ORIGINAL ARTICLE

Structural Evaluation of an Agricultural Trailer Axle Subjected to Impact Loads

M.Sc. Raudel Flores Moreno^{I  *} 

Dr.Cs. Arturo Martínez Rodríguez^III 

Dr.C. Gilberto de Jesús López Canteñs^II 

Dr.C. Eugenio Romantchik Kriuchkova^II 

Dr.C. Pedro Ramón Mayans Céspedes^II 

M.Sc. Geisy Hernández-Cuello^III 

^I Universidad Autónoma Chapingo (UACh), Posgrado en Ingeniería Agrícola y Uso Integral del Agua, Chapingo, Texcoco, México.

^II Universidad Autónoma Chapingo (UACh), Departamento de Ingeniería Mecánica Agrícola (DIMA), Chapingo, Texcoco, México.

^III Universidad Agraria de La Habana (UNAH), Centro de Mecanización Agropecuaria (CEMA), San José de las Lajas, Mayabeque, Cuba

ABSTRACT

The dynamic load coefficients allow obtaining the tensile and deformational states in parts and structures subjected to dynamic loads with an acceptable degree of accuracy. In the present investigation, the dynamic load coefficients are determined and a structural evaluation is carried out on an agricultural trailer axle, subjected to a static vertical load of 20 kN. The energy method was used to determine the dynamic load coefficients and the simulation by the finite element method was performed to determine static stresses and deformations. Applying this method, the structural evaluation of the agricultural trailer axle subjected to impact loads was achieved, with a low computational requirement. For a free fall height of the trailer of 200 mm, with a load of 20 kN on each axle, if the wheels were rigid, an excessively high dynamic load coefficient would occur. It would cause exceeding the elastic limit of the axis material more than five times, while an impact height of that same level, can be damped by the tires, without using other damping means (springs), with a safety coefficient of 2.5.

Keywords: Dynamic stresses; numerical simulation; deflections

INTRODUCTION

The loads that act in agricultural machines are generally dynamic, this type of loads can cause serious effects, since they are powerful to cause plastic deformations (^{Flores et al., 2010b}). Frequent overloads provoke that many machines and implements suffer deformations in their structure or breaks during work (^{Paneque et al., 2018}).

The determination of dynamic load coefficients in an analytical way in agricultural machine structures, subjected to the effects of low speed impacts, presents a high level of difficulty. For this reason, it is necessary to use a methodology that allows determining the dynamic load coefficients and evaluate structures in a simple and precise way (^{Martínez et al., 2009}).

Studies that include analysis of forces, efforts, deflections and other aspects of physical design behavior can be addressed with computer-aided engineering tools, which encompasses the use of computer-aided design (CAD) and the method of elements. finite (FEM).

The numerical simulation methods have been applied in studies related to impact loads, like in the works developed by ^{Gin & Manikandan (2014)}, who performed a review related to the dynamic response of metal fiber laminates, subjected to an impact low speed, which include results on experimental, numerical and analytical works. Likewise, ^{Singh and Singh (2015)}, studied the effect of projectile characterization, fiber orientation and impact behavior on certain polymer compounds. On the other hand, ^{Untaroiu et al. (2013)},developed the model of a lower limb of a human body using the finite element method, to study injuries during an impact in a vehicle accident.

In the pneumatic soil interaction, the finite element method has been used, like in the study of ^{Lee and Gard (2014)}, who built a model of interaction between the soil and the tire. On the other hand, ^{Li et al. (2014)} investigated a five-piece wheel rim-tire system and a two-piece wheel rim connected to bolts, to examine stress levels and fatigue in critical regions, while ^{Xu and Zhai (2017)} formulated a stochastic model for the coupling between a vehicle and the ground, subject to shocks due to irregularities in the terrain. ^{Reina et al. (2017)} carried out the estimation of the terrain from chromatic, geometric properties and of functions based on the contact of the vehicle with the terrain, by measuring experimentally the operation of an off-road vehicle on different surfaces to validate the system studied. On the other hand, ^{Kong et al. (2016)} and ^{Kumar & Aggarwal (2017)} studied leaf spring suspension designs and their optimization. Finally, ^{Romero et al. (2018)}, propose an integrated model to simulate the vehicle-infrastructure interaction coupled. They performed a parametric analysis to examine the effect of the operational conditions and the characteristics of the vehicle design, on the dynamic responses of bridges and flexible pavements.

