Dynamic analysis of microrobots with Coulomb friction using harmonic balance method

In this paper, we investigate the dynamic analysis of a strongly nonlinear microrobot using a three-term harmonic balance method. The employed locomotion concept, namely “friction drive principle,” is based on the superposition of a horizontal vibration at the interface between the robot and work floor and an active variation of friction force, obtained by the vertical vibration of the base at the same interface. The equation of motion for the system reveals a parametrically excited oscillator with discontinuity for which the elastic force term is proportional to a signum function. The obtained periodic solution not only is of high accuracy, but also can predict the contribution of the friction coefficient in the average velocity of the slider. Results show that the velocity and the step efficiency of motion depend almost sinusoidally on the phase shift between the horizontal and the vertical vibration. Unlike traditional analytical techniques and in agreement with both numerical simulations and experimental results reported in the literature, the utilized method demonstrates that the maximum average velocity occurs at a phase shift that varies with respect to system’s configuration parameters. Besides, the effect of variation of different configuration parameters on the behavior of this type of microrobots has been studied and the maximum achievable performance in terms of velocity and the step efficiency has been evaluated.     

A new approach for dynamic analysis of flexible manipulator systems

In this paper, a new approach for dynamic analysis of the flexible multibody manipulator systems is described. The organization of the computer implementations which are used to automatically construct and numerically solve the system of loosely coupled dynamic equations expressed in terms of the absolute, joint and elastic coordinates is discussed. The main processor source code consists of three main modules: constraint module, mass module and force module. The constraint module is used to numerically evaluate the relationship between the absolute and joint accelerations. The mass module is used to numerically evaluate the system mass matrix as well as the non-linear Coriolis and centrifugal forces associated with the absolute, joint and elastic coordinates. At the same time, the force module is used to numerically evaluate the generalized external and elastic forces associated with the absolute, joint and elastic coordinates. Computational efficiency is achieved by taking advantage of the structure of the resulting system of loosely coupled equations. The absolute, joint and elastic accelerations are integrated forward in time using direct numerical integration methods. The absolute positions and velocities can then be determined using the kinematic relationships. The flexible 2-DOF double-pendulum and spatial manipulator systems are used as illustrated examples to demonstrate and verify the application of the computational procedures discussed in this paper.     

A modular algorithm for linear, periodic train-track models

Summary  An algorithm is presented which can be used for the investigation of a large variety of train-track models. These models only have to fulfil the requirements of linearity and periodicity with respect to the track length direction. A steady-state solution is obtained for a vehicle moving on a tangent track with constant velocity. The algorithm itself can be split into three modules: one for the whole train-track system, one for the track, and one for a single rail support. These modules and their interfaces are described in detail. The article demonstrates the applicability of the algorithm by means of four examples. The first example shows the influence of the sleeper elasticity on the sleeper motion. The second one illustrates the effect of an advanced subsoil model on the wheel/rail contact force. Subsequently, as a further example, the compliance frequency-response functions of a ballasted track and a rigid track are compared. The last example deals with the sleeper passing excitation. Here, it is shown that even in the case of resonance, the wheel/rail contact-force fluctuations remain below ten percent of the static value. Received 17 January 2000; accepted for publication 18 August 2000     

Nonlinear Oscillations of a Nonresonant Cable under In-Plane Excitation with a Longitudinal Control

The nonlinear oscillations of a controlled suspended elastic cable under in-plane excitation are considered. Active control realized by longitudinal displacement of one support is introduced in order to reduce the transverse in-plane and out-of-plane vibrations. Linear and quadratic enhanced velocity feedback control laws are chosen and their effects on the cable motion are investigated using a two degree-of-freedom model. Perturbation analysis is performed to determine the in-plane steady-state solutions and their stability under an out-of-plane disturbance. The analysis is extended to the bifurcated two-mode steady-state oscillations in the region of parametric excitation. The dependence of the control effectiveness on the system parameters is investigated in the case of the first symmetric mode and the range of oscillation amplitudes in which the proposed control ensures a dissipation of energy is determined. Although control based only on in-plane response quantities is effective in reducing oscillations with a prevailing in-plane component, addition of out-of-plane measures has to be considered when the motion is characterized by two comparable components.     

