Using numerical simulation to analyze the strength properties of the developed demountable body of a trolley

One of the safest types of public transport is the metro, which is actively developing in many countries. Despite a number of advantages, the construction of metro tunnels is a rather labor-intensive process, which involves complex technical equipment in the form of tunnel boring complexes. Tunnel boring complexes include locomotives that perform the functions of hauling away rock using trolley with removable body. Trolley differs from their usual characteristics - in weight, dimensions, as well as the component composition of individual systems, in particular the compressed-air braking system. The article is devoted to the analysis of the parameters of the stress-strain state of one of the main load-bearing elements of a trolley- the casing. As a result of the analysis, design loading cases were selected, the most loaded parts of the body were determined, recommendations were formed for choosing the optimal material thickness of various elements and increasing the load-bearing capacity of the body.


Introduction
The rapid development of rail transport, including those used in the construction of tunnels and subways as elements for hauling rock, puts forward higher demands on the efficiency and safety of vehicle operation [1].
The direction to increase the productivity, load capacity and durability of many mechanical engineering structures is intensifying.However, in most engineering industries, design decisions made decades ago are still relevant.Traditional technical products are gradually exhausting their resources, and the development of radically different, alternative solutions is required.In addition, for a wide class of mechanical engineering structures, there are quite strict standards for strength, stability, and deformability.Thus, these established factors hinder the creation of innovative products with a sharply increased level of technical characteristics [2].
In accordance with the requirements of state standards, in order to extend the service life of loadbearing structures of rolling stock, it is necessary to study the stress-strain state (SSS) of these structures.Bearer frames are subjected to strong static and dynamic loads, and are made mainly of solid casting, which makes them difficult to process due to their bulkiness.There may be casting cavities that lead to the initiation of cracks [3].Welded structures of frame elements are also known [4,5], in which fatigue stresses of welds arise, the prediction of which is advisable to carry out using computer simulation.Elements of the supporting body structure may be damaged as a result of shunting operations, docking or loading of cars [6].A number of works have considered the issue of ensuring the necessary strength of freight cars under special operating conditions: during transportation [7] and during loading [8].In [9] the use of energy-absorbing materials for pipe loadbearing structures of a car is described in order to increase their dynamic characteristics [9].Wheel pairs are the most loaded components of car, therefore the determination of their strength properties is one of the most important studies in railway production [10].The influence of the rigid and elastic connection of the wheel pair with the frame on the dynamics and stability of the car in motion is also considered [11].

Calculation model
An element of a trolley with removable body, which is part of a tunnel boring complex, in the form of a removable body and contact elements, is considered as an object for research.Figure 1 shows a sketch of a detachable body suspended on cross arms.All parts are made of steel 09Г2С [4].The use of a removable turning body as part of the trolley will significantly speed up operational processes for mining rocks, increase automation of the processes of emptying trains, however, this imposes additional requirements on the elements of the body design.

Figure 1. Sketch of removable body suspended on cross arms
During technological operations, housing elements are subjected to various types of loading.In particular, to assess the SSS of structural elements of the trolley body, loads on the bilge, side surface, rotary rollers, and side stops are side walls.The use of a removable reversible body involves the transportation of bulk cargo.Spacer loads of granular bodies in the general case are determined by formulas and constructions given in courses on the statics of granular bodies [12].
The maximum load on the bilge of the trolley will be reached at the moment the body is torn off by the cross arms from the trolley frame.To calculate the strength of the elements of the side walls of the body supporting bulk cargo, the values of the angle of repose and volumetric mass of bulk cargo are taken according to [12].During the calculation process, the volumetric mass and angle of repose of the heaviest load -ore are taken: 2.5 t/m 3 and 35, respectively.Figure 2 shows the design diagram for design case No. 1, where p is the active pressuren the vertical wall of the car with a horizontal surface of the bulk cargo, Pa; mgcargo -gravity force applied to the bottom, N; mcargo -weight of transported cargo, kg; g -acceleration of gravity, m/s 2 .
The most loaded state of the side surface will be achieved at the moment of turning the body over for emptying, namely the moment when the load completely affects the side wall, which corresponds to turning the body over 90 degrees.At this moment, the turning rollers are engaged with the hooks of the turning mechanism.Figure 3 shows the design diagram for design case 2.  The most loaded state of the turning rollers is achieved at the moment of overturn in design case 3, when the centers of the circles of the turning rollers and side stops are on the same straight line, parallel to the base surface indicated in figure 4. In the design of the turning body, two rollers are used on each side (figure 4 ) each of which is fixed in two places on the eyes.It is worth noting that for better convergence of the problem, the roller is limited in all movements except the axis of action of the reaction force.By analogy with design case 3, the SSS of the side supports of the trolley body is calculated (design case No. 4).Obviously, the maximum load on this unit is achieved at the moment the body is torn off by the cross arm.In this setting, it will be convenient to apply a pulling force to the cross arm, and fix traverse stop, which belongs to the structure of the removable body.Figure 5 shows the application of forces and fastenings to surfaces for design case No. 4. It is worth noting that for better convergence of the problem, the cross arm is limited in all movements except the axis of action of the reaction force.

