Traction Distribution Research Articles

An Equivalent Indentation Method for the External Crack with a Dugdale Cohesive Zone

An equivalent indentation method is developed for the external crack problem with a Dugdale cohesive zone in the both axisymmetric and two-dimensional (2D) cases. This is achieved based on the principle of superposition by decomposing the original problem into two simple boundary value problems, with one considering action of a constant traction within the cohesive zone, and the other corresponding to indentation by a rigid concave punch. Closed-form expressions are derived for the distributions of displacement and traction on the crack interface, which are consistent with the classical results in fracture mechanics. Results show that the interfacial traction distributions in the axisymmetric and 2D cases share the similar mathematical forms except for different coordinate parameters. Finite element analysis is performed to validate the obtained analytical solutions. The proposed method relies solely on a few contact solutions on the surface irrespective of a general elasticity solution in the whole body, and it may find applications in the external crack analysis and adhesive contact model involving functionally graded elastic solids or piezoelectric materials.

A theoretical model for the study of thermal fracture of functionally graded thermal barrier coatings with a system of edge and internal cracks

The problem of fracture of functionally graded coatings (FGCs) on a homogeneous substrate (a semi-infinite medium) is investigated under the influence of thermal and/or mechanical loads (e.g. a heat flux, residual thermal stresses caused by cooling-heating, tension). These loads reflect the most important cases, which arise during the exploitation of FGC structures. The FGC contains pre-existing systems of cracks, such as edge, internal and interface cracks. The mathematical description of the model is based on singular integral equations. The properties of the FGC are continuous functions of the thickness coordinate. Furthermore, the non-homogeneity of the functionally graded material is revealed in the form of corresponding inhomogeneous traction distributions on the surfaces of cracks. This method is approximate and used with the assumption, that the gradation of material properties of the FGC with the depth of the layer is not abrupt. The influence of residual stresses caused by temperature changes on ΔT (e.g. cooling from operating temperatures) is investigated in detail. Different crack patterns (which are reported in experiments and available in the literature) are studied by carrying out numerical experiments with respect to stress intensity factors and fracture angles (a deviation of cracks from the initial direction of propagation). The proposed model in combination with a detailed parametric analysis can help to optimize FGCs in order to improve the fracture resistance of FGC/homogeneous structures.

Mathematical modelling of torque vectoring differentials

Active safety systems which distribute forces between the wheels are an integral part of a modern vehicle. The vast majority of systems are based on the brake systems, and reducing engine power, which certainly reduces the vehicle speed. However, the needs of car owners are constantly changing, there is a need for devices capable of ensuring the distribution of traction between the wheels without having to reduce speed. With this task perfectly cope with the main transmission containing the mechanisms of power distribution (MPD). Power distribution mechanisms have a greater impact on vehicle handling. More often meet term, Torque Vectoring Differential (TVD). They began to be used for the first time since the mid-1990s, and found their application in sports cars, and then in executive cars. The described main gears are an integral part of dynamic stabilization systems. During the vehicle development, these systems are developed and investigated using mathematical modeling methods. Therefore, the paper describes the design, operation principle and kinematic design of the most common. The equations systems describing the dynamics of the links and the mechanism as a whole are also composed. The mathematical modeling of vehicles equipped with TVD is modelled.

Application of ETAPTM eTraXTM software package for digital simulation of distribution network that feeds an AC traction power supply system

Voltage unbalance in power systems feeding AC traction power systems is a worldwide known problem. One of the main aspects of this problem is the negative effect of voltage unbalance on motor loads causing operating problems and economic damage. It is necessary to perform unbalanced power flow studies and calculate voltage unbalance indexes to assess this negative effect of voltage unbalance and the develop of compensating measures during the design stage. Usually, calculations of the AC traction power supply system and the distribution network feeding it are carried out separately during the design of new lines of railways electrified by alternating current (AC) and reconstructing of existing ones. This approach is a source of deviations in the power flow studies because the lack of consideration of mutual influences between the traction power system and the distribution power system. In this paper, we compare a digital model in which the traction power supply system and the distribution network are modeled separately with a model that considers mutual influences between the traction and external power supply systems, including power flows through the traction network caused by the distribution network (transit currents). For digital modeling of these processes, authors used ETAPTM software with eTraXTM package. It allows to run unbalanced power flow studies when the generation and load are being changed over time, including train movement. During a separate simulation of the traction power system and distribution network, traction network was modelled using the equivalent sources connected to traction substation buses and the distribution network was modeled taking into account the fact that traction load was given from the simulation of the traction power system. The traction load was considered as lumped loads connected to the traction substation buses.At the same time, in both cases, the unbalanced power flow study was carried out by the phase domain method. Based on the results of two models comparison, it was concluded that the combined model containing a traction power supply system and distribution network, is more effective in terms of improving the accuracy of assessment voltage unbalance in accordance with current regulatory and technical documents on power quality.

