Transformation of sliding motion to rolling during spheres collision

In this research, we have investigated the three-dimensional elastic collision of two balls, based on friction in the tangential plane. Our aim is to offer analytical closed form relations for post collision parameters such as linear and angular velocities, collision time and tangential and normal impulse in three dimensions. To simplify the problem, stick regime is not considered. In other words, balls have a low tangential coefficient of restitution. Sliding, sliding then rolling, and rolling at the beginning of contact are three cases that can occur during impact which have been considered in our research. The normal interaction force is described by the Hertz contact force and dimensionless analysis is used for investigating normal interaction force; furthermore, Coulomb friction is considered during sliding. Experimental data for collisions show when sliding exists through the impact, tangential impulses can be taken as frictional impulses using the Coulomb law if the dynamic regime is not stick regime. To identify transformation of sliding motion to rolling or sticking during the impact process, linear and trigonometric functions are considered as an approximation for the normal interaction force. Afterwards, we have obtained the condition for the possibility of this transformation; moreover, we can estimate the duration of sliding and rolling or sticking. We have obtained an analytical solution for maximum force and deformation, collision time, impulses and post-collision linear and angular velocities in three dimensions.     

基于增量耦合预测控制的风电叶片打磨机械臂末端颤振抑制研究

针对风电叶片打磨过程中,末端执行器与叶片表面发生刚性接触而引起末端执行器切向颤振问题,提出一种基于力反馈与加速度前馈复合结构的末端执行器增量耦合预测控制方法。在末端执行器柔性驱动单元数学建模的基础上,基于增量耦合动态矩阵预测控制算法对复合PID控制策略进行改进,将不可控但可预知输入加速度作为磨削轴向力预测序列的一部分。同时,在有限时域内采用二次型性能指标最小化的方式对控制目标进行滚动优化,以确保末端执行器与风电叶片表面柔顺接触。仿真及实验结果表明,此方法可以快速地实现末端执行器的切向颤振抑制,并能最大限度地减小因控制时滞、环境时变、模型失配等带来的误差。     

3D contact modelling of large plastic deformation in powder forming processes

In this paper, the three-dimensional large frictional contact deformation of powder forming process is modeled using a node-to-surface contact algorithm based on the penalty and augmented-Lagrange approaches. The technique is applied by imposing the normal and tangential contact constraints and modifying the contact properties of frictional slip. The Coulomb friction law is employed to simulate the friction between the rigid punch and the work piece. It is shown that the augmented-Lagrange technique significantly improves imposing of the constraints on contact surfaces. In order to predict the non-uniform relative density and stress distributions during the large deformation of powder die-pressing, the nonlinear contact friction algorithm is employed within the framework of large finite element deformation, in which a double-surface cap plasticity model is used for highly nonlinear behavior of powder. Finally, the numerical schemes are examined for accuracy and efficiency in modeling of a set of powder components.     

Contact algorithms for the material point method in impact and penetration simulation

The inherent no‐slip contact constraint in the standard material point method (MPM) creates a greater penetration resistance. Therefore, the standard MPM was not able to treat the problems involving impact and penetration very well. To overcome these deficiencies, two contact methods for MPM are presented and implemented in our 3D explicit MPM code, MPM3D. In MPM, the impenetrability condition may not satisfied on the redefined regular grid at the beginning of each time step, even if it has been imposed on the deformed grid at the end of last time step. The impenetrability condition between bodies is only imposed on the deformed grid in the first contact method, while it is imposed both on the deformed grid and redefined regular grid in the second contact method. Furthermore, three methods are proposed for impact and penetration simulation to determine the surface normal vectors that satisfy the collinearity conditions at the contact surface. The contact algorithms are verified by modeling the collision of two elastic rings and sphere rolling problems, and then applied to the simulation of penetration of steel ball and perforation of thick plate with a particle failure model. In the simulation of elastic ring collision, the first contact algorithm introduces significant disturbance into the total energy, but the second contact algorithm can obtain the stable solution by using much larger time step. It seems that both contact algorithms give good results for other problems, such as the sphere rolling and the projectile penetration. Copyright © 2010 John Wiley & Sons, Ltd.     

A parallel finite element contact/impact algorithm for non-linear explicit transient analysis: Part I—The search algorithm and contact mechanics

A contact algorithm has been developed and implemented in a non-linear dynamic explicit finite element program to analyse the response of three-dimensional shell structures. The contact search algorithm accounts for initial contact, sliding, and release through the use of a parametric representation of the motion of points located on the surface of the structure combined with a contact surface representation which approximates the actual surface by means of triangular search planes. The mechanics of contact is handled by taking advantage of the fact that an explicit time integration scheme results in very small displacements during a time step. The amount of overlap of the discrete representation of the surfaces which occurs at contact is taken as a measure of the approach of the surfaces. Hence, experimental data which relates approach to normal contact pressure can be used to determine the contact pressure applied to the finite element model of the surface as contact evolves. The friction model also incorporates experimental data on the dependence of the coefficient of friction on both the relative sliding velocity and on the relative tangential displacement between surfaces in contact observed in friction tests. The parallel implementation of this contact algorithm and its performance on a 128-processor distributed-memory multiprocessor computer is discussed in Part II of this paper.     

