Parameterization and modelling of large off-road tyres for ride analyses: Part 2 – Parameterization and validation of tyre models

Every mathematical model used in a simulation is an idealization and simplification of reality. Vehicle dynamic simulations that go beyond the fundamental investigations require complex multi-body simulation models. The tyre–road interaction presents one of the biggest challenges in creating an accurate vehicle model. Many tyre models have been proposed and developed but proper validation studies are less accessible. These models were mostly developed and validated for passenger car tyres for application on relatively smooth roads. The improvement of ride comfort, safety and structural integrity of large off-road vehicles, over rough terrain, has become more significant in the development process of heavy vehicles. This paper investigates whether existing tyre models can be used to accurately describe the vertical behaviour of large off road tyres while driving over uneven terrain. [1] Presented an extensive set of experimentally determined parameterization and validation data for a large off-road tyre. Both laboratory and field test are performed for various loads, inflation pressures and terrain inputs. The parameterization process of four tyre models or contact models are discussed in detail. The parameterized models are then validated against test results on various hard but rough off-road terrain and the results are discussed.     

Reconstruction of road defects and road roughness classification using Artificial Neural Networks simulation and vehicle dynamic responses: Application to experimental data

This paper reports the performance of an Artificial Neural Network based road condition monitoring methodology on measured data obtained from a Land Rover Defender 110 which was driven over discrete obstacles and Belgian paving. In a previous study it was demonstrated, using data calculated from a numerical model, that the neural network was able to reconstruct road profiles and their associated defects within good levels of fitting accuracy and correlation. A nonlinear autoregressive network with exogenous inputs was trained in a series–parallel framework. When compared to the parallel framework, the series–parallel framework offered the advantage of fast training but had a shortcoming in that it required feed-forward of true road profiles. In this study, the true profiles are not available and the test data are obtained from field measurements. Training data are numerically generated by making minor adjustments to the real measured profiles and applying them to a full vehicle model of the Land Rover. This is done to avoid using the same road profile and acceleration data for training and testing or validating the neural network. A static feed-forward neural network is trained and consequently tested on the real measured data. The results show very good correlations over both the discrete obstacles and the Belgian paving. The random nature of the Belgian paving necessitated correlations to be made using their displacement spectral densities as well as evaluations of RMS error percent values of the raw road profiles. The use of displacement spectral densities is considered to be of much more practical value than the road profiles since they can easily be interpreted into road roughness measures by plotting them over an internationally recognized standard roughness scale.     

原子尺度摩擦行为的分子动力学模拟

应用大规模分子动力学方法,模拟了具有原子级光滑和原子级粗糙形貌的刚性球形探头与弹性平面基体的干摩擦行为,研究了无/有粘附条件下的载荷与摩擦力、载荷与真实接触面积,以及摩擦力与真实接触面积之间的关系,对纳米尺度下的摩擦行为规律进行了分析。几种系统的真实接触面积－载荷关系都与相应的连续力学接触模型定性的一致,它们分别是Hertz光滑表面接触模型、Greenwood-Williamson粗糙表面接触模型和Maugis-Dugdale粘着接触模型。无论是由光滑表面还是粗糙表面构成的摩擦系统,在无粘附条件下摩擦力与载荷成正比,而摩擦力与真实接触面积之间没有一个简单的关系;在粘附条件下摩擦力与真实接触面积成正比,而摩擦力与载荷之间表现为Maugis-Dugdale模型预测的亚线性关系。我们的研究表明,当表面作用从无粘附到粘附时,控制摩擦力的决定因素从载荷转变为接触面积,摩擦行为从载荷控制摩擦转变为粘着控制摩擦。     

Direct numerical simulation of turbulent heat transfer on the Reynolds analogy over irregular rough surfaces

The effect of rough surface topography on heat and momentum transfer is studied by direct numerical simulations of turbulent heat transfer over uniformly heated three-dimensional irregular rough surfaces, where the effective slope and skewness values are systematically varied while maintaining a fixed root-mean-square roughness. The friction Reynolds number is fixed at 450, and the temperature is treated as a passive scalar with a Prandtl number of unity. Both the skin friction coefficient and Stanton number are enhanced by the wall roughness. However, the Reynolds analogy factor for the rough surface is lower than that for the smooth surface. The semi-analytical expression for the Reynolds analogy factor suggests that the Reynolds analogy factor is related to the skin friction coefficient and the difference between the temperature and velocity roughness functions, and the Reynolds analogy factor for the present rough surfaces is found to be predicted solely based on the equivalent sand-grain roughness. This suggests that the relationship between the Reynolds analogy factor and the equivalent sand-grain roughness is not affected by the effective slope and skewness values. Analysis of the heat and momentum transfer mechanisms based on the spatial- and time-averaged equations suggests that two factors decrease the Reynolds analogy factor. One is the increased effective Prandtl number within the rough surface in which the momentum diffusivity due to the combined effects of turbulence and dispersion is larger than the corresponding thermal diffusivity. The other is the significant increase in the pressure drag force term above the mean roughness height.     

