Steering forces on undriven tractor wheel

The steering forces on an undriven, angled wheel mounting a 6-16 8PR tire were measured on a wheel test carriage at zero camber angle and at 1.5 km/h forward speed in a soil bin with sandy clay loam soil. The lateral force developed was found to be a function of slip angle, normal load, and inflation pressure for a particular soil condition. An exponential relationship could estimate the coefficient of lateral force of the 6-16 tire. The coefficients of this equation were found to be linearly related to inflation pressure. Rolling resistance of the wheel tested was found to be a function of slip angle, normal load, and inflation pressure for the soil condition tested. A linear relationship existed between the rolling resistance and slip angle, where the coefficients were found to be a function of inflation pressure and normal load. The generalized equations developed in the present study for estimating coefficients of lateral force and rolling resistance by taking both the tire and operating parameters into account, were found to be reasonably good by looking at the high coefficient of determination between experimental and estimated values.     

Experimental analysis of vertical soil reaction and soil stress distribution under off-road tires

In this study, the vertical soil reaction acting on a driven wheel was measured by strain gages bonded to the left rear axle of a 2WD tractor driven under steady-state condition on different soil surfaces, tractor operations, and combinations of static wheel load and tire inflation pressure. In addition, the measurements of radial and tangential stresses on the soil–tire interface were made simultaneously at lug’s face and leading side near the centerline of the left rear tire using spot pressure sensors. The experimental results indicate that the proposed method of vertical soil reaction measurement is capable of monitoring the real-time vertical wheel load of a moving vehicle and provides a tool for further studies on vehicle dynamics and dynamic wheel–soil interaction. Furthermore, the measured distributions of soil stresses under tractor tire could provide more real insight into the soil–wheel interactions.     

载重子午线轮胎帘线受力的有限元分析

以10.00R20轮胎为原型,针对特定的断面轮廓形状和帘线结构形式建立了轮胎结构计算的有限元模型,着重研究了额定充气压力状态以及受静负荷作用时各部分帘线受力的基本特征。结果表明:(1)充气状态下胎冠部和胎圈部的帘线结构参数之间的相互影响很小,因而在分析设计中可以相对独立地考虑;(2)静负荷作用下帘线受力在接地面附近的分布情况较复杂,尤其是负荷较大时可能出现胎冠中部帘线张力不足甚至受压以及0°带束层边缘受拉力过大的情况,这些对轮胎使用性能不利的受力状况可以通过帘线结构的合理设计来克服。     

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.     

Tire and soil effects on power loss: Measurement and comparison with finite element model results

In the present study, the effect of vertical load, tire inflation pressure and soil moisture content on power loss in tire under controlled soil bin conditions were investigated. Also a finite element model of tire-soil interaction in order to achieve a suitable model for predicting power loss in tire was created. Increasing the vertical load on the tire had a noteworthy impact on increasing the tire contact volume with the soil, reducing the percentage of slip, and increasing the rolling resistance; although, reducing the load on the tire had the opposite effect. At a constant inflation pressure, by increasing the vertical load on the tire, the amount of power loss due to the rolling resistance and the total power loss in the tire increased. Increase in soil moisture content increased the power loss caused by slip. Increasing the inflation pressure at a constant vertical load, also increasing the soil moisture content, led to an increase in the power loss caused by rolling resistance, and increase total power loss. The obtained error for estimating power loss of rolling resistance and total power loss was satisfactory and confirmed the acceptability of the model for power loss estimation.     

Rolling deformation of truck tires: Measurement and analysis using a tire sensing approach

Measurements on rolling tire deformation provide deep insights into the mechanism of generating tire forces and moments. For free rolling tires, substantial attention has been given to the rolling resistance because of its significant impact on the fuel consumption and CO₂ emissions. This paper attempts to investigate the rolling resistance force through measurements of the rolling deformation of truck tires using a tire sensing approach. An optical tire sensor system is used to measure rolling tire deformation, which includes the deformed inner profile, sidewall deformation, and tread deformation. Measurements were conducted on a test truck for both new and used tires. In addition, the influences from operational factors such as wheel load and inflation pressure on tread deformation were examined and analyzed.     