Coordinated Chassis Control of 4WD Vehicles Utilizing Differential Braking, Traction Distribution and Active Front Steering

This paper proposes a coordinated chassis control (CCC) utilizing four-wheel differential braking, electronically controlled real-time four-wheel drive (4WD) and active front steering (AFS), aiming to improve the driving performance and handling stability during cornering. First, the performance of the single system is tested; then the hierarchical-structure control algorithm is designed: a supervisory controller to monitor vehicle states and determine the desired yaw rate, upper-level controller to decide the desired longitudinal forces and the desired yaw moment based on the driver intention and the consideration of vehicle stability, and the control allocation layer to distribute the actual control inputs to the actuators applying an optimal control allocation algorithm. Simulations of moderate driving/aggressive deceleration scenarios and a comprehensive test on a handling road are conducted to validate the effectiveness of the proposed control algorithm. The results of the simulations suggest that the proposed algorithm can effectively improve the driving speed in limit cornering without losing lateral stability, and reduce the tire dissipation energy compared with other control algorithms such as the electronic stability control system, the four wheel independent brake system and an integrated chassis control system proposed in a previous research.

The Fretting Contact of Coated Bodies. Part I – Contact Parameters

In case of a mismatch between the elastic properties of the contacting bodies, the solution of the fretting contact can only be achieved numerically due to the connection between the contact pressure and the shear tractions. The numerical treatment of the contact processes employs an iterative strategy, and therefore requires the computation of the displacement response of the elastic body, assumed as an elastic half-space, subjected to general loadings. Unlike the case of homogeneous bodies with known Green’s functions, a closed-form expression of the response of layered semi-infinite solids to unit point loads has only been attained in the frequency domain. The latter formulas are used in this paper to assess the displacement due to arbitrary normal and shear surface tractions, thus empowering the application of a trial-and-error approach in finding the parameters of a fretting contact: the contact area, the slip and the stick regions, and the distributions of pressure and shear tractions. The contact parameters are assessed in a nested loop strategy, involving three levels of iterations. The inner level, based on the conjugate gradient method for linear systems of equations, finds the pressure when solving the contact problem along the normal direction, disconnected from any tangential effects, or the shear tractions when considering the contact equations in the tangential direction, disconnected from the pressure influence. The middle level stabilizes the pressure with respect to the shear tractions, thus assuring that the global instantaneous contact solution is achieved. The outer level manages the reproduction of the loading history in a fretting loop, by load incrementation. The proposed strategy proves itself as a robust tool for the prediction of the fretting contact process involving coatings.

Модель динамики колесной машины для комплекса натурно-математического моделирования

Introduction. The use of the method of full-scale-mathematical modeling in “real time” opens up wide opportunities associated with the analysis of the modes of operation of the “man – vehicle – environment” system, as well as the study of the loading of units and assemblies of vehicles. The existing research complexes of full-scale mathematical modeling are suitable for obtaining most of the indicators usually determined by full-scale tests. The difference lies in the ability to fully control the course of virtual testing, recording any parameters of the vehicle movement, taking into account the “human factor”, as well as complete safety of the experiment. Purpose of research. The purpose of this work is to create a mathematical model of the dynam-ics of a wheeled vehicle, suitable for use in such a complex of full-scale mathematical modeling and assessment of the load of transmission units in conditions close to real operation. Methodology and methods. The proposed model is based on the existing model of the dynamics of a wheeled vehicle developed at Bauman Moscow State Technical University. Within the framework of the model, the dynamics of a vehicle is described as a plane motion of a rigid body in a horizontal plane. The principle of possible displacements is applied to determine the normal reac-tions of the bearing surface. The interaction of the wheel with the ground in the plane of the support base is described using an approach based on the “friction ellipse” concept. To enable the driver and operator of the full-scale mathematical modeling complex to drive a virtual vehicle in “real time” mode, the mathematical model is supplemented with a control system that communicates between the control parameter set by the driver by pressing the accelerator and brake pedals and the control actions of the vehicle's transmission units, such as: an electric machine, an internal combustion en-gine, a hydrodynamic retarder and a brake system. The article presents a block diagram of the de-veloped control algorithm, as well as approbation of the system's operation in a complex of full-scale mathematical modeling. Results and scientific novelty. A mathematical model of the dynamics of a wheeled vehicle was developed. It opens up wide possibilities for studying the modes of operation of the “driver-vehicle-environment” system in “real time”, using a complex of full-scale mathematical modeling. Practical significance. A mathematical model of the dynamics of a wheeled vehicle was devel-oped. It is supplemented with an algorithm for the distribution of traction / braking torques between the transmission units, which provide a connection between the driver's pressing on the accelerator / brake pedal and the control parameters of each of the units.

