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Talaş kaldırma işleminin sonlu elemanlar yöntemi yardımıyla analizi

Talaş kaldırma işleminin sonlu elemanlar yöntemi yardımıyla analizi

##### Dosyalar

##### Tarih

1997

##### Yazarlar

Kaya, Vahit

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

##### Özet

Metal talaş kaldırma, aczu edilen boyut hassasiyetini ekle etmek için iş par- çağından istenmeyen nwbwneyi kaldırmak ipin loıflamlan imalat işlemidir. Sonhıe- leman yöntemi gibi sayısal yöntemlerin gelişin*^ dijitd bilgisayariardalri hesapsal güçlükler ve model simrlamalwrmin üstesinden gelindi (izah eden sonuçlar veren çeşitli analizler). Bu yüzden bu yalıamanın amact sonbı elemanlar yöntemim kullanarak ortogonal metal talaş kaldırma işlemini analiz etmektir. İlk olarak ortogo- nal metal talaş kakbzma işleminin sonlu eleman moa^tanmılandı ve talaş oluşumunu nıoddlemekiçm takım ucu onnııde^ Plastik şe- kfl değiştinne bnynklflğnne dayanan eleman ayama kriteri de incelendi Euler ve Taranga modellerinden elde edilen sonuçlar alüminyumun dnşuk hız ile kesilmesinde ölçülen takım kuvvetleri üe mukayese «*tiMffinA> mükemmel bir uyuşma gösteriyor. Rıttvfan haşin» annhı ffanan mnAtjj ila Infytfrjlen mt4a\ talaa VaMırma îafagrmıin çaafrli yönleri de deneysel sonuçlar ve fenomennlojik gözlemlerie iyi uyuştu. Sonhı eleman simûlasyomı da geıçekteştirikti. örneğin, dengesiz kuvvetleri indirgeme yöntemi daha kamrh ve hassas sonhı eleman simolasyonu içm incelendi ve gem Düzlem şekil değiştinne sonhı eleman yöntemi sürekli talaş ohışumhı karbon çeliğinin ortogo nal metal keamesmi simûle etmek içm geliştirildi ve genyideştirik