Motion of a sphere colliding with a rough surface

The following problems of inertial motion of a sphere are considered: between two parallel planes, inside another sphere, and inside a circular cylinder. It is assumed that, at the instant of impact, the no-slip condition is fulfilled: the tangential velocity of the contact point of the sphere is equal to zero; in other words, a constraint is imposed and removed instantaneously. It is shown in the above cases that in the limit the motion of the sphere becomes steady in velocity: the angular velocity of the sphere tends to be constant and the velocity of its center becomes periodic in the first case or conditionally periodic in the second and third cases. In certain cases, the coordinates specifying the position and orientation of the sphere also reach the steady-state regime.     

Working Processes of cyclic-action machinery for soil deformation—part IIDer arbeitsvorgang von maschinen mit zyklischer bewegung im hinblick auf die bodenverformung - teil II

The analysis deals with machinery for horizontal boring, consisting of a main unit moving with constant velocity and a slider-crank mechanism providing reciprocating motion of the tool. Special emphasis is placed on the force and energy aspects of the working process. It is established that the basic parameters of the process, including the velocity of the main unit, the maximum tractive force in the working cycle, the crank throw, the energy consumption and other, are largely dependent on the displacement of the tool in the loading stage (‘displacement per cycle’ for short). Each value of this displacement is associated with a set of the above parameters, a change in one of which affects the others. The optimal value is determined here, corresponding to the minimum energy consumption, which is considerably lower than that of the corresponding continuous (quasistatic) process. The reduction of the tractive force, compared with the latter, is attributable to the toughening effect of non-recoverable deformation at prelimiting levels of the frontal resistance force of the soil.     

Working Processes of cyclic-action machinery for soil deformation—part II

The analysis deals with machinery for horizontal boring, consisting of a main unit moving with constant velocity and a slider-crank mechanism providing reciprocating motion of the tool. Special emphasis is placed on the force and energy aspects of the working process. It is established that the basic parameters of the process, including the velocity of the main unit, the maximum tractive force in the working cycle, the crank throw, the energy consumption and other, are largely dependent on the displacement of the tool in the loading stage (‘displacement per cycle’ for short). Each value of this displacement is associated with a set of the above parameters, a change in one of which affects the others. The optimal value is determined here, corresponding to the minimum energy consumption, which is considerably lower than that of the corresponding continuous (quasistatic) process. The reduction of the tractive force, compared with the latter, is attributable to the toughening effect of non-recoverable deformation at prelimiting levels of the frontal resistance force of the soil.     

Vibration of a Non-Linear Self-Excited System with Two Degrees of Freedom under External and Parametric Excitation

Vibration analysis of a non-linear parametrically self-excited system with two degrees of freedom under harmonic external excitation was carried out in the present paper. External excitation in the main parametric resonance area was assumed in the form of standard force excitation or inertial excitation. Close to the first and second free vibrations frequency, the amplitudes of the system vibrations and the width of synchronization areas were determined. Stability of obtained periodic solutions was investigated. The analytical results were verified and supplemented with the effects of digital and analog simulations.     

Modeling of vibrational impact motion of mobile-based body

The paper deals with vibrational impact motion of a mobile-based body on an inclined plane, which is a characteristic for vibrational alignment of components subjected to an automated assembly. The alignment model is presented by a two-degree-of-freedom vibro-impact system in which the moving body is impacting the plane obliquely. Properties of the vibrational impact motion under kinematical excitement of the moving body and under the excitement of the plane in two perpendicular directions were investigated by numerical methods. It was determined that impact displacement occurs under transient regimes of motion from static to dynamic state of equilibrium. Dependencies of maximum displacement of the body and average displacement velocity on force of elastic resistance, amplitude of plane vibration in the direction of the displacement, and phase angle between the perpendicular members of vibration components were established. Zones of system and excitement parameter combination when the vibrational impact motion occurs were defined.     

