Edge Force Coefficients Research Articles

Estimation of Hardness and Residual Stress on End-Milled Surfaces Using Linear Regression Model

This study presents a novel method for estimating the surface integrity of end-milled workpieces. It is well known that the mechanical properties of machined surfaces in cutting affect the quality of the final product. In particular, hardness and residual stress often require strict control; however, nondestructive inspection remains a challenge. This study proposes a method to estimate the hardness and residual stress of end-milled surfaces by analyzing cutting forces and images of the tool during machining to obtain approximate temperature and stress distributions. These state quantities are highly correlated with the dislocation density and its distribution on the machined surface, which in turn is strongly correlated with residual stress and surface hardness. Despite this strong correlation, few research studies have been conducted on the topic. In the proposed method, cutting forces, measured by a dynamometer, are analyzed to estimate the specific cutting forces and edge force coefficients. Simultaneously, the flank wear width is recorded using an image-based on-machine measuring device installed in the machine tool. From this information, the average stresses at the primary and tertiary cutting zones are estimated, while the cutting temperature in the primary cutting zone is roughly estimated by considering the traditional shear-angle prediction theory. Using these estimations, hardness and residual stress are calculated based on a simple linear regression model. Parameter identification for the model is performed based on measured hardness and residual stress in end-milling experiments. The model was validated against experimental measurements, which showed that the proposed method can accurately estimate hardness and residual stress, although it was observed that the selection of explanatory variables has a significant effect on accuracy.

Tool wear area estimation through in-process edge force coefficient in trochoidal milling of Inconel 718

The rapid wear and premature failure of the cutting tool are prone to happen due to increased forces during machining difficult-to-cut materials such as Inconel 718. The application of alternative toolpath such as trochoidal milling has significantly improved tool life and reduced the overall cycle time of the process. The wear pattern of the tool has a direct impact on the cutting forces, which increases with tool deterioration. The cutting forces in milling are modeled through the mechanistic force model and can be designated through a set of force coefficients, i.e. cutting and edge representing the shearing and ploughing phenomenon of metal removal. It has been established in the literature that tool wear has a considerable effect on the value of edge force coefficients. This paper aims to determine the in-process edge force coefficients for the trochoidal toolpath and correlates them with the corresponding flank wear area. The proposed correlation will further assist in predicting the level of flank wear area based on the force values in trochoidal milling.

Determination of force coefficient based on instantaneous forces and linear mechanistic model in ball end milling

Due to the intricate geometry, force prediction in the ball end milling process (BMP) is a challenging task. Cutting forces generated during BMP have an impact on important aspects of machining characteristics such as form error, chatter and vibration, surface finish, tool wear, and dimensional accuracy. These machining problems might be resolved by foreknowledge of the cutting forces. In the present research, a new and quick mathematical model based on the linear mechanistic method is reported to determine the force coefficients. The cutter’s hemispherical part is discretized into five discs along the axis at 0.4 mm uniform spacing in the range of 0.2–1.8 mm. For one cutter revolution, forces in the tangential, radial, and axial directions are measured for each disc to prevent radial runout. The current disc makes use of the preceding disc’s cutting force. To derive the shear and edge force coefficients, these are further divided into edge and shear forces. Validation experiments have been conducted and compared with the simulated forces to assess the predictive power of the developed force coefficient model. The predicted results are found to be remarkably close to the experimental results with an error of 5.5%, −8.6%, and 8.9% at 6631 rpm and 2.8%, −4.4%, and 2.21% at 10,052 rpm in tangential, radial, and axial forces, respectively.

Analysis of cutting forces at different spindle speeds with straight and helical-flute tools for conventional-speed milling incorporating the effect of tool runout

This paper is concerned with the experimental investigation and mechanistic prediction of cutting forces for flat-end milling with tool runout. The effects of the tool geometry, the workpiece material and cutting parameters such as spindle speed, tool engagement and cutting direction are investigated. The mechanistic force model uses the trochoidal flute path to calculate the undeformed chip thickness. Average cutting force and linear regression model are applied for identifying the coefficients of the force model, and tool runout parameters are established from the radii of all flutes at the free end of the cutting tool. A series of milling processes are conducted on AZ31 Magnesium (Mg) alloy and titanium alloy (Ti6Al4V) to analyze the instantaneous cutting force curves, amplitudes of cutting forces and peak forces over a wide range of conventional spindle speeds, namely 600, 1200 and 3000 rev/min. It is found that the values of the cutting force coefficients are higher at lower spindle speed and decrease with an increase in spindle speed, especially when machining Ti6Al4V alloy. For the edge force coefficients, it is observed a slight variation when using cutting tools with different helix angles. Besides, the cutting force amplitudes strongly depend upon the workpiece material. The helix angle has a significant influence on the transverse force amplitude at the spindle speed of 600 rev/min. The cutting forces obtained mechanistically are also substantiated by comparison with measurements.

