Effects of coefficient of friction and coefficient of restitution on static packing characteristics of polydisperse spherical pebble bed

The effects of the coefficient of friction and coefficient of restitution on the static packing characteristics of a polydisperse spherical pebble bed are numer...     

Oblique Bounce of a Rubber Ball

Measurements are presented on the oblique impact of a hollow rubber ball incident on a polished granite surface, and the results are compared with those for a solid rubber superball. The hollow ball had a much higher coefficient of sliding friction than the superball, resulting in significant differences in all bounce parameters, at all angles of incidence. The hollow ball gripped the surface at all observed angles of incidence, resulting in one or two reversals in the direction of the friction force during the impact. The friction force was measured directly, as was the rotation speed of the ball during the impact. The results show that the tangential coefficient of restitution of a ball depends on both the coefficient of sliding friction and the ratio of the tangential to the normal vibration frequency of the ball.     

STABILITY ANALYSIS OF REUSABLE LAUNCH VEHICLE LANDING STRUCTURE$^{\bf 1)}$

近年来,包括中国在内的诸多国家相继开展垂直起降重复使用火箭的研究,运载火箭在平台上垂直着陆时的着陆稳定性为实现运载火箭重复使用的关键问题. 由于在运载火箭设计初期结构设计尚未完成,不具有供着陆稳定性分析的详细的动力学模型,难以开展着陆过程动力学仿真,故对运载火箭着陆稳定性评估方法的研究尤为必要. 本文基于广义碰撞定律,对二维运动模式下运载火箭与着陆平台的多点碰撞过程进行了分析,切向采用库伦摩擦模型给出了切向运动学恢复系数的表达式. 本文首先通过机械能约束和接触碰撞中的单边约束给出了一般运动形式下广义运动学恢复系数的值域,再对两种典型运动模式,给出了该两种典型运动模式下广义运动学恢复系数的值域. 然后考虑着陆腿中缓冲器的作用,将运载火箭与平台的碰撞近似为完全非弹性碰撞,得到了其广义运动学恢复系数,并结合运动学分析和能量法提出了一种基于碰撞后速度的着陆稳定性的判别方法. 最后以某型运载火箭着陆样机的参数为例,分析了碰撞前速度、着陆腿跨距、摩擦系数对着陆稳定性的影响,结果表明,本文提出的稳定性判别方法较能量法更为精确,可以考虑触地速度、角速度、摩擦系数等参数间的耦合关系.     

重复使用火箭着陆结构稳定性分析

近年来,包括中国在内的诸多国家相继开展垂直起降重复使用火箭的研究,运载火箭在平台上垂直着陆时的着陆稳定性为实现运载火箭重复使用的关键问题.由于在运载火箭设计初期结构设计尚未完成,不具有供着陆稳定性分析的详细的动力学模型,难以开展着陆过程动力学仿真,故对运载火箭着陆稳定性评估方法的研究尤为必要.本文基于广义碰撞定律,对二维运动模式下运载火箭与着陆平台的多点碰撞过程进行了分析,切向采用库伦摩擦模型给出了切向运动学恢复系数的表达式.本文首先通过机械能约束和接触碰撞中的单边约束给出了一般运动形式下广义运动学恢复系数的值域,再对两种典型运动模式,给出了该两种典型运动模式下广义运动学恢复系数的值域.然后考虑着陆腿中缓冲器的作用,将运载火箭与平台的碰撞近似为完全非弹性碰撞,得到了其广义运动学恢复系数,并结合运动学分析和能量法提出了一种基于碰撞后速度的着陆稳定性的判别方法.最后以某型运载火箭着陆样机的参数为例,分析了碰撞前速度、着陆腿跨距、摩擦系数对着陆稳定性的影响,结果表明,本文提出的稳定性判别方法较能量法更为精确,可以考虑触地速度、角速度、摩擦系数等参数间的耦合关系.     

Rigid body impact with moment of rolling friction

In this paper, the impact between a rigid pendulum and rough surfaces is studied. The rolling friction moment and the coefficient of rolling friction are introduced, and an improved mathematical model of the planar impact with friction is presented. The influence of the moment of rolling friction on the energy dissipated by friction during the impact is analyzed. For a simple pendulum, using the energetic coefficient of restitution, more energy is dissipated for larger values of the coefficient of kinetic friction and contact radius, and for smaller values of the length of the beam. For a double pendulum using the kinematic coefficient of restitution, some energetically inconsistent results can be solved for some values of the coefficient of rolling friction.     