A slip-line plasticity analysis of sliding friction of rough surfaces exhibiting self-affine (fractal) behavior

A plasticity analysis of sliding friction of rough (fractal) surfaces sliding against smooth surfaces was developed based on a slip-line model of a rigid spherical asperity (wear particle) plowing and cutting through a soft semi-infinite medium. Solutions of the fraction of fully plastic asperity microcontacts responsible for the evolution of friction and energy dissipation were obtained in terms of the total normal load (global interference), interfacial adhesion characteristics, topography (fractal) parameters of the hard surface, and elastic–plastic material properties of the soft surface. This was accomplished by incorporating the slip-line model of a single microcontact into a friction analysis of sliding surfaces demonstrating multi-scale roughness. Numerical results provide insight into the effects of global interference (normal load), fractal parameters (surface roughness) of the hard surface, interfacial shear strength (adhesion), and material properties of the soft surface on plastic deformation at the microcontact level, global coefficient of friction, and frictional energy dissipated during sliding.     

A slip-line plasticity analysis of abrasive wear of a smooth and soft surface sliding against a rough (fractal) and hard surface

Abrasive wear of a soft and smooth surface sliding against a rough (fractal) and hard surface was analyzed by the slip-line theory of plasticity. The analysis is based on a slip-line model of a rigid spherical asperity (wear particle) plowing through a soft surface and removing material by microcutting. Integration of this single-contact model into a three-dimensional contact mechanics analysis of an abrasive surface exhibiting multi-scale roughness described by fractal geometry yielded relationships of the abrasive wear rate and wear coefficient in terms of the interfacial shear strength (adhesion), topography (fractal) parameters of the hard/rough surface, elastic–plastic material properties of the soft/smooth surface, and total normal load. Analytical results from the single-contact analysis provide insight into the deformation of a perfectly plastic material caused by the abrasive action of a rigid asperity/wear particle under different normal load and interfacial friction (adhesion) conditions. The dependence of the abrasive wear rate and wear coefficient on normal load (global interference), roughness of the abrasive surface, elastic–plastic material properties of the abraded surface, and interfacial shear strength (lubrication effect) is interpreted in the context of numerical results obtained for representative ceramic/ceramic, ceramic/metallic, and metal/metal sliding systems.     

Steady Sliding Frictional Contact Problems in Linear Elasticity

The existence and uniqueness of an equilibrium solution to frictional contact problems involving a class of moving rigid obstacles is studied. At low friction coefficient values, the steady sliding frictional contact problem is uniquely solvable, thanks to the Lions-Stampacchia theorem on variational inequalities associated with a nonsymmetric coercive bilinear form. It is proved that the coerciveness of the bilinear form can be lost at some positive critical value of the friction coefficient, depending only on the geometry and the elastic properties of the body. An example presented here, shows that infinitely many solutions can be obtained when the friction coefficient is larger than the critical value. This result is paving the road towards a theory of jamming in terms of bifurcation in variational inequality. The particular case where the elastic body is an isotropic half-space is studied. The corresponding value of the critical friction coefficient is proved to be infinite in this case. In the particular case of the frictionless situation, our analysis incidentally unifies the approaches developed by Lions-Stampacchia (variational inequalities) and Hertz (harmonic analysis on the half-space) to contact problems in linear elasticity.     

引入特征粗糙度参数的Stribeck曲线试验研究

为探讨表面粗糙度对Stribeck曲线的影响,对不同初始表面的不锈钢销试件与45#钢盘试件在浸油润滑条件下进行摩擦磨损试验,研究摩擦系数的变化规律.结果表明:摩擦副表面越粗糙,对应Stribeck曲线上混合润滑区域面积越大,曲线斜率越小,使得不同表面粗糙度下的摩擦系数试验模型不具有唯一性.因此,将由分形参数导出的能客观表征粗糙表面的"特征粗糙度"参数引入Stribeck动压参数,从而提出新的动压参数.在新的动压参数下,具有不同表面粗糙度摩擦副的Stribeck曲线具有较好的一致性,继而可建立与粗糙度无关的摩擦系数试验模型.     

