Slip-line Model Research Articles

Prediction of tool-chip contact length based on slip-line modeling of orthogonal cutting with rounded-edge cutting tools

It is known that no cutting tool has a perfectly sharp cutting edge and that there is always a small rounding on the cutting edge of the tool. In this study, a new tool-chip contact length equation is presented for cutting tools with rounded-edge in orthogonal cutting. This equation was obtained based on a newly developed slip-line model. This newly developed slip-line model has rounded-edge cutting and considers the presence of a dead metal zone in front of the cutting edge. To verify the newly developed tool-chip contact length equation, experimental studies were conducted at various cutting speeds and uncut chip thickness values at both 0° and 6° rake angles, using cutting tools with 50 μm–100 μm–150 μm edge radii. Orthogonal cutting experiments were carried out using the shaping-based quick stop device and brass (CuZn30) material was chosen as a workpiece that allows continuous chip formation without built-up edge. Strong correlation was observed between the experiment results and values that were obtained from the newly developed tool-chip contact length equation.

Frictional behavior of tool-workpiece on surface quality of glow discharge polymer during micro-milling

Machining of concavities and other complex microstructures on glow discharge polymer (GDP) films is critical to its high laser power performance, especially in the inertial confinement nuclear fusion. This study mainly investigated the effect of tool-workpiece frictional mechanism on the quality of machined surface in micro-milling of GDP. A series of milling tests of micro-grooves with different spindle speeds (n) and spindle axis deflection angles (θ) were conducted using a cubic boron nitride (CBN) milling tool. The orthogonal cutting slip line model was adopted to reveal the material removal mechanism of GDP. The wear mechanism and friction coefficient of the contact area between GDP material and the CBN tool were analyzed. The chip thickness and shear stress were innovatively used to characterize the surface roughness. The regression models of milling forces, surface profiles, shear stresses and surface roughness with chip thickness were established. The tribo-performance of the CBN tool on GDP material was characterized using cutting specific energy and a friction coefficient. Research results show that θ has a significant effect on the surface quality than n. At θ of 20° and n of 30,000 rpm, the contour error of the micro-groove structure is about 0.11 μm, a reduction of 93.9% compared with at θ of 0°. Thermal softening and strain hardening are found the keys affecting surface morphology. Chip morphology such as segmental, granular, and crack chips was observed. The adhesion wear on the CBN tool surface was found critical to its machining performance.

The relationship between adhesion morphology and cutting force in orthogonal cutting of 6061-T6 aluminum alloy

Due to the sticky and soft characteristics of aluminum alloy, it is easy to form adhesion on the tool rake face during cutting process. In this work, the orthogonal cutting tests for 6061-T6 aluminum were carried out at cutting speeds of 20–300 m/min and feed rates of 0.05–0.3 mm, and the relationship between adhesion and cutting force has been explored. A slip-line model was used to separate the edge force of cutting edge to obtain the pure friction force of tool rake face, thereby obtaining the average friction coefficient. Adhesion morphologies were observed under the scanning electron microscope (SEM) and compared with the average friction coefficients. It was found that different adhesion morphologies correspond to different friction coefficient ranges. Simultaneously, the relationship between the temperature and normal stress on the tool rake face and the adhesion morphology and friction coefficient was investigated. The results showed that the temperature is the major factor of adhesion evolution and friction coefficient change. Combining the tool rake face temperature and the adhesion morphology, it was noted that the reduction of the friction coefficient is not only owing to the self-lubrication caused by thermal softening, but also due to the decrease of the total shear force caused by the incomplete contact. Finally, the relationship between the friction coefficient of tool rake face and the cutting force and specific cutting energy was discussed, with the conclusion that the friction coefficient has an impact on the cutting force and specific cutting energy by changing the shear angle.

