Development and evaluation of an in-situ tire testing facility with variable side slip angles

An in-situ tire test rig was developed for field research on tire tractive and maneuverability performances. The Single Wheel Tester (SWT) was mounted on a tractor and a tested wheel was driven by a hydromotor, along a frame of 3 m length. In the SWT, four load cells were utilized to measure longitudinal and lateral forces, input and self-aligning torques, and two optical counters were applied to calculate forward and angular velocities. Response Surface Methodology was used to execute experimental design and to analyze the collected data. Afterwards, reduced form of a 2 Factor Interaction model was extracted to predict rolling resistance using seven factors. The test results show that increasing the normal load and side slip angle will cause an increment of rolling resistance. The incremental growth rate of the rolling resistance due to the normal load increment was observed. At higher cone index values, increasing the angular velocity reduces the rolling resistance, although at lower cone index values, the effect of angular velocity on rolling resistance is in reverse order. In addition, the increasing moisture content effect on rolling resistance at lower side slip angle values was observed.     

Brachistochrone for a rolling cylinder

The motion of a heavy homogeneous cylinder is considered as a no-slip rolling along the desired curve. We obtain a functional in the form of the total time of the cylinder rolling and solve the corresponding variational problem of minimizing this functional. We obtain an algebraic equation for the directional line of steepest descent, brachistochrone, in parametric form. We use the equation of motion of the cylinder with constraint reaction to determine the conditions of implementation of its pure rolling without separation and slip with respect to the brachistochrone.     

Friction force model and rolling dynamics for a ball on a rough surface with presliding displacement taken into account

A model of sliding and spinning friction forces for a ball in the form of finite relations obtained by integrating the tangential stresses over the contact area whose parameters are determined by Hertz’s theory for the “ball-rough horizontal surface” tribological conjunction pair is supplemented with a model of rolling friction torques. The combined model is peculiar in that the presliding displacement effect in rolling and spinning friction torques is taken into account. It is shown that the ball motions in the presliding displacement zone are of quasilinear character and, under shock perturbations, have the form of damping vibrations in the three orientation angles. The numerical parameters of the rolling and spinning friction model are experimentally determined for the presliding displacement zones, while the sliding friction parameters and partly the spinning friction parameters are calculated. Mathematical modeling permits one to discover new properties of the ball, namely, its deceleration in rolling, the onset of damping vibrations at the beginning and end of motion, and the transient process parameters.     

Cycloidal pendulum with a rolling cylinder

Free vibrations of a heavy homogeneous cylinder rolling in a cylindrical cavity whose directing curve is a brachistochrone are considered. The equation of motion of the cylinder is derived and the circular frequency of free vibrations of the cylinder center of mass is determined. An analogy between the cycloidal pendulum with a rolling cylinder and the classical cycloidal pendulum in the form of a material point is obtained.     

原始组织对ER9车轮钢滚动接触疲劳性能的影响

利用双盘滚动接触疲劳试验机对原始组织分别为片状珠光体+先共析铁素体(P+PF)和回火索氏体(TS)的ER9车轮钢试样进行滚动接触疲劳试验,并对结果进行了分析。结果表明:在油润滑条件下,原始P+PF试样的滚动接触疲劳寿命是TS试样的2.8倍.?其原因是原始的P+PF的试样表面存在厚约1?μm的机加工细晶层,而TS试样无明显细晶层,在疲劳过程中,P+PF试样会优先在细晶层内萌生浅层裂纹并平行于表面扩展形成浅层剥落,而后在细晶层剥落的区域萌生疲劳裂纹,而TS试样则直接在试样表面萌生疲劳裂纹.?经过1×105周次在空气中的预磨损后,两种不同原始组织的试样表面均被强化,滚动接触疲劳寿命均有大幅度的提升.?但由于P+PF试样预磨损过程中机加工细晶层的剥落以及产生了少量的疲劳磨损,部分疲劳磨损裂纹成为滚动接触疲劳裂纹的裂纹源,而预磨损后的TS试样的表层形成分布更为均匀的细晶层,故预磨损后的TS试样的滚动接触疲劳寿命远高于P+PF试样.      

