滚动问题中摩擦力的判断

刚体滚动时摩擦力的判断是工程力学中极易引起学生困惑的问题. 在对摩擦力产生原因进行分析的基础上, 确定了刚体纯滚动时静摩擦力的计算公式和判定方法. 刚体作纯滚动时静摩擦力所作总功为零, 仅实现刚体平动动能和转动动能之间的相互转化, 其方向总是阻碍主动力引起的物体运动趋势并使其向另一种运动转化; 刚体作有滑滚动时滑动摩擦力所作总功为负, 其方向与刚体滑动方向相反, 并实现刚体平动动能和转动动能之间的相互转化.     

摩擦与滚阻对被动行走器步态影响的研究

本文研究了圆弧足被动行走器支撑足与地面间的摩擦系数和滚阻系数对被动行走器步态的影响. 首先分别利用扩展的 赫兹接触力模型和LuGre摩擦模型描述了支撑足与地面接触点处的法向支撑力和切向摩擦力,并考虑了行走过程中支撑足 所受的滚动摩阻;其次利用第二类Lagrange方程推导出了该系统的动力学方程,并通过与已有成果的对比确定 了合适的LuGre摩擦模型参数;最后仿真分析了摩擦系数和滚阻系数对被动行走器步态的影响. 研究发现:摩擦系数的改变 虽然对被动行走器行走的平均速度、步幅,以及支撑足接触点处的最大法向接触力的影响较小,但摩擦系数的减小 会改变其行走步态类型,如发生倍周期分岔甚至混沌现象;然而,滚阻系数的改变会对行走器行走的 平均速度、步幅,以及支撑足接触点处的最大法向接触力的影响较大,尚未发现滚阻系数的改变会引起其行走步态的变化.      

Friction force model and rolling dynamics for a ball on a rough surface with presliding displacement taken into account

A model of sliding and spinning friction forces for a ball in the form of finite relations obtained by integrating the tangential stresses over the contact area whose parameters are determined by Hertz’s theory for the “ball-rough horizontal surface” tribological conjunction pair is supplemented with a model of rolling friction torques. The combined model is peculiar in that the presliding displacement effect in rolling and spinning friction torques is taken into account. It is shown that the ball motions in the presliding displacement zone are of quasilinear character and, under shock perturbations, have the form of damping vibrations in the three orientation angles. The numerical parameters of the rolling and spinning friction model are experimentally determined for the presliding displacement zones, while the sliding friction parameters and partly the spinning friction parameters are calculated. Mathematical modeling permits one to discover new properties of the ball, namely, its deceleration in rolling, the onset of damping vibrations at the beginning and end of motion, and the transient process parameters.     

Variational principles for constrained systems: Theory and experiment

In this paper we present two methods, the nonholonomic method and the vakonomic method, for deriving equations of motion for a mechanical system with constraints. The resulting equations are compared. Results are also presented from an experiment for a model system: a ball rolling without sliding on a rotating table. Both sets of equations of motion for the model system are compared with the experimental results. The effects of various forms of friction are considered in the nonholonomic equations. With appropriate friction terms, the nonholonomic equations of motion for the model system give reasonable agreement with the experimental observations.     

Influence of rolling friction on single spout fluidized bed simulation

In this paper we study the effect of rolling friction on the dynamics in a single spout fluidized bed using Discrete Element Method (DEM) coupled to Computational Fluid Dynamics (CFD). In a first step we neglect rolling friction and show that the results delivered by the open source CFD–DEM framework applied in this study agree with previous simulations documented in literature. In a second step we include a rolling friction sub-model in order to investigate the effect of particle non-sphericity. The influence of particle–particle as well as particle–wall rolling friction on the flow in single spout fluidized bed is studied separately. Adequate rolling friction model parameters are obtained using first principle DEM simulations and data from literature. Finally, we demonstrate the importance of correct modelling of rolling friction for coupled CFD–DEM simulations of spout fluidized beds. We show that simulation results can be improved significantly when applying a rolling friction model, and that experimental data from literature obtained with Positron Emission Particle Tracking (PEPT) technique can be satisfactorily reproduced.     

