The stiffness of an elastic solid with an embedded,nominally spherical inclusion subjected to a small arbitrary motion

The article examines the problem of translation and rotation of a nominally (slightly deformed) spherical rigid inclusion embedded into an unbounded elastic medium. To the first order in the small parameter characterizing the boundary perturbation, explicit expressions are deduced for the induced displacement field as well as for the net force and net torque required to produce the applied translation and rotation.     

A technique for studying interaction between a screw dislocation dipole or a concentrated load and a mode III crack crossing an interface

A method of potentially wide application is developed for deriving analytical expressions of the elastic interaction between a screw dislocation dipole or a concentrated force and a crack cutting perpendicularly across the interface of a bimaterial. The cross line composed of the interface and the crack is mapped into a line, and then the complex potentials are educed. The Muskhelishvili method is extended by creating a Plemelj function that matches the singularity of the real crack tips, and eliminates the pseudo tips’ singularity induced by the conformal mapping. The stress field is obtained after solving the Riemann–Hilbert boundary value problem. Based on the stress field expressions, crack tip stress intensity factors, dislocation dipole image forces and image torque are formulated. Numerical curves show that both the translation and rotation must be considered in the static equilibrium of the dipole system. The crack tip stress intensity factor induced by the dipole may rise or drop and the crack may attract or reject the dipole. These trends depend not only on the crack length, but also on the dipole location, the length and the angle of the dipole span. Generally, the horizontal image force exerted at the center of the dislocation dipole is much smaller than the vertical one. Whether the dipole subjected to clockwise torque or anticlockwise torque is determined by whether the Burgers vector of the crack-nearby dislocation of the dipole is positive or negative. A concentrated load induces no singularity to crack tip stress fields as the load is located at the crack line. However, as the concentrated force is not located on the crack line but approaches the crack tip, the nearby crack tip stress intensity factor K_IIIu increases steeply to infinity.     

Disturbance compensation of a dual-arm underwater robot via redundant parallel mechanism theory

Disturbance compensation is one of the major issues for underwater robots to hover as a mobile platform and to manipulate an object in an underwater environment. This paper presents a new strategy of disturbance compensation for a mobile dual-arm underwater robot using internal torques derived from redundant parallel mechanism theory. A model of the robot was analyzed by redundant serial and parallel mechanisms at the same time. The joint torque to operate the robot is obtained from a redundant serial mechanism model with null-space projection due to redundancy. The joint torque derived from the redundant parallel kinematic model is calculated to perfectly compensate for disturbances to the mobile platform and is included in the solution of the joint torque based on the serial redundant model. The resultant joint torque can generate force on the end-effector for required tasks and forces for disturbance compensation simultaneously . A simulation shows the performance of this disturbance compensation strategy. The joint torque based on the algorithm generates the desired task force and the disturbance compensation force together, and a little additional joint torque can generate a large internal force effectively due to the characteristics of a redundant parallel mechanism. The proposed method is more effective than compensation methods using thrusting force on the mobile platform.     

Hydrodynamic force and torque models for a particle moving near a wall at finite particle Reynolds numbers

This research work is aimed at proposing models for the hydrodynamic force and torque experienced by a spherical particle moving near a solid wall in a viscous fluid at finite particle Reynolds numbers. Conventional lubrication theory was developed based on the theory of Stokes flow around the particle at vanishing particle Reynolds number. In order to account for the effects of finite particle Reynolds number on the models for hydrodynamic force and torque near a wall, we use four types of simple motions at different particle Reynolds numbers. Using the lattice Boltzmann method and considering the moving boundary conditions, we fully resolve the flow field near the particle and obtain the models for hydrodynamic force and torque as functions of particle Reynolds number and the dimensionless gap between the particle and the wall. The resolution is up to 50 grids per particle diameter. After comparing numerical results of the coefficients with conventional results based on Stokes flow, we propose new models for hydrodynamic force and torque at different particle Reynolds numbers. It is shown that the particle Reynolds number has a significant impact on the models for hydrodynamic force and torque. Furthermore, the models are validated against general motions of a particle and available modeling results from literature. The proposed models could be used as sub-grid scale models where the flows between particle and wall can not be fully resolved, or be used in Lagrangian simulations of particle-laden flows when particles are close to a wall instead of the currently used models for an isolated particle.     

