两光滑球体斜碰时的恢复系数问题

本文首先就两球正碰的情况阐述了碰撞材质恢复系数的定义,着重指出根据碰撞冲量所给出的定义,即恢复系数等于碰撞过程中恢复冲量值与压缩冲量值之比.据此,进而分析两光滑球斜碰的情况,明确了引用“接近速度”与“分离速度”来表征恢复系数的确切含义。本文最后结合工科物理通用教材中的一道典型习题,具体验算了两弹性粒子斜碰时的恢复系数值。     

黏附性颗粒团撞击平面的离散元模拟

黏附性颗粒团的撞击和破碎存在于众多自然现象和工业过程中。本文采用离散元(DEM)方法模拟了微米颗粒组成的球形颗粒团与平面撞击的动力学过程,研究了表面能、撞击速度、弹性恢复系数和摩擦力等关键因素对碰撞过程及其特征时间、颗粒团破碎率的影响。不同表面能下颗粒团的破碎率与无量纲碰撞能存在归一化的关系,颗粒团破碎程度最高的时刻与直观的视觉判断差异明显,弹性恢复系数和滑动摩擦对临界碰撞能影响显著。     

关于恢复系数e的讨论

定义了物体的绝对恢复系数、计算一两物体碰撞时的共同恢复系数与两物体各自绝对恢复系数的关系，讨论了碰撞中的两物体各自因范性形变而损失的机械能。     

关于恢复系数计算公式问题的讨论

计算恢复系数的一般公式为一般书上由恢复系数的原始定义导出此公式时,都只考虑了碰撞双方在碰撞过程中在碰撞方向上所受冲量大小相等、方向相反的情形,而对于一般的情形没有讨论.这在解某些非此类特殊情形的问题时,能否用此公式常会产生疑问.本文拟就较一般的情形由恢复系数的原始定义导出公式(A).先从一个例题谈起. [题][1]质量为m2的光滑球用一不可伸长的绳系于固定点 A,另一质量为m1的球以与绳成 θ角的速度v1与m1正碰,试求m1及m2碰后开始运动的速度v1'及v2'.设恢复系数e为已知.(答案是: in。十inISill“0～ (1 e)m;sinH\ in。十wi18i…     

甘油液滴与水平固壁面碰撞力的试验研究

本文通过搭建液滴碰撞试验台,研究了甘油液滴分别撞击干燥水平壁面和带液滴壁面时碰撞力随时间的变化规律。研究结果显示:液滴撞击干燥壁面时,碰撞力峰值随碰撞速度与液滴直径的增大而增大;不同液滴直径与碰撞速度下的无因次碰撞力-无因次时间曲线明显贴近,无因次碰撞力峰值随液滴雷诺数增大而具有下降趋势;撞击带液滴壁面会使碰撞力峰值减小,碰撞力持续时间延长,液滴撞击带液滴壁面与干燥壁面的碰撞力峰值之比随碰撞速度增加先减小后趋于平缓。     

弹体材料在超高速碰撞过程中的物相演化

在碰撞速度大于10 km/s的超高速碰撞问题中,弹体材料大部分发生液化、汽化,以现有技术手段对此类问题进行实验研究存在一定难度。为深入了解超高速碰撞过程中材料物相的演化规律,揭示不同密度、熔点的材料在超高速碰撞过程中的物相演化特征,采用物质点法,结合GRAY三相物态方程,对铜、镍、铝3种金属材料的超高速碰撞问题进行数值模拟研究,得到不同碰撞速度下弹体材料物相分布随时间变化曲线,并总结出材料特性和碰撞速度对物相演化的影响规律,为开展超高速碰撞等效实验提供参考。     

