ELASTIC-PLASTIC FINITE ELEMENT ANALYSIS OF THREE-DIMENSIONAL CONTACT-IMPACT AT RAIL JOINT

Using the finite element code ANSYS/LS-DYNA, a dynamic finite element modelwith an elastic-linear-kinematic-hardening plastic material is established to analyzeelastic-plastic stresses in the railhead in the impact process of wheel and rail occurring at thegap of rail joint. The model is based on the discrete elastic support condition of the rails, whichis suitable for the actual situation of wheel/track rolling contact. In the analysis the influencesof axle load, yield stress and tangent modulus of rail material on the stresses and strains areinvestigated in detail. The distribution of stresses and strains in the jointed railhead are given.It is found that the axle load, yield stress and tangent modulus of rail material greatly affect thestresses and strains in the railhead during impacting. The study provides a reliable method anduseful datum for the further research on fatigue and wear of railhead and improving the rail jointmode.

A CONTACT SEARCHING ALGORITHM FOR CONTACT-IMPACT PROBLEMS

A new contact searching algorithm for contact-impact systems is proposed in this paper.In terms of the cell structure and the linked-list,this algo- rithm solves the problem of sorting and searching contacts in three dimensions by transforming it to a retrieving process from two one-dimensional arrays,and binary searching is no longer required.Using this algorithm, the cost of contact searching is reduced to the order of O(N)instead of O(Nlog_2N)for traditional ones,where N is the node number in the system.Moreover,this algorithm can handle contact systems with arbitrary mesh layouts.Due to the simplicity of this algorithm it can be easily implemented in a dynamic explicit finite element program.Our numerical experi- mental result shows that this algorithm is reliable arid efficient for contact searching of three dimensional systems.

An efficient formulation based on the Lagrangian method for contact–impact analysis of flexible multi-body system

In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are the most commonly used methods in engineering applications.However,these methods are highly dependent on various non-physical parameters,which have great effects on the simulation results.Moreover,a tremendous number of degrees of freedom in the contact–impact problems will influenc thenumericalefficien ysignificantl.Withtheconsideration of these two problems,a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in fl xible multi-body system numerically.Meanwhile,the finit element meshing laws of the contact bodies will be studied preliminarily.A numerical example with experimental verificatio will certify the reliability of the presented formulationincontact–impactanalysis.Furthermore,aseries of numerical investigations explain how great the influenc of the finit element meshing has on the simulation results.Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficien y.

Modeling and Calculation of Impact Friction Caused by Corner Contact in Gear Transmission

Corner contact in gear pair causes vibration and noise,which has attracted many attentions.However,teeth errors and deformation make it difficulty to determine the point situated at corner contact and study the mechanism of teeth impact friction in the current researches.Based on the mechanism of corner contact,the process of corner contact is divided into two stages of impact and scratch,and the calculation model including gear equivalent error-combined deformation is established along the line of action.According to the distributive law,gear equivalent error is synthesized by base pitch error,normal backlash and tooth profile modification on the line of action.The combined tooth compliance of the first point lying in corner contact before the normal path is inversed along the line of action,on basis of the theory of engagement and the curve of tooth synthetic complianceload-history.Combined secondarily the equivalent error with the combined deflection,the position standard of the point situated at corner contact is probed.Then the impact positions and forces,from the beginning to the end during corner contact before the normal path,are calculated accurately.Due to the above results,the lash model during corner contact is founded,and the impact force and frictional coefficient are quantified.A numerical example is performed and the averaged impact friction coefficient based on the presented calculation method is validated.This research obtains the results which could be referenced to understand the complex mechanism of teeth impact friction and quantitative calculation of the friction force and coefficient,and to gear exact design for tribology.

