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Procedía

Procedía Engineering 206 (2017) 1388-1394

www.elsevier.com/loeate/procedia

International Conference on Industrial Engineering, ICIE 2017

Application of the Laws of Mechanics of Granulated Solidsin Studies to Loader Bucket Interaction with Bulk Material Stack

Yu.M. Lyashinkoa, E.A. Rivyakinab'*, D.N. Shurygina

a Platov South-Russian State Polytechnic University (NPI), 132, St. Prosvescheniya, Rostov region, Novocherkassk 346428, Russia bDonState Technical University, 1, Gagarina Sq., Rhetov-na-Don 3460on, Russia

Abstract

Today the industrial complex needs sophisticated machines to perform loading operations. In the mechanized loading theory, one of the approdches to the description of the interaction processes between the bucket working bodies and the stocgpile of bulk material, ir the use of a dtatic granular medium method developed in the papers by Ch. (Coulomb, and St. S. Golushkovich's. Further development of progressive loading equipment i s required to elab orate modern methods bor rids earch of physievl and technological processes of interaction of executive bodie s with dhe essternal envlronment through the use of the numerical methods such as the discrete element method.

©2017 The Authore. Publidied by Eleevier Ltd.

Peer-review under resperLsibllity of the ¡s^pen^i^c committee of the; International Coherence on Industrial Engineering Keywords: mechanized loading;resistance to implementation; static granular medium; graphic-analytical method.

1. Introduction

The resistance of the jhili to introduce the working body is a chiractiristic that defines its basic parameters. Therefore, all the researchers involmed in the study of loading in one way or another, concerned the question of determining the efforts in thee implementation of the working body and the drawing of the goods [1-6]. To identify way s of further development of the studying of the mteraction o f loading machines with the external environment and impfoving the working bodies, the following is an analysis of* existing analytical methods. In theory mechanized loading one of the approaches to the description of processes of interaction of working bodies of the bucket with the

* Corresponding author. Tel.: +7-918-515-1070; fax: +7-8636-22-3088. E-mail address: revyelena@yandex.ru

1877-7058 © 2017 The Authors. Published by Elsevier Ltd.

Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering. 10.1016/j.proeng.2017.10.650

stockpile bulk material is the use of the method is a static granular medium developed in the writings of Ch. Coulomb, and S. S. Golushkevich's [7-9].

2. Application of the Ch. Coulomb'smethod in studies of the process of loading packaged material bucket working body

The possibility of applying the Ch. Coulomb's method for describing the interaction of the front loader bucket to a stack tested in the works of I. V. Boyarkina [10]. According to the considered on the basis of the Ch. Coulomb's law interaction of the loader bucket with the pile of loose material at the first stage of introduction of the front wall of the bucket in a bulk material slip occurs cut the prism along the plane of the bucket (Fig. 1). At the same time there is a second sliding plane in an array of material on line OB, located at an angle y2 with the horizontal. In the plane of the slides OB are the complex physical phenomena that require detailed consideration and study. In cake-stack material plane slip, line OB, is an imaginary plane. The real slide of the prism bounded by the cross section OA1Bmay not occur on the line OB, since it is impossible to cut all pieces of material shown black fill (Fig. 1). In real conditions of digging the material is not subject to destruction. However, this does not mean that in this case the Ch. Coulomb's theory does not work. Shear volume of bulk material in its thickness occurs, the active layer separating the movable and fixed volume of material, having a thickness of d/p. This layer is at an angle y2 and acts as a Ch. Coulomb's slip plane. As a result of the phenomena in the slip plane OAi on the prism side of the bottom of the bucket is the force of sliding friction F1 and the normal force N1 and the sliding surfaces Ch. Coulomb's force: the frictional force F2 of the soil on the ground, the force of cohesion of the soil F^ and normal force N2. These forces are calculated values in the developed analytical calculation method:

where accordingly, the coefficients of sliding friction of soil on the bottom of the bucket and the ground.