The impact of the concave distribution of rolling friction coefficient on the seismic isolation performance of a spring-rolling system

A complex yet realistic nonuniform rolling friction force distribution of a spring-rolling isolation system could lead to great complexity in determining its seismic response. This paper investigates the isolation performance of a spring-rolling isolation system assuming that the rolling friction force gradually and linearly increases with the relative displacement between the isolator and the ground. A series of ground motions with different characteristics were applied to this system. The analysis results show that the considered concavely distributed friction force is capable of dissipating the earthquake energy, and it is also able to modify the structural natural period. These merits combined help to improve the isolating efficacy of the spring-rolling isolation system compared with scenarios with uniform distribution pattern, and more importantly lead to a relatively optimum isolation state, avoiding a sudden amplification of the structural seismic response, regardless of the input motion characteristics.     

Dynamic Modes of One Seismic-Damping Mechanism with Frictional Bonds

The possible states of a system of interacting solids with rolling friction and unilateral sliding friction bonds are analyzed. The system can be used for seismic isolation of buildings. The structures (modes) of motion are established. The basic analytical relations are derived, which are needed to construct a dynamic model of variable structure     

两种型面轮轨滚动接触蠕滑率和摩擦功

采用数值分析方法详细分析了2种型面轮对与轨道在滚动接触过程中的接触几何、蠕滑率和摩擦功。在摩擦功分析计算中利用了Kalker三维弹性体非赫兹滚动接触理论,并考虑了轮轨的结构变形的影响。分析计算表明,在轮对运动相同的情况下,磨耗型轮对与轨道之间的蠕滑率和摩擦功与锥型轮对轨道之间的蠕滑率和摩擦功相差甚大。数值分析结果表明,现行铁路中正在推广使用的磨耗型轮对并不能减少轮轨接触表面之间的磨损,磨损型车轮的型面与钢轨尺寸的匹配还有待进一步改进。     

Rolling resistance of a rigid sphere with viscoelastic coatings

We present a novel three-dimensional boundary-element formulation that fully characterizes the mechanical behavior of the external boundary of a multi-layered viscoelastic coating attached to a hard rotating spherical core. The proposed formulation incorporates both, the viscoelastic, and the inertial effects of the steady-state rolling motion of the sphere, including the Coriolis effect. The proposed formulation is based on Fourier-domain expressions of all mechanical governing equations. It relates two-dimensional Fourier series expansions of surface displacements and stresses, which results in the formation of a compliance matrix for the outer boundary of the deformable coating, discretized into nodes. The computational cost of building such a compliance matrix is optimized, based on configurational similarities and symmetry. The proposed formulation is applied, in combination with a rolling contact solving strategy, to evaluate the viscoelastic rolling friction of a coated sphere on a rigid plane. Steady-state results generated by the proposed model are verified by comparison to those obtained from running dynamic simulations on a three-dimensional finite element model, beyond the transient. A detailed application example includes a verification of convergence and illustrates the dependence of rolling resistance on the applied load, the thickness of the coating, and the rolling velocity.     

On a Paradox in the Motion of a Rigid Particle along a Wall in a Fluid

The results of an experimental investigation of spherical particles with different surface roughnesses rolling under their own weight down an inclined pipe wall in a Newtonian fluid at low Reynolds numbers, both with (friction should be taken into account) and without contact with the wall, are presented. It is shown that a fixed particle moves differently in different fluids with similar viscosities and densities. This fact, as well as the possibility of particle motion without contact with the wall, cannot be explained within the framework of the usual hydrodynamic theories. An example is the dependence of the particle motion on the static pressure.     

Dynamic Processes in a Spheroidal Seismic-Damping Mechanism

A mathematical model of a variable-structure system of solids with rolling friction and unilateral sliding friction bonds is described. The model can be applied to seismic isolation mechanisms. Conditions for transition between the possible structures of the equations of state are formulated. The behavior of the system with kinematically defined motion of the base is analyzed as an example__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 119–127, January 2005.     