Based on this background, the present work aims to determine the dynamic load system acting on an agricultural cart axle devoid of suspension system and subjected to dynamic impacts. For that purpose, they determined the static deflections by applying the method of finite elements, from which, the dynamic load coefficients are calculated using traditional methods.

METHODS

Theoretical-Methodological Foundation

Description of the mechanical system

As an object of study, an agricultural trailer axle that supports a load equivalent to 20,000 N was used. It consists of two wheel hubs coupled to the central bar (Figure 1) on which, a couple of 7.50-20-6 tires, typical of agricultural machines (Figure 2) with their wheel rims, are attached.

Figure 1. Representation of the axle and tire of the agricultural trailer. a) 3D axis view developed using CAD tools; b) Plan of the central bar of the wheel axle; c) Wheel hub plane; d) 7.50-20-6 tire.

FIGURE 1 Representation of the axle and tire of the agricultural trailer. a) 3D axis view developed using CAD tools; b) Plan of the central bar of the wheel axle; c) Wheel hub plane; d) 7.50-20-6 tire. 

The axle material studied is 30 G steel according to GOST, 8632 steel according to AISI / SAE 30 Ni Cr Mo 2 K D. In the case of the tire, the mechanical properties required for processing during finite element analysis were previously determined in experimental form (^{Flores, et. al., 2010a}).

Determination of Dynamic Load Coefficients

The method used to determine the dynamic load coefficients, based on the energy method, starts from the approach that the potential energy of the impacting body (m.g.H) is converted into elastic potential energy that the impacted body accumulates during deformation.

According to classical theory (Pisarenko, 1989) the maximum dynamic stresses (σdmax) during flexion caused by impact are determined by means of the expression:

$\sigma d_{máx}=kd\cdot {\sigma }_{es{t}_{\max }}$………………….……………….… (1)

where: σest, is the static tension; kd, is the coefficient of dynamic loads, which in the simplest traditional method (Pisarenko, 1989) is given by the expression.

$kd=1+\sqrt{1+\frac{2H}{{\delta }_{est}}}$....................................................................... (2)

Being: δest, the deflection or displacement of the point of the beam or impacted body (in which it is desired to determine the coefficient of dynamic loads) under the action of the static load (m.g in this case).

In the case under study, the static arrow is taken as the sum of the deflection ${\delta }_{est\left(eje\right)}$ , corresponding to the beam or axis and the deflection ${\delta }_{est\left(neum\right)}$ of the tire at the point of union with the axis:

${\delta }_{est}={\delta }_{est\left(eje\right)}+{\delta }_{est\left(neum\right)}$……………………………………… (3)

The calculation of the tensions, as well as the static deflections in the elements under study, required for the determination of the dynamic load coefficients, was made from the digitized modeling of these elements using computer-aided design tools (CAD) and the determination of displacements through a static analysis using the finite element method (MEF). For their application, the corresponding stages were followed: selecting the type of study, applying properties of the materials involved in the system, establishing boundary conditions (loads, restrictions and contacts between components), creating mesh according to convergence analysis and running the program.

For the determination of the coefficient of dynamic loads, the value obtained from static deflection through finite element analysis is replaced in expression (2), for whose evaluation, a software was developed in Mathcad 2000 Professional support. This software makes it possible to vary the values ​​of the different input data, offering the results, both in tabulated form, and graphically. The deflections, both of the axle and of the tire, were determined separately, and then the principle of superposition was applied through the expression (3).

RESULTS AND DISCUSSION

Figure 2a shows the digitized model of the axle of the agricultural trailer, as well as the mesh configuration of finite elements applied (Figure 2c) of finite elements applied. Mesh size was defined on the basis of a convergence analysis shown in Figure 2b. Convergence analysis shows that from a size of the element close to 40 mm, the convergence of the results occurs.

