading to an enhanced heat flux. The experimental results are compared to validate the influence of droplet motion/departure on condensation heat transfer performance, especially for steam–air mixture with the presence of high fractional NCG.     

Influence of heat transfer on the dynamic response of a spherical gas/vapour bubble

The standard approach to analyse the bubble motion is the well known Rayleigh–Plesset equation. When applying the toolbox of nonlinear dynamical systems to this problem several aspects of physical modelling are usually sacrificed. Particularly in vapour bubbles the heat transfer in the liquid domain has a significant effect on the bubble motion; therefore the nonlinear energy equation coupled with the Rayleigh–Plesset equation must be solved. The main aim of this paper is to find an efficient numerical method to transform the energy equation into an ODE system, which, after coupling with the Rayleigh–Plesset equation can be analysed with the help of bifurcation theory. Due to the strong nonlinearity and violent bubble motions the computational effort can be high, thus it is essential to reduce the size of the problem as much as possible. In the first part of the paper finite difference, Galerkin and spectral collocation methods are examined and compared in terms of efficiency. In the second part free and forced oscillations are analysed with an emphasis on the influence of heat transfer. In the case of forced oscillations the unstable branches of the amplification diagrams are also computed.