Modern computer technology allows the numerical method to determine the actual value of the slip angle y2, which eliminates the necessity of finding the analytical formulas to determine the slip angle y2 as complex functions of the parameters. The analytical method of power calculation of the process of interaction of the loader bucket with loose material based on the theory of grip and the limit Ch. Coulomb's equilibrium. In the process of thrusting the bucket into bulk material in the array of material when it is loading external shearing forces there is a shear plane at an angle y2, which are the shear stress t and normal stress c and the coupling C, between which is established an analytical relationship for the Ch. Coulomb's law:

At the beginning of the implementation process of the bucket the prism of material having a section OA1B and the weight of G is free to slide along the flat wall of the bucket. The pressure of the front wall of the bucket on the soil, numerically coincident with the N1 response, tends to move the prism OBA1 parallel to the plane OB at an angle y2, and the force of normal pressure from the slip plane OB, which is numerically coincident with the reaction N2 is the force driving the prism OBA1 inside of the bucket. Considered forces are distributed forces acting in the respective faces of the prism slides OA1B.

In this case the normal forces N1 and N2 can be shown in the form of linear normal distributed strength with maximum values of intensity triangular plot q1max and q2max(H/M), which can be calculated by the formulas:

N2 = N1(^1,^2,Ml,Ml ,C, LBH )

t = C + atgPo

Mathematical models derived from Ch. Coulomb's laws, enabled a study of the process of implementation in a pile of bulk material flat front wall of the bucket.

Fig. 2. Scheme of distributed forces acting in the respective faces of the prism slides OA1B.

Considered phenomena accompanying the process of implementation of the bucket into the pile, and the method of calculation of forces and parameters are the basis for the creation of the modern theory of digging material with a front loader bucket.

3. The study of the process of loading of rocks bucket working on a method of Professor S. S. Golushkevich's

The possibility of applying of the Professor S. S. Golushkevich's method to describe the interaction of the bucket with the pile tested in the works of V. G. Silnya and V. D. Ereiskii [11-13].When you create a new form of bucket for loading the machine PPM-4M V. G. Silnya and V. D. Ereiskiietc. was used, considered in work [2], the energy theory of the implementation process of the bucket into the pile, was developed by staff of the laboratory of mechanization of mining operations the mining Institute of USSR Academy of Sciences under the leadership of G. V. Rodionov. According to the results of experimental studies carried out under the direction of G. V. Rodionova on model installations, the ideas of physics of the interaction of the bucket with the rock mass are as follows.

When introduced into the stack of the bottom of the bucket or inclined plate (Fig.3, a) is the displacement at the sliding planes I-I and II-II, delineation of the prism shift F1 and F2. These lines arise from the violation of the limit stress state caused by movement of the inclined plane. Displacement of particles above the bottom in the area of Fi

is similar to the processes occurring at the passive pressure on the friable mass retaining walls, tilted at an angle a0on to the base of the pile. Experiments show that when a0= 0 the displacement of the particle over the plane is in the area Fx does not occur. The front edge of the bottom of the bucket formed of the sealing material - the core of the seal (Fig. 3, a), the length of which increases with the penetration depth S, of the angle of inclination of the plane a0 and particle size. If the base of the pile is smooth, and the sharp edge of the bottom of the bucket held tightly to the base, the core of the seal does not occur. This allows you to imagine the emergence of such a nucleus as moving in the pile of the piece, located in front of the front edge of the bottom of the bucket, which plays the role of an additional retaining wall of small height (Fig.3, b).Similar phenomena take place in the implementation of the side walls of the bucket (Fig.3, c). With the increase in the angle of the front edge of the implement element A and the

Fig. 3. Deformation of the stack when introducing elements of the bucket (a, b, c); the interaction of the bottom of the bucket to a stack when drawing (d, e,f)

When you rotate the bucket in a vertical plane, scooped up - in the initial period there is a seal part of the pile located above the bottom (Fig.3, d). Upon further rotation occurs, the shift of the particles first in lines 1-2, a later -along the lines of 1-3. Education and the position of the slip lines 1-2 explains how and when implementation, violation of condition of limit equilibrium of the pile under the action of pressure from the bottom of the bucket. The shape and volume of the prism with base ABC is independent of the initial resistance to drawing, line 1-3 - reflects the influence on the volume occupied by the bucket load. The nature of the interaction of the bottom of the bucket to a stack when drawing depends on the position of the trajectory of the front edge of the bucket relative to the initial line slip sun (Fig.4, e); the trajectory is divided into steep 1 and shallow 2. For steep trajectories characterized by a decrease in shift amount with the increase of the angle of rotation of the bucket 9K, to, for shallow - plot BB2 move the volume of the pile increases. Therefore, the dependence of the moments of resistance of the scoop M3 (9) for the trajectories of the first and second types differ in the position of the point and the value of the max M3max(Fig. 3, f). The analytical determination of the resistance to the introduction and scooped up bucket loading on the interaction with the bulk material of the bottom and walls is regarded as the work of retaining walls. In Fig. 4 shows a stack having a slope angle (angle between the surface slope and the horizontal OC), is equal to the angle of repose 97, or less than, the angle of dumping 5. Line AB defines part of the bottom of the bucket, introduced in the stack, a and as - respectively, the angles of inclination of the soil generation on the horizon and the bottom of the bucket to soil excavation. Build to determine the body bulging BCEMA (Fig.4, b), is made by characteristic circles (Fig. 4, c).