FIGURE 2 Digitization and meshing of the agricultural trailer axle: a) three-dimensional model; b) convergence analysis; c) detail of the finite element mesh restrictions applied to the model 

For an agricultural trailer that has a maximum load capacity of 40 000 N, of them, 20 000 N correspond to each of the two axels and each tire will receive a vertical static load of 10 000N. These loads are applied at the points of the axes on which the structure of the cart rests, indicating with red arrows the applied forces (Figure 2a and c). The type of application applied for the study is shown in Figure 3, where the red arrows that indicate the point of application of the static load are appreciated. Movement restrictions were applied to the wheel hubs, to determine the deformations of the axle with respect to the point of attachment with the wheel rims.

As for the wheel, Figure 3 shows the meshing performed for the analysis, as well as the places of application of the loads and the pressure inside the tire (red color), and the restrictions (green color). The selected option of contact between the wheel rim and the tire was of the welded type. The applied load level was 10,000 N and the air pressure supplied to the tire was selected from 0.3 MPa, coinciding with the recommended value for this load level. A rigid surface was selected for the support surface, which constitutes the most dangerous situation.

FIGURE 3 Tire model with mesh configuration, applied loads and restrictions. 

A convergence analysis was applied to the selection of the meshing of the tire-wheel rim assembly. The characteristics of both meshes are shown in Table 1.

TABLE 1 Characteristics of the mesh used for the axle and the wheel rim-tire assembly 

	Axis	Wheel rim-tire
Mesh type	Standard. Solid tetrahedral element	Standard. Solid tetrahedral element
Item size	40 mm	30,5 mm
Tolerance	1.374 mm	1,5247 mm
Mesh quality	High order	High order
Total number of nodes	47 276	81 810
Total number of items	16 016	29 493

The distribution of the equivalent voltages of Von Mises for the axis is shown in Figure 4, showing that the maximum static stresses occur at the end of the axis, reaching a maximum value of 9.44 MPa for the applied static load of 20 kN, well below the elastic limit of the material (325 MPa).

FIGURE 4 Distribution of equivalent stresses of Von Mises on the shaft. 

Figure 5 shows the distribution of deflections in the axis, producing the maximum values ​​(0.0284 mm) in the center of the axis.

FIGURE 5 Distribution of deflections on the axis. 

The distribution of the deformations in the wheel, subjected to a static load of 10 kN and an internal pressure of 0.3 MPa, is shown in Figure 6, and it can be seen that, in the area of coupling with the hub of the axle, the deformation reaches 2.55 mm.

The distribution of stresses and deformations along the axis for a static load of 20 kN is shown in Figure 7.

In the figure it can be seen, both, the deflections on the axle (expressed in tenths of mm), and the total deflections (in mm) that take into account the sum of the deflections of the tire and those of the axle.

FIGURE 6 Distribution of deformations in the wheel. 

The distribution of stresses and deformations along the axis for a static load of 20 kN is shown in Figure 7. In the figure you can see both the deflections on the axle (expressed in tenths of mm), and the total deflections (in mm) that take into account the sum of the deflections of the tire and those of the axle. As it can be seen, the maximum deflections occur in the center of the beam, where the tensions are minimal, while the minimum total deflections (2,556 mm), which cause the maximum dynamic load coefficients (according to expression 2), coincide with the point of maximum tensions, so it is undoubted that, also from the dynamic point of view, the most dangerous point coincides with the ends of the axis where the Von Mises tension under static load reaches 9.44 MPa.

FIGURE 7 Variation of tensions and deflections along the axis. 

Table 2 shows the values ​​of the tensions and deflections along the axis, and it can be seen that the deflections of the axle are extremely small in relation to the deflections caused by the tires.