Dynamic load and inflation pressure effects on contact pressures of a forestry forwarder tire

A Trelleborg Twin 421 Mark II 600/55-26.5 steel-reinforced bias-ply forwarder drive tire at inflation pressures of 100 and 240 kPa and dynamic loads of 23.9 and 40 kN was used at 5% travel reduction on a firm clay soil. Effects of dynamic load and inflation pressure on soil–tire contact pressures were determined using six pressure transducers mounted on the tire tread. Three were mounted on the face of a lug and three at corresponding locations on the undertread. Contact angles increased with decreases in inflation pressure and increases in dynamic load. Contact pressures on a lug at the edge of the tire increased as dynamic load increased. Mean and peak pressures on the undertread generally were less than those on a lug. The peak pressures on a lug occurred forward of the axle in nearly all combinations of dynamic load, inflation pressure, and pressure sensor location, and peak pressures on the undertread occurred to the rear of the axle in most of the combinations. Ratios of the peak contact pressure to the inflation pressure ranged from 0 at the edge of the undertread for three combinations of dynamic load and inflation pressure to 8.39 for the pressure sensor on a lug, near the tire centerline, when the tire was underinflated. At constant dynamic load, net traction and tractive efficiency decreased as inflation pressure increased.     

交通荷载下沥青路面车辙三维非线性有限元分析

建立了半刚性沥青路面和柔性沥青路面的三维有限元模型,采用非线性粘弹塑性理论分析了不同交通荷载对沥青路面车辙变形和切应力的影响,并考虑了刹车、路面纵坡对路面车辙的影响。结果表明:在相同荷载作用下,两种路面结构的车辙变形和切应力分布随着路面深度呈非线性分布,但不同路面结构对交通荷载变化的敏感性存在较大的差异;不同的胎压、轮载以及刹车产生的水平力对路面车辙变形有着较大的影响。当胎压为1 050 kPa及轮载为62.5 kN时,路面产生的车辙都大于在标准荷载及标准胎压时路面产生的车辙;在坡度为1%～6%时,路面纵坡对沥青路面车辙深度的影响不明显;在坡道上行车(特别是下行)时刹车是路面车辙过大的主要原因。     

Soil displacement beneath an agricultural tractor drive tire

Soil strain transducers were used to determine strain in an initially loose sandy loam soil in a soil bin beneath the centerline of an 18.4R38 radial-ply tractor drive tire operating at 10% travel reduction. The initial depth of the midpoints of the strain transducers beneath the undisturbed soil surface was 220 mm. Strain was determined in the vertical, longitudinal, and lateral directions. Initial lengths of strain transducers were approximately 118 mm for the longitudinal and lateral transducers and 136 mm for the vertical transducer. The tire dynamic load was 25 kN and the inflation pressure was 110 kPa, which was a recommended pressure corresponding to the load. In each of four replications, as the tire approached and passed over the strain transducers, the soil first compressed in the longitudinal direction, then elongated, and then compressed again. The soil was compressed in the vertical direction and elongated in the lateral direction. Mean natural strains of the soil following the tire pass were −0.200 in the vertical direction, +0.127 in the lateral direction, and −0.027 in the longitudinal direction. The mean final volumetric natural strain from the strain transducer data was −0.099, which was only 35% of the mean change in natural volumetric strain calculated from soil core samples, −0.286. This difference likely resulted from the greater length of the lateral strain transducer relative to the 69 mm lateral dimension of the soil cores. The strain transducer data indicated the occurrence of plastic flow in the soil during one of the four replications. These results indicate the complex nature of soil movement beneath a tire during traffic and emphasize a shortcoming of soil bulk density data because soil deformation can occur during plastic flow while soil bulk density remains constant.     

冰面上轮胎摩擦牵引力的实验研究

研制开发了测试冰雪面轮胎力学特性的试验装置,该装置具有可作往复运动的平台冰槽。在不同冰基体温度下,分析了轮胎摩擦引力受侧偏角,载荷和轮胎充气压力的影响,从试验角度论证了轮胎中央充放气系统对改善冬季轮胎牵引性能的作用,该装置的建立将有利于轮胎新结构和新材料的开发,并起到完善现有轮胎力学模型的作用。     

Soil stress state orientation beneath a tire at various loads and inflation pressures