Analytical modelling of the trans-scale cutting forces in diamond cutting of polycrystalline metals considering material microstructure and size effect

In diamond cutting of polycrystalline metals, the influence of size effect and microstructure on the cutting force is prominent due to the trans-scale variation of undeformed chip thickness (UDCT) from microscale to nanoscale. This study proposes a trans-scale cutting force model for diamond cutting of polycrystalline metals with the full consideration of microstructure, material elastic recovery, size effect and round-tool-edge effect. Specifically, by corelating micro-forming theory and crystal plastic theory, a hybrid slip-line model (HSLM) is developed to determine the flow stress in the primary deformation zone, which can quantify the influence of size effect and microstructure, such as grain size, grain boundary and crystal anisotropy, on flow stress. Then, the normal cutting force and frictional cutting force are determined by analysing the stress distribution and frictional states at tool-chip interface using a tool-chip contact model. The rubbing force induced by material elastic recovery at very small UDCT is determined based on indentation theory. Through diamond cutting of polycrystalline copper with different grain sizes, it is experimentally demonstrated that the proposed HSLM can capture the cutting mechanism transformation phenomenon from shearing (tensile stress) to ploughing (compressive stress) with increasing size factor. Besides, the proposed force model has the improved estimation accuracy compared with the conventional force models developed based on Johnson-Cook constitutive equation.

Analysis of slip-line model for serrated chip formation in orthogonal machining of AISI 304 stainless steel under various cooling/lubricating conditions

In the past, numerous slip-line models have been developed and presented for continuous chip formation. However the authors of this paper recently proposed a new slip-line model for serrated chip formation in machining with rounded cutting edge. In that model, Oxley’s predictive machining theory was integrated for machining of stainless steel material and the model was validated under dry cutting. The current study extends the previously developed slip-line model for orthogonal turning of AISI 304 austenitic stainless steel for various cooling/lubricating conditions. The orthogonal machining experiments were performed under dry, flood cooling, MQL (Minimum Quantity Lubrication) and cryogenic cooling conditions. Good correlations are observed between experimental work and predictions under various cooling/lubricating conditions for cutting force components and maximum and minimum chip thickness values. After achieving the good correlation, several important outputs such as the shear stress, flow stress, ploughing force, stagnation point angle, chip up-curl radius, which are difficult or impossible to measure experimentally were determined by solving the extension of the previously developed model. The lowest tool-chip frictional shear stress was achieved under MQL method whereas the highest was obtained in dry cutting. In addition, the minimum ploughing force was obtained in cryogenic cooling while the maximum value occurred in dry cutting. The stagnation point angle decreased when applying lubricant or coolant and increased with increasing cutting speed. The tool-chip contact length slightly decreased, the chip up-curl radius increased and the thickness of the primary shear zone reduced with increasing cutting speed. Additionally, lower tool-chip contact length, larger chip up-curl radius and larger primary shear zone thickness occurred while using lubricant or coolant. Higher cutting speed caused lower shear strain and flow stress and higher shear strain-rate. The highest and lowest flow stresses were obtained under cryogenic cooling and dry cutting, respectively.

A Machining Program Employing a Slip Line Field Modelling Technique Over Other Constitutive Models

Machining involves complex plastic material flow at the chip separation site which makes it difficult to predict forces and other machining outputs to higher accuracy. Modelling is a common technique which facilitates incorporation of analytical and experimentally derived equations to visualize the process and analyses the mechanism. It saves time and machining factors can be optimized without any trial and error method. In this paper, the significance of slip line field model over other constitutive laws in defining the complex regions in machining are thoroughly reviewed and a slip line field model is chosen which incorporates build up edge (BUE) of a larger size than the other previously defined slip line models for machining. The modified model also incorporate a region of shear zone instead of a shear line, takes into account the chip curl effect and conform to the velocity discontinuity and stress equilibrium. The slip line fields are generated using MATLAB and employing Dewhurst-Collin's matrix technique.

An analytical force model for ultra-precision diamond sculpturing of micro-grooves with textured surfaces

The investigation on the cutting force for ultra-precision diamond sculpturing (UPDS) is important to understand its material removal mechanism and tool-workpiece reaction behaviors during cutting. However, few studies have focused on the cutting force model for UPDS of micro-grooves with textured surfaces. The prediction of the cutting force for UPDS is complicated due to its unique kinematics featuring oscillated servo motions, which inevitably leads to the dynamic material removal process featuring time varying plastic deformation directions. In the present study, an analytical cutting force model for UPDS of textured micro-grooves is proposed with the full consideration of the oscillations induced dynamic cutting conditions, round-edged effect as well as the shearing and ploughing mechanisms. Specifically, the nominal shearing force is derived by a dynamic slip-line model involving the time varying shear angle, stress, strain and strain rate in the deformation zone. A two-state model is adopted to describe sticking and sliding states of the chip on the tool rake face, based on which the frictional shearing force is calculated. When the depth of cut is lower than the critical chip thickness, the material is removed by the ploughing force that is of proportional relation to the tool-workpiece interference volume according to the indentation theory. Finally, the whole cutting force is obtained by discretization method, and the model is experimentally validated through sculpturing two types of textured micro-grooves with harmonic structures.