Slow motions of a circular cylinder experiencing slip near a plane wall

A theoretical study is presented for the two-dimensional creeping flow caused by a long circular cylindrical particle translating and rotating in a viscous fluid near a large plane wall parallel to its axis. The fluid is allowed to slip at the surface of the particle. The Stokes equations for the fluid velocity field are solved in the quasi-steady limit using cylindrical bipolar coordinates. Semi-analytical solutions for the drag force and torque acting on the particle by the fluid are obtained for various values of the slip coefficient associated with the particle surface and of the relative separation distance between the particle and the wall. The results indicate that the translation and rotation of the confined cylinder are not coupled with each other. For the motion of a no-slip cylinder near a plane wall, our hydrodynamic drag force and torque results reduce to the closed-form solutions available in the literature. The boundary-corrected drag force and torque acting on the particle decrease with an increase in the slip coefficient for an otherwise specified condition. The plane wall exerts the greatest drag on the particle when its migration occurs normal to it, and the least in the case of motion parallel to it. The enhancement in the hydrodynamic drag force and torque on a translating and rotating particle caused by a nearby plane wall is much more significant for a cylinder than for a sphere.     

Aerodynamic coefficients of a spinning sphere in a rarefied-gas flow

A three-dimensional rarefied-gas flow past a spinning sphere in the transitional and near-continuum flow regimes is studied numerically. The rarefaction and compressibility effects on the lateral (Magnus) force and the aerodynamic torque exerted on the sphere are investigated for the first time. The coefficients of the drag force, the Magnus force, and the aerodynamic torque are found for Mach numbers ranging from 0.1 to 2 and Knudsen numbers ranging from 0.05 to 20. In the transitional regime, at a certain Knudsen number depending on the Mach number the Magnus force direction changes. This change is attributable to the increase in the role of normal stresses and the decrease in the contribution of the shear stresses to the Magnus force with decrease in the Knudsen number. A semi-empirical formula for the calculation of the Magnus force coefficient in the transitional flow regime is proposed.     

Second-order effect of an elastic circular shaft during torsion

In this paper we deal with the second-order effect of an elastic circular shaft duringtorsion.The analysis is based on the method of co-moving coordinates and the strain-rotation decomposition theorem in continuum mechanics.By using asymptotic expansionmethods,we comfirm that the effect of axial elongation and distortion of plane cross-section exists in an elastic circular shaft during large torsion and give the expressions ofthe axial force and the torque.     

静压气体球轴承支承球形转子的干扰力矩分析

中心小孔供气单向受载球面气体轴承可以用于球形转子的静平衡测量。对作用于转子上的干扰力矩进行估算是平衡装置设计的重要部分。本在一定假设条件下推导了由粘性剪切应力和气膜支撑力引起的作用于转子上的干扰力矩。干扰力矩以轴承包角、中心气室张角、气膜压力、转子转速、转子旋转轴位置、失中度、转子非球表示。以干扰力矩最小为准则分析了这些参数的影响，结论有助于静平衡装置的优化设计以及对精度的进一步分析。     

Power spectral density analysis of draft and torque fluctuations of a PTO powered disk tiller

Experiments were conducted in a typical Bangkok clay soil with a PTO driven disk tiller to collect the draft force and torque variation data. Tests were conducted at different forward speeds of 0.29, 0.59, 0.86, 1.08 and 1.37 m/s and at 28° and 33° disk gang angle settings. Average soil moisture content was 26% and average cone index of the test soil was 1870 kPa during all the tests. The draft force was measured by a three point linkage dynamometer. The PTO torque was measured by a slip ring type torque transducer. Tests were also conducted in the unpowered mode. Fast Fourier transform (FFT) and power spectral density (PSD) analysis techniques were used to analyse the draft force and torque variations in a time domain. The results indicated that the dominant frequencies of the draft force variations were within the range of 2.5–5.5 cycles/m of forward travel. The wave length was longer at a higher disk gang angle setting. The dominant frequency component of the torque variations varied from 3.3 to 4.3 cycles/revolution of the disk. In the unpowered mode the dominant frequencies of the draft signals had less magnitude than those of the powered mode for the same operating conditions at both disk gang angle settings of the powered disk.     

