Strojniški vestnik - Journal of Mechanical Engineering 51(2005)2, 95-102 UDK - UDC 621.923:539.3 Pregledni znanstveni članek - Review scientific paper (1.02) Prehodni pojavi pri postopku brušenja Transient Phenomena in the Grinding Process Vladas Vekteris Lokalne stične premike, ki so posledica elastičnih deformacij orodja in obdelovanca, smo proučevali z uporabo končnih elementov in s preskusi. Izdelali smo grafične in analitične prikaze rezalne sile s harmoničnimi in stohastičnimi elementi. Predhodno objavljene raziskave stika med brusilnim kolesom in obdelovancem temeljijo na predpostavki, da predstavljajo stične deformacije neposredno funkcijo normalnih in tangencialnih sil, ki med postopkom brušenja delujejo na kolo oz. njegova zrna, brez upoštevanja obrabe in lomljenja zrn. V prispevku smo, s pomočjo metode končnih elementov in preskusa krožnega polirnega brušenja z velikimi hitrostmi, opisali postopek raziskave in grafično prikazali prehodne pojave in vzorec uničenja brusilnih zrn znotraj stične zone kot posledico impulznih obremenitev. Prej omenjeno metodo lahko uporabimo pri prožnih, togih, plastičnih in drugih nelinearnih materialih, ki jih obdelujemo z brušenjem. Uporabo nelinearnih lastnosti materiala, modul prostornine in modul pomika v stični coni med brusilnim kolesom (vrsta 24A12TICM28K5) in obdelovancem (jeklo 45), smo pri preskusu simulirali z uporabo tri-parametričnih elementov. S predstavljeno metodo lahko izračunamo prehodne napetosti in deformacije med krožnim polirnim brušenjem z velikimi hitrostmi ter proučujemo uničenje brusilnih zrn na dvorazsežnem modelu z nedoločenimi mejami in nelinearlnimi značilnostmi. Namen predstavljene razsikave je določitev vpliva prehodnih pojavov na sestavo rezalne sile med postopkom brušenja. © 2005 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: postopek brušenja, napetosti, deformacije, simuliranje, analize eksperimentalne) Local contact displacements resulting from the elastic deformation of the tool and the blank, were studied using the finite-element and by experiments. Graphical and analytical expressions for the cutting force, with harmonical and stochastic components, were obtained. Previously published research on the behaviour of the contact between the grinding wheel and the workpiece has been based, on the assumption that the contact deformations represent a direct function of both the normal and the tangent forces acting on the wheel or its grains during the grinding process, without taking into account the attrition and breaking of the grains. This paper covers the procedure for researching and graphically representating transient processes and the pattern of the abrasive grains’ destruction within the contact zone under impulse loads, which is based on the method of finite elements and the results of a high-speed circular plunge-grinding experiment. The above-mentioned method can be applied to elastic, inelastic, plastic and other nonlinear materials machined by grinding. To introduce the nonlinear properties of the material in the experiment, the modulus of the volume and the modulus of the shift in the contact zone between the grinding wheel (grade 24A12TICM28K5) and the workpiece (steel 45) are simulated by three-parametric elements. The presented method makes it possible to calculate transient stress and deformations during high-speed circular plunge grinding and to study the destruction of abrasive grains in a two-dimensional medium with indefinite boundaries and nonlinear characteristics. The present research is aimed at finding out the influence of transient phenomena on the structure of the cutting force during the process of grinding. © 2005 Journal of Mechanical Engineering. All rights reserved. (Keywords: grinding process, stress, strain, simulation, experimental analysis) 95 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)2, 95-102 0 INTRODUCTION Factory-wide automation, the increase in machining precision and operational concentration, as well as the intensification of cutting processes, and other important factors for increasing the output and efficiency of adaptive production, constitute the objective rules of the development of technological equipment. On the whole, these trends in the development of industrial production bring forth new problems when developing grinding equipment, particularly of the spindle systems based on the intensification of cutting processes. The intensification of cutting processes is one of the basic methods of scientific and technical progress in the machine-tool building industry. An increase in the grinding speed up to 60 m/s (instead of 30 to 35 m/s) has drastically increased the efficiency of grinding equipment. Nowadays, there are all the necessary grounds for applying grinding speeds od up to 100 to 120 m/s ([1] to [3]). Despite this, a simple increase in the cutting speed by increasing the grinding wheel’s velocity will not produce a tangible effect unless all the grinding system’s reserves are used together, particularly the radial and circular feeds. Reference [4] shows that an increase in the circular feeding velocity of circular grinders is particularly effective when CBN grinding wheels are used. In such cases of high-speed grinding, as well as in cases of normal-velocity grinding, the quality of the work surface increases in proportion to the reduction of the cutting force. A large number of abrasive grains per unit time take part in the metal-cutting process during a high-speed grinding operation. This results in a decrease in the depth of cut-offs per abrasive grain and, consequently, in a lower stress on the grain, thus reducing its rate of wear. At present the relative speed of the tool and the workpiece in metal machining is considered to be in the range from 25 to 500 m/s ([1] to [3]). Information is rather scarce about the phenomena occurring under such heavy-duty velocity and stress conditions. Here, theoretical physical investigations indicate that high-velocity grinding is characterized by the occurrence of the temperature field ([5] and [6]) and the field of forces during the grinding process. At the present time there is a lot of activity to simulate the properties of abrasive tools with a particular grain and cutting-edge microgeometry in order to develop grinding wheels with new structures to operate under n-fold load and allow functional cutting speeds of up to 300-500 m/s ([1] to [3]). However the phenomena that take place during the interaction of the two elements with particular stochastic properties are still insufficiently studied. This includes the characteristics of the force field, generated during high-velocity cutting, and those of the field’s stochastic components. To make use of all the specific advantages of high-speed grinding it is necessary to clearly understand the mechanism of the wheel and workpiece interaction in the contact zone. A number