Validation of the slip-line model for serrated chip formation in orthogonal turning under dry and MQL conditions

In this study, the previously developed slip-line model for serrated chip formation was validated in orthogonal turning under dry and MQL (Minimum Quantity Lubrication) conditions. Face turning experiments were conducted on grooved AISI 304 austenitic stainless steel workpiece with tool inserts having cutting edge radius of 50 μm. The cutting force components and the maximum and minimum chip thicknesses were measured to validate the model. In dry cutting, the average prediction errors are 9.44%, 4.78% and 7.69% for cutting, thrust, and resultant forces, respectively. In machining with MQL, the average prediction errors are 10.79%, 11.49% and 2.46% for cutting, thrust, and resultant forces, respectively. In addition, the average prediction errors for maximum and minimum chip thicknesses are determined as 6.38% and 9.12% in dry cutting and 7.79% and 4.35% in MQL, respectively.

A slip-line model for serrated chip formation in machining of stainless steel and validation

Machining of difficult-to-cut materials producing serrated chip formation has generated a significant interest among academic researchers and industry groups because of the need for understanding the fundamental mechanisms to model the process. Therefore, various analytical and numerical models have been developed in the recent past to investigate such machining operations. The slip-line theory is one of the established modeling methods, but slip-line modeling of serrated chip formation has not been investigated adequately. In this study, a new slip-line model for serrated chip formation in machining with rounded cutting edge tool is presented along with its associated hodograph. In addition, Oxley’s theory was integrated to the proposed slip-line model for stainless steel material, and the model was validated by experimental results. A good agreement between the experimental and analytically predicted results was obtained. The proposed slip-line model offers predictions of cutting and thrust forces, ploughing force, maximum and minimum chip thickness values, tool–chip contact length, chip up-curl radius, thickness of the primary shear zone, angular position of the stagnation point, shear strain, shear strain rate at the shear plane, and the prevalent flow stress.

A thermo-mechanical coupled model of derivative cutting of microtextured tools

In our previous works, the revelation of the significance of derivative cutting in the cutting process with microtextured tools, which occurs because of the finite sharpness of the texture edge at the tool-chip interface, serves as a starting point for exploring of the cutting mechanism. At present, a thermo-mechanical coupled model for orthogonal cutting process is formulated to predict cutting force under effect of derivative cutting in terms of the structural and positional parameters of textures, cutting conditions, and material properties. The flow stress model considering size effect is combined with the Oxley’s cutting model to predict derivative chip formation force. Meanwhile, the Waldorf’s slip-line model is applied to evaluate plowing force in derivative cutting. The cutting temperature is predicted based on the heat source theory, which is integrated with the proposed model of derivative cutting to build up the coupled iterative model. A series of orthogonal cutting tests are carried out to validate the prediction model by using different types of microtextured tools. The measured values of cutting force show a good agreement with the predictions. Furthermore, the proposed method provides some insights into ways to diminish the adverse effect of derivative cutting. Results show that the reductions in the edge radius and the inclined angle of textures contribute to decreasing derivative cutting force with increasing cutting velocity.