Interactions between a rectangular cylinder and a free-surface flow

The salient features of the interaction between a free-surface flow and a cylinder of rectangular cross-section are investigated and discussed. Laboratory-scale experiments are performed in a water channel under various flow conditions and elevations of the cylinder above the channel floor. The flow field is characterized on the basis of time-averaged and fluctuating local velocity measurements. Dynamic loadings on the cylinder are measured by two water-insulated dynamometers placed inside the cylinder structure. Starting from frequency and spectral analyses of the force signals, insights on the relationship between force dominant frequencies and the Strouhal number of the vortex shedding phenomenon are provided. Experimental results highlight the strong influence of the asymmetric configuration imposed by the two different boundary conditions (free surface and channel floor) on (i) the mean force coefficients and (ii) the vortex shedding frequencies. We provide an analysis of the nature of the dependence of average force coefficients on relevant dimensionless groups, i.e., the Reynolds number, normalized flow depth and cylinder submersion.     

The hydrodynamic force and torque on a bounded sphere in Poiseuille flow

The lattice Boltzmann (LB) method is used to study the hydrodynamic force and torque acting on a sphere held stationary between parallel plates in pressure‐driven flow. This and associated flow configurations are explored in this paper. LB results are in excellent agreement with existing theory and numerical results for simple pressure‐driven flow between parallel plates, for flow through a periodic medium of spheres [Zick AA, Homsy GM. Stokes flow through periodic arrays of spheres. Journal of Fluid Mechanics 1982; 115: 13], and for the force and torque acting on a sphere held fixed at the quarter vertical position in a pressure‐driven flow between parallel plates. In the latter case, LB calculations reveal a screening effect caused by neighboring periodic images of the test sphere. It is shown that the test sphere is hydrodynamically decoupled from its periodic images when separated by approximately 30 sphere radii. LB results for force and torque as a function of sphere height and flow cell height are also reported. Copyright © 2001 John Wiley & Sons, Ltd.     

A NUMERICAL AND ANALYTICAL STUDY ON A TAIL-FLAPPING MODEL FOR FISH FAST C-START＊

The force production physics and the flow control mechanism of fish fast C-start are studied numerically and theoretically by using a tail-flapping model. The problem is simplified to a 2-D foil that rotates rapidly to and fro on one side about its fixed leading edge in water medium. The study involves the simulation of the flow by solving the two-dimensional unsteady incompressible Navier-Stokes equations and employing a theoretical analytic modeling approach. Firstly, reasonable thrust magnitude and its time history are obtained and checked by fitting predicted results coming from these two approaches. Next, the flow fields and vortex structures are given, and the propulsive mechanism is interpreted. The results show that the induction of vortex distributions near the trailing edge of the tail are important in the time-averaged thrust generation, though the added inertial effect plays an important role in producing an instant large thrust especially in the first stage. Furthermore, dynamic and energetic effects of some kinematic controlling factors are discussed. For enhancing the time-averaged thrust but keeping a favorable ratio of it to time-averaged input power within the limitations of muscle ability, it is recommended to have a larger deflection amplitude in a limited time interval and with no time delay between the to-and-fro strokes. The project supported by the CAS (KJCX-SW-L04)     

螺栓扭矩系数影响因素的试验研究

在螺栓连接结构中,为保证连接的可靠性,必须为螺栓提供合适的预紧力。工程中通常采用扭矩法装配螺栓连接结构,因此需要确定预紧力与扭矩之间的关系(即扭矩系数),以施加合适的装配扭矩。本文对输电塔中常用的M16镀锌螺栓进行预紧力试验研究,测试分析了螺栓强度等级、有无垫圈和有无润滑对螺栓连接副扭矩系数的影响。研究结果表明,高强度螺栓比普通螺栓的扭矩系数小,数据离散性也小;无垫圈的螺栓比有垫圈的螺栓扭矩系数小,但数据离散性大;有润滑的螺栓比无润滑的螺栓扭矩系数小,数据离散性也小。本文同时探讨了如何控制、调整扭矩系数,以及螺栓连接中要注意的问题,为设计和施工单位提供参考。     

Forces on a porous sphere spinning in a fluid flow

Exact expressions are found for the drag (modified Stokes force) and the lift (modified Magnus force) on a porous sphere spinning slowly in a viscous fluid flowing slowly and uniformly past it.     

Mathematical model for cold rolling based on energy method

There is an increasing requirement for improved accuracy of the rolling models which are widely used in rolling plant in order to produce high-quality products, because this accuracy is important for rolling schedule setup and automatic control. A three-dimensional mathematical model for cold rolling using tangential velocity field and energy method is firstly proposed to investigate the deformation of the strip at the roll gap based on elastic and plastic mechanics. The field and geometrical approximation yield criterion are used to integrate the internal plastic deformation power. The friction power is analyzed using the co-line vector inner product method. Finally, the analytical expressions of roll separating force and roll torque are obtained quickly considering the effect of roll flattening on the roll separating force. The predicted roll separating forces are consistent with other researchers’ models, especially for on-line measured roll separating forces in a tandem cold rolling plant. The accurate predicted results provide valuable guidelines for optimization of rolling process.     