硅酸钠缓蚀液润滑下氮化硅—灰铸铁磨损表面膜的形成机理研究

通过摩擦磨损试验，发现氮化硅与灰铸铁配副在硅酸钠缓蚀液润滑下，氮化硅磨损表面由于发生摩擦化学反应而变得超光滑；灰铸铁磨损表面则经历局部表面膜的反复形成与剥落过程，最终形成一支含硅胶，硅酸盐和石墨的表面膜，表面膜的形成使灰铸铁磨损表面光滑化。超光滑的氮化硅表面与光滑的灰铸铁表面的润滑条件下表现出优异的摩擦学性能。     

A tire–ice model (TIM) for traction estimation

Increased traffic safety levels are of highest importance, especially when driving on icy roads. Experimental investigations for a detailed understanding of pneumatic tire performance on ice are expensive and time consuming. The changing ambient and ice conditions make it challenging to maintain repeatable test conditions during a test program. This paper presents a tire–ice contact model (TIM) to simulate the friction levels between the tire and the ice surface. The main goal of this model is to predict the tire–ice friction based on the temperature rise in the contact patch. The temperature rise prediction in the contact patch is based on the pressure distribution in the contact patch and on the thermal properties of the tread compound and of the ice surface. The contact patch is next classified into wet and dry regions based on the ice surface temperature and temperature rise simulations. The principle of thermal balance is then applied to compute the friction level in the contact patch. The tire–ice contact model is validated by comparing friction levels from simulations and experimental findings. Friction levels at different conditions of load, inflation pressure, and ice temperatures have been simulated using the tire–ice contact model and compared to experimental findings.     

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.     

Tire-ice model development for the simulation of rubber compounds effect on tire performance

The material properties of the rubber compounds, which are highly dependent on temperature, have a vital role in the tire behavior. A comprehensive study on the effect of the rubber properties on tire performance, for different temperatures, as well as different road conditions is required to adequately predict the performance of tires on ice.In this study, a theoretical model has been developed for the tire-ice interaction. The temperature changes obtained from the model are used to calculate the height of the water film created by the heat generated due to the friction force. Next, the viscous friction coefficient at the contact patch is obtained. By using the thermal balance equation at the contact patch, the dry friction is obtained. Knowing the friction coefficients for the dry and wet regions, the equivalent friction coefficient is calculated. The model has been validated using experimental results for three similar tires with different rubber compounds properties. The model developed can be used to predict the temperature changes at the contact patch, the tire friction force, the areas of wet and dry regions, the height of the water film for different ice temperatures, different normal load, etc.     

The test and simulation of ABS on rough,non-deformable terrains

It is well known that the performance of many antilock braking systems (ABS) deteriorate on rough, non-deformable surfaces due to a number of factors such as axle oscillations, wheel speed fluctuations and deficiencies in the algorithms. Rough terrain excitation further contribute to dynamic tyre effects such as loss of vertical contact and poor contact patch generation that leads to reduced longitudinal force generation. In this study, a slightly modified version of the Bosch ABS algorithm is implemented in Matlab/Simulink using co-simulation with a validated full vehicle ADAMS model that incorporate a valid high-fidelity FTire model. A non-ABS test vehicle is fitted with a commercial ABS modulator controlled by an embedded computer. The co-simulation model is validated with vehicle test data on both smooth and rough terrains. Initial results show that wheel speed fluctuations on rough terrain cause inaccuracies in the estimation of vehicle velocity and excessive noise on the derived rotational acceleration values. This leads to inaccurate longitudinal slip calculation and poor control state decisions respectively. It is concluded that, although the correlation is not yet as desired, the combined use of a simulation model and test vehicle can be a useful tool in the research of ABS braking on rough terrains.     

表面形貌变形对塑性成形滑动接触界面摩擦的影响

为了更好地理解塑性成形滑动接触界面的摩擦行为,构建了一种新型的摩擦试验装置,运用表面纹理化技术制备了两类表面形貌的1050铝材试件,在不同的接触压力和滑动速度条件下进行一系列拉伸摩擦试验.对试验前后试件三维表面形貌进行了测量;提取真实接触面积比、封闭空体面积比和开放空体面积比等三维表面参数,来描述试件表面形貌的变化.试验发现:摩擦系数随名义接触压力和滑动速度增加而逐渐减小;试件初始表面形貌对摩擦有明显的影响;试件表面形貌和参数随接触条件出现了规律性变化.基于机械流变模型的分析表明:随着试件表面形貌变形,不同的机理决定界面摩擦行为,摩擦系数对名义接触压力和滑动速度的依赖性可分别归因于微观塑性流体动压润滑效应和入口区流体动压牵引效应.     