Nanomachines: a general approach to inducing a directed motion at the atomic level

The motion of bodies in a periodic potential relief with weak damping is discussed. A spontaneous directed motion of particles at a velocity unambiguously defined by the frequency of a periodic action and spatial period of the potential is shown to be possible in the presence of external periodic actions of different type. The principles of inducing the directed motion at a precisely controlled velocity discussed here can be used to develop: (i) means of handling with individual molecules or molecular clusters on crystalline surfaces; (ii) “nanomachines”—objects capable of spontaneous motion not only in the absence of the external force but also under the action of the force reverse to the direction of motion (thereby capable of carrying other particles); (iii) drives providing precisely controlled velocity of motion; (iv) controllable tribological systems by profiling of friction surfaces in a specified manner and applying an ultrasonic excitation. The dependence of the average system velocity on the average applied force (perceived as “the law of friction of the system” at the macroscopic level) is shown to have plateaus of constant velocity at a zero velocity and a set of equidistant discrete velocities in the presence of periodic external perturbations. The problem of developing fully controlled nanomachines can be formulated as the problem of controlling the width and position of the plateaus.     

Motion of two interconnected mass points under action of non-symmetric viscous friction

This paper deals with the analysis of a one-dimensional motion of two mass points in a resistive medium. The force of resistance is described by small non-symmetric viscous friction acting on each mass point. The magnitude of this force depends on the direction of motion. The mass points are interconnected with a kinematic constraint or with an elastic element. Using the averaging method the expressions for the stationary “on the average” velocity of the systems’s motion as a single whole is found. In case of a small degree of non-symmetry an explicit expression for the stationary “on the average” velocity of the system is derived. For the other case we obtained algebraic equations for the corresponding stationary velocity.     

ROBUST CONTROL OF VORTEX-INDUCED VIBRATION OF A RIGID CYLINDER SUPPORTED BY AN ELASTIC BEAM USING μ -SYNTHESIS

For lightweight and flexible structures, it is important to suppress the vibrations induced by interactions between fluid and structures. This paper presents the robust control of the vortex-induced vibration of a rigid circular cylinder supported by an elastic cantilever beam in which the fluid force is considered as an external excitation on the structure. For the problems considered here, the excitation frequency is assumed to be equal to the natural frequency of the structure or the “lock-in” frequency. The natural frequencies of this analytical model are calculated by using the modal analysis method and then modal coordinates are introduced to obtain the state equations of the structural system. A pair of piezoelectric devices fixed under the base plate, on which the elastic beam is clamped, were used as actuators. A robust controller satisfying the nominal performance and robust performance is designed using μ -synthesis theory based on the structured singular value. Simulation and experiment were carried out with the designed controller and the effectiveness of the robust control strategy was verified by both experimental and simulation results.     

Vibration drift with quadratic drag

The motion of a mechanical system in which one of the bodies experiences drag proportional to the squared velocity is considered. The motion is assumed to be caused by a harmonic internal force. Approximate expressions determining the velocity of the system relative to the medium are obtained.     

基于遗传算法的温差发电系统模块布局优化设计

温差发电在航空航天等极端环境供电和汽车余热利用等领域具有重要的应用,然而低的热电转换效率严重限制了其发展.目前主要从提高材料本身性能和优化热电模块结构两方面提升性能.本文从整体出发,建立了基于遗传算法的温差发电系统模块布局优化设计方法.融合已有的解析模型,发展了能够快速获得系统电输出功率的性能评估方法;通过遗传算法,以...     

The ultratough peeling of elastic tapes from viscoelastic substrates

The peeling of an elastic thin tape from a flat smooth viscoelastic substrate is investigated. Based on a Green function approach and on the translational invariance, a closed form analytical solution is proposed, which takes into account the viscoelastic dissipation in the substrate material.We find that peeling is prevented from taking place, only when the external force is smaller than the one predicted by Kendall's formula for elastic tapes on rigid substrates. However, we also find that, regardless of the value of the applied force, steady state detachment may occur when the elastic tape is sufficiently stiff. In this case, the constant peeling velocity can be modulated by properly defining the geometrical parameters and the material properties of tape and viscoelastic foundation. On the other hand, for relatively high peeling angles or compliant tapes a threshold value of the peeling force is found, above which the steady-state equilibrium is no longer possible and unstable detachment occurs.The present study contributes to shed light on the behavior of pressure sensitive adhesives in contact with viscoelastic substrates like the human skin. At the same time, it can be considered a first step towards a better understanding of the effect of viscoelastic dissipation on the fracture behavior of solids.     