A Model for the Determination of the Resisting Torque of the Rolling Bearing Cage Motion of Slow-Speed Kinematic Pairs

A simplified, plane model for determination of resisting torques of the rolling bearing cage motion of low speed kinematic pairs is presented. The considerations are devoted to an arbitrary character of the point contact of a rolling element–cage pairs lying in a plane which is crossing the rolling elements in their geometrical centre. The model has been developed on the basis of the analysis of motion kinematics of a bearing track and rolling elements. The proposed algorithm allows for continuous tracking the resisting torque of the cage and its components during the kinematic pair motion.     

An evaluation of the concept of rolling resistance

Certain fundamental equations are part of every scientific discipline. These can form the starting point of relevant research. Later on, however, these equations themselves should be further developed. The fundamental equations in terrain-vehicle mechanics are those which deal with the peripheral force and rolling resistance. Both have formed the subject of numerous investigations, yet many open questions remain. An example is the interpretation of the properties of rolling resistance. According to the present study the mechanical conditions are identical for both towed and driving wheels. Rolling resistance is essentially a moment, but an active force is needed to move the wheel forward. This force acts in the travel direction at the axle of a towed wheel and at the perimeter of a driving wheel.     

A novel analytical model based on arc tangent velocity field for prediction of rolling force in strip rolling

Accurate prediction of rolling force is an effective method to improve strip quality in rolling process. To achieve this goal, a novel arc tangent velocity field model based on the upper bound method is proposed to evaluate the rolling force. The mathematical expression of rolling force is derived from the virtual work principle and maximum plastic work principle. Comparing the experimental results with the proposed analytical model prediction, it has been found that this model is good for estimation of rolling force. Meanwhile, the finite element method is also used to simulate the rolling process to verify the validity of the analytical model. It is shown that this model can be used for prediction of rolling force in practice.

     

Transient rolling friction model for discrete element simulations of sphere assemblies

The rolling resistance between a pair of contacting particles can be modeled with two mechanisms. The first mechanism, already widely addressed in the DEM literature, involves a contact moment between the particles. The second mechanism involves a reduction of the tangential contact force, but without a contact moment. This type of rotational resistance, termed creep-friction, is the subject of the paper. Within the creep-friction literature, the term “creep” does not mean a viscous mechanism, but rather connotes a slight slip that accompanies rolling. Two extremes of particle motions bound the range of creep-friction behaviors: a pure tangential translation is modeled as a Cattaneo–Mindlin interaction, whereas prolonged steady-state rolling corresponds to the traditional wheel–rail problem described by Carter, Poritsky, and others. DEM simulations, however, are dominated by the transient creep-friction rolling conditions that lie between these two extremes. A simplified model is proposed for the three-dimensional transient creep-friction rolling of two spheres. The model is an extension of the work of Dahlberg and Alfredsson, who studied the two-dimensional interactions of disks. The proposed model is applied to two different systems: a pair of spheres and a large dense assembly of spheres. Although creep-friction can reduce the tangential contact force that would otherwise be predicted with Cattaneo–Mindlin theory, a significant force reduction occurs only when the rate of rolling is much greater than the rate of translational sliding and only after a sustained period of rolling. When applied to the deviatoric loading of an assembly of spheres, the proposed creep-friction model has minimal effect on macroscopic strength or stiffness. At the micro-scale of individual contacts, creep-friction does have a modest influence on the incremental contact behavior, although the aggregate effect on the assembly's behavior is minimal.     