Fig. 4. Graphic-analytical method for determination of resistance the scoop, S>0.

To do this, the circle pads built tangent line ab that is parallel to the bottom of the ladle AB. Through the point of tangency is perpendicular to OO6 intersection with a circle of poles. From the point O6 to the intersection with the circle vertices is video O6m, parallel by R. Connecting point m with points a and b, obtain the direction of slip lines in the zone of maximum stress BAM. To determine the directions of slip lines in the zone of minimum stress BCE to the range of venues is tangent cb ' parallel to the surface slope of the pile - CB; built perpendicular OO2 and from point O2; O2e is a direct parallel to the direction of gravity. Connecting point e to points c and b ' get the desired direction.The length of the straight BE restricting a special area BEM, is determined by the following formula:

r = r орХ%ф, r = BE, r = BM (4)

кон нач ' кон ' нач V '

where y -the angle between the slip lines, which determines the magnitude of the special zone.

To complete the construction of the body bulging, you need the points M and E to combine the logarithmic spiral. To determine the value of resistance R of the stack, you must calculate the space in all areas of the body bulging, the area of the special zone is determined by the formula

Fmbe = "IT—(BE 2 - MB2) (5)

After finding space easily determined by the gravity of individual body parts bulging Gh G2, G3. In a designated area of the centre of gravity is on the straight line VD. Knowing the gravity of certain body parts bulging and of the force direction with a polygon of forces is easy to determine the value of resistance of the pile R (Fig. 4, a). This method gives the best results for the flat trajectory, the maximum approaching the sliding surface. A fairly accurate correlation between theoretical and experimental curves suggests that the theoretical methods can be used not only to predict the design parameters influence the loading of bodies on to resist, but in determining the law WBH = f (S) in order to reduce the volume of experimental studies.

4. Computer modeling of graphic images underlying of the Professor S. S. Golushkevich's graphic method

Application of the Professor S.S. Golushkevich's method received development in researches of process of loading of rocks bucket working body of the excavator with a bottom in the form of a roller surface. Designed

bucket with roller bottom provides the reduction of energy consumption one of the most labor-intensive operations of the operating cycle of the shovel excavator of the implementation process of the bucket, by lowering the coefficient of friction rocky soils on the bottom by switching from sliding friction to rolling friction [14]. The level of development of modern computational tools allows to create mathematical models of processes of constructing graphic images, with subsequent implementation with the help of software, including build, underlying the graphic of Professor S. S. Golushkevich's method: the characteristic circles and zones of the stress state. To write a program that implements the graphical-analytical of Professor S. S. Golushkevich's method, was drawn up a mathematical model that implements the above algorithm [15]. Fig. 5 shows the simulation results of the characteristic circles and lines slip zones of strong and weak stresses.

The characteristic circles

Circle of poles K

Fig. 5 - The characteristic circles and lines slip zones of strong and weak stresses.

The program is implemented with the software product from Microsoft: Visual Studio .Net (C programming language).

5. Conclusion

The analysis of publications devoted to the simulation results, the state of the "loose body" in a wide range of technological processes, indicate a promising numerical methods. Priorities in the research process, the interaction of the loader bucket with the pile of the bulk material lies in the approaches to system modeling "loose body -retaining element" on the basis of application for the analysis zones of the stress state of the array bulk environment numerical methods such as discrete element method [17-21]. Thus, the importance of the possibility of detailed visualization of the processes under study and consideration of important factors not considered in other approaches. The development of this area may provide an impetus to the development of new effective machines and technologies.

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