Scattering of Surface Waves by a Three-Dimensional Cavity of Arbitrary Shape: Analytical and Experimental Studies

The scattering of surface waves by a three-dimensional shallow cavity of arbitrary shape at the surface of a homogenous, isotropic, linearly elastic half-space is theoretically investigated. A novel analytical approach based on a reciprocity consideration is introduced in this article to determine the particle displacements of the scattered wave field generated by the interaction between the surface waves and the cavity. In the usual manner, the scattered field was shown to be equivalent to the radiation from the distribution of tractions, calculated from the incident wave, on the surface of the cavity. The radiation of surface waves subjected to the computed tractions applied at a single location was found using reciprocity theorems. The field scattered by the cavity was subsequently obtained from the superposition of displacements due to all the forces applied on the cavity surface. Solutions for the scattering of surface waves by a spherical, a circular cylindrical (coin-shaped) and a square cylindrical cavity are presented in detail. We here derive the closed-form expressions of the displacement amplitudes, which represent the far-field scattered waves produced by each of the cavities. An experimental setup using the ultrasonic pulse-echo technique was then carried out to record the scattered echoes of surface waves from these cavities in order to provide practical validation of the analytical findings. The vertical displacements measured at a significant distance of about twenty-five wavelengths from the cavities of the same width and different depth were compared with the corresponding theoretical predictions. The comparisons show excellent agreement for the case of a spherical cavity and good agreement in the cases of a circular and a cylindrical cavity in terms of trends and magnitudes. It is followed by a discussion on the results of the comparison and the limitations of the proposed approach regarding the degree of smoothness and the size of cavity.

Measurement of mixed mode interfacial strengths with cementitious materials

In the oil and gas industry, a successful zonal isolation, which is the primary goal of cementing, is achieved by a strong bond at the cement-rock and the cement-casing interfaces. We introduce a universal test in conjunction with an analytical solution to measure the mixed mode interfacial strength of cementitious materials at the casing-cement or rock-cement interfaces. To this end, the most practical method is employed, which is the direct measurement of adhesion at the interface. This experimental setup is consisted of a rotational disk composed of two identical halves. Each half includes a cylindrical hole at its center, which can be filled by cement slurry, a rock cylinder or a steel bar. Therefore, different interfaces i.e. cement-cement, cement-steel, and cement-rock can be examined. After curing, the disk is subjected to two diametral point loads using a compressive frame. By adjusting the angle between the load direction and the overlapping interface, we can examine different combinations of modes I and II. On the other hand, an analytical elasticity solution is developed to calculate the critical shear strength that would initiate sliding between the interfaces. Analytical results show a non-uniform distribution of shear tractions along the sliding interface. Having the peak load obtained from experiment, derived formulations are used to evaluate the bonding strength of cementitious materials corresponding to different loading modes of pure shear, the combination of tension/compression and shear. The value of the current analytical derivation can be appreciated by comparison with the typical approach that assumes a uniform traction distribution along the sliding interface. We find that assuming uniform distribution will overestimate the shear strength at the cement-casing interface. The analytical solution in conjunction with the experimental results can also be used to calibrate cement interfacial friction properties.