Conditions for pure rolling of a heavy cylinder along a brachistochrone

Algebraic equations for the line of steepest descent of a cylinder are derived in parametric form. Conditions for rolling without slipping and separation of the cylinder along a brachistochrone are established based on the equations of motion with constraint reaction. The important conclusion is drawn that the center of mass of a cylinder moving along a brachistochrone describes a cycloid     

The Bekker theory of rolling resistance amended to take account of skid and deep sinkage

The Bekker theory of rolling resistance of free rolling, towed, rigid wheels is amended to take account of both skid and deep sinkage without leading to excessive complexity in the predictive equations. Theoretical relationships between skid and sinkage are derived for a free rolling, towed, rigid wheel on a purely cohesive soil ( = 0) and on a purely frictional soil (c = 0) with a sinkage exponent of unity. Generally, good agreement is found between predicted and measured values of rolling resistance and sinkage at a given vertical load, on both sand and clay soils, at shallow and deep sinkage.     

接触应力对FCB车轮钢组织演变与性能的影响

利用双盘滚动摩擦磨损试验机进行了贝氏体车轮钢的滚动磨损试验,采用扫描电子显微镜(SEM)、电子背散射衍射(EBSD)分析不同接触应力条件下贝氏体车轮钢次表层微观组织演变. 结果表明:在滚动磨损条件下,磨损机制由黏着磨损转变为疲劳磨损,增大接触应力对黏着磨损阶段的磨损量影响不大,但会显著增加疲劳磨损阶段的磨损量;贝氏体车轮钢在塑性变形的过程中,贝氏体铁素板条中位错逐渐增值、先累积形成小角度晶界,而后形成大角度晶界,使贝氏体铁素体发生细化;接触应力的大小影响表层组织的演变,当接触应力增至1 150 MPa时,晶粒细化为超细等轴晶,继续增加接触应力,组织变化并不明显. 接触应力大小会影响贝氏体车轮钢的表面硬度. 接触应力增加使贝氏体车轮钢的表面硬度增高,硬化层深度增大.      

Vibration analysis of a circular disk tensioned by rolling using finite element method

Summary The paper proposes a method in finite element analysis for estimating natural frequencies of a disk tensioned by rolling, without the use of eigenvalue analysis. The natural frequencies of a disk vary when the localized plastic deformation caused by roll-tensioning induces residual stresses. Tensioning is used for improving the dynamic stability of circular saws; the optimal condition of rolling can be predicted from natural frequency characteristics. In the proposed method, the natural frequencies after rolling are easily estimated from the mode shapes of the disk before rolling and the stress distribution after rolling. The method is based on ideas similar to thermal stress and sensitivity analysis rather than on eigenvalue analysis. The effectiveness of the method is shown by comparing the natural frequency characteristics obtained by this method with those by eigenvalue analysis. Received 18 June 1998; accepted for publication 8 April 1999     

Theory of rolling: Solution of the Coulomb problem

A theory of rolling of round bodies in the normal mode with adhesion conditions satisfied on the entire contact area is proposed. This theory refines the classical Coulomb’s theory of rolling in which the rolling moment is directly proportional to the pressing force (e.g., the weight of the rolling body). The rolling moment of cylinders is found to be directly proportional to the pressing force raised to a power of 3/2, and the rolling moment of balls and tori is proportional to the pressing force raised to a power of 4/3. It is shown that the normal mode of uniform rolling can only be provided for a certain ratio of the elastic constants of the materials of the round body and the base forming an ideal pair. The Coulomb problem is solved for the cases of rolling of an elastic cylinder over an elastic half-space, of an elastic ball over an elastic half-space, of an elastic torus over an elastic half-space, and of a cylinder and ball over a tightly stretched membrane. The rolling law is derived for such cases. The rolling friction coefficients, the rolling moment, and the rolling friction force are calculated.     

Establishment of the tension stress model considering metal lateral flow for foil rolling

In rolling production, the foil flatness quality is judged by detecting the lateral distribution of the front tension stress. Currently, because of the inaccuracy of the tension control model, there are still many flatness defects in foil rolling production. For the tension stress model of foil rolling, the primary problem is the inaccuracy of the metal lateral flow model. Therefore, based on Fleck’s foil rolling theory, a new model of the lateral displacement in the foil deformation region is established by using the principle of minimum potential energy. Next, a tension stress model is established, which takes the effect of the metal lateral flow into account. Last, using a laboratory 20-high rolling mill as the research object, the finite element model of foil rolling is established, and the accuracy of the new model is demonstrated by comparing the theoretical calculations with the simulation results.

