Elastoplastic formulation for friction with orthotropic anisotropy and rotational hardening

In various fields of engineering, it is important to clarify the frictional sliding behavior over a wide scale. In this study, we formulate an anisotropic friction model with the orthotropy and rotation of a sliding surface based on the elastoplastic theory. This model can also describe preliminary microscopic sliding and rate-dependent frictional response. Further, basic experimental results of anisotropic frictional sliding can be pertinently represented by the present model. We also employ this model with the finite element method and analyze typical frictional contact problems. We then demonstrate the effect of anisotropy parameters on the numerical results.     

Agricultural tire deformation in the 2D case by finite element methods

The mechanical characteristics of the rubber tire and the interaction between a tire and a rigid surface were investigated by a two-dimensional (2D) finite element (FE) model. The FE model consists of a rigid rim and a rigid contact surface which interact with the elastic tire. Four distinct sets of elastic parameters are used to represent beads, sidewall, tread and lugs. Several sets of tire loads and inflation pressures were applied to the FE model as boundary conditions, together with various displacements and friction conditions. The deformation of the tire profile, the tire displacements in the vertical and lateral directions, the normal contact pressures, the frictional forces and the stress distribution of the tire components were investigated by the 2D FE model under the above boundary conditions. The calculated tire deflections were compared with the measured data. The results show a good fit between calculated and measured data, especially at high load and inflation pressure. The comparison shows that the FE analysis is suitable to predict aspects of the tire performance like its deflection and interactions with the contact surface. Compared with the experimental methods, the FE methods show many advantages in the prediction of tire deformation, contact pressure and stress distribution.     

一种考虑剪切作用的各向异性超弹性本构模型

基于纤维增强复合材料连续介质力学理论,提出了一种轮胎帘线/橡胶复合材料的各向异性超弹性本构模型. 应变能被分解为分别代表橡胶、帘线、帘线/橡胶之间的角剪切和正剪切应变能4个部分. 给出了模型参数的简单确定方法,通过拟合文献中的实验数据,得到了本构模型参数,并用该模型预测了其他变形条件下的力学行为,得到了和实验数据较一致的结果,验证了该模型的有效性,为整体轮胎的有限元分析打下了基础.     

Traveling and abrasion characteristics of wheels for lunar exploration rover in vacuum

This paper investigates the traveling and abrasion characteristics of rigid wheels for a lunar exploration rover at atmospheric pressure and in a vacuum. For this investigation, a traveling test system that enables the wheel to continuously travel over a long distance was developed. Using this system, tests on traveling performance and abrasion were conducted with the wheel on a lunar regolith simulant surface. In the initial tests, various wheels traveled over different ground conditions and their performances were evaluated based on the relationship between the drawbar pull and slippage. In the later tests, a wheel with grousers traveled a distance of 3 km and the abrasion was analyzed at various intervals. From the traveling performance tests, it was found that for a soft ground condition, the traveling performance of the wheels in vacuum was slightly lower than that in atmosphere. This indicates that ground tests performed in atmosphere overestimate the actual performance on the lunar surface. The abrasion tests suggested that the scratching of wheels occurs more easily in vacuum than in atmosphere. These experiments confirmed that the abrasion of the wheels do not cause any critical problem for a traveling distance of up to 3 km in a simulated lunar environment.     

Finite element modeling of tire/terrain interaction: Application to predicting soil compaction and tire mobility

Tire/terrain interaction has been an important research topic in terramechanics. For off-road vehicle design, good tire mobility and little compaction on terrain are always strongly desired. These two issues were always investigated based on empirical approaches or testing methods. Finite element modeling of tire/terrain interaction seems a good approach, but the capability of the finite element has not well demonstrated. In this paper, the fundamental formulations on modeling soil compaction and tire mobility issues are further introduced. The Drucker-Prager/Cap model implemented in ABAQUS is used to model the soil compaction. A user subroutine for finite strain hyperelasticity model is developed to model nearly incompressible rubber material for tire. In order to predict transient spatial density, large deformation finite element formulation is used to capture the configuration change, which combines with soil elastoplastic model to calculate the transient spatial density due to tire compaction on terrain. Representative simulations are provided to demonstrate how the tire/terrain interaction model can be used to predict soil compaction and tire mobility in the field of terramechanics.     

