Geosciences and Engineering, Vol. 1, No. (01), pp. 337 34. EXAMINATION OF AN OPTIMIZED REPLACEABLE CUTTING TOOTH OF EXCAVATOR ZOLTÁN VIRÁG 1 SÁNDOR SZIRBIK 1 Department of Geotechnical Equipment, University of Miskolc Department of Mechanics, University of Miskolc 3515 Miskolc-Egyetemváros, Hungary 1 gtbvir@uni-miskolc.hu ; Sandor.Szirbik@uni-miskolc.hu Abstract This paper briefly outlines the design of replaceable cutting teeth, which are attached to a holder with detachable joint [1]. The description of the rock cutting process is very complex. Thus the investigation of the effect of lateral forces is complicated through cutting tests. We have to use accordingly numerical analysis to examine some segment of the cutting process. Our main objective is to present a finite element analysis of cutting teeth in which the linear increase of the lateral force is taken into consideration. The finite element analysis is a powerful technique, which is enabled to obtain the stress and displacement distribution in cutting teeth. The simulation results have shown that the maximum stresses decrease if the lateral force increases. The geometry of the optimized cutting teeth will be safe under the given loading conditions. 1. Introduction An important and complex issue in mining is the rock cutting mechanization. The high cutting tooth wear and the high specific power demand are the long-standing problem of mining technique. New cutting tooth was designed in order to eliminate problems. Rock cutting tests were carried out, where winning experiments on the large sample from the mine were made using chisels modeling the in-plant winning chisels (cutting teeth), with cutting parameters close to reality []. To determine the geometric configuration of the cutting teeth and the cutting edges the knowledge of the mining technology is inevitable. The measurement data of cutting is collected and registered by a computer aided measurement system. On rock samples we recorded 165 measurement cycles. In each measurement cycle the following data and cutting characteristics were recorded: cutting direction, form, depth, average chip area, average cutting force F V, average pressing force F R and average lateral force F O. As a result of the measurements a new cutting geometry was developed []. The experiments prove that it should pay attention to the wears and the geometry of cutting teeth because of the increasing of the cutting, pressing and lateral force. Considering the laboratory cutting test results a FEM was created for further investigations.. Mathematical procedure In this section we give a brief introduction to displacement-based finite element methods. We remark that several books have given the basic concepts of finite element analysis. Although we have other alternatives, the principle of minimum potential energy is taken here as a starting point. First consider an elastic body V bounded by a surface A. The surface can be divided into two parts denoted by A p and A u. We shall assume that A p is the union of those surface patches on which loads are imposed and A u is the union of those
338 Zoltán Virág Sándor Szirbik surface patches on which displacements are prescribed. The total potential energy of the e- th element after finite element discretization can be defined as e 1 et e et e et e Π P = dv ρ dv da ε σ u k u p (1) e e e V V A p where σ e, ε e and u e are stress, strain and displacement vectors, respectively. Using approximation u e = Nq e, constitutive equation σ e = Cε e and strain displacement relation ε e = Bq e we have e 1 et T e et T e T e Π P = q dv ( ρ dv da) B CB q q N k + N p e e e V V A p e K e f () where N is the shape function matrix, B is the strain-displacement matrix, C is the matrix of elastic coefficients for an isotropic material and the nodal displacement vector is denoted by q. The total potential energy of the elastic body is n e 1 Π T T P = Π P = q Kq q f (3) e= 1 where n is the number of finite elements of the body, The first order variation of equation (3) assumes the form T T δπ P = δq Kq δq f = 0 (4) Finally the finite element approach leads to an algebraic equation system as follows: Kq = f (5) where K is the stiffness matrix, f is the vector of loads. This equation system can be solved for unknown nodal displacement using commercial FEM software. More detailed descriptions of finite element procedures can be found in Bathe s book [3]. 3. Model description In order to investigate the distribution of stresses in the cutting tooth, we set up a finite element model. Consider the solid model shown in Figure 1, consisting of a holder, a part from the cutting edge and an optimized cutting tooth. The cutting tooth is jointed into the holder as a removable piece. The holder is actually a steel rectangular structural tube, and of course it is possible the remaining parts of structure are made of a different kind of steel.
Examination of an Optimized Replaceable Cutting Tooth of Excavator 339 Figure 1: 3D assembly of solid models: the cutting tooth (1), the cutting edge () and the holder (3) Because of the detachable contact joint we should describe five contact pairs between the appropriate surfaces of the tooth and holder in the finite element model. The contact pair consists of the two contact surfaces. One of them in the pair is selected to be the contactor surface on the tooth and the other contact surface to be the target surface on the holder. For simplicity the contact surfaces of holder are regarded as stationary, rigid surfaces. It follows that these surfaces are used in our model to simplify the contact searching instead of modeling the holder as a solid structure. We assume that the coefficient of friction is equal to zero between the contact surfaces. Under these conditions we should solve this contact problem by using finite element technique. Further details of contact problems are presented in [4, 5]. Figure : Geometrical model of cutting tooth for finite element analysis The finite element mesh of cutting tooth is of free type using 10-node tetrahedral elements and so this solid structure is divided into 5 937 finite elements. The geometrical model of tooth is illustrated in Figure. The mechanical properties of steel used in linear elastic finite element analysis are also taken: Young s modulus (E) is.1 10 5 MPa and Poisson s ratio (ν) is 0.3. This material behaviour is assumed to be linear elastic until the effective stress reaches proportional limit and in this region the stress-strain relation is represented by Hooke s law.