     

一种滞弹簧耗能的新型离散元滚动阻力模型研究

颗粒间滚动阻力对颗粒体系的稳定性起着重要作用. 在传统的离散元法中, 滚动阻力模型通常由转动弹簧、转动黏壶和摩擦元件表达, 颗粒滚动动能由黏滞力(矩)和摩擦力做功耗散. 由于黏滞力(矩)与滚动速度相关, 临近静止状态的颗粒滚动速度变小, 动能耗散减弱, 传统的离散元模拟得到颗粒由滚动到静止耗费的时间比试验观测的结果要长. 为解决这一问题, 基于摩擦学理论分析了滚动阻力产生的材料滞弹性机理, 将其引入离散元滚动阻力模型, 提出了一种速度无关型动能耗散的滞弹簧, 给出了滞弹簧的弹性恢复力计算公式, 建立了一种新型的离散元滞弹性滚动阻力模型(HDEM). 为验证新型滚动阻力模型的正确性, 通过一个光学物理试验对单个圆形颗粒试件的自由滚动过程进行了测量, 将测量数据与新型的滞弹型离散元模型和传统离散元模型计算结果进行了对比. 结果显示, 基于滞弹性滚动阻力模型HDEM计算结果与试验数据吻合程度更高, 而且模拟得到的颗粒摆动频率更符合试验现象.      

Winkler partial slip solution for harmonic oscillations in steady rolling contact problems

A Winkler model (Kalker’s simplified theory) is adopted for solving analytically partial slip rolling contact problem in the first order perturbation form of small periodic oscillations of generally both normal and tangential load about a steady state. At present, only numerical investigations exist for this problem, with various approximations to deal with the transient effects (often, simply neglected), and particularly the effect of varying normal load and hence contact area, has not been investigated in detail, despite the problem of corrugation is essentially driven by the change of normal load.The linear perturbation analysis is used to obtain closed form expressions for the receptances of the tangential load. Also, similar expressions are obtained for the energy dissipation, which is correlated with the local wear.     

Nondestructive evaluation of plastic deformation in AA6061 aluminum alloy by electromagnetic discharge image

The electromagnetic discharge imaging (EDI) technique is combined with image analysis methods and used as a nondestructive method to evaluate the amount of plastic deformation of AA6061 aluminum alloy. Various amounts of plastic deformation was introduced mechanically by cold rolling on specimens having identical surface conditions to the specimen. Since the EDI discharge characteristics and intensity are affected by plastic deformation, the results can be used as a correlation. It is shown that the EDI discharge intensity increases with increasing rolling ratio up to 25% and reaches a saturation limit, beyond which the discharge intensity is inversely proportional to the rolling ratio. Since the changes of the internal energy and the electrical properties of the specimen caused by cold rolling has opposing effects on the EDI discharge intensity. That would eventually be saturated. Further analysis shows that the high intensity region of EDI discharge pattern is increased from 0–10% rolling ratio and then from 30% and up. As the AC frequency increased, the discharge intensity becomes proportional to the increase rolling ratio.     

低速下润滑接触区补充供油机制的研究

在滚动轴承运行的过程中,滚道上的润滑剂在滚动体的反复碾压下,厚度不断减小,轴承最终进入乏油润滑状态.为了解释长期工作在乏油条件下的轴承依旧能够保持较长时间的良好工作状态,有必要研究在轴承中是否存在某种自发的补充供油机制.本文作者基于球盘接触模型,分别考虑毛细力和分离压力在润滑油迁移过程中的作用,建立赫兹接触区附近油层分布模型,并以此修正弹流计算中的入口供油条件,采用统一Reynolds方程法计算在静止或低速条件下的润滑油膜厚度和压力分布,研究毛细力和分离压力的补充供油机制对润滑条件的改善作用.