Stress state transducers (SSTs) were used to determine the orientation of the major principal stress, σ₁, in soil beneath the centeline of an 18.4R38 radial-ply R-1 drive tire operated at 10% slip. Two soils, a sandy loam and a clay loam, were each prepared twice to obtain two density profiles. One profile of each soil had a hardpan and the soil above the hardpan was loose. The soil in the second profile was loosely tilled. The stress state was determined at a depth of 358 mm in the sandy loam and 241 mm in the clay loam soil. The tire was operated at two dynamic loads (13.2 and 25.3 kN), each at two levels of inflation pressure (41 and 124 kPa). When the orientation of σ₁ was determined directly beneath the axle, the mean angles of tilt in the direction of travel ranged from 6 to 23 degrees from vertical. Inflation pressure did not significantly affect the angle when the dynamic load was 13.2 kN in the sandy loam soil, and neither inflation pressure nor dynamic load significantly affected the angle in the clay loam soil. When the dynamic load was 25.3 kN in the sandy loam soil, the orientation of the major principal stress determined directly beneath the axle was tilted significantly more in the direction of travel when the tire was at 41 kPa inflation pressure than when at 124 kPa. These changes in stress orientation demonstrate the importance of measuring the complete stress state in soil, rather than stresses along only one line of action. The changing orientation of σ₁ as the tire passes over the soil indicates the soil undergoes kneading and supports future investigation of the contribution of changes in stress orientation to soil compaction.     

Reaction Forces under Static Loading of a Wheel Pair with Camber

The static loading of a wheel pair with a deformable periphery is considered when the wheels are mounted on a common axle with a non-zero camber angle. A tire tread (protector) is modeled by a set of elastic rods interacting with the motion plane according to the dry friction law. The wheel camber effect on the slip in the contact zone and on the magnitude of reaction forces from the road is studied. An analog of the continuous model for a rod tread is discussed. The normal and tangential reaction forces are found depending on the vertical displacement of the center of the mechanical system under discussion.     

ANALYTICAL STUDY ON GROUND VIBRATION INDUCED BY MOVING VEHICLE 1)

本文从汽车动力学出发,建立 1/4 汽车与半空间地基耦合振动的动力学模型,并采用弹性滚子接触模型来反映轮胎包容性. 模型中同时考虑轮-地之间的纵向和竖向作用力,构建系统动力控制方程,利用 Fourier 和 Laplace 积分变换进行求解,推导出地表振动位移的解析解. 在数值算例中,利用离散傅里叶逆变换和 Crump 法进行数值反演,得出地表振动位移的空间分布,由此讨论了轮胎着地长度和轮-地相互作用力的变化规律,并对地表振动位移的参数影响作出分析. 结果表明,地面不平度对轮-地之间作用力的影响最为显著,地面越不平顺则轮-地作用力和地表振动位移越大. 车速对轮-地作用力的大小影响有限,但对载荷激励频率影响较大,车速增大则激励频率增大,地表振动位移随之增大. 在较低车速时,轮胎包容性对轮-地作用力和地表振动产生一定影响,轮胎充气压力增大,轮-地作用力和地表振动位移增大,但随着车速升高,这种影响将逐渐消失.     

汽车行驶诱发地表振动的解析研究

本文从汽车动力学出发,建立 1/4 汽车与半空间地基耦合振动的动力学模型,并采用弹性滚子接触模型来反映轮胎包容性. 模型中同时考虑轮-地之间的纵向和竖向作用力,构建系统动力控制方程,利用 Fourier 和 Laplace 积分变换进行求解,推导出地表振动位移的解析解. 在数值算例中,利用离散傅里叶逆变换和 Crump 法进行数值反演,得出地表振动位移的空间分布,由此讨论了轮胎着地长度和轮-地相互作用力的变化规律,并对地表振动位移的参数影响作出分析. 结果表明,地面不平度对轮-地之间作用力的影响最为显著,地面越不平顺则轮-地作用力和地表振动位移越大. 车速对轮-地作用力的大小影响有限,但对载荷激励频率影响较大,车速增大则激励频率增大,地表振动位移随之增大. 在较低车速时,轮胎包容性对轮-地作用力和地表振动产生一定影响,轮胎充气压力增大,轮-地作用力和地表振动位移增大,但随着车速升高,这种影响将逐渐消失.      

Modeling compaction in agricultural soils

Research was conducted to quantify the effect of tire variables (section width, diameter, inflation pressure); soil variables (soil moisture content, initial cone index, initial bulk density); and external variables (travel speed, axle load, number of tire passes) on soil compaction and to develop models to assess compaction in agricultural soils. Experiments were conducted in a laboratory soil bin at the Asian Institute of Technology in three soils, namely: clay soil (CS), silty clay loam soil (SCLS), and silty loam soil (SLS). A dimensional analysis technique was used to develop the compaction models. The axle load and the number of tire passes proved to be the most dominant factors which influenced compaction. Up to 13% increase in bulk density and cone index were observed when working at 3 kN axle load in a single pass using a 8.0–16 tire. Most of the compaction occurred during the first three passes of the tire. It was also found that the aspect ratio, tire inflation pressure and soil moisture content have significant effect on soil compaction. The initial cone index did not show significant effect. The compaction models provided good predictions even when tested with actual field data from previous studies. Thus, using the models, a decision support system could be developed which may be able to provide useful recommendations for appropriate soil management practices and solutions to site-specific compaction problems.     