Slip line model for forces estimation in the radial-axial ring rolling process

In the research presented in this paper, a slip line-based model is proposed for the estimation of both radial and axial force in the radial-axial ring rolling (RARR) process. Based on the shape of the contact arcs between ring and tools in the two deformation gaps present in the ring rolling process, a recursive algorithm for the calculation of the two slip line fields starting from the two pairs of opposite tools is derived and implemented in a commercial spreadsheet software (MS Excel). By considering the stress boundary conditions applied to the portion of material undergoing the deformation, both for the radial and axial deformation gaps, the pressure factors those make the two slip line fields starting from the two opposite tools to intersect are calculated and utilized for the estimation of radial and axial forces, for each round of the process. The developed model has been validated by cross-comparing its results with those of laboratory experiment and numerical simulation. For the validation study case, the average deviations, in comparison to the experimental results, are calculated in 1.86% and 4.55% for the slip line force model whereas in 6.86% and 0.88% for the numerical simulation, for the radial and axial forces respectively. The proposed slip line model has been also utilized for the estimation of radial and axial forming forces of nine different study cases of flat rings having the outer diameter ranging from 800 mm to 2000 mm, observing a maximum deviation, in comparison to the relevant FEM simulation, of 4.92% (radial force) and 5.88% (axial force). The developed slip line force model allows estimating almost in real time and with a reasonable accuracy the process forces and, for this reason, it may be of interest for both industrial and academic researchers dealing with the set-up and control of the radial-axial ring rolling process.

Chip inward curl and its influence on dimensional accuracy in groove cutting with a novel restricted contact tool

Tool geometry has a significant influence on cutting force, cutting temperature, and surface quality. Restricted contact tools show good advantages in reducing cutting force, decreasing temperature, and improving surface quality. In this article, a new pattern of chip curl, “chip inward curl,” and its influence on dimensional accuracy were investigated using a novel restricted contact tool when cutting grooves. This novel restricted contact tool has symmetrical tool/chip contact length which varies along the main cutting edge and has a smaller tool land length in the middle of the rake face. In order to analyze the chip inward curl and its influence on dimensional accuracy with this novel restricted contact tool, a theoretical method to predict the chip back-flow angle using a slip-line model taking into consideration of cutting tool edge was proposed. Dimensional accuracy of the grooves achieved by this novel restricted contact tool in groove cutting tests was investigated and compared with those cut by a conventional flat-faced tool. Also, three-dimensional finite element models were developed to analyze the chip back-flow angle and chip inward curl. Results indicate that this new type of restricted contact tool has significant advantages in the control of chip curl and obtains better dimensional accuracy in groove cutting.

Effect of Ploughing Force on Cutting Forces in Micro-cutting with a Rounded-edge Cutting Tool

In micro- and nano-machining operations, the importance of cutting edge radius attracts attention to understand the mechanics of micro-cutting operations. In addition, the cutting edge radius causes higher ploughing forces and the ploughing force has many effects on the mechanics on micro- and nano-machining such as increasing the resultant force and making difficult the cutting. In this study, the previously developed slip-line model for orthogonal machining with a rounded-edge cutting tool was used to determine the effect of the ploughing force on the cutting and thrust forces in micro-cutting. The cutting and thrust forces were experimentally obtained and the ploughing force was calculated from the model. The effect of the ploughing force upon cutting and thrust forces was determined. This effect was higher on thrust force and increased when cutting edge radius, uncut chip thickness, cutting speed, and rake angle increased.

Predictive modeling of machining residual stresses considering tool edge effects

The surface integrity of machined components is defined by several characteristics, of which residual stress is extremely important. Residual stress is known to have an effect on critical mechanical properties such as fatigue life, corrosion cracking resistance, and dimensional tolerance of machined components. Among the factors that affect residual stress in machined parts are cutting parameters and tool geometry. This paper presents a method of modeling residual stress for hone-edge cutting tools in turning. The model utilizes analytical cutting force models in conjunction with an approximate algorithm for elastic–plastic rolling/sliding contact. Oxley’s cutting force model is coupled with a slip line model proposed by Waldorf to estimate the cutting forces, which are in turn used to estimate the stress distribution between the tool and the workpiece. A rolling/sliding contact model, which captures kinematic hardening, is used to predict the machining residual stresses. Additionally, a moving heat source model is applied to determine the temperature rise in the workpiece due to the cutting forces. The model predictions are compared with experimental data for the turning of AISI 52100. Force predictions compare well with experimental results. Similarly, the predicted residual stress distributions correlate well with the measured residual stresses in terms of magnitude of stresses and depth of penetration.