Dynamic properties of automotive damper modules

This paper addresses the dynamic properties of automotive shock absorber modules. Analyzing an equivalent linear system, a set of characteristic dimensionless numbers are introduced in order to qualify the dynamic performance of the damper and the damper module. The dependency of these numbers on the main parameters of the module like the damping constant, the spring stiffness of the damper, the top mount stiffness and the piston rod mass is shown. These numbers may also serve as similarity coefficients for quite different dampers regarding their dynamic behavior. Furthermore, they can be used to adjust the stiffness of the different force elements of the damper module to achieve an optimal damping quality.     

串列布置三圆柱涡激振动频谱特性研究

对串列三圆柱体双自由度涡激振动问题进行了数值计算, 并分析了雷诺数、固有频率比和约化速度对串列三圆柱体结构动力响应及频谱特性的影响. 研究发现: 雷诺数、频率比对上游圆柱的振幅和流体力系数的影响较小. 中游圆柱频率锁定区域随着雷诺数的增大而增大, 其动力响应受上游圆柱尾流的影响较大, 但频率比的影响较小. 同时, 流体力系数在约化速度较小时受雷诺数和频率比的影响较大. 另外, 下游圆柱的振幅和流体力系数受雷诺数及频率比的影响较大. 雷诺数、频率比和约化速度对圆柱流体力系数能量谱密度(PSD)曲线中主峰幅值、频谱成分及波动性的影响较大. 流体力系数PSD曲线波动性的增强, 导致圆柱运动轨迹会从"8"字形转变成不规则形状. 当频率比为2.0时, 上游圆柱尾流出现P$+$S模式, 导致其发生非对称运动, 且升、阻力系数PSD曲线主峰重合. 最后, 激励荷载平均功率值随约化速度的变化趋势与对应的结构动力响应的变化类似. 在同一约化速度区间内, 结构振动响应的强弱与位移的平均功率值成正比. 对不同约化速度区间内的升力系数功率谱密度分析时, 振动频率比($f_{s}/f_{n, y})$对结构振动响应的影响更大.      

An experimental and analytical study of autoparametric resonance in a 3DOF model of cable-stayed-beam

Autoparametric interaction and the associated phenomenon of amplitude saturation are experimentally observed in a physical model of cable-and-beam structure. In this system, the horizontal beam is fixed at one end and supported at the other end by an inclined taut cable. The longitudinal axes of beam and cable are in a vertical plane. Three natural frequencies of the system are approximately of the ratio 1:1:2. This is a combination of two conditions that are very likely to occur in relatively long-span, multi-stay-cable bridges, namely, 1:1 tuning and 1:2 superharmonic tuning. While the beam is vertically excited with sufficiently large force near a primary resonance, the cable vibrates horizontally at half of excitation frequency. The beam also vibrates horizontally at half-frequency, as well as vertically. As the vertical excitation on the bean is further increased in amplitude, the vertical vibration amplitude gets saturated instead of increasing proportionately. A 3DOF analytical model of the structure is also derived, where the finite motion of the cable introduces geometric nonlinearities in quadratic and cubic forms. The system parameters having been carefully measured from the experimental model, steady-state solutions of the coupled nonlinear equations of motion are obtained, by the perturbation method of multiple time scales. Agreement between experimental observation and analytical prediction is very good, both qualitatively and quantitatively. Very good agreement is found also in the case of horizontal excitation of the beam, where effects of linear and nonlinear interaction are apparent.     

Transverse Elastic–Friction Vibrations of a Running Aircraft

An analytical model of the plane-parallel running of an aircraft under crosswind load is proposed. The compliance of the internal constraints of the aircraft and the nonlinearity of the side force on the landing gear wheels are taken into account. The model is intended to study the transverse elastic friction vibrations of the aircraft hull and landing gears. The steady motion of the aircraft is considered. The dependence of the lateral friction force on the slip angle is assumed to have the form of a sinusoidal segment. The Routh–Hurwitz instability conditions are derived in an explicit form