Transient dynamic response analysis of 3-D patterned tire rolling over cleat

Transient dynamic response of a rolling tire impacting with a small cleat is analyzed by an explicit finite element method. A 3-D tire model considering detailed tread blocks is used to accurately simulate the local tire-cleat impact process. The frictional dynamic contact problem is formulated by making use of total Lagrangian scheme and the penalty method. By imposing mass-proportional damping to only the tire parts showing the significant lateral deformation, the dynamic viscosity effect is artificially reflected. Time-history and frequency responses of the dynamic forces exerted on the tire axis are numerically predicted and assessed through the comparison with experimental results. As well as, the effects of the tire rolling speed and the inflation pressure on the transient dynamic response are parametrically investigated.     

Off-road tire modeling and the multi-pass effect for vehicle dynamics simulation

Off-road operations are critical in many fields and the complexity of the tire-terrain interaction deeply affects vehicle performance. In this paper, a semi-empirical off-road tire model is discussed. The efforts of several researchers are brought together into a single model able to predict the main features of a tire operating in off-road scenarios by computing drawbar pull, driving torque, lateral force, slip-sinkage phenomenon and the multi-pass behavior. The approach is principally based on works by Wong, Reece, Chan, and Sandu and it is extended in order to catch into a single model the fundamental features of a tire running on soft soil. A thorough discussion of the methodology is conducted in order to highlight strengths and weakness of different implementations. The study considers rigid wheels and flexible tires and analyzes the longitudinal and the lateral dynamics. Being computationally inexpensive a semi-empirical model is attractive for real time vehicle dynamics simulations. To the best knowledge of the authors, current vehicle dynamics codes poorly account for off-road operations where tire-terrain interaction dominates vehicle performance. In this paper two soils are considered: a loose sandy terrain and a firmer loam. Results show that the model realistically predicts longitudinal and lateral forces providing at the same time good estimates of the slip-sinkage behavior and tire parameters sensitivity.     

扁平化对子午线轮胎力学性能影响的有限元分析

以185/60R14半钢子午线轮胎为参考轮胎,通过改变断面高和改变断面宽两种方式构建了不同扁平率的一系列轮胎模型,采用ABAQUS/Standard软件对不同高宽比的轮胎进行了系统的研究.结果表明,通过减小断面高和增大断面宽两种方式实现轮胎的扁平化,将会产生不同的效果:前者会导致轮胎胎圈部三角胶内的应变能密度明显增大:后者则会使带束层帘线拉力的最大值明显降低,带束层帘线中部的应力状态由受压变为受拉,轮胎胎冠部橡胶结构危险区域的Mises应力和应变能密度均明显减小,对胎侧部和胎圈部的力学行为影响则很小.由此,可以利用增大胎冠部宽度而保持轮胎其他部位结构不变的简单方法实现子午线轮胎的扁平化.     

不同材料参数和内压的轮胎对单腹板轮毂变形的影响

将轮胎材料简化为各向同性超弹性材料特性，考虑轮胎与轮毂和地面之间的三维接触以及轮胎中钢丝圈的影响，建立飞机单腹板机轮整体结构有限元模型。主要分析不同轮胎材料参数和内压下，单腹板轮毂轮缘处的径向变形，结果表明；轮毂剖面上测点的应变值与实验结果基本一致。轮胎下沉量与轮毂测点的径向变形和轮毂所受的载荷基本呈线性关系；凸出一侧的轮缘变形最大；轮胎下沉量较大时。轮胎材料参数对轮毂的径向变形影响明显；轮毂测点径向变形在1-2.5mm时，相同的径向变形，轮毂受到的总载荷受轮胎材料参数变化而变化，而在变形较大或较小时，影响不明显。对于同一种轮胎材料，不同的内压，轮毂的变形减轻比较大，气压越高，对于相同的轮胎下沉量，轮毂受到总体荷载也越高。     

不同类型地震波作用下地下综合体结构地震反应分析

为探究不同类型地震波作用下地下综合体结构的地震反应特征,本文以上海某地下综合体为工程背景,采用ABAQUS软件建立土-地下综合体结构相互作用体系三维有限元模型,利用Davidenkov模型模拟土的非线性,以不同类型的单向地震波和双向地震波（含水平向和竖向）作为输入,对软土场地中地下综合体结构进行了地震反应分析,比较了不同类型地震波作用下地下综合体结构地震反应的差异,探讨了地下综合体结构的竖向地震动效应问题．本文的算例结果表明：在长周期地震波作用下地下综合体结构的位移响应和内力响应峰值均明显大于普通地震波作用下的结果;考虑竖向地震动时地下综合体结构的柱轴力较单一水平向地震动作用情形有明显增大;在本文地下综合体结构算例中,地下三层柱底、四层柱顶、五层柱底、以及底板与侧墙连接处为受力较大部位．     