In the second section several finite element model of orthogonal metal cutting is described. First part of the second section a finite element model of orthogonal metal cutting is described. The model is used to predict chip geometry, plastic deformation and residual stresses in the workpiece, and the associated tool forces as a function of various cutting conditions, such as workpiece material properties, friction, depth of cut, and tool geometry. The model is based on the general purpose two-dimensional finite deflection code NIKE2D. The part also describes several modification to the program which make it more suitable for studying metal cutting problems. The first is a parting line criterion which allows for separation of the chip from the workpiece. The second consist of an adiabatic heating model to simulate the heat generation ef fects due to plastic work of the workpiece and chip, from which nodal temperatures are determined and the temperature-dependent material properties are updated. The final modification involves calculating tool forces at each incremental movement of the tool. To allow for separation of the chip from the workpiece, the model employs a ma terial parting (or separation) criterion based on the effective plastic strain at the tool tip region of the workpiece. The strain separation criterion is assessed in light of its effect on the calculated residual stresses and tool forces. Results from the model for machining 2024 aluminium alloy with a tool rake angle of 20 deg and a friction coeffi cient of 0.3 indicates that varying the separation criteria over the range 0.25 to 1.00 has little effect on the resulting chip geometry and tool forces. However, variations in the criteria significantly alter the residual stresses in the workpiece. First part of the second section demonstrates that the finite element method pro vides an appropriate means for predicting residual stresses and tool forces in ortho gonal machining. Furthermore, there are no theoretical limitations to applying the model to other types of metal cutting, such as high speed machining. However, this part point out that caution must be exercised in selecting a physically valid separation criterion. Second part of the second section the finite element method was used to model chip formation in orthogonal metal cutting. Emphasis was given on analyzing the ef fect of important factors, such as plastic flow of the workpiece material, friction at the tool-workpiece interface, and wear of the tool, on the cutting process. To simulate separation of the chip from the workpiece, superposition of two nodes at each nodal location of a parting line of the initial mesh was imposed. According to the developed algorithm, the superimposed nodes were constrained to assume identical displace ments, until approaching to a specified small distance from the tool tip. At that xxxu juncture, the displacement constraint was removed and separation of the nodes was allowed. Under the usual plane strain assumption, quasi-static finite element simulations of orthogonal metal cutting were performed for interfacial friction coefficients equal to zero, 0.15, and 0.5 and unworn or worn (cratered) tools having a strongly adherent built-up edge. To investigate the significance of the deformation of the workpiece material on the cutting process, elastic-perfectly plastic and elastic- plastic with isotropic strain hardening and strain rate sensitivity constitutive laws were used in the analysis. For simplicity, the tool material and the built-up edge were modeled as perfectly rigid. In all cases analyzed, the cutting speed and depth of cut were set equal to 183 m/min and 1.27 mm, respectively. Experiments confirmed that cutting of AISI 4340 steel with ceramic-coated tools under similar conditions led to the development of a built-up edge and the formation of continuous chips. The dimensions of the cra-ter, assumed in the finite element simulations involving a cratered tool, were also de-termineted from the same cutting experiments. Spatial distributions of the equivalent total plastic strain and the von Mises equivalent stress corresponding to steady-state cutting conditions and the normal and shear stresses at the rake face are contrasted and interpreted qualitatively in terms of critical parameters. The influence of interfacial friction, metal flow characteristics, and wear at the rake face of the tool on the steady-state magnitudes of the cutting forces, shear plane angle, chip thickness, and chip-tool contact length are also elucidated. Several aspects of the metal cutting process predicted by the finite element model agreed well with experimental results and phenomenological observations. In third part of the second section the development and implementation of a plane-strain finite element method for the simulation of orthogonal metal cutting with continuous chip formation are presented. Detailed work-material modeling, including the effects of elasticity, viscoplasticity, temperature, large strain, and high strain-rate, is used to simulate the material deformation during the cutting process. The unbalan ced force reduction method and sticking-sliding friction behavior are implemented to analyze the cutting process. The deformation of the finite element mesh and compa risons of residual stress distributions with X-ray diffraction measurements are pre sented. Simulation results along the primary and secondary deformation zones and under the cut surface, e.g., the normal and shear stresses, temperature, strain-rate, etc., are presented revealing insight into the metal cutting process. In this part, a plane-strain finite element method is developed and implemented to simulate the orthogonal metal cutting of AISI 1020 carbon steel with continuous chip formation. The unbalanced force reduction method and sticking-sliding friction mo deling are first introduced. The deformation of the finite element mesh and validation of the residual stress distribution are then discussed. Distributions of normal and shear stresses in the primary and secondary deformation zones and various other para meters, such as the temperature and plastic strain, along three sections inside the workpiece are also presented. In Fourth part of second section two computer models are described that treat the special case of orthogonal cutting. The models are based on the finite element method, which is used to discretize a portion of the workpiece in the vicinity of the xxxin cutting tool. From the models, the detailed stress and strain fields in the chip and workpiece, chip geometry and tool forces can be determined. The first model is based on a specially modified version of a large deformation updated Lagrangian code developed at Lawrence Livermore National Laboratory called NIKE2D, which employs an elastic-plastic material model. The second model treats the region in the vicinity of the cutting tool as an Eulerian flow field. Material passing through the field is modeled as viscoplastic. Results obtained from both mo dels show excellent agreement when compared with measured tool forces for slow speed cutting of aluminium 2024-T361. These two orthogonal cutting models are reviewed. Both models provide de tailed information about chip geometry, stress and strain fields and tool forces. The fundamental difference between them is the choice of coordinate reference frame. In the updated-Lagrangian formulation, the elements are attached to the workpiece ma terial. These elements move with the material as it undergoes the large deformation found in the chip. In contrast, the Eulerian method treats the finite element grid as spatially fixed. The Lagrangian model