Contact-impact formulation for multi-body systems using component mode synthesis

The efficiency and accuracy are two most concerned issues in the modeling and simulation of multi-body systems involving contact and impact. This paper proposed a formulation based on the component mode synthesis method for planar contact problems of flexible multi-body systems. A flexible body is divided into two parts： a contact zone and an un-contact zone. For the un-contact zone, by using the fixed-interface substructure method as reference, a few low-order modal coordinates are used to replace the nodal coordinates of the nodes, and meanwhile, the nodal coordinates of the local impact region are kept unchanged, therefore the total degrees of freedom （DOFs） are greatly cut down and the computational cost of the simulation is significantly reduced. By using additional constraint method, the impact constraint equations and kinematic constraint equations are derived, and the Lagrange equations of the first kind of flexible multi-body system are obtained. The impact of an elastic beam with a fixed half disk is simulated to verify the efficiency and accuracy of this method.

Reduced projection augmented Lagrange bi-conjugate gradient method for contact and impact problems

Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formulation of non-linear program- ming. For contact-impact problems, a larger time-step can be adopted arriving at numer- ical convergence compared with penalty method. By establishment of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to im- prove precision and efficiency of numerical solutions. A numerical example shows that the algorithm we suggested is valid and exact.

AN IMPROVED CONTACT-IMPACT ALGORITHM FOR EXPLICIT INTEGRATION FEM

Although the penalty algorithm is simple and direct in concept, it has a defect that the contact forces are badly dependent on the chosen penalty factor. An improved contact-impact algorithm for the explicit integration FEM is proposed in the present paper. Based on the fact that bodies cannot penetrate into each other on the contact faces, a set of equations with the additional unknown contact forces on the slave nodes can be formed in a new system configuration. By solving these equations, the correct contact forces could be obtained without using the penalty factor.

Numerical simulation on impact-contact between the tips of a pair of blades

To study the dynamic characteristics and damping mechanism of impact-contact between the tips of blades further more,the impact-contact between the tips of a pair of blades was studied through numerical simulation.In this paper,the dynamic equation of contact-impact between the tips was established and Newmark direct integration method was adopted in numerical simulation.The nonlinear response characteristics and damping mechanism of impact-contact system are obtained.The results of numerical simulation were obtained as follows:As the clearance between blade shrouds is smaller,the vibration amplitude is smaller.The clearance between blade shrouds has a great influence on the input energy of the aerodynamic-excitation-vibration force.As the clearance of blade shrouds increases,the input energy of the aerodynamic-excitation-vibration force increases rapidly.

The efficiency of direct integration methods in elastic contact-impact problems

A comparison of direct integration methods is madeand their efficiency is investigated for impact problems.New-mark,Wilson-θ,Central Difference and Houbolt Methodsare used as direct integration methods.Impact analysisincludes that of elastic and large deformation based uponupdated Lagrangian including buckling check.The resultsshow that the direct integration methods give differentresults in different contact-impact cases.

Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.

REDUCED AUGMENTED LAGRANGIAN BI-CONJUGATE GRADIENT METHOD FOR IMPACT-CONTACT PROBLEMS

To avoid the numerical oscillation of the penalty method andnon-compatibility with ex- plicit operators of conventional Lagrangemultiplier methods used in transient contact problems to en- forcesurface contact conditions, a new approach to enforcing surfacecontact constraints for the tran- sient nonlinear finite elementproblems, referred to as 'the reduced augmented Lagrangianbi-conjugate gradient method (ALCG)', is developed in this paper.Based on the nonlinear constrained optimization theory and iscompatible with the explicit time integration scheme, this approachcan also be used in implicit scheme naturally.