Modeling of softsphere normal collisions with characteristic of coefficient of restitution dependent on impact velocity

This letter presents a theoretical model of the normal (head-on) collisions between two soft spheres for predicting the experimental characteristic of the coefficient of restitution dependent on impact velocity. After the contact force law between the contacted spheres during a collision is phenomenologically formulated in terms of the compression or overlap displacement under consideration of an elastic—plastic loading and a plastic unloading subprocesses, the coefficient of restitution is gained by the dynamic equation of the contact process once an initial impact velocity is input. It is found that the theoretical predictions of the coefficient of restitution varying with the impact velocity are well in agreement with the existing experimental characteristics which are fitted by the explicit formula.     

Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres

The current work presents a different methodology for modeling the impact between elasto-plastic spheres. Recent finite element results modeling the static deformation of an elasto-plastic sphere are used in conjunction with equations for the variation of kinetic energy to obtain predictions for the coefficient of restitution. A model is also needed to predict the residual deformation of the sphere during rebound, or unloading, of which several are available and compared in this work. The model predicts that a significant amount of energy will be dissipated in the form of plastic deformation such that as the speed at initial impact increases, the coefficient of restitution decreases. This work also derives a new equation for the initial critical speed which causes initial plastic deformation in the sphere that is different than that shown in previously derived equations and is strongly dependant on Poisson’s Ratio. For impacts occurring above this speed, the coefficient of restitution will be less than a value of one. This work also compares the predictions between several models that make significantly different predictions. The results of the current model also compare well with some existing experimental data. Empirical fits to the results are provided for use as a tool to predict the coefficient of restitution.     

考虑摩擦因素的结合面切向接触刚度分形预估模型及其仿真分析

为建立更完善和精确的结合面接触刚度模型,本文根据分形理论和摩擦学原理,从微观角度建立了考虑摩擦因素的结合面切向接触刚度分形预估模型.通过数值仿真分析研究了接触载荷、分形维数、摩擦系数和接触面积等因素对结合面切向接触刚度的影响.分析结果表明:结合面切向接触刚度随法向载荷和分形维数的增加而增大,而随分形尺度参数的增大而减小;摩擦系数对结合面切向接触刚度的影响较大,不同实际接触面积下的切向刚度相差较大;当分形维数较小时,摩擦系数对结合面切向刚度的影响将降低.这些研究对于进一步开展结合面的动力学特性研究具有重要意义.     

Dynamic Deformation Behavior of a Golf Ball during Normal Impact

The normal impact between a golf ball and a rigid steel target was studied to examine ball deformation and the contact force during the impact. Using high-speed video images, the normal and tangential compression ratios of the ball were measured to analyze the ball deformation quantitatively. In addition, the inbound and rebound ball velocities, contact time, and coefficient of restitution were determined as basic parameters of the impact. As the inbound ball velocity increased, the maximum normal compression ratio increased while the maximum tangential compression ratio, contact time and coefficient of restitution decreased. The ball center displacements during the impact were measured to determine the ball center velocity and acceleration, and the contact force was calculated by the product of the mass and acceleration. The contact force increased almost linearly with the inbound ball velocity, and its relationship agreed well quantitatively with the results from a load-cell, and also agreed well qualitatively with Hertz contact theory.     

Micromechanical analysis of friction anisotropy in rough elastic contacts

Computational contact homogenization approach is applied to study friction anisotropy resulting from asperity interaction in elastic contacts. Contact of rough surfaces with anisotropic roughness is considered with asperity contact at the micro scale being governed by the isotropic Coulomb friction model. Application of a micro-to-macro scale transition scheme yields a macroscopic friction model with orientation- and pressure-dependent macroscopic friction coefficient. The macroscopic slip rule is found to exhibit a weak non-associativity in the tangential plane, although the slip rule at the microscale is associated in the tangential plane. Counterintuitive effects are observed for compressible materials, in particular, for auxetic materials.     

基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究

基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究.首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模,在碰撞时采用冲量动量法求出跳跃速度,其次在法向上引入接触约束求解出碰撞力,在切向上采用LuGre摩擦模型分两种方式求解...     

一般运动刚体的恢复系数公式的适用条件

一般文献中,当用到关于恢复系数的牛顿公式时,都是针对两体碰撞的.该文针对两个受到一定外力作一般运动的刚体之间的碰撞,导出了牛顿恢复系数公式的适用条件.     