Robotic grasp analysis using deformable solid mechanics

Given an object and a hand, identifying a robust grasp out of an infinite set of grasp candidates is a challenging problem, and several grasp synthesis approaches have been proposed in the robotics community to find the promising ones. Most of the approaches assume both the object and the hand to be rigid and evaluate the robustness of the grasp based on the wrenches acting at contact points. Since rigid body mechanics is used in these works, the actual distribution of the contact tractions is not considered, and contacts are represented by their resultant wrenches. However, the tractions acting at the contact interfaces play a critical role in the robustness of the grasp, and not accounting for these in detail is a serious limitation of the current approaches. In this paper, we replace the conventional wrench-based rigid-body approaches with a deformable-body mechanics formulation as is conventional in solid mechanics. We briefly review the wrench-based grasp synthesis approaches in the literature and address the drawbacks present in them from a solid mechanics standpoint. In our formulation, we account for deformation in both the grasper and the object and evaluate the robustness of grasp based on the distribution of normal and tangential tractions at the contact interface. We contrast how a given grasp situation is solved using conventional wrench space formulations and deformable solid mechanics and show how tractions on the contacting surfaces influence the grasp equilibrium. Recognizing that contact areas can be correlated to contact tractions, we propose a grasp performance index, $$\pi $$ , based on the contact areas. We also devise a grasp analysis strategy to identify robust grasps under random perturbations and implement it using Finite Element Method (FEM) to study a few grasps. One of the key aspects of our Finite Element (FE)-based approach is that it can be used to monitor the dynamic interaction between object and hand for judging grasp robustness. We then compare our measure, $$\pi $$ , with conventional grasp quality measures, $$\epsilon $$ and v and show that it successfully accounts for the effect of the physical characteristics of the object and hand (such as the mass, Young’s modulus and coefficient of friction) and identifies robust grasps that are in line with human intuition and experience.

Investigation of Rayleigh wave interaction with surface defects

The current article is concerned with the interaction of Rayleigh waves with surface defects of arbitrary shape in a homogeneous, isotropic, linearly elastic half-space. Using a linear superposition principle, the interaction generates a scattered field which is equivalent to the field radiated from a distribution of horizontal and vertical tractions on the surface of the defect. These tractions are equal in magnitude but opposite in sign to the corresponding tractions obtained from the incident wave. The scattered field is then computed as the superposition of the displacements radiated from the tractions at every point of the defect surface using the reciprocity theorem approach. The far-field vertical displacements are compared with calculations obtained by the boundary element method (BEM) for circular, rectangular, triangular and arbitrary-shaped defects. Comparisons between the theoretical and BEM results, which are graphically displayed, are in excellent agreement. It is also discussed the limitations of the proposed approximate theory.
 Keywords:
 half-space; Rayleigh wave; surface defect; reciprocity theorem; boundary element method (BEM).

MPTC for PMSMs of EVs With Multi-Motor Driven System Considering Optimal Energy Allocation

This paper presents a compound propulsion system with a high-speed permanent-magnet synchronous motor (PMSM) and two in-wheel motors for electric vehicles (EVs). In this paper, the longitudinal dynamic model of EVs is first presented. Then traction distribution ratio α is introduced to express the traction distribution between the front and the rear axles. Moreover, the function of power consumption concerned with the traction distribution ratio α is established. Therefore, the α that minimizes the power consumption function is selected as the optimal traction distribution ratio. To improve the performance of motor controllers, the model predictive torque control (MPTC) method is employed for high-speed and in-wheel motor drives. Experimental comparison with field-oriented control (FOC) shows the advantages of MPTC in dynamic response. Finally, experimental comparisons and hardware-in-loop (HiL) tests are presented to verify the MPTC method and the proposed energy allocation method, respectively.

A simple numerical approach for reconstructing the atomic stresses at grain boundaries from quantum-mechanical calculations.

The atomistic stress state at a metal grain boundary is an intrinsic attribute which affects many physical and mechanical properties of the metal. While the virial stress is an accepted measure of the atomistic stress in molecular dynamics simulations, an equivalent definition is not well-established for quantum-mechanical density functional theory (DFT) calculations. Here, we introduce a numerical technique, termed the sequential atom removal (SAR) approach, to reconstruct the atomic stresses near a symmetrical-tilt Σ5(310)[001] Cu grain boundary. In the SAR approach, individual atoms near the boundary are sequentially removed to compute the pair (reaction) force between atoms, while correcting for changes to the local electron density caused by atom removal. We show that this SAR approach accurately reproduces the spatially-varying virial stresses at a grain boundary governed by an embedded atom method potential. The SAR approach is subsequently used to extract the atomistic stresses of the grain boundary from DFT calculations, from which we reconstruct a continuum-equivalent grain boundary traction distribution as a quantitative descriptor of the grain boundary atomic structure.