340 Zoltán Virág Sándor Szirbik The aim of previous works [1, ] is to simulate the cutting load from real cutting conditions on the surface, which is cross-hatched and painted with yellow color in Figure 3. The resultant force from the pressure on the surface consists of three components: cutting force F V, lateral force F O and a pressing force F R, as see in Figure 3. These forces were determined by means of laboratory cutting experiments [1]. We assume that now the values of the resultant of cutting and lateral forces are 100 kn, and pressing force is always 100 kn. In order to investigate the rock cutting action for cutting forces in different directions we have to define various direction angles. Figure 3: Cutting, lateral and pressing force The direction angle α, which is measured in degrees positive clockwise between the direction of cutting force and the y axis of the global coordinate system, specifies the magnitudes of lateral and cutting forces. Thus F R = F = 100 kn, F V = F cos α and F O = F sin α are imposed on the appropriate surface as specified loads. 4. Results of finite element analyses In the preceding section a contact problem is proposed to determine the stress and displacement distribution in the tooth. The given problem is solved in ADINA [5]. To preserve the integrity of the teeth, the maximum stresses should be kept under the proportional limit of the material. The finite element analysis helps accordingly to qualify the strength of the new cutting tooth. The program computes effective stress (also called equivalent or von Mises stress) at each arbitrary point from the stress components using the formula σ [(σ σ ) + (σ σ ) + (σ σ ) + 6(τ + τ τ )] 1 = x y x z y z xy xz yz (6) red + As appeared from the numerical simulation the maximum effective stress is about 900 MPa in the case of α = 0 and it occurs in front of the tooth (see Figure 4). However the stresses decrease quickly below 60 MPa in the remaining part and so in the shank of the tooth.
Examination of an Optimized Replaceable Cutting Tooth of Excavator 341 Figure 4: Effective stress distribution in the tooth The maximum displacement occurs also in front of the tooth, where the loading condition is imposed. The maximum value of deformation is 0.46 mm. In the remaining part displacements decrease also quickly. Figure 5: Displacement distribution in the tooth The corresponding results after changing the direction angle have been tabulated in Table 1, where the maximum effective stress is denoted by σ max and the maximum displacement by u max and as mentioned previously, the angle α is measured in degrees. Maximum values of numerical results Table 1 α [degree] σ max [MPa] u max [mm] 0 933.3 0.46 10 884.9 0.389 0 850.3 0.4 30 89.3 0.53
34 Zoltán Virág Sándor Szirbik The simulation results show differences in the values of displacements. However the stresses decrease if the angle increases. We remark that these results show good analogy with those obtained in the previous study [6], where the whole stucture is modeled as a solid structure. Finally the theoretical optimized cutting tooth is realized. 5. Conclusions It is established that the development of cutting teeth could be improved by using finite element analysis. This technique is applicable to compare different types of teeth easily. It leads to an assessment of the effect of the main parameters on the behaviour of the geometric configuration of the cutting teeth. Consequently the results of finite element analysis show that the head of cutting tooth is the most critical point and so we conclude that high strength steel will be adequate because of the extreme loads. The obtained results can be useful in practice. List of Symbols A Surface K Stiffness matrix ε Strain vector B Strain-displacement matrix q Nodal displacement vector ν Poisson s ratio C Matrix of elastic coefficients u Displacement σ Normal stress E Modulus of elasticity u Displacement vector σ Stress vector f Vector of loads V Volume p Potential energy F Force α Angle τ Shearing stress Acknowledgment. This work was carried out as part of the TÁMOP-4..1.B-10//KONV-010-0001 project in the framework of the New Hungarian Development Plan. The realization of this project is supported by the European Union, co-financed by the European Social Fund. REFERENCES [1] Ladányi, G. Sümegi, I. Virág, Z.: Meríték- és bontófogfejlesztések első fázisának eredményei a Mátrai Erőmű ZRt. bányáiban üzemelő merítéklétrás kotróknál. 43. Bányagépészeti és Bányavillamossági Konferencia kiadványa, 010, 135 148. [] Ladányi, G. Sümegi, I. Virág, Z.: Laboratory rock cutting tests on rock samples from Visonta South Mine. Annals of the University of Petroşani, Mechanical Engineering, 9, 007, 09 18. [3] Bathe, K. J.: Finite Element Procedures. Prentice-Hall, Inc., New Jersey, 1996. [4] Wriggers, P.: Computational Contact Mechanics. Spinger-Verlag, Berlin Heidelberg, 006. [5] ADINA theory and modeling guide. Report ARD 10-5, ADINA R&D, Inc; 010. [6] Virág, Z. Szirbik, S.: Merítéklétrás kotró technológiájához optimált cserélhető bontófog vizsgálata. LXII. évfolyam, 011/11, III. kötet, 48 51.
University of Miskolc, Department of Research Management and International Relations Responsible for publication: Prof. Dr. Mihály Dobróka prorector Miskolc-Egyetemváros Editor: László Kis Published by the Miskolc University Press under leadership of Erzsébet Burmeister Responsible for duplication: Erzsébet Pásztor Number of copies printed: 00 Put to the Press on 01 TU 01 397 ME ISSN 063-6997