A Contact Force Model Considering Meshing and Collision States for Dynamic Analysisin Helical Gear System

The current research on gear system dynamics mainly utilizes linear spring damping model to calculate the contact force between gears. However, this linear model cannot correctly describe the energy transfer process of collision that often occurs in gear system. Focus on the contact-impact events, this paper proposes an improved gear contact force model for dynamic analysis in helical gear transmission system. In this model, a new factor associated with hysteresis damping is developed for contact-impact state, whereas the traditional linear damping factor is utilized for normal meshing state. For determining the selection strategy of these two damping factors, the fundamental contact mechanics of contact-impact event a ected by supporting forces are analyzed. During this analysis, an e ect factor is proposed for evaluating the influence of supporting forces on collision. Meanwhile, a new restitution of coe cient is deduced for calculating hysteresis damping factor, which suitable for both separation and non-separation states at the end of collision. In addition, the time-varying meshing sti ness(TVMS) is obtained based on the potential energy approach and the slice theory. Finally, a dynamic analysis of a helical gear system is carried out to better understand the contact force model proposed in this paper. The analysis results show that the contribution of supporting forces to the dynamic response of contact-impact event within gear pair is important. The supporting forces and dissipative energy are the main reasons for gear system to enter a steady contact state from repeated contact-impact state. This research proposes an improved contact force model which distinguishes meshing and collision states in gear system.

Influence of Pseudoelasticity on Mechanical Behavior of TiNi Alloy under Dynamic Impact Loading

The mechanical behavior of TiNi alloy and Cr12MoV alloy under dynamic impact loading was investigated with a self-made impact testing system. The real-time contact force was measured with a piezoelectric force sensor and digital signal processing system during impact. Equations for predicting instantaneous velocity anti displacement were presented. The results showed that the TiNi alloy exhibited a plateau of maximum contact force with increasing impact height. At the plateau stage, TiNi alloy in the parent phase can absorb impact energy and keep the maximum contact force nearly identical due to its pseudoelasticity.

Mechanical Behaviors of TiNi Alloy under Dynamic Impact Loading Conditions

The mechanical behaviors of Ti-50.7%Ni shape memory alloy under a dynamic impact loading condition were investigated by a home-built impact testing system. Both the contact force and the contact time during the impact process were measured with a piezoelectric force sensor and a digital signal processing system in real time. The predicted instantaneous velocity and the displacement formulae are presented. Results show that the maximum contact force increased, while the contact time decreased with the increase of the temperature when the TiNi alloy was in a martensitic state. When the compressive stress during the impact process was higher than the critical stress of the stress-induced martensitic transformation, the TiNi alloy specimen in the parent phase left no permanent deformation but could dissipate the impact energy.

空间连杆引纬机构的刚柔耦合磨损分析

为准确预测空间连杆引纬机构间隙磨损机制,通过结合Lankarani-Nikravesh与Bai碰撞力模型,建立可变刚度与阻尼系数非连续接触碰撞力模型,采用改进的Coulomb摩擦力模型描述含间隙机构旋转铰的切向摩擦力,通过Lagrange方法对系统动力学建模;其次选取空间连杆为柔性化对象,综合Ansys与Adams分析,对空间连杆引纬机构进行刚柔耦合动力学仿真;最后将系统的动态仿真响应结果与Archard模型相结合,求解运动副磨损情况。结果表明:柔性构件可以有效缓解机构间隙碰撞的冲击作用,间隙为0.15 mm条件下,剑头加速度振荡最大幅值缩减53.2%;当间隙升至0.5 mm后,虽磨损范围大幅增加,但间隙磨损深度并未随之大幅提升。

滚动球轴承局部故障引起滚珠负载振荡性分析

为深入剖析滚动球轴承局部故障对轴承整体振动特性的影响,利用Hertz接触理论构建了转子偏心力激励下的球轴承-转子系统动力学数字仿真模型,并结合深沟球轴承外圈、内圈、滚珠的局部故障引起的轴承间隙变化,推演了滚珠与各类故障区域间的冲击激励响应方程。在此基础上通过分析单点损伤引起的滚珠内部接触负载变化,揭示了单个滚珠接触应力对相邻滚子负载与系统整体振动特性的影响规律。通过分析轴承转动过程中有效承载滚珠个数的变化情况,建立了的滚珠负载占比时间对故障冲击振荡幅值的影响关系。分析结果表明,滚珠与故障区域的接触分离会使其负载发生振荡,且各故障状态下的振荡频率都为系统共振频率;在2个等效承载滚珠上的运转时间占比越大,故障冲击振荡的强度越大;各类型早期故障状态下的Poincaré映射点的保持在相同幅值附近;当局部故障程度增大到一定程度时,系统振动混沌特性增强,振动幅值相应增大。