Subcritical and critical states of a crack with failure zones

• A new semi-analytical technique is developed to solve the problems of crack mechanics within the cohesive zone model . • Proposed technique implicitly takes into account the finite stress condition. • New dependencies for critical crack lengths are obtained for the non-uniform traction-separation laws. The problem on the stress–strain state near a mode I crack in an infinite plate is solved in the frame of a cohesive zone model. The complex variable method of Muskhelishvili is used to obtain the crack opening displacements caused by the cohesive traction , which models the failure zone at the crack tip, as well as by the external load. The finite stress condition and logarithmic singularity of the derivative of the separation with respect to the coordinate at the tip of a physical crack are taken into account. The cohesive traction distribution is sought in a piecewise linear form, nodal values of which are being numerically chosen to satisfy the traction-separation law. According to this law, the cohesive traction is coupled with the corresponding separation and fracture toughness . The tips of the physical crack and cohesive zone (geometric variables) along with the discrete cohesive traction are used as the problem parameters determining the stress-strain state. If the crack length is included in the set, then the critical crack size can be found for the given loading intensity. The obtained determining system of equations is solved numerically. To find the initial point for a standard numerical algorithm, the asymptotic determining system is derived. In this system, the geometric variables can be easily eliminated, which make it possible to linearize the system. In the numerical examples, the one-parameter traction-separation laws are used. Influence of the shape parameters of the law on the critical crack size and the corresponding cohesive length is studied. The possibility of using asymptotic solutions for determining the critical parameters is analysed. It is established that the critical crack length slightly depends on the shape parameter, while the cohesive length shows a strong dependence on the shape of cohesive laws .

A theoretical model for the study of thermal fracture of functionally graded thermal barrier coatings

The problem of fracture of functionally graded coatings (FGCs) on a homogeneous substrate (a semi-infinite medium) is investigated under the influence of thermal and/or mechanical loads (e.g. a heat flux, residual thermal stresses caused by cooling-heating, tension). These loads reflect the most important cases, which arise during the exploitation of FGC structures. The FGC contains pre-existing systems of cracks, such as edge, internal and interface cracks. The mathematical description of the model is based on singular integral equations. The properties of the FGC are continuous functions of the thickness coordinate. Furthermore, the non-homogeneity of the functionally graded material is revealed in the form of corresponding inhomogeneous traction distributions on the surfaces of cracks. This method is approximate and used with the assumption, that the gradation of material properties of the FGC with the depth of the layer is not abrupt. The influence of residual stresses caused by temperature changes on ΔT (cooling) is investigated in detail. Different crack patterns (which are reported in experiments and available in the literature) are studied by carrying out numerical experiments with respect to stress intensity factors, fracture angles (a deviation of cracks from the initial direction of propagation) and critical loads, when the propagation of cracks starts. The proposed model in combination with a detailed parametric analysis can help to optimize FGCs in order to improve the fracture resistance of FGC/homogeneous systems.

On the contact and adhesion of a piezoelectric half-space under a rigid punch with an axisymmetric power-law profile

The present paper provides a theoretical study on the axisymmetric contact and adhesive behaviors of a transversely isotropic piezoelectric half-space under a rigid punch, with an emphasis on Hertzian contact and JKR-type adhesion solutions for the conducting punch of power-law profile. The Hertzian piezoelectric contact model and JKR-type adhesion model are established by cumulative superposition and equivalent energy release rate approaches, respectively. Closed-form expressions are derived for the applied load, indentation depth, distributions of contact traction and surface displacement, which are able to link existing solutions for non-adhesive and adhesive contact problems for transversely isotropic and isotropic elastic materials, and to include the corresponding Hertz-n and JKR-n solutions as special cases. Similar mathematical forms are found between the elastic solids and the piezoelectric materials under a conducting grounded punch except for different material moduli. These results can serve as benchmarks for checking the validity of numerical methods.