described here includes a general capability to define the interaction of multiple bodies along an initially tied line in accordance with a material failure criterion. The model uses a chip separation criterion based on total effective plastic strain. When the total effective plastic strain ahead of the cutting tool reaches a previously defined threshold value, the chip is allowed to separate from the work- piece material. The Eulerian model treats the workpiece material as rigid-viscoplastic and so strain-rate effects can be included directly. Velocity contour near the cutting tool edge can be predicted, which is useful for detecting the onset of built-up edge. Chip geometry is determined by comparing velocity vectors with the assumed position of the chip. The free surface of the chip is adjusted until the normal component of the surface velocity is zero. Cutting models are applied to single point diamond turning of aluminum 2024- T361. Excellent agreement based on cutting forces was found for cutting over a range of rake angles from -20 to 20° for various cutting speeds up to 6.2 nuns'1 and cutting depths from 1.3 to 21.3 um. In the first part of section three a numerical modeling method for predicting chip form and power requirements in three-dimensional cutting processes is described. The method is based on variational (energy) results from the theory of rigid-plastic materials and is applicable to the steady-state cutting of ductile metals. The analysis involves mainly material behavior assumptions and for simple material models yield results similar to the widely-used minimum work approach. In that part the theore tical basis of the method and the appropriate numerical algorithm (gradient search or steepest descent) for implementation in specific processes are described. Results for the oblique end turning and drilling processes are compared with experimental data in the second part of the section three. xxxiv Second part of section three using the method described in the first part of section three, numerical models for predicting chip form and the principal components of po wer consumption are developed for oblique end turning and drilling. Applying the method involves mainly specifying appropriate sets of independent variables for mini mization calculations. Results predicted using the rigid-viscoplastic material model are compared with measurements from unlubricated tests on steel and aluminum alloy samples. The agreement between predicted and measured results for turning is gene rally good, particularly for chip thickness values, chip-tool contact lengths, and the qualitative effect of varying the depth of cut. The agreement is not as good for dril ling; in drilling the main cutting edge torque contribution and qualitative effects of varying the spindle speed and feed rate are accurately predicted, but the average chip thickness is consistently underestimated while chip radii of curl are overestimated. The lack of agreement for the last two outputs appears to be due to constraint from the hole drill flute surfaces which would limit maximum radii of curl. Third part of the section three proposes a new model of chip forming process in three dimensional cutting with single point tool, in which the process is interpreted as a piling up of orthogonal cutting along the cutting edge. Based upon the proposed model, an energy method similar to the upper bound approach, which enables to pre dict the chip formation and the three components of cutting force by using only the orthogonal cutting data, is developed. The method is also applied to predict chip formation and cutting force in oblique cutting, plain milling, and groove cutting ope rations. In the fourth part of section four the cutting model and energy method to predict chip formation and cutting force, which were proposed in previous part of this study, are extended to machining with conventional single-point tool. The prediction is al ways possible in the practical range of cutting conditions regardless of size of cutting and tool geometry, if only orthogonal cutting data under equivalent cutting conditions are in hand. The predicted results are verified to be in good agreement with the expe rimental results in a wide variety of depth of cut, side and back rake angles, side cut ting edge angle, and nose radius. Fourth section presents a finite element model of orthogonal machining by using a 2-node link element to simulate chip separation. The chip and workpiece are connec ted by these link elements along a predefined separation line. The chip separation will be initiated when the distance between the leading node and the tool edge is equal to or smaller than given value. Consequently, as the tool advances, these link elements will be separated one by one resulting in the formation of the chip and the machined surface. Work material behavior is described by true stress-strain curves for a 0-3 strain range. The chip-tool interaction is modeled as sliding/sticking. In the sliding region a constant coefficient of friction is employed and in the sticking region the shear strength of workpiece is used. Comparison between simulated and experimental results for machining 70/30 brass and OFHC copper shows a maximum difference of 20 percent, which is acceptable considering the assumptions and the approximations made in the analysis. XXXV In the fifth section the plane-strain finite element method is developed and applied to model the orthogonal metal cutting of annealed low carbon steel with continuous chip formation. Four sets of simulation results for cutting with -2°, 0°, 5°, and 15° rake angle are summarized and compared to analyze the effects of rake angle in cut ting processes. The initial and deformed finite element meshes, as the cutting reaches steady-state condition, are first presented. Simulation results of the cutting forces and residual stresses, along with the X-ray diffraction measurements of the residual stress es generated using a worn cutting tool with 5° rake angle, are used to identify the in fluences of the rake angle and tool sharpness. Elements are selected to represent three sections along the shear and contact zones and under the cut surface. The normal and shear stresses, distributions of parameters along these three sections, and contours of temperature, plastic strain, and effective stress are then presented. Limi tations of the finite element method for metal cutting simulation are discussed. In the sixth section results of simulation of an orthogonal cutting process with artificial tool flank wear are presented in this section. The historical stress, strain, and the distribution of stress, strain, strain rate, and the temperature are obtained from an incremental displacement method. The simulation and experimental results for cutting force, fiictional force, the chip thickness and contact length are in good agreement with each other. The shear angle can be determined from the maximum strain energy density curve and the value obtained agrees well with that obtained from the experi ments. In the seventh section a finite element program developed for calculating the temperature distributions in the chip and tool in metal machining has been extended in its range of application. Specifically, the program no longer needs a flow field as in put and it can accommodate a wide range of shear angle and contact lengths. An im portant feature of this section is that temperature fields from the finite element method have been compared with temperatures obtained with a metallographic method. This is the first time these two techniques have been used for the same machining condi tions and the comparisons are very good.