Monitoring of in-process force coefficients and tool wear

Mechanistic modeling of the milling forces is described by a set of cutting and edge force coefficients that characterize the shearing and ploughing actions of the metal removal process. The force coefficients are traditionally calibrated under a series of dedicated milling experiments. However, due to the force coefficients’ process-dependency, such an approach can become cumbersome if the machining conditions deviate from those of the milling experiments. In this paper, a method for monitoring the in-process force coefficients is proposed for toolpaths that exhibit varying radial immersions or feed rates. The proposed methodology was experimentally validated, and it is demonstrated that the edge force coefficients can be used to estimate the tool’s flank wear. In the absence of a force dynamometer, force coefficients as estimated under spindle current measurements were evaluated and also shown to be a viable solution for tool wear monitoring.

Estimation of hardness and residual stress of finished surface by linear regression model

This study presents a novel method for estimating the surface integrity in end-milling. The mechanical properties of the machined surfaces in cutting affect the quality of the final product. In particular, hardness and residual stress often require strict control, but nondestructive inspection is not easy. This study proposes a method to estimate the hardness and residual stress of end-milled surfaces by analyzing the cutting forces measured on the machine and the tool image. The measured cutting force is analyzed to estimate the specific cutting forces and edge force coefficients. The flank wear width is measured using an on-machine measuring device installed in the machine tool. From this information, the average stresses at the primary and tertiary cutting zones are estimated. The cutting temperature in the primary cutting zone is roughly estimated by considering the shear angle theory. These state quantities are highly correlated with the dislocation density and its change on the machined surface. Therefore, hardness and residual stress are estimated based on a simple linear regression model. Parameter identification was performed based on measured hardness and residual stress in end milling experiments. The experimental results validated that the proposed method can accurately estimate hardness and residual stress.

Effects of Machining Parameters on Cutting Force of Endmilling of Inconel 718 Using Wavy-Edge Bull-Nose Helical End-Mill under Minimum Quantity Lubrication

This paper investigates effects of machining parameters: cutting speed (CS), feedrate (FR), and axial depth of cut (DC), on cutting force of endmilling of Inconel 718. A Wavy-edge bull-nose helical endmill (WEBNHE) was simulated cutting this material, at different levels of these parameters, then the maximum values of cutting force components (FxMax, FyMax, FzMax), as well as the resultant (FMax) were predicted using a mechanistic cutting force prediction model developed and cited from references [1-3]. The mechanistic model predicts the cutting force based on instantaneous cross-sectional area of the chip, and the local differential cutting-edge length, whereas minimum quantity lubrication (MQL) cooling strategy was incorporated into the mechanistic model via experimentally-identified cutting force and edge force coefficients which were identified and cited from the reference [4]. The simulated experimental runs in this research were designed based on Full-factorial principle, whereas MATLAB was used to simulate the mechanistic model and predict the cutting forces. The resultes showed that depth of cut contributed the most (by 78.94%) on the predicted resultant force (FMax), Followed by Feedrate, which contributed by 20.56%, and last was the cutting speed which contributed only by7.13%. Resultes also showned that, increasing feedrate and depth of cut resulted in increasing the three cutting force components and the resultant, Whereas increasing the cutting speed resulted in decreasing the FxMax and FyMax, but increasing the FzMax. Furthemore, by focusing on the axial force component (FzMax), it was observed that the effect of cutting speed was completelly reversed when the feedrate reached 41 mm/min and depth of cut reched 25 mm. At these conditions, cutting speed 93 produced more FzMax than 62. This can be justified by the wavy-cutting edge affecting cutting force direction

Mechanistic modeling of cutting forces in high-speed microturning of titanium alloy with consideration of nose radius

Microturning is a micromechanical machining process used to produce microcylindrical or axially symmetrical parts. Microcylindrical parts are mainly used in microfluidic systems, intravenous micromotors, microsurgical applications, optical lens applications, and microinjection systems. The workpiece diameter is very small in microturning and therefore is greatly affected by the cutting forces. For this reason, it is important to predict the cutting forces when machining miniature parts. In this study, an analytical mechanistic model of microturning is used to predict the cutting forces considering the tool nose radius. In the semi-empirically developed mechanistic model, the tool radius was considered. A series of semi-orthogonal microturning cutting tests were carried out to determine the cutting and edge force coefficients. The mechanistic model was generalized depending on the cutting speed and depth of cut by performing multilinear regression analysis. In the study, the depth of cut (ap = 30–90 µm) and feed values (f = 0.5–20 µm/rev) were selected considering the nose radius and edge radius of the cutting tool. The experiments were carried out under high-cutting speeds (Vc = 150–500 m/min) and microcutting conditions. Ti6Al4V alloy was used as the workpiece material and the tests were carried out under dry cutting conditions. Validation tests for different cutting parameters were carried out to validate the accuracy of the developed mechanistic model. The results showed that the difference between the mechanistic model and the experimental data was a minimum of 3% and a maximum of 24%. The maximum difference between the experimental and the model usually occurs in forces in the tangential direction. It has been observed that the developed model gives accurate results even at a depth of cut smaller than the nose radius and at feed values smaller than the edge radius.