脆性物质碰撞恢复系数e的测量

在科研中需要用煤炭与钢板碰撞的恢复系数,但在现有资料中无法查出,所以我们只好自己动手测量。最初用传统的方法进行测量都未能成功,失败的原因多数是作好的试样(煤炭球)与钢板碰撞时就破裂了。后来改用气垫导轨测量,由于碰前的速度可以人为控制,效果较好。现将测试的有关情况和结果分述如下。一、测试原理根据材料碰撞恢复系数的定义e=(u_2-u_1)/(v_1-v_2),即二碰撞物体碰后的相对速度(u_2-u_1)与碰撞前相对速度(v_1-v_2)之比。把用炭块作好的煤球与从测试件上取出的一小块钢板,分别紧密地固定在     

入射速度对颗粒/平板撞击过程影响的实验研究

以燃煤锅炉积灰为背景,对不同入射速度条件下SiO_2颗粒与光滑表面撞击特性进行实验研究。实验采用高速摄像机得到了颗粒法向的入射速度和反弹速度,重点研究了颗粒载体与撞击平台温差相同时,入射速度对粒径约为20μm颗粒的撞击特性影响。结果表明,不同温度场内颗粒法向恢复系数随法向入射速度的增大先急剧增大后平缓最后减小;颗粒入射法向速度相同时,法向恢复系数随平台温度的升高而减小;临界捕集速度随平台及气流的温度升高而增大。     

再谈恢复系数的物理意义

1998年第4期<物理通报>发表了徐志和的文章"恢复系数的意义及范围"[1],这篇文章是从动量的角度讨论恢复系数的物理意义,<大学物理>上也发表过有关恢复系数的文章[2～3],他们也只是从速度或者动量的角度去讨论恢复系数,并没有从能量方面去探讨.本文完全从能量的角度去讨论这个问题,而且结论简单富有意义,使得恢复系数的物理含义更加丰富多彩.     

冲击载荷下分层梯度泡沫材料中的应力波传播特性

以一维应力波传播理论为基础,建立了3层金属泡沫材料受到刚性块撞击时的理论模型,研究了刚性块撞击3层泡沫圆杆时的动力响应过程,从理论上给出了刚性块在撞击过程中的速度衰减规律数值解。利用ANSYS/LS-DYNA分析了受刚性块撞击时塑性应力波在3层泡沫材料中的传播过程,比较了刚性块以及层间界面处节点速度的变化规律。通过对比有限元结果与理论结果发现:理论模型能够较好地预测冲击载荷下分层泡沫材料各界面的速度衰减规律;3层梯度泡沫材料比相同质量的单层均质泡沫材料具有更加高效的吸能和缓冲能力。由于理论假设忽略了反射波以及泡沫材料应变硬化效应的影响,理论解与有限元模拟结果之间存在一定的误差。     

Rolling as a “continuing collision”

We show that two basic mechanical processes, the collision of particles and rolling motion of a sphere on a plane, are intimately related. According to our recent findings, the restitution coefficient for colliding spherical particles , which characterizes the energy loss upon collision, is directly related to the rolling friction coefficient for a viscous sphere on a hard plane. We quantify both coefficients in terms of material constants which allows to determine either of them provided the other is known. This relation between the coefficients may give rise to a novel experimental technique to determine alternatively the coefficient of restitution or the coefficient of rolling friction. Received 5 May 1999     

Coefficient of tangential restitution for viscoelastic spheres

The collision of frictional granular particles may be described by an interaction force whose normal component is that of viscoelastic spheres while the tangential part is described by the model by Cundall and Strack (Géotechnique 29, 47 (1979)) being the most popular tangential collision model in Molecular Dynamics simulations. Albeit being a rather complicated model, governed by 5 phenomenological parameters and 2 independent initial conditions, we find that it is described by 3 independent parameters only. Surprisingly, in a wide range of parameters the corresponding coefficient of tangential restitution, epsilont, is well described by the simple Coulomb law with a cut-off at epsilont = 0. A more complex behavior of the coefficient of restitution as a function on the normal and tangential components of the impact velocity, gn and gt, including negative values of epsilont, is found only for very small ratio gt/gn. For the analysis presented here we neglect dissipation of the interaction in normal direction.     

Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution epsilon which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, epsilon=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of epsilon on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for epsilon=const both methods lead to the same result for the self-diffusion coefficient. For the case of impact-velocity dependent coefficients of restitution, the Green-Kubo method is, however, either restrictive or too complicated for practical application, therefore we compute the diffusion coefficient using the Chapman-Enskog method. We conclude that in application to granular gases, the Chapman-Enskog approach is preferable for deriving kinetic coefficients.     

Dynamic Model of Elastoplastic Normal Collision of a Spherical Particle with a Half-Space with Allowance for Adhesion Interaction in a Contact Zone

Physics of the Solid State - The problem of a collision of a spherical homogeneous particle with a half-space is solved numerically. The coefficient of the normal velocity restitution is calculated...     

Collision dynamics of two adjacent oscillators

A linear analysis is made of a single collision between two single-degree-of-freedom systems separated by a gap. The contact is modelled by a spring and a viscous damper. The approach is to describe the motion of the pair as being composed of sum and difference displacements. The equation of motion during contact is found and the solution is obtained from the conditions at initial contact. The main parameters are the ratio of strain energy to kinetic energy at initial contact, and the damping of the contact. The contact time and the energy loss are calculated, which gives an expression for the coefficient of restitution for the collision. This coefficient is found to be dependent on the collision velocity, but becomes constant for strong collisions.     

Stationary states and energy cascades in inelastic gases

We find a general class of nontrivial stationary states in inelastic gases where, due to dissipation, energy is transferred from large velocity scales to small velocity scales. These steady states exist for arbitrary collision rules and arbitrary dimension. Their signature is a stationary velocity distribution f(v) with an algebraic high-energy tail, f(v) approximately v(-sigma). The exponent sigma is obtained analytically and it varies continuously with the spatial dimension, the homogeneity index characterizing the collision rate, and the restitution coefficient. We observe these stationary states in numerical simulations in which energy is injected into the system by infrequently boosting particles to high velocities. We propose that these states may be realized experimentally in driven granular systems.     

Scattering of particles with internal degrees of freedom

The scattering of particles with a small number of internal degrees of freedom is considered. Billiard formalism is used to study the scattering of two such structurally complex particles. The main scattering characteristics are found. Various types of scattering modes are revealed. In particular, a mode is detected when the velocity of motion of such particles away from each other is higher than their approach velocity before the collision. The scattering of such particles is shown to occur after a finite number of collisions. A generalized Newton law is proposed for the collision of particles with a small number of degrees of freedom, and the form of the effective coefficient of restitution is found.     

Behavior of one inelastic ball bouncing repeatedly off the ground

An experimental study of the behavior of one bead bouncing repeatedly off a static flat horizontal surface is presented. We observe that the number of bounces made by the bead is finite. When the duration between two successive bounces becomes of the order of the impact duration, the bead no longer bounces but oscillates on the elastically deformed surface before coming to rest. This transition is explained with a modified Hertz interaction law in which gravity is taken into account during the interaction. For each bounce, measurement of both the duration of collision and the restitution coefficient have been done. The effective restitution coefficient is essentially constant and close to 1 during almost all bounces before decreasing to zero when the impact velocity vanishes. This is due to an interplay between gravity and viscoelastic dissipation. Received: 2 December 1997 / Accepted: 5 March 1998     

Numerical simulation of powder transport behavior in laser cladding with coaxial powder feeding

Laser cladding with coaxial powder feeding is one of the new processes applied to produce well bonding coating on the component to improve performance of its surface. In the process, the clad material is transported by the carrying gas through the coaxial nozzle, generating gas-powder flow. The powder feeding process in the coaxial laser cladding has important influence on the clad qualities. A 3D numerical model was developed to study the powder stream structure of a coaxial feeding nozzle. The predicted powder stream structure was well agreed with the experimental one. The validated model was used to explore the collision behavior of particles in the coaxial nozzle, as well as powder concentration distribution. It was found that the particle diameter and restitution coefficient greatly affect the velocity vector at outlet of nozzle due to the collisions, as well as the powder stream convergence characteristics below the nozzle. The results indicated a practical approach to optimize the powder stream for the coaxial laser cladding.