In the second section several finite element model of orthogonal metal cutting is described. First part of the second section a finite element model of orthogonal metal cutting is described. The model is used to predict chip geometry, plastic deformation and residual stresses in the workpiece, and the associated tool forces as a function of various cutting conditions, such as workpiece material properties, friction, depth of cut, and tool geometry. The model is based on the general purpose two-dimensional finite deflection code NIKE2D. The part also describes several modification to the program which make it more suitable for studying metal cutting problems. The first is a parting line criterion which allows for separation of the chip from the workpiece. The second consist of an adiabatic heating model to simulate the heat generation ef fects due to plastic work of the workpiece and chip, from which nodal temperatures are determined and the temperature-dependent material properties are updated. The final modification involves calculating tool forces at each incremental movement of the tool. To allow for separation of the chip from the workpiece, the model employs a ma terial parting (or separation) criterion based on the effective plastic strain at the tool tip region of the workpiece. The strain separation criterion is assessed in light of its effect on the calculated residual stresses and tool forces. Results from the model for machining 2024 aluminium alloy with a tool rake angle of 20 deg and a friction coeffi cient of 0.3 indicates that varying the separation criteria over the range 0.25 to 1.00 has little effect on the resulting chip geometry and tool forces. However, variations in the criteria significantly alter the residual stresses in the workpiece. First part of the second section demonstrates that the finite element method pro vides an appropriate means for predicting residual stresses and tool forces in ortho gonal machining. Furthermore, there are no theoretical limitations to applying the model to other types of metal cutting, such as high speed machining. However, this part point out that caution must be exercised in selecting a physically valid separation criterion. Second part of the second section the finite element method was used to model chip formation in orthogonal metal cutting. Emphasis was given on analyzing the ef fect of important factors, such as plastic flow of the workpiece material, friction at the tool-workpiece interface, and wear of the tool, on the cutting process. To simulate separation of the chip from the workpiece, superposition of two nodes at each nodal location of a parting line of the initial mesh was imposed. According to the developed algorithm, the superimposed nodes were constrained to assume identical displace ments, until approaching to a specified small distance from the tool tip. At that xxxu juncture, the displacement constraint was removed and separation of the nodes was allowed. Under the usual plane strain assumption, quasi-static finite element simulations of orthogonal metal cutting were performed for interfacial friction coefficients equal to zero, 0.15, and 0.5 and unworn or worn (cratered) tools having a strongly adherent built-up edge. To investigate the significance of the deformation of the workpiece material on the cutting process, elastic-perfectly plastic and elastic- plastic with isotropic strain hardening and strain rate sensitivity constitutive laws were used in the analysis. For simplicity, the tool material and the built-up edge were modeled as perfectly rigid. In all cases analyzed, the cutting speed and depth of cut were set equal to 183 m/min and 1.27 mm, respectively. Experiments confirmed that cutting of AISI 4340 steel with ceramic-coated tools under similar conditions led to the development of a built-up edge and the formation of continuous chips. The dimensions of the cra-ter, assumed in the finite element simulations involving a cratered tool, were also de-termineted from the same cutting experiments. Spatial distributions of the equivalent total plastic strain and the von Mises equivalent stress corresponding to steady-state cutting conditions and the normal and shear stresses at the rake face are contrasted and interpreted qualitatively in terms of critical parameters. The influence of interfacial friction, metal flow characteristics, and wear at the rake face of the tool on the steady-state magnitudes of the cutting forces, shear plane angle, chip thickness, and chip-tool contact length are also elucidated. Several aspects of the metal cutting process predicted by the finite element model agreed well with experimental results and phenomenological observations. In third part of the second section the development and implementation of a plane-strain finite element method for the simulation of orthogonal metal cutting with continuous chip formation are presented. Detailed work-material modeling, including the effects of elasticity, viscoplasticity, temperature, large strain, and high strain-rate, is used to simulate the material deformation during the cutting process. The unbalan ced force reduction method and sticking-sliding friction