Soil compaction and tires for harvesting and transporting sugarcane

Four tire types (A, block-shape tread; B, rib-shape tread; C, low-lug tread; D, high-lug tread) used to harvest and transport sugarcane were compared regarding the compaction induced to the soil. Tires were tested at three inflation pressures (207, 276, 345 kPa) and six loads ranging from 20 to 60 kN/tire. Track impressions were traced, and 576 areas were measured to find equations relating inflation pressure, load, contact surface and pressure. Contact surface increased with increasing load and decreasing inflation pressure; however, the contact pressure presented no defined pattern of variation, with tire types A and B generating lower contact pressure. The vertical stresses under the tires were measured and simulated with sensors and software developed at the Colombian Sugarcane Research Center (Cenicaña). Sensors were placed at 10, 30, 50 and 70 cm depth. Tire types A and B registered vertical stresses below 250 kPa at the surface. These two tires were better options to reduce soil compaction. The equations characterizing the tires were introduced into a program to simulate the vertical stress. Simulated and measured stresses were adjusted in an 87–92% range. Results indicate a good correlation between the tire equations, the vertical stress simulation and the vertical stress measurement.     

Tire deflection and contact studies

Dimensional variations of pneumatic tires influence off-road locomotion and more particularly their aptitude for the transmission of high propulsive torques to the tire-soil contact area.Height variation of the tire when load increases is linear and allows a classification of the casings by means of the angular coefficients for the straight lines expression this relationship.Variation in the level where the enlarging of the torus is maximum is directly connected with the applied load and inversely proportional to the inflation pressure. Ply rating and inflation pressure define a stiffness coefficient for a tire, while the ratio of height to width under load specifies a deformation coefficient, a squash rate and a flattening rate. These three parameters characterize the elasticity of the tire and so are connected to the effective tire-soil contact areas.Compressive effects of the vertical stress as well as the transmitted torques are in relation with tire deformability. The study points to the need for better specification of the parameters for the choice, or for the definition of the desired characteristics for manufacturing, of tires.Experiments already done on superficial compaction effects concluded with a new type of cross section for the tire called the camel shoe.     

The determination of deflection and contact characteristics of a pneumatic tire on a rigid surface

The contact pressure, contact area, contact width, contact length and vertical deflection of a pneumatic tire on a rigid surface depend on tire size, load and inflation pressure and can be derived by means of mathematical expressions. These expressions have been widely utilized and checked in practice for different tires.     

子午线轮胎接触变形的结构有限元分析

针对195／60R14子午线轮胎建立了三维非线性有限元模型，着重研究了额定充气压力及静载荷作用下帘线承受拉应力和剪应力的基本特征。计算结果表明，接地区域摩擦力呈斜对称分布，反映了轮胎中帘线-橡胶复合材料存在变形耦合效应；冠带层、带束层、胎体帘线应力分布较为复杂，载荷变化对其应力水平和分布影响较大；在胎肩部位应力较高，且随载荷变化局部帘线应力变化剧烈，在承受交变载荷时，易形成层间剥落。分析结果有助于预测轮胎的使用性能，可以针对性地应用于因轮胎结构设计引起的质量损坏，某些对轮胎使用性能不利的受力状态可通过结构的优化设计来克服。     

基于动量原理的大坡度沥青路面动水压力计算及影响因素分析Calculation and influence factors analysis for hydrodynamic pressure of asphalt pavement with large slope based on momentum theorem

在多雨地区长大纵坡沥青路面是雨天事故多发区域。应用动量定理,建立了沥青路面动水压力的力学计算模型,并系统分析了车辆荷载、行车速度和道路纵坡对动水压力的影响。结果表明,当水膜厚度＜3 mm时,动水压力随车速及车辆荷载的增大而增大,上坡时,动水压力随着纵坡坡度的增大而增大,下坡时,动水压力随着纵坡坡度的增大而减小。当水膜厚度＞3 mm时,动水压力随车速、车辆荷载增大而增大,上坡时,动水压力随着纵坡坡度的增大而增大,下坡时,动水压力随着纵坡坡度的增大呈先缓慢增加然后又缓慢减小的变化趋势;无论是上坡还是下坡,动水压力都随着车轮半径的增大而增大。本研究成果为多雨地区长大纵坡沥青路面重载交通高速行车易发生交通事故提供了理论分析依据。