A fractal study of sound propagation characteristics in roughened porous materials

The influence of rough elements of porous materials on sound propagation characteristics in roughened porous materials is investigated. Rough surface topography on the roughened porous materials is simulated by the fractal geometry theory, in which relative roughness is defined clearly as a function of the fractal dimension, porosity, average diameter and diameter ratio of the hexagonal elements on pore wall of the porous materials. Based on the sound propagation model of the smooth porous materials, a sound propagation model of the roughened porous materials is built. The effective density and bulk modulus, acoustic impedance and propagation constant, flow resistivity and sound absorption coefficient of the roughened porous materials are derived and discussed as a function of the relative roughness. It is demonstrated that the sound absorption coefficient of the roughened porous materials is improved as the relative roughness increases. The model predictions for the sound absorption coefficient of the roughened porous materials are well agreed with that of the existing test results.     

Friction factor in micropipe gas flow under laminar,transition and turbulent flow regime

The present work deals with the compressible flow of nitrogen gas inside microtubes ranging from 30 to 500 μm and with different values of the surface roughness (<1%), for different flow regimes. The first part of the work is devoted to a benchmark of friction factor data obtained at DIENCA (University of Bologna) and the ENEA laboratories, using fused silica pipes of 50 and 100 μm. Data overlapping is excellent thus evidencing how the agreement of the experimental data with the classic theory is independent of the measurement system. The second part of the work demonstrates that classic correlations can predict friction factor in laminar flow without revealing any evident influence of the surface roughness. The laminar-to-turbulent transition starts for Reynolds number not lower than 2000 for smooth pipes, while tending to larger values (3200–4500) for rough pipes. Anyway, contrarily to other available results, no dependence of the critical Reynolds number on the L/D has been observed. Changes in the flow regime have been found of the sharp and smooth type, like for larger pipes; smooth transition looks typical of smooth pipes while the sharp transition in the flow pattern is associated with rough pipes. In the fully developed turbulent regime, obtained for both smooth and rough pipes, an agreement between experimental data and the Blasius correlation has been verified for smooth pipes, while for rough pipes the agreement with predictions given by the Colebrook equation is rather modest.     

A method for predicting the internal motion resistance of rubber-tracked undercarriages,Pt. 2. A research on the motion resistance of road wheels

In spite of an increasing number of rubber-tracked crawlers, the literature provides few guidelines and calculation models suitable for minimizing their internal motion resistance. This article presents a model where the internal resistance of double-flanged road wheels for rubber-tracked vehicles is calculated as a sum of the losses resulting from the indentation of the wheels into the track surface and friction of the wheels against the track guide lugs. The model allows for vertical and lateral load of the wheels, the non-uniform distribution of the wheel pressure on the track, and the relationship between the friction coefficient and normal reaction force in the interface between the wheel and track guide lugs. The model has been verified by experiments. According to the results of model computations and experiments discussed in the article, the internal losses of a given rubber-tracked undercarriage might be reduced if: the road wheels are covered with a material that exhibits low friction coefficient and mechanical hysteresis, the vehicle suspension system features oscillating bogie wheels, the undercarriage is fitted with the largest possible number of road wheels, and the vehicle weight is evenly distributed to all of the road wheels.     

仿生非光滑表面铸铁材料的常温摩擦磨损性能

模仿动物体表形态,在试样表面通过激光雕刻出有规则分布的凹坑以及条纹等非光滑单元体,研究了具有非光滑表面材料的摩擦磨损性能.结果表明:非光滑表面材料的耐磨性较光滑表面提高1倍以上,摩擦系数提高66%以上;当非光滑表面的单元体硬度越高、直径越大和间距越小时,其耐磨性能越好,摩擦系数越大.这是由于激光加工的单元体相当于在母体上增加了许多强化质点,比母体具有较高的硬度和致密性,能够提高抗磨性,增加表面粗糙度,所以其耐磨性提高,摩擦系数增大.     

A roll stability performance measure for off-road vehicles

The roll stability is significant for both road and off-road commercial vehicles, while the majority of reported studies focus on road vehicles neglecting the contributions of uneven off-road terrains. The limited studies on roll stability of off-road vehicles have assessed the stability limits using performance measures derived for road vehicles. This study proposes an alternative performance measure for assessing roll stability limits of off-road vehicles. The roll dynamics of an off-road mining vehicle operating on random rough terrains are investigated, where the two terrain-track profiles are synthesized considering coherency between them. It is shown that a measure based on steady-turning root-mean-square lateral acceleration corresponding to the sustained period of unity lateral-load-transfer-ratio prior to the absolute-rollover, could serve as a reliable measure of roll stability of the vehicle operating on random rough terrains. The robustness of proposed performance measure is demonstrated considering sprung mass center height variations and different terrain excitations. The simulation results revealed adverse effects of terrain elevation magnitude on the roll stability, while a relatively higher coherency resulted in lower terrain roll-excitation and thereby enhanced vehicle roll stability. Terrains with relatively higher waviness increased the magnitude of lower spatial frequency components, which resulted in reduced roll stability limits.