behavior are implemented to analyze the cutting process. The deformation of the finite element mesh and compa risons of residual stress distributions with X-ray diffraction measurements are pre sented. Simulation results along the primary and secondary deformation zones and under the cut surface, e.g., the normal and shear stresses, temperature, strain-rate, etc., are presented revealing insight into the metal cutting process. In this part, a plane-strain finite element method is developed and implemented to simulate the orthogonal metal cutting of AISI 1020 carbon steel with continuous chip formation. The unbalanced force reduction method and sticking-sliding friction mo deling are first introduced. The deformation of the finite element mesh and validation of the residual stress distribution are then discussed. Distributions of normal and shear stresses in the primary and secondary deformation zones and various other para meters, such as the temperature and plastic strain, along three sections inside the workpiece are also presented. In Fourth part of second section two computer models are described that treat the special case of orthogonal cutting. The models are based on the finite element method, which is used to discretize a portion of the workpiece in the vicinity of the xxxin cutting tool. From the models, the detailed stress and strain fields in the chip and workpiece, chip geometry and tool forces can be determined. The first model is based on a specially modified version of a large deformation updated Lagrangian code developed at Lawrence Livermore National Laboratory called NIKE2D, which employs an elastic-plastic material model. The second model treats the region in the vicinity of the cutting tool as an Eulerian flow field. Material passing through the field is modeled as viscoplastic. Results obtained from both mo dels show excellent agreement when compared with measured tool forces for slow speed cutting of aluminium 2024-T361. These two orthogonal cutting models are reviewed. Both models provide de tailed information about chip geometry, stress and strain fields and tool forces. The fundamental difference between them is the choice of coordinate reference frame. In the updated-Lagrangian formulation, the elements are attached to the workpiece ma terial. These elements move with the material as it undergoes the large deformation found in the chip. In contrast, the Eulerian method treats the finite element grid as spatially fixed. The Lagrangian model described here includes a general capability to define the interaction of multiple bodies along an initially tied line in accordance with a material failure criterion. The model uses a chip separation criterion based on total effective plastic strain. When the total effective plastic strain ahead of the cutting tool reaches a previously defined threshold value, the chip is allowed to separate from the work- piece material. The Eulerian model treats the workpiece material as rigid-viscoplastic and so strain-rate effects can be included directly. Velocity contour near the cutting tool edge can be predicted, which is useful for detecting the onset of built-up edge. Chip geometry is determined by comparing velocity vectors with the assumed position of the chip. The free surface of the chip is adjusted until the normal component of the surface velocity is zero. Cutting models are applied to single point diamond turning of aluminum 2024- T361. Excellent agreement based on cutting forces was found for cutting over a range of rake angles from -20 to 20° for various cutting speeds up to 6.2 nuns'1 and cutting depths from 1.3 to 21.3 um. In the first part of section three a numerical modeling method for predicting chip form and power requirements in three-dimensional cutting processes is described. The method is based on variational (energy) results from the theory of rigid-plastic materials and is applicable to the steady-state cutting of ductile metals. The analysis involves mainly material behavior assumptions and for simple material models yield results similar to the widely-used minimum work approach. In that part the theore tical basis of the method and the appropriate numerical algorithm (gradient search or steepest descent) for implementation in specific processes are described. Results for the oblique end turning and drilling processes are compared with experimental data in the second part of the section three. xxxiv Second part of section three using the method described in the first part of section three, numerical models for predicting chip form and the principal components of po wer consumption are developed for oblique end turning and drilling. Applying the method involves mainly specifying appropriate sets of independent variables for mini mization calculations. Results predicted using the rigid-viscoplastic material model are compared with measurements from unlubricated tests on steel and aluminum alloy samples. The agreement between predicted and measured results for turning is gene rally good, particularly for chip thickness values, chip-tool contact lengths, and the qualitative effect of varying the depth of cut. The agreement is not as good for