Slip-line metal cutting model with negative rake angle

A small dead region is seen in front of the rake face of the tool during cutting with negative rake. The lack of knowledge about the stagnant region in the cutting with negative rake requires researching new models. In this work, cutting mechanism of the metal cutting with negative rake angle tools and the stagnation zone formation were studied. A model was generated from the experimental work by usage of the Dewhurst and Collins' matrix technique for solving the slip-line problem numerically. This model was applied at negative rake angles from 0o to -70o. All slip line angles in the slip line model that consist of three regions were resolved with the help of the experimental data. Variation of the dead metal zone and slip line regions with negative rake angle was determined. Effects of the negative rake angle on the cutting and thrust forces were investigated according to the cutting speed.

SLIP-LINE MODELING OF MACHINING AND DETERMINE THE INFLUENCE OF RAKE ANGLE ON THE CUTTING FORCE

In this study, the effects of the rake angle on main cutting force (Fc), and thrust forces (Ft) was investigated. A new slip line model approach for modelling the orthogonal cutting process was proposed. This model was applied at negative rake angles from 0° to –60° and consists of three regions. The main forces were measured with a computer aided quick stop device. Variance Analysis (ANOVA) was utilized to analyze the effects of the cutting parameters on cutting and thrust forces accordingly. Multi-variable regression analysis was also employed to determine the correlations between the factors and the cutting forces. The cutting forces could be calculated by equation parameters which are the rake angle and the uncut chip thickness.

A slip-line approach to the machining with rounded-edge tool

In this paper, a new slip-line model approach for modeling the orthogonal cutting process with rounded-edge tools and its associated hodograph are proposed. This model consists of eight regions, which include a dead region in front of the rake face of tool. Dewhurst and Collins’s matrix technique for numerically solving the slip-line problem is employed in the mathematical formulation of the new model. The experimental results show that a small dead region is seen in front of the rake face of tool during cutting with a rounded-edge cutting tool. The unknown slip-line angle pair was solved depending on the force data obtained experimentally and variation of the subregions with cutting edge radius was determined. Cutting force, thrust force, and dead zone grow as cutting edge radius increases in cutting edge-radiused tools.

A Slip-Line Approach to the Micro-Cutting Process with a Rounded-Edge Tool

The effect of tool edge roundness attracts growing attention due to increasing applications of precision, micro-and nanomachining technologies. A new slip-line model and its associated hodograph are proposed for cutting with a rounded-edge tool in this paper. New model considers stagnant metal region called as dead metal zone formed in front of the rake face of tool during cutting process. Dewhurst and Collinss [ matrix technique for numerically solving the slip-line problem is employed in the mathematical formulation of the new model. The unknown slip-line angles were solved depending on the force data obtained from experiments and variation of the sub-regions with cutting edge radius was determined.

A Slip-Line Approach to the Micro-Cutting Process with a Rounded-Edge Tool

The effect of tool edge roundness attracts growing attention due to increasing applications of precision, micro-and nanomachining technologies. A new slip-line model and its associated hodograph are proposed for cutting with a rounded-edge tool in this paper. New model considers stagnant metal region called as dead metal zone formed in front of the rake face of tool during cutting process. Dewhurst and Collinss [ matrix technique for numerically solving the slip-line problem is employed in the mathematical formulation of the new model. The unknown slip-line angles were solved depending on the force data obtained from experiments and variation of the sub-regions with cutting edge radius was determined.

A slip-line plasticity analysis of sliding friction of rough surfaces exhibiting self-affine (fractal) behavior

A plasticity analysis of sliding friction of rough (fractal) surfaces sliding against smooth surfaces was developed based on a slip-line model of a rigid spherical asperity (wear particle) plowing and cutting through a soft semi-infinite medium. Solutions of the fraction of fully plastic asperity microcontacts responsible for the evolution of friction and energy dissipation were obtained in terms of the total normal load (global interference), interfacial adhesion characteristics, topography (fractal) parameters of the hard surface, and elastic–plastic material properties of the soft surface. This was accomplished by incorporating the slip-line model of a single microcontact into a friction analysis of sliding surfaces demonstrating multi-scale roughness. Numerical results provide insight into the effects of global interference (normal load), fractal parameters (surface roughness) of the hard surface, interfacial shear strength (adhesion), and material properties of the soft surface on plastic deformation at the microcontact level, global coefficient of friction, and frictional energy dissipated during sliding.