Formulation of the problem of the motion of a small body in a perturbed flow

The classical problem of the hydrodynamic reactions on a body of arbitrary shape moving in a fluid at rest [1] was generalized by Sedov to the case of an accelerated translational flow [2]. In the expressions for the hydrodynamic reactions, the shape of the body is represented only by the coefficients λ_ij of the added masses and the volume Ω of the body. In the general case of motion of a body in a nontranslational flow the shape of the body cannot be represented by a finite set of coefficients in the determination of the hydrodynamic reactions. An important simplification occurs in the small-body formulation, which again leads to expressions for the force and torque similar to the classical expressions. The problem of the motion of a small body in a perturbed nontranslational flow was posed by Grigoryan and Yakimov [3], and with allowance for deformation of the body by Yakimov [4]. Later studies containing this formulation have been reviewed by Vil'khovchenko and Yakimov [5]. The aim of the present paper is to formulate the small-body problem more precisely. The order of smallness of the terms in the earlier studies was estimated solely as a function of the power of a small parameter — the size of the body. In the present paper it is shown that if it is additionally required that the final expression for the reactions should contain only principal terms containing the components ν_i and ω_i of the translational and angular velocities, and also terms describing the flow structure, then the expression found by Grigoryan and Yakimov [3] for the hydrodynamic reaction is valid. The terms are estimated on the basis of dimensional analysis. Such arguments have already been used by the author for special examples [6, 7].     

Stereo-PIV study of flow around a maneuvering fish

Stereoscopic PIV was used to measure the three-component velocity distribution around a live fish. At the same time, shadow images of the fish were captured by additional cameras in order to reconstruct the three-dimensional shape of the fish. The side jet shed against the swept tail during turning was evident in the results. The height of the jet was approximately equal to the height of the tail fin, and a vortex ring was observed around the side jet. Based on the circulation and diameter of the vortex ring, the impulse and time-averaged force in terms of the side jet were estimated.     

On the moment of forces acting on a body in a ferrofluid

Attention is drawn to the appreciable torque which acts on a nonmagnetic body in a ferrofluid when a field is applied. The contribution to the torque made by an external inhomogeneity of the field and the perturbation introduced by the body is considered. It is shown that in fields obtained in practice they may be comparable. A method of calculating the resultant force and the resultant torque is considered. The moment of the forces that act on a cylinder of elliptic section in homogeneous and inhomogeneous fields is calculated. An experimental investigation confirmed the theoretical calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 132–136, July–August, 1980.     

外环干扰力矩对陀螺加速度计测试精度的影响

摆式积分陀螺加速度计的外环干扰力矩包括仪表外环轴的摩擦力矩和交叉轴加速度引起的交变力矩。作者分析了引起摆式积分陀螺加速度计外环干扰力矩的主要原因,提出一种在高精度三轴测试转台上分离摆式积分陀螺加速度计外环干扰力,测试摆式积分陀螺加速度计精度的试验方法。该试验采用三轴转台中环转动速度随动摆式积分陀螺加速度计外环进动角速度,同时摆式积分陀螺加速度计陀螺摆的输出轴在整个试验中保持水平,从而分离仪表外环干扰力的方案。通过对试验数据进行分析,得出外环干扰力的存在影响了摆式积分陀螺加速度计测试精度,为改善摆式陀螺加速度计工艺以提高摆式陀螺加速度计的测试精度提供了依据。     

Design of multi-degree motion haptic mechanisms using smart fluid-based devices

This article presents two different types of haptic masters capable of 4-degree- of-freedom (DOF) force feedback utilizing magnetorheological fluid (MR) and electrorheological (ER) fluid. The proposed ER master consists of a spherical joint for 3-DOF rotational motion and a linear device for 1-DOF translational motion, the MR haptic master consists bi-directional clutches associated with a planetary gear system and one-directional clutch with a bevel gear system. After showing the configuration of each haptic mechanism, the torque and force models of the actuators are derived based on the field-dependent Bingham model. After undertaking optimal design with spatial limitation and desired torque level, two different types of haptic master systems are manufactured. The torque and force responses are experimentally evaluated to validate practical feasibility of the proposed haptic masters for medical application.