dril ling; in drilling the main cutting edge torque contribution and qualitative effects of varying the spindle speed and feed rate are accurately predicted, but the average chip thickness is consistently underestimated while chip radii of curl are overestimated. The lack of agreement for the last two outputs appears to be due to constraint from the hole drill flute surfaces which would limit maximum radii of curl. Third part of the section three proposes a new model of chip forming process in three dimensional cutting with single point tool, in which the process is interpreted as a piling up of orthogonal cutting along the cutting edge. Based upon the proposed model, an energy method similar to the upper bound approach, which enables to pre dict the chip formation and the three components of cutting force by using only the orthogonal cutting data, is developed. The method is also applied to predict chip formation and cutting force in oblique cutting, plain milling, and groove cutting ope rations. In the fourth part of section four the cutting model and energy method to predict chip formation and cutting force, which were proposed in previous part of this study, are extended to machining with conventional single-point tool. The prediction is al ways possible in the practical range of cutting conditions regardless of size of cutting and tool geometry, if only orthogonal cutting data under equivalent cutting conditions are in hand. The predicted results are verified to be in good agreement with the expe rimental results in a wide variety of depth of cut, side and back rake angles, side cut ting edge angle, and nose radius. Fourth section presents a finite element model of orthogonal machining by using a 2-node link element to simulate chip separation. The chip and workpiece are connec ted by these link elements along a predefined separation line. The chip separation will be initiated when the distance between the leading node and the tool edge is equal to or smaller than given value. Consequently, as the tool advances, these link elements will be separated one by one resulting in the formation of the chip and the machined surface. Work material behavior is described by true stress-strain curves for a 0-3 strain range. The chip-tool interaction is modeled as sliding/sticking. In the sliding region a constant coefficient of friction is employed and in the sticking region the shear strength of workpiece is used. Comparison between simulated and experimental results for machining 70/30 brass and OFHC copper shows a maximum difference of 20 percent, which is acceptable considering the assumptions and the approximations made in the analysis. XXXV In the fifth section the plane-strain finite element method is developed and applied to model the orthogonal metal cutting of annealed low carbon steel with continuous chip formation. Four sets of simulation results for cutting with -2°, 0°, 5°, and 15° rake angle are summarized and compared to analyze the effects of rake angle in cut ting processes. The initial and deformed finite element meshes, as the cutting reaches steady-state condition, are first presented. Simulation results of the cutting forces and residual stresses, along with the X-ray diffraction measurements of the residual stress es generated using a worn cutting tool with 5° rake angle, are used to identify the in fluences of the rake angle and tool sharpness. Elements are selected to represent three sections along the shear and contact zones and under the cut surface. The normal and shear stresses, distributions of parameters along these three sections, and contours of temperature, plastic strain, and effective stress are then presented. Limi tations of the finite element method for metal cutting simulation are discussed. In the sixth section results of simulation of an orthogonal cutting process with artificial tool flank wear are presented in this section. The historical stress, strain, and the distribution of stress, strain, strain rate, and the temperature are obtained from an incremental displacement method. The simulation and experimental results for cutting force, fiictional force, the chip thickness and contact length are in good agreement with each other. The shear angle can be determined from the maximum strain energy density curve and the value obtained agrees well with that obtained from the experi ments. In the seventh section a finite element program developed for calculating the temperature distributions in the chip and tool in metal machining has been extended in its range of application. Specifically, the program no longer needs a flow field as in put and it can accommodate a wide range of shear angle and contact lengths. An im portant feature of this section is that temperature fields from the finite element method have been compared with temperatures obtained with a metallographic method. This is the first time these two techniques have been used for the same machining condi tions and the comparisons are very good.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Sosyal Bilimler Enstitüsü, 1977

##### Anahtar kelimeler

Sonlu elemanlar yöntemi,
Talaş kaldırma,
Finite element method,
Layer removal