TABLE 2 Tensions and deflections along the axis 

Distance from the shaft end, mm	Shaft deflection, mm	Wheel deflection, mm	Total deflection, mm	Static Tension of Von Mises, σ est., MPa.	Kd (axis + wheel) para H=200 mm	kd (axis) for H = 200 mm	Dynamic tension σ din (a + w), MPa	Dynamic tension σ din (a, MPa
0	0,014	25,555	2,556	9,444	13,548	168,830	127,950	1594,5
20	0,026	25,555	2,557	3,211	13,545	123,860	43,495	397,72
40	0,037	25,555	2,558	2,271	13,542	104,140	30,756	236,51
100	0,070	25,555	2,562	0,557	13,534	76,384	7,538	42,546
120	0,080	25,555	2,563	0,568	13,532	71,717	7,686	40,735
140	0,088	25,555	2,563	0,568	13,530	68,123	7,685	38,693
160	0,097	25,555	2,564	0,568	13,528	65,026	7,684	36,934
180	0,106	25,555	2,565	0,568	13,526	62,379	7,682	35,431
200	0,704	25,555	2,625	0,568	13,383	24,850	7,601	14,115
400	1,880	25,555	2,743	0,568	13,117	15,620	7,450	8,872
600	2,410	25,555	2,796	0,568	13,002	13,921	7,385	7,907
800	2,730	25,555	2,828	0,568	12,934	13,145	7,347	7,466
896	2,840	25,555	2,839	0,568	12,911	12,909	7,333	7,332

The table also shows the calculation of the dynamic load coefficients for a drop height of the cart with the undercarriage H = 200 mm. For this height of impact, if the wheels and the soil were rigid, the coefficient of dynamic loads kd (axle) would reach the value of 168.83 at the end of the axles, when the dynamic tension reached a value of σ din (a) = 1594.5 MPa, five times higher than the elastic limit of the shaft material. However, with the damping effect of the tire the dynamic load coefficient, for the same drop height, decreases to a kd (axis + well)=13,548, reaching the dynamic tension σ din (a + w) = 127.95 MPa , lower than the elastic limit with a safety coefficient of n = 2.5.

CONCLUSIONS

• By combining the energy method and the analysis of stresses and deformations using the finite element method, the structural evaluation of the agricultural trailer axle subjected to impact loads was achieved, with a low computational requirement;

• For a free fall height of the cart of 200 mm, with a load of 20 kN on each axle, if the wheels were rigid, an excessively high dynamic load coefficient would occur, causing to exceed in more than five times the elastic limit of the shaft material;

• An impact height of that same level can be damped by the tires, without using other damping means (springs), with a safety coefficient of 2.5;

THANKS

The development of this research is gratefully acknowledged to the National Council of Science and Technology (CONACYT) for its support for professional development and scientific improvement. To the Chapingo Autonomous University for becoming part of the group of students and to the Agrarian University of Havana for my professional training.

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Received: September 25, 2019; Accepted: December 19, 2019

^*Corresponding author: Raudel Flores Moreno, e-mail: [e-mail]

Raudel Flores-Moreno, Estudiante de doctorado, Universidad Autónoma Chapingo, Posgrado en Ingeniería Agrícola y Uso Integral del Agua,. Carretera México-Texcoco km 38.5, Chapingo, Texcoco, México, C.P. 56230, MÉXICO. e-mail: [e-mail]

Arturo Martínez Rodríguez, Profesor Titular, Universidad Agraria de La Habana (UNAH), Facultad de Ciencias Técnicas, Centro de Mecanización Agropecuaria (CEMA), San José de las Lajas, Mayabeque, La Habana, Cuba, C.P: 32700, e-mail: [e-mail]

Gilberto de Jesús López-Canteñs, Profesor Titular, Universidad Autónoma Chapingo (UACh), Departamento de Ingeniería Mecánica Agrícola (DIMA), km 38.5 carr. México-Texcoco. CP 56230, Chapingo, Texcoco, Estado de México, e-mail: [e-mail].

Eugenio Romantchik-Kriuchkova, Profesor Titular, Universidad Autónoma Chapingo (UACh), Departamento de Ingeniería Mecánica Agrícola (DIMA), km 38.5 carr. México-Texcoco. CP 56230, Chapingo, Texcoco, Estado de México, e-mail: [e-mail].

Pedro Ramón Mayans-Céspedes, Profesor Titular, Universidad Autónoma Chapingo (UACh), Departamento de Ingeniería Mecánica Agrícola (DIMA), km 38.5 carr. México-Texcoco. CP 56230, Chapingo, Texcoco, Estado de México, [e-mail].

Geisy Hernández-Cuello, Inv. Auxiliar, Universidad Agraria de La Habana (UNAH), Centro de Mecanización Agropecuaria (CEMA), San José de las Lajas, Mayabeque, La Habana, Cuba, C.P: 32700, e-mail: [e-mail]

The authors of this work declare no conflict of interests.