Analytical model of longitudinal tire traction in snow

An analytical model to estimate longitudinal traction of a tire in snow was developed and verified to have good predictability in comparison with measurements. Snow traction of a tire is composed of four kinds of forces in this model: braking force attributable to snow compression, shear force of snow in void (space between tread blocks), frictional force, and digging force (edge effect generated by sipes and blocks). The mechanical characteristics of snow were considered in the prediction of braking force and shear force, but were not considered in the prediction of other forces. The contribution of shear force of snow in void and the frictional force was large in static traction (traction just before a tire slips). On the other hand, the contributions of digging force and frictional force were large in situations involving high slip ratios.     

An investigation of intelligent tires using multiscale modeling of cord-rubber composites

A computational model based on the multiscale progressive failure analysis is employed to provide the theoretical predictions for damage development in the cord-rubber composites in tires. Vulcanized rubber, reinforcing belts, and carcass used in tire structures cause the anisotropic behavior under different loading conditions. Steel reinforcement layers made of steel wires combined with rubber complicate the macro-scale finite element modeling of tires. This paper presents a new three-dimensional model of the cord-rubber composite used in tires in order to predict the different types of damage including matrix cracking, delamination, and fiber failure based on the micro-scale analysis. Additionally, intelligent tires have the potential to be widely used to enhance the safety of road transportation systems, and this paper provides an estimation of the effects of void volume fraction, fiber volume fraction, and stacking sequence of the cord-rubber composites on the acceleration profile of the tire measured at the inner-liner.     

Effect of plastic zone on the fatigue crack propagation behavior between two fatigue cracks

In this study, the fatigue crack propagation behavior in the stress interaction field between two different fatigue cracks is studied by experiment and finite element analysis. In the experiment, the offset distance between two cracks and the applied stress are varied to create different stress interaction fields. The size of the plastic zone area is used to examine the crack propagation path and rate. Three types of crack propagation in the interaction field were found by experiment, and the crack propagation behavior of two cracks was significantly changed as different stresses were applied. The size of the plastic zone obtained by finite element analysis can be used to explain crack propagation behavior qualitatively.     

帘线/橡胶复合材料各向异性黏-超弹性本构模型

帘线/橡胶复合材料广泛应用于轮胎等重要工程领域,为了描述其在服役条件下的大变形、非线性、各向异性和高应变率等材料力学行为,基于纤维增强复合材料连续介质力学理论,提出了一种考虑应变率效应的帘线/橡胶复合材料各向异性黏-超弹性本构模型. 该模型中单位体积的应变能被解耦为便于参数识别的基体等容变形能、帘线拉伸变形能、剪切应变能和黏性应变能四部分. 给出了模型参数的确定方法,并通过拟合文献中单轴拉伸、偏轴拉伸实验数据,得到了模型参数. 利用该模型预测了不同加载和变形条件下的力学行为,并将预测结果与实验结果对比分析. 结果表明, 考虑黏性模型和不考虑黏性模型对不同应变率变形条件下的预测结果相差很大,且考虑黏性模型的预测结果与实验结果吻合很好. 因此,与不考虑黏性模型相比,所提出的各向异性黏-超弹性本构模型能更好地表征帘线/橡胶复合材料在大变形、高应变率条件下的力学特性.      

On the interaction of frictional formulations with bifurcation phenomena in hyperelastic steady state rolling calculations

A finite element formulation for hyperelastic steady state rolling of inflated tires is analyzed. In particular, numerical difficulties associated with enforcing frictional conditions within such a framework are discussed. We focus in this work on adherent (i.e., no slip) friction formulations, and in addition to analyzing the numerical difficulties associated with such problems, we also study the interaction of frictional conditions with bifurcation phenomena. Such phenomena are observed in the context of multiple solutions (both stable and unstable) of the discretized system, and are also manifested in the behavior of the iterative map used to solve the nonlinear algebraic system of equations.     