Complete analytical solutions for double cantilever beam specimens with bi-linear quasi-brittle and brittle interfaces

In this work we develop a complete analytical solution for a double cantilever beam (DCB) where the arms are modelled as Timoshenko beams, and a bi-linear cohesive-zone model (CZM) is embedded at the interface. The solution is given for two types of DCB; one with prescribed rotations (with steady-state crack propagation) and one with prescribed displacement (where the crack propagation is not steady state). Because the CZM is bi-linear, the analytical solutions are given separately in three phases, namely (i) linear-elastic behaviour before crack propagation, (ii) damage growth before crack propagation and (iii) crack propagation. These solutions are then used to derive the solutions for the case when the interface is linear-elastic with brittle failure (i.e. no damage growth before crack propagation) and the case with infinitely stiff interface with brittle failure (corresponding to linear-elastic fracture mechanics (LEFM) solutions). If the DCB arms are shear-deformable, our solution correctly captures the fact that they will rotate at the crack tip and in front of it even if the interface is infinitely stiff. Expressions defining the distribution of contact tractions at the interface, as well as shear forces, bending moments and cross-sectional rotations of the arms, at and in front of the crack tip, are derived for a linear-elastic interface with brittle failure and in the LEFM limit. For a DCB with prescribed displacement in the LEFM limit we also derive a closed-form expression for the critical energy release rate, G_c. This formula, compared to the so-called ‘standard beam theory’ formula based on the assumptions that the DCB arms are clamped at the crack tip (and also used in standards for determining fracture toughness in mode-I delamination), has an additional term which takes into account the rotation at the crack tip. Additionally, we provide all the mentioned analytical solutions for the case when the shear stiffness of the arms is infinitely high, which corresponds to Euler–Bernoulli beam theory. In the numerical examples we compare results for Euler–Beronulli and Timoshenko beam theory and analyse the influence of the CZM parameters.

Methods to solve half-plane partial slip contact problems

There exists a family of methods for finding the extent of partial slip in contact problems between elastically similar bodies, capable of idealisation by half-planes. Closed form solutions are given to problems subject to a constant normal load and subsequent application of either an increasing shear force or differential bulk tension parallel with the surface. The starting point may be either a sliding contact (as is customary), or a fully adhered contact. The corrections required to impose a point-wise interpretation of Coulomb’s law of friction may be either in the form of a shear traction distribution or as dislocation arrays. The latter, when applied to the fully adhered contact, has the merit of automatically preserving the locked-in relative surface strains.

The role of traction in membrane curvature generation.

Curvature of biological membranes can be generated by a variety of molecular mechanisms including protein scaffolding, compositional heterogeneity, and cytoskeletal forces. These mechanisms have the net effect of generating tractions (force per unit length) on the bilayer that are translated into distinct shapes of the membrane. Here, we demonstrate how the local shape of the membrane can be used to infer the traction acting locally on the membrane. We show that buds and tubes, two common membrane deformations studied in trafficking processes, have different traction distributions along the membrane and that these tractions are specific to the molecular mechanism used to generate these shapes. Furthermore, we show that the magnitude of an axial force applied to the membrane as well as that of an effective line tension can be calculated from these tractions. Finally, we consider the sensitivity of these quantities with respect to uncertainties in material properties and follow with a discussion on sources of uncertainty in membrane shape.

Synchronous control system based on wireless data transmission for 50,000-t heavy-haul trains

In order to meet the ever-increasing freight capacity demand, operation of heavy-haul freight trains with a 50,000 t capacity has been widely studied for a decade in China. A typical heavy-haul train with a large capacity employs multiple locomotives that are evenly distributed along the train, and each locomotive, or two or more locomotives, hauls a certain amount of freight cars. The synchronicity among locomotives is of great importance to safety. A 50,000-t train developed in China will be pulled by 10 locomotives, and the uneven distribution of traction or brake force, caused by the asynchronous command execution of different locomotives, could eventually lead to severe accidents such as decoupling. This article focuses on how to apply the existing wireless-based multi-locomotive synchronous control system to the trains with the capacity of 50,000 t. The modular functionality of the control system is introduced, and some methods aiming to enhance the reliability of wireless communication are discussed. Then four experiments conducted on real trains or in laboratory are described. Test results show that the wireless synchronous control system can meet the technical requirements of 50,000-t trains and its operation is feasible.