Grid model
The peculiarities of solving each of the calculated cases deserve special attention.Thus, for design cases No. 1 and No. 2, bends of the rolled sheet from which the sides and bottom of the body are made will be characteristic.The finite element method is based on the domain discretization method, which indicates a direct relationship between the number of elements, the accuracy of the results obtained and the physical modeling time

Calculation and conclusion
Figure 10 shows the distribution field of equivalent stresses over the body for the first design case.Maximum stresses occur in the corners where the transverse reinforcement is attached to the underbody.When lifting the body on traverses, the stress from the thrust of the bulk cargo on the side surface does not exceed 50 MPa.Application of steel grade sheet metal 09Г2С on a bottom with a thickness of 10 mm, under given loads entails a deflection of the bottom by more than 10 mm.It is worth noting that the side surfaces also suffered deformations of 3-5 mm.Due to the presence of an amplifier, the end surfaces have significantly lower stresses (about 15 MPa) and deformations (about 1 mm).Application of steel 09Г2С thickness of the bottom sheet is 10 mm, strength class 325 allows you to obtain a safety factor on the bottom of 1.1.Thus, it is advisable at future design stages to increase the thickness of the rolled sheet or the strength class of the steel used.Implementation of these recommendations will increase the service life of the bottom, but will entail an increase in monetary costs for the purchase of materials, and will also slightly reduce the efficiency of the entire trolley as a whole due to an increase in the mass of the structure.
Figure 11 shows the distribution field of equivalent stresses over the body for the second design case.Maximum stresses occur in the corners of the end and side surfaces.Application of steel grade sheet metal 09Г2С on a side surface with a thickness of 8 mm, under given loads entails a deflection of 26 mm.The end surfaces, due to the attachment of traverse stops to them, have significantly less deformation (about 2 mm).Application of steel 09Г2С a bottom sheet thickness of 8 mm of strength class 325 is unacceptable, since the safety factor is below unity.Thus, it is necessary to increase the thickness of the rolled sheet.Increasing the strength class of steel is not effective in this case, since steel of strength class 390 will allow you to have a safety margin in the region of 1, however, any internal defects in the rolled product can cause destruction of the entire product.Figure 12 shows the distribution field of equivalent stresses for the third design case.Maximum stresses are observed at the contact points between the roller and the hook.Average stresses in the rest of the structure do not exceed 70 MPa.This is due to the bending of the roller relative to the edges of the hook.The stress at the contact point is 111 MPa.Thus, the safety factor is 2.92.
Figure 13 shows the distribution field of equivalent stresses for the fourth design case.The safety factor is equal to 1.48.Based on the distribution of pressure resulting from pressing the traverse against the stop along the contact area, we can conclude that the greatest pressure occurs on the lower area of the traverse stop.The maximum contact pressure is about 170 MPa.Most design cases record rather low safety factors.On the one hand, this indicates the efficiency and high mass perfection of the body, therefore this design is the cheapest in terms of the unit cost of materials, however, such limiting values of safety factors can lead to frequent breakdowns of body elements and low reliability.The results of the second design case demonstrated the inconsistency of using a rolled sheet 8 mm thick for the side wall of the body.Increasing the strength class of steel for the side wall is not advisable.The key direction for increasing the strength of the body at the future stage of product development should be the design of additional stiffeners, increasing the thickness of the rolled sheet, or replacing the material altogether.A similar solution should be applied to the bottom.A safety margin of only 10% does not guarantee trouble-free operation of the body, subject to welding of elements, technological defects in the production of steel sheets and human factor.To increase reliability and safety when transporting a body on traverses, it is recommended to increase the thickness of the traverse to increase the contact area and reduce stress at the contact points.This will allow the loaded body to be transported more safely.At the same time, this will extend the service life of the traverses themselves.

Figure 4 .Figure 5 .
Figure 4. Determination of the most loaded state of the rotary rollers for the design case №3 (dimensions in mm) [13].To reduce time costs, in design cases No. 1 and No. 2, Shell elements were used for the sides and bottom, with different thicknesses depending on the thickness of the product in each specific place.Moreover, to simplify the model in these design cases, all parts are rigidly connected.Design cases No. 3 and No. 4 are characterized by friction of elements.For better contact resolution, an increased number of nodes on each contact surface is required.Also, the correct Anchorage of nodes will make a significant contribution to the convergence of the problem.Figures6-9show grid models for all calculation cases.

Figure 10 .Figure 11 .
Figure 10.Field of distribution of equivalent stresses over the body for the first design case (MPa)

Figure 12 .Figure 13 .
Figure 12.Field of distribution of equivalent stresses over the body for the third design case (MPa)