固体火箭发动机滚动球窝喷管弹塑性摩擦接触承载性能分析

固体火箭发动机滚动球窝喷管的弹塑性摩擦接触承载性能,属于复杂结构在复杂载荷作用下的弹塑性摩擦接触问题,它直接决定着系统的结构设计和功能发挥。为保证系统在承受极端工作载荷时,喷管不产生大的轴向位移,阴球、阳球与滚动体间具有一定的接触强度,同时不产生过量的塑性变形,设计阶段,基于计算精度高的三维摩擦接触问题的Lagrange乘子法,解决了与弹塑性耦合的算法问题;在滚动体运动分析及摩擦测试的基础上,模拟系统冷试车冲压试验,充分考虑材料表面强化层,建立了各构件间的弹塑性摩擦接触模型。有限元计算结果及冷试车分解试验、系统作动力矩测试试验结果表明,系统弹塑性摩擦接触承载性能满足结构设计要求,有限元建模及计算结果正确。     

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.     

Dynamics of a homogeneous ball on a horizontal plane with sliding,spinning, and rolling friction taken into account

We analyze the dynamics of a homogeneous ball on a horizontal plane with friction of all kinds, namely, sliding, spinning, and rolling friction, taken into account. The qualitative-analytic study of the ball dynamics is supplemented with numerical experiments.     

A Model for the Determination of the Resisting Torque of the Rolling Bearing Cage Motion of Slow-Speed Kinematic Pairs

A simplified, plane model for determination of resisting torques of the rolling bearing cage motion of low speed kinematic pairs is presented. The considerations are devoted to an arbitrary character of the point contact of a rolling element–cage pairs lying in a plane which is crossing the rolling elements in their geometrical centre. The model has been developed on the basis of the analysis of motion kinematics of a bearing track and rolling elements. The proposed algorithm allows for continuous tracking the resisting torque of the cage and its components during the kinematic pair motion.     

在微粗糙平面上滚动的Chaplygin球的稳定性

本文利用文献[1]的结果,继续讨论 Chaplygin 球在微粗糙平面上滚动的稳定性。严格证明了在粘性和库仓两种磨擦条件下球绕最大惯量主轴滚动的一致稳定性,和在粘性摩擦条件及球的最大与中间主惯量矩十分接近的前提下球绕最小惯量主轴滚动的不稳定性。     

车轮钢滚动剥离摩擦磨损特性研究

在NENE-2型摩擦磨损试验机上利用往复滚动试验装置研究了不同滚滑状态下车轮钢的剥离摩擦磨损特性和碳含量对车轮钢滚动剥离磨损性能的影响.结果表明:在不同滚滑状态下摩擦副之间的摩擦力不同,平面试样的表面磨痕形貌随着不同的切向摩擦力而明显不同,随着切向摩擦力的增大滚动磨损机制亦发生改变,剥离磨损加剧且磨损深度变大,当相对滑动量增大到一定程度后,磨损表现为明显的剥层机制;碳含量对车轮钢的滚动磨损表面磨痕形貌影响显著,碳含量低时磨痕以犁沟为主,碳含量高时剥离磨损发生的概率增加.     

Theory of rolling: Solution of the Coulomb problem

A theory of rolling of round bodies in the normal mode with adhesion conditions satisfied on the entire contact area is proposed. This theory refines the classical Coulomb’s theory of rolling in which the rolling moment is directly proportional to the pressing force (e.g., the weight of the rolling body). The rolling moment of cylinders is found to be directly proportional to the pressing force raised to a power of 3/2, and the rolling moment of balls and tori is proportional to the pressing force raised to a power of 4/3. It is shown that the normal mode of uniform rolling can only be provided for a certain ratio of the elastic constants of the materials of the round body and the base forming an ideal pair. The Coulomb problem is solved for the cases of rolling of an elastic cylinder over an elastic half-space, of an elastic ball over an elastic half-space, of an elastic torus over an elastic half-space, and of a cylinder and ball over a tightly stretched membrane. The rolling law is derived for such cases. The rolling friction coefficients, the rolling moment, and the rolling friction force are calculated.     

Brachistochrone for a rolling cylinder

The motion of a heavy homogeneous cylinder is considered as a no-slip rolling along the desired curve. We obtain a functional in the form of the total time of the cylinder rolling and solve the corresponding variational problem of minimizing this functional. We obtain an algebraic equation for the directional line of steepest descent, brachistochrone, in parametric form. We use the equation of motion of the cylinder with constraint reaction to determine the conditions of implementation of its pure rolling without separation and slip with respect to the brachistochrone.