On Cutter Deflection Profile Errors in End Milling: Modeling and Experimental Validation

In the present paper three dimensional cutter deflections and the corresponding profile errors during end milling are predicted by finite element and bond graph modeling approach. The deflections have been modeled considering the cutter as a cantilever beam fixed at the collet end. Rayleigh beam model is used for modeling to consider the shear force effect, and Castigliano's theorem of strain energy is used to predict the deflections due to radial, tangential, and axial cutting forces. The tool-workpiece contact region is sliced into small elements to apply the forces on the entire contact region and predict deflections more accurately. The predicted deflections at different parametric settings are compared with experimental measurements by measuring the geometric accuracy of the cut profiles. The depth of cut has the most significant influence on profile deviations, while feed and speed have marginal effects. The results reveal that the predictions by finite elements and the bond graph closely matches with the experimental results, and errors of the machined profile are significantly influenced by the radial and tangential deflections. The axial deflection is negligible and leads to insignificant deviation in depth of the cut profile. The proposed model shows that the bond graph simulation takes significantly less computational time and space as compared to the finite element technique.     

A combined approach for modeling particle behavior in granular impact damper using discrete element method and cellular automata

A particle impact damper is a vibration absorber type that consists of a container attached to a primary vibrating structure. It also contains many particles that are constrained to move inside the container, whereby the damping effect can be obtained by collision between particles and the container. The discrete element method (DEM) has been developed for modeling granular systems, where the kinematics of each particle are calculated numerically using the equations of motion. However, the computational time is significant since the algorithm checks for particle contacts for all possible particle combinations. The use of a cellular automata (CA) modeling technique may provide increased computational efficiency due to the local updating of variables, and the discrete treatment of time and space. In this study, we propose a new approach combining DEM with CA for modeling a granular damper under a forced excitation. We use DEM to describe the particle motion according to the equations of motion, while CA is introduced for the particle contact checks in discrete space. We also investigate the effect of simplification in the contact force model, which allows the unit time step of numerical integration to become larger than that used in the strict model. It is shown that the suggested particle contact scanning method and the force approximation model contribute to the reduction of the computational time, and neither degenerates the calculation accuracy nor causes the numerical instability.     

A finite sliding model of two identical spheres under displacement and force control—part I: static analysis

A simplified analytical model of tangential contact engagement, sliding and separation of two elastic, identical spheres is developed assuming the kinematically induced sphere motion trajectory or load controlled sliding motion. The evaluation of driving force during contact sliding motion is determined for both monotonic and reciprocal sliding motion. The analytical formulae and diagrams of driving force versus sliding path are specified for linear and circular paths. The sliding trajectories are also determined for the load controlled programs. The results presented can be applied in the experimental testing of frictional response of contacting bodies, in a wear study of rough surfaces or in the contact interaction analysis of granular material during flow. The results can also be relevant for the development of the discrete element method widely applied in simulation of granular material flow, where the sliding regime conditions prevail in grain contact interaction.     

Partial slip problem for two semi-infinite strips in contact

Two semi-infinite strips brought into frictional contact, end-to-end, by a normal pressure are then subjected to a monotonically increasing or oscillating tangential force remote from the interface. The full stress tensor for the partial slip regime is found.     

轮对运动状态对轮轨滚动接触应力的影响

分析计算了锥型踏面轮对沿轨道滚动接触时轮轨接触几何参数和不同运动状态下的轮轨之间的刚性蠕滑率。根据确定的轮轨接触几何参数和轮轨接触界面之间的蠕滑率,利用非Hertz滚动接触理论分析计算了锥型轮对和钢轨滚动接触斑作用力的分布。再利用弹性力学中Bossinesq-Cerruti力/位移计算公式并借助Gauss数值积分方法,确定了轮轨滚动接触时体内的弹性位移、应变和应力随轮对运动状态变化情况。数据结果为轮轨强度设计提供了重要的参考依据。     

DAE for Frictional Contact Modeling of Constrained Multi-Flexible Body Systems

A general formulation for modeling frictional contact interactions in a constrained multi-flexible body system is outlined in this paper. The governing differential-algebraic equations (DAE) for the constrained motion contains not only a frictional term but also, the unknown contact conditions. These contact conditions are characterized by a set of nonlinear complementarity equations. To demonstrate the model, a falling-spinning beam impacting a rough elastic ground with damping is solved and comparison with Stewart-Trinkles' results provided.     

Dynamic large deflection response of composite laminates subjected to impact

Impact responses of composite laminates with and without initial stresses are investigated using the finite element method. A nine-node isoparametric quadrilateral element based on the Mindlin plate theory and the von Karman large deflection assumptions is developed. An experimentally established contact law which accounts for the permanent indentation is incorporated into the finite element program to evaluate the impact force. In the time integration, the Newmark constant acceleration algorithm is used in conjunction with successive iterations within each time step. Numerical results, including the contact force histories, deflections and strains in the plate, are presented.     