A method of optimal wheel torque determination for independent wheel drive vehicles

A method of optimal wheel torque determination for electric motor vehicles is presented. Electric motor vehicles are increasing with the rise of public interest in environmental protection. In the case of vehicles driven by controllable motors on each individual wheel, the determination of the wheel torque is an essential factor for efficient driving. In this research, a method of optimal torque determination has been formulated by using the variational principle to minimize frictional work done by the tires with the ground contact. Optimal torque on each wheel for a four-wheel vehicle was numerically obtained by solving the equations under several driving conditions. The result of the numerical simulation is useful as a guide to control the motor torque of electric vehicles for efficient driving.     

A new indentation model for snow

Plate indentation tests have been used widely to characterize the properties of terrains. In particular, pressure-sinkage curves obtained from these tests have been used for vehicle-terrain interaction predictions. However, there is a lack of physical basis to properly interpret the meaning of these empirical curves such that they cannot be related to fundamental material properties. Also, the relation between the plate indentation tests and static (non-rolling) pneumatic tire indentation is not clear. In this paper, we conducted finite element analysis of circular plate indentation and static tire indentation simulations for fresh snow of different depths. The results indicate that the pressure-sinkage relationship for the plate indentation test is qualitatively similar to that for static tire indentation. Three deformation zones have been identified for these tests using pressure-sinkage and density-sinkage data: a small elastic zone (Zone I), a propagating hardening plastic zone (Zone II) and a densification (finite depth) zone (Zone III). The onset of a finite-depth zone was identified where the pressure bulb beneath the plate/tire has reached the bottom of snow. It is shown that Zone I and Zone II correspond to a semi-infinite terrain typical of vehicle-soil interaction, whereas Zone III corresponds to a finite-depth domain for snow and other multilayered media. The plastic constraint underneath the indenters suggests a quasi-uniaxial stress state such that a simple 1-D indentation model was proposed for Zone I, a spherical cavity expansion solution was adapted for Zone II, and an upper bound solution was adapted for Zone III. The results of the prediction of the transition between Zone II and Zone III as well as the pressure-sinkage relationships compared well with finite element solutions of plate indentation and static tire indentation tests, and with field data.     

Traveling performance analysis of planetary rovers using a repeatable test system in vacuum

In this study, the effect of a vacuum environment on the traveling characteristics of planetary rovers is experimentally investigated. For this study, a wheel traveling test system that enables a wheel to travel at various speeds and traction loads in a vacuum chamber was developed. In this system, the ground can be prepared before each run, and the wheel can travel in similar ground conditions repeatedly. Subsequently, using this system, traveling tests of the wheel were conducted in the atmosphere and medium vacuum. The wheel was tested at different speeds and various traction loads (i.e., drawbar pulls) on a sandbox filled with three types of material. Wheel slip and sinkage were quantitatively compared in the atmosphere and vacuum. From the experiment, it was confirmed that the medium vacuum environment does not significantly affect the traveling performance of the wheel.     

Development and validation of off-road tire-gravelly soil interaction using advanced computational techniques

This paper presents a novel modelling technique to compute the interaction between an 8x4 off-road truck and gravelly soil (sand with gravel soil). The off-road truck tire size 315/80R22.5 is modelled using the Finite Element Analysis (FEA) technique and validated using manufacturer-provided data in static and dynamic responses. The gravelly soil is modelled using Smoothed-Particle Hydrodynamics (SPH) technique and calibrated against physical measurements using pressure-sinkage and direct shear-strength tests. The tire-gravelly soil interaction is captured using the node symmetric node to segment with edge treatment algorithm deployed for interaction between FEA and SPH elements. The model setup consists of four tires presenting the four axles of the truck, the first tire is a free-rolling steering tire, the second and third tires are driven tires and the fourth tire is a free-rolling push tire. The truck tires-gravelly soil interaction is computed and validated against physical measurements performed in Göteborg, Sweden. The effect of gravelly soil compaction and truck loading on the tire performance is discussed and investigated.     

机械密封补偿机构中辅助O形密封圈的性能分析

采用有限单元法建立了机械密封O形辅助密封圈的数值分析模型.利用非线性有限元软件MSC.MARC计算了VonMises应力和接触密封界面之间的接触应力.采用高频疲劳试验机和高压水润滑O形密封圈试验单元组成的试验装置测得了摩擦力,并结合数值计算结果求得了摩擦系数.分析了O形辅助密封圈的压缩量及滑移速度对摩擦力的影响,讨论了O形辅助密封圈对机械密封的密封能力、泄漏特性的影响.结果表明:O形密封圈用于机械密封中的补偿机构会有微量泄漏;水润滑状态下接触密封界面能形成润滑水膜,摩擦力较小,有利于密封稳定运转.