of researchers studied local elastic deformations in the contact zone between the grinding wheel and the workpiece by applying different approaches and methods. Reference [7] provides a review of this research. According to this research the deformation in the contact zone under the effect of normal and tangent forces is determined by the elastic properties of the tool and the elastoplastic properties of the workpiece. The local elastic displacements of the abrasive grains inside an abrasive tool, caused by normal and tangent forces, are transferred to the adjacent grains thtough intergranular contacts (directly or through the binder). The intensity of these displacements depends on the geometry of an abrasive grain, the stress value, the amount and the properties of the intergranular contacts. It is common ([1], [2] and [7]) knowledge that abrasive grains have a random shape and geometry, they are also randomly oriented during the production of the abrasive tool, and the grains differ considerably from each other as regards shape, size, thickness and the number of binding ties ([2] and [7]). Because of this their displacement in the normal direction and the rotation in the tangent direction, resulting from the shock of their interaction with the billet, contributes to the activation of vibration in the cutting zone. The pulse stress waves generated in this zone spread over the material of the abrasive grains and binder ([1] and [2]). For this reason the material particles in the cutting zone vibrate at a very high frequency and produce a certain effect on the system’s state and the chip-grinding process. This paper presents a method for calculating the transient stress and the deformations in the contact zone between the grinding wheel and the workpiece, and the destruction of abrasive grains in the two-dimensional medium with indefinite boundaries and nonlinear characteristics. The 96 Vekteris V. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)2, 95-102 suggested method and the program designed on the basis thereof ([16] and [17]) were verified with experimental data obtained during the process of grinding a steel workpiece (steel 45) with a grinding wheel (grade 24A12ÜCM28K5), which made it possible to substantiate the structure of the cutting force. 1 STRESS AND STRAIN In order to understand the mechanism of the grinding processes and to determine the degree of system strain let us discuss local (contact) shifts resulting from the elastic deformation of the tool and workpiece during the penetration of the tool into the workpiece. Let us assume that the tools with determined geometry are not deformed whereas the grinding system undergoes eccentric deformation, though the cutting section later undergoes local thermoelastic deformations. The machining of materials using a tool with a stochastic micro-geometry is associated with local transient deformation at the contact of the interaction and the deformation of the grinding system ([1] and [8]). In the case of a rigid system the contact deformation changes the shape of the interacting bodies ([1], [8] and [9]). If r is the radius of the non-deformed tools, then the change in the curvature determined by the force Fij per unit of width and acting upon the contact will be as follows [10]: --- = % (1) ri ri Cnlk where r is the curvature of the deformed tool; ln is the contact; C is a constant depending on the elastic properties of the tool (Cn =pEi/16(1-v 2 )), where nI is Poisson’s ratio. The dependence of the elasticity modulus on the temperature of a tool with a ceramic binder according to [11] is expressed with the exponential dependence Ei =E0exp(aTT), where E0 is the modulus of elasticity at room temperature (E0=(50...100).103 MPa), E is the modulus of elasticity at higher temperatures, aT is a constant dependent on temperature (aT =(3...6)-10-4), and T is the temperature. Then ri, =ri(1 + Fij/Cnlk2), where lk=(1 + 1q *)-Jri,t0~; q* = vi / vj, vi is the speed of the grinding wheel, vj is the speed of the work piece, and t0 is the real value of the depth of cut in one revolution. The transient force field Fij is an unknown parameter in these expressions; it determines the degree of strain in the system. Control of the value of strain also guarantees appropriate control of the elasticity, the vibration resistance and the damping ability of the system. The shaping process strain and its field of forces are determined by the normal and tangent voltages caused by the changing characteristics of the integrating elements (instrument and part). The elastic displacements of abrasive grains at the point of interaction contact were determined by calculation and by experiment [7]. However, neither the strained state [12] nor the beginning of the transient processes with accompanying fracture of abrasive grains under the effect of impulse loads (Fig. 1) were observed. This can be explained by complicacy on account of lots of factors, particularly during the non-linear behavior of the instrument’s and the part’s material. The nonlinear behavior of the material can be simulated by rheological equations on the basis of a three-parametrical model, including the model of Kelvin-Foight and spring (elastic materials, materials with Poisson’s ratio and plastic flow). It is known from [7] that it is the removable layer that possesses the greatest elasticity, which is why it can be modulated as a spring and as a plastic flow of metal, it can also be modulated as a model of Kelvin-Foight. In this case the bulk modulus will be represented by a rigid spring, and the modulus of shear by a dashpot. Then the relation between the stress and the strain can be expressed as follows [13]: s=[C]{} +[C]{} i =1|[C]0 e - {e ( x}dx (2). Where s is the stress; C, C0,and Ci are the matrixes characterising the material properties; x is the integration variable; and e is the strain. The application of the principle of conformity [13] makes it possible to automatically calculate the ratio of the stresses and strains_(i.e., to calculate the values of the matrixes \C , \C0\, and Ci ). The transient grinding process with the resulting ractures of abrasive grains during an impulse load (Fig. 1) belong to the type of problems for which no analytical solutions can be found. Therefore, in this case a widely known method of finite elements ([14] to [17]) to structurally idealize the continuous medium, to evaluate the rigidity of elements through the following node movement and Prehodni pojavi pri postopku brušenja - Transient Phenomena in the Grinding Process 97 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)2, 95-102 ab c d Fig. 1. Basic types of destruction of abrasive grains: a - rotation and wear of grinding grains; b - crack-formation; c - destruction of grains with the separation of large particles; d - pull-out of grains from the binder; 1 - abrasive grain; 2 - binder of the grinding wheell;