旋转型行波超声电机理论模型的仿真研究

建立了旋转型行波超声电机定、转子间的摩擦驱动模型，不仅考虑了接触界面上的纵向分布力，而且分析接触力沿周向和径向上的分量，在此基础上结合定子和转子的动力学模型得到了整个电机的机电耦合模型。文章分析了预压力影响电机驱动频率的本质原因，说明该频率不能直接通过分析自由定子得到，最后通过数值计算分析了接触界面力对电机工作频率的影响，取得了与实验一致的结果。     

Friction drive of an SAW motor. Part IV: physics of contact

A procedure for modeling the frictional heating and electricity of a surface acoustic wave (SAW) motor is proposed. The frictional heat is developed during friction drive when sliding occurs at the frictional interface; the heat is conducted into the solids, resulting in an increase in temperature. The spatial distribution of the heat source was associated with the contact pressure distribution, and the heat conduction from the heat source was formulated. Owing to the piezoelectricity and pyroelectricity of the stator used in the present study, the elastic deformation and temperature increase produce the electric fields. The electric fields in the stator were determined with respect to each cause. Electric discontinuity at the boundary between the stator and the slider, moreover, produces electrostatic force, which was calculated using a Maxwell stress tensor. All the analyses revealed the underlying physical fields in addition to the mechanical fields of the SAW motor. By the use of those analytical methods, the frictional properties of the SAW motor were discussed. We pointed out that another physical phenomenoniquestcontact electrificationiquestcould arise at the contact interface. The electrostatic force due to contact electrification had sufficient strength to change the friction property, which corresponded to the variation of the friction coefficient from 0.1 to 1.     

静动力弹塑性分析的杆系离散单元计算理论研究

杆系离散单元法的现有研究成果均假定接触本构模型的切向弹簧仅用于描述剪力引起的纯剪切变形,这与弯曲梁理论下剪力引起的变形情况不相符。该文针对该问题重新定义了切向弹簧,并根据能量等效原理系统推导了不考虑或考虑剪切变形工况接触本构模型的切向接触刚度系数计算公式。在此基础上,提出了杆系离散单元精细塑性铰法以描述结构的塑性开展问题,推导了颗粒间的弹塑性接触本构模型。采用自编程序对两个大型网壳结构分别进行了静、动力弹塑性行为分析,验证了接触本构模型正确性和精细塑性铰法的适用性。该文将杆系离散单元法的基本计算理论系统化,并补充了杆系离散单元法的弹塑性计算理论,为结构静、动力分析提供了新思路。     

回转窑滚圈与托轮接触应力解析

 滚圈与托轮接触应力的计算对回转窑滚动接触疲劳寿命预测起到至关重要的作用。考虑滚圈与托轮在牵引滚动接触状态下相互之间传递法向力和切向摩擦力的综合作用,将其简化为二维平面应变问题,然后从经典Hertz理论中弹性半空间在分布法向力和切向力作用下受载区应力分量的积分表达式出发,对接触区对称平面上各点的应力进行分析与计算,得出受载区各主应力的解析表达式,并采取最优函数逼近法求得半解析解,确定了最大主剪应力及其位置,能满足工程应用的要求。     

Analysis of the apparent friction of polymeric surfaces

The apparent friction coefficient is the ratio between the tangential force and the normal load applied to moving body in contact with the surface of a material. This coefficient includes a so-called “true local friction” at the interface and a “geometrical friction” which is the ploughing effect. The material underneath a moving tip may display various types of behaviour: elastic, elastic–plastic where elastic and plastic strain are present in the contact area, or fully plastic. As is usual in polymers, the material behaviour is time and temperature dependent and may exhibit strain hardening. A surface flow line model of a scratching tip which links the apparent friction to the local friction and contact geometry was recently proposed. An inverse analysis is used in the present work to estimate the local friction from the measured apparent friction and a knowledge of the contact area and tip shape. The polymer true friction coefficient displays temperature and sliding speed dependency, which may be attributed to the surface thermodynamics. It is shown that the local friction depends on the level of strain in the polymer at the contact interface.     

受冲板壳结构的弹塑性力学特性分析

采用基于随动坐标系的 4节点假设应变场壳单元及显式有限元方法分析受冲板壳结构的弹塑性力学特性。材料模型采用弹塑性等向强化模型 ,接触搜寻采用一体化接触搜寻方法 ,接触力由罚参数法计算 ,算例表明 :该方法简明、直观、快捷、方便     

A revised ice pressure-area curve and a fracture mechanics explanation

In the context of ice-structure interactions, data from measurements of forces indicate that for areas smaller than 10 m² contact pressure is proportional to area to the power − 0.7, in contrast to larger areas for which the area dependence is much weaker. A simple model is presented, where the basic idea is that the area over which the force is measured is not the same as the area that controls the force. It takes the force as that from one high-pressure zone (HPZ), determined by linear elastic fracture mechanics and the distance to the nearest edge of the total area, and assumes that the largest force occurs when only one HPZ is present within the measurement area. The model generates an area dependence close to the observed data.