Measurements of impact properties of small, nearly spherical particles

The authors report impact properties for collisions of small, nearly spherical particles that present interesting experimental challenges. They consider difficulties arising with surface reflectivity, slight asphericity, surface damage and collisions with particles affixed to a rigid plate. To measure these impact properties, the authors refine the experimental technique of Foersteret al. To permit straightforward incorporation in rapid granular theories, the impacts are described with three coefficients. The first is the Newtonian coefficient of normal restitution. The second represents the frictional properties of the contact surfaces. The last characterizes the restitution of the tangential component of the contact point velocity for impacts that involve negligible sliding.     

Unsteady mixed convection flow from a rotating vertical cone with a magnetic field

An analysis is developed to study the unsteady mixed convection flow over a vertical cone rotating in an ambient fluid with a time-dependent angular velocity in the presence of a magnetic field. The coupled nonlinear partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The local skin friction coefficients in the tangential and azimuthal directions and the local Nusselt number increase with the time when the angular velocity of the cone increases, but the reverse trend is observed for decreasing angular velocity. However, these are not mirror reflection of each other. The magnetic field reduces the skin friction coefficient in the tangential direction and also the Nusselt number, but it increases the skin friction coefficient in the azimuthal direction. The skin friction coefficients and the Nusselt number increase with the buoyancy force.     

The prediction of the coefficient of restitution between impacting spheres and finite thickness plates undergoing elastoplastic deformations and wave propagation

Nonlinear Dynamics - The coefficient of restitution (COR) is a pragmatic analytical tool needed to solve impact problems. The coefficient is customarily obtained empirically by executing...     

Surface friction in a turbulent boundary layer with a positive pressure gradient

A dependence of the relative friction coefficient on the form parameter of the aerodynamic curvature is proposed on the basis of measurements of the tangential stress on the wall during the flow of a liquid in a diffusor using the electrodiffusion method. The intensity of fluctuations of the tangential stress at the wall and the instant of appearance of reverse flows are investigated. The results of measurement of the friction coefficient by the electrodiffusion method and Clauser method are compared.     

Collisions in a liquid fluidized bed

Collisional phenomena in a solid–liquid flow were studied in terms of two parameters: the collision frequency and the coefficient of restitution. Experimental measurements of these parameters were conducted inside a liquid fluidized bed by particle tracking in an index-matched array. Collision detection was based on the use of a peak acceleration threshold of the instantaneous speed of colored tracers. The measurements of collision frequency were compared with the theoretical expression derived from the kinetic theory for granular flow (KTGF). The normal and tangential restitution coefficients were measured from the trajectories before and after contact for both particle–particle and particle–wall collisions. A comparison with previous theoretical and experimental works is presented and discussed.     

受限颗粒体对制动系统非线性振动的影响

制动系统在工作时,往往受到沙粒、尘土以及磨屑等受限颗粒体的影响,这些受限颗粒体在摩擦副中的高度分布具有较强的随机性,一定程度诱发了制动系统的非线性振动. 本文中基于制动片切向振动模型,引入了新的受限颗粒体摩擦模型,提出了用波动系数来描述受限颗粒体高度分布随机性的强弱. 发现在特定参数下,当此系数为0时,制动片切向振动为周期运动;但是当此系数不为0时,制动片切向振动呈现拟周期或混沌运动,此时的切向振动分岔特性图的稳定轨道也会出现数量或分布的变化,甚至表现出混沌特性. 同一时变信号内,受限颗粒体引发制动片切向非线性振动包括发散、收敛以及拟周期运动等多种形式.      

干气密封滑动摩擦界面切向接触刚度分形模型

为揭示干气密封滑动摩擦界面高频微幅自激摩擦振动规律,用分形参数表征摩擦界面形貌特性,根据重新建立的微凸体接触变形方式,以及对非协调弹性体在切向力作用下初始滑动问题的研究,建立了干气密封滑动摩擦界面切向接触刚度分形模型. 通过数值对切向接触刚度的影响因素进行了分析,研究结果表明:切向接触刚度随分形维数、真实接触面积和材料特性系数的增大而增大;切向接触刚度随特征尺度、摩擦系数的增大逐渐减小. 相比于分形维数、特征尺度和材料特性系数对切向接触刚度的影响,摩擦系数的影响相对较小. 这些研究结果为进一步研究干气密封高频微幅自激摩擦振动奠定了基础.