Study of rail-wheel contact problem by analytical and numerical approaches

This study presents the rail wheel contact problems under normal and tangential categories. Both analytical and numerical approaches were used for modelling, where the analytical approach assumed elliptical contact patches based on the Hertz theory. In the numerical approach, 3D finite element models were used to investigate non-elliptical contact patches. The only elastic material model was considered in the case of Hertz theory. However, in the case of finite element analysis, both elastic and elastoplastic material models were used to simulate the material's behavior under the applied load. The elastoplastic material model was used to determine the amount of stress at which the plastic deformation starts, which enables determining the rail wheel's critical load. The commercial software ABAQUS was employed for 3D modeling and contact stress analysis. The study shows maximum stress at 3 mm from the rail wheel contact surface when the maximum load of 85 kN is applied. This initiates the cracks in the subsurface and causes the portion of the rail wheel to break off in the form of spalling after a certain time.

Nonlinear Dynamics Analysis of a Rolling Bearing

A numerical analysis of the nonlinear bearing model about two degrees of freedom has been presented in this paper. The contact between a ball and ring by Hertz theory is described. Influence of the number of balls, shaft rotation and clearance on the acceleration were investigated in detail. Three numbers of balls from 11 to 16 were analyzed. The clearance level in the range of 0-71μm has been studied. It has been shown that the acceleration responses are different, depending on the vibration direction and are usually higher when the radial internal clearance and the shaft speed are increased. The higher ball number caused that the accelerations decreased in both directions. Moreover, two dynamic indicators that can be used for comparison bearing dynamics have been proposed. These obtained results are useful for understanding the vibration response mechanism from a practical point of view.

The problem of the interaction of a conical indenter with an elastic cylinder

В данной работе исследуется поведение эластомера при взаимодействии с жестким штампом, вершина которого имеет форму конуса. В качестве определяющих соотношений используются модель материала Генки и ее обобщение для описания физически-нелинейного отклика. Проведено сравнение результатов численного решения с кривыми, полученными из рассмотрения поставленной задачи в рамках линейной модели с использованием теории Герца. В работах [10, 11] показана принципиальная возможность определения параметров модели гиперупругости на основе определяющих соотношений Генки-Мурнагана из экспериментов по индентированию сферическим штампом. Результаты, полученные в данной работе, могут быть использованы для построения методики определения параметров нелинейно-упругой модели из экспериментов по индентированию коническим штампом. In this paper, we investigate the behavior of an elastomer when interacting with a rigid punch, the top of which is cone-shaped. Hencky’s material model and its generalization to describe the physically nonlinear response are used as the constitutive relations. The results of the numerical solution are compared with the curves obtained from considering the problem in the framework of a linear model using the Hertz theory. The works [10, 11] show the fundamental possibility of determining the parameters of the hyperelasticity model based on the Hencky- Murnaghan constitutive relations from experiments on indentation with a spherical stamp. The results obtained in this work can be used to construct a method for determining the parameters of a nonlinear elastic model from experiments on indentation with a conical stamp.

Modeling of braking thermal effect for wheel-rail contact parameters

The Hertzian contact parameters are evaluated by taking into account the increase in temperature of the wheel due to braking under a steady mechanical loading. An equivalent mechanical load is evolved by Finite Element Analysis (FEA) to produce the same effect of the mechanical and thermal loading. The values obtained by FEA and Hertz theory for steady mechanical loading as well as for equivalent mechanical loading are matching. The contact parameters are found to vary linearly with temperature and equations are developed to obtain these parameters under thermal and mechanical loading. For 146.3 °C temperature of wheel due to braking, the contact pressure is 941.3 MPa, shear stress is 378 MPa and for solo mechanical loading, they are 519.8 MPa and 191 MPa correspondingly. The area of contact patch has increased from 0.0652 m2 to 0.142 m2 by 2.2 times due to thermal effect.

Simulation and measurement study of metro wheel wear based on the Archard model

PurposeThe purpose of this paper is to study the wear evolution of metro wheels under the conditions of different track sequences, track composition and vehicle load and then to predict wheel wear and to guide its maintenance.MethodologyBy using the SIMPACK and MATLAB software, numerical simulation analysis of metro wheel wear is carried out based on Hertz theory, the FASTSIM algorithm and the Archard model. First of all, the vehicle dynamics model is established to calculate the motion relationship and external forces of wheel-rail in the SIMPACK software. Then, the normal force of wheel-rail is solved based on Hertz theory, and the tangential force of wheel-rail is calculated based on the FASTSIM algorithm through the MATLAB software. Next, in the MATLAB software, the wheel wear is calculated based on the Archard model, and a new wheel profile is obtained. Finally, the new wheel profile is re-input into the vehicle system dynamics model in the SIMPACK software to carry out cyclic calculation of wear.FindingsThe results show that the setting order of different curves has an obvious influence on wear when the proportion of the straight track and the curve is fixed. With the increase in running mileage, the severe wear zone is shifted from tread to flange root under the condition of the sequence-type track, but the wheel wear distribution is basically stable for the unit-type track, and their wear growth rates become closer. In the tracks with different straight-curved ratio, the more proportion the curved tracks occupy, the closer the severe wear zone is shifted to flange root. At the same time, an increase in weight of the vehicle load will aggravate the wheel wear, but it will not change the distribution of wheel wear. Compared with the measured data of one city B type metro in China, the numerical simulation results of wheel wear are nearly the same with the measured data.Practical implicationsThese results will be helpful for metro tracks planning and can predict the trend of wheel wear, which has significant importance for the vehicle to do the repair operation. At the same time, the security risks of the vehicle are decreased economically and effectively.Originality/valueAt present, many scholars have studied the influence of metro tracks on wheel wear, but mainly focused on a straight line or a certain radius curve and neglected the influence of track sequence and track composition. This study is the first to examine the influence of track sequence on metro wheel wear by comparing the sequence-type track and unit-type track. The results show that the track sequence has a great influence on the wear distribution. At the same time, the influence of track composition on wheel wear is studied by comparing different straight-curve ratio tracks; therefore, wheel wear can be predicted integrally under different track conditions.

Comparison of analytical and numerical solution of bearing contact analysis

In this paper, an effort has been put to analyze the rolling ball bearing using finite element analysis the contact pressure level, stress or displacement behavior of rolling ball bearing. The obtained results were then compared with the analytical results obtained through the methodology of Hertz theory, which means composition and solution of analytical formulas and equations based on specific ball bearing parameters in order achieve optimal results to demonstrate an almost identical similarity of results of numerical and analytical solution and correct setting up of the given simulation in computational software ANSYS Workbench.