渐开线变齿厚齿轮啮合冲击分析

基于弹性接触动力学理论和齿轮传动物理模型,对渐开线变齿厚齿轮啮合冲击问题进行了分析,建立了变齿厚齿轮全齿啮合接触冲击模型.通过模拟轮齿啮合接触状态,对轮齿啮合区域展开了讨论,利用LS-DYNA软件进行接触碰撞分析,分别研究了冲击合力和冲击应力随转速和冲击位置的变化规律.结果表明:转速和冲击位置对冲击合力和冲击应力影响显著,且冲击最大应力主要集中在齿顶和轮齿的大小端附近;转速越大,轮齿受载面与非受载面之间的冲击应力相差越大.

半刀宽插铣冲击力有限元分析与实验研究

半刀宽插铣是一种常见的型腔加工方式,在顺铣切入和逆铣切出时由于刀—屑接触宽度突变会产生较大冲击,严重影响刀具使用寿命。通过有限元计算与实验相结合的方式,对半刀宽逆铣加工中的冲击力学行为进行研究。以40Cr合金钢为研究对象,建立半刀宽逆铣有限元计算模型,根据加工中刀—屑接触宽度与切削力的变化特点,以刀—屑接触宽度发生突变对应时刻的切向力表征冲击力,采用极差分析法与单因素分析法研究各切削参数对刀具冲击力的影响规律,并通过实验验证了模型的有效性。实验结果表明,仿真与实验冲击力的相对误差在10%以内,证明该有限元模型可用于半刀宽插铣冲击力预测和切削参数优化;冲击力与插铣步距和每齿进给量成正比,随着切削速度的增加,冲击力先增加后减小。

Discrete state space method and modal extension method based impact sound synthesis model

The efficient and accurate synthesis of physical parameter-controllable impact sounds is essential for sound source identification. In this study, an impact sound synthesis model of a cylinder is proposed based on discrete state space（DSS） method and modal extension method（MEM）. This model is comprised of the whole three processes of the physical interaction, i.e., the Hertz contact process, the transient structural response process, and the sound radiation process. Firstly,the modal expanded DSS equations of the contact system are constructed and the transient structural response of the cylinder is obtained. Then the impact sound of the cylinder is acquired using improved discrete Raleigh integral. Finally, the proposed model is verified by comparing with existing models. The results show that the proposed impact sound synthesis model is more accurate and efficient than the existing methods and easy to be extended to the impact sound synthesis of other structures.

双块式无砟轨道轨枕与道床板界面脱空损伤识别

为准确识别双块式无砟轨道轨枕与道床板连接面脱空损伤,建立了双块式无砟轨道冲击回波有限元模型,分析界面损伤对弹性波传播规律的影响。在室内浇筑含有不同损伤位置和不同损伤程度的混凝土复合试件,采用冲击回波法进行损伤识别。研究结果表明:脱空损伤会显著影响弹性波在界面处的传播,基于回波信号分析可识别损伤;弹性波频率主要受激振锤大小的影响,应结合结构易损位置和理论计算选取合适的激振锤;混凝土复合试件的试验厚度值与理论厚度值相差仅为1 cm,测试结果合理,可用于判断脱空损伤程度,但不能确定损伤区域;利用平面成像技术可准确识别轨枕与道床板界面脱空范围,为双块式无砟轨道结构养护维修提供一定参考,试验结果验证了冲击回波法用于双块式轨道层间脱空识别的可行性和合理性。