A development method of cutting force coefficients in face milling process using parallelogram insert

This paper presents a modeling method of cutting force and a combination approach of theory and experimental methods in the determination of cutting force coefficients in the face milling process using a parallelogram insert. By the theoretical method, the cutting forces were modeled by a mathematical function of cutting cutter geometry (Cutter diameter, the number of inserts, the insert nose radius, insert cutting edge helix angle, etc.), cutting conditions (depth of cut, feed per flute, spindle speed, etc.), and cutting force coefficients (shear force coefficients, edge force coefficients). By the theoretical method, the average cutting forces in three directions (feed – x, normal – y, and axial – z) were modeled as the linear functions of feed per flute. By the experimental method, the average cutting forces in these three directions were also regressed as the linear functions of feed per flute with quite large determination coefficients (R2 were larger than 92 %). Then, the relationship of average cutting forces and feed per flute was used to determine all six cutting force coefficient components. The validation experiments were performed to verify the linear function of average cutting forces, to determine the cutting force coefficients, and to verify the cutting force models in the face milling process using a cutter with one parallelogram insert. The cutting force models were successfully verified by comparison of the shape and the values of predicted cutting forces and measured cutting forces. These proposed methods and models can be applied to determine the cutting force coefficients and predict the cutting force in the face milling process using a parallelogram insert and can be extended with other cutting types or other insert types

Establishment of instantaneous milling force prediction model for multi-directional CFRP laminate

Carbon fiber reinforced polymer (CFRP) is widely used in the aerospace field due to its light weight and high strength. The CFRP milling process is prone to damage such as burrs and tears. The cutting force is closely related to the damage of CFRP and tool wear. In this paper, a back propagation (BP) neural network model of cutting force and edge force coefficients was established. The model considers the effects of instantaneous uncut chip thickness, fiber cutting angle, spindle speed, and axial depth of cut. The unidirectional CFRP laminate instantaneous milling model considering the cutting edge force was further established. The instantaneous milling force prediction model was extended to multi-directional CFRP laminates. And the relationship between the damage mechanism of CFRP and the instantaneous milling force was analyzed. Experiments have proved that the instantaneous milling force prediction model built in this paper has high accuracy.

Chatter stability and surface quality in milling of unidirectional carbon fiber reinforced polymer

Carbon fiber reinforced polymers (CFRPs) are typical difficult-to-machine materials. Due to their anisotropic material property, chatter and poor surface quality are easy to occur during machining. In this paper, the mechanical cutting force model and dynamic milling system model considering the anisotropy of unidirectional CFRP (UD-CFRP) were established. The cutting force coefficients and the edge force coefficients in the cutting force model were calculated as functions of fiber cutting angle. The cutting force model can accurately describe the variation laws of milling force in different fiber directions. The chatter stability of milling UD-CFRP was analyzed and the influence of the fiber direction on it was studied. The influence laws of the fiber directions and chatter stability on surface quality were discussed, and a variable related to cutting stability, chatter factor, was defined, which provides a novel method for predicting surface quality of machined UD-CFRP.

A PSO-based semi-analytical force prediction model for chamfered carbide tools considering different material flow state caused by edge geometry

The prediction of force in metal cutting is essential when estimating tool wear, surface quality and energy consumption. As a significant characteristic in tool design, edge geometry results in more challenges in force modeling especially under the condition of cutting with chamfered insert. In this paper, a semi-analytical model is proposed to describe the effect of chamfered edge on cutting force considering multiple material flow state. In orthogonal cutting, shear effect is calculated based on the unequal division shear-zone model and Johnson-Cook's material constitutive law. Two kinds of chip-tool contact patterns are considered to discuss the effect of tool edge, chip flows on both chamfered edge and rake face when chamfer length is close to Uncut Chip Thickness (UCT), or chip flows only on chamfered edge when chamfer length is much larger than UCT. Edge force coefficients of chamfered edge are modeled as linear functions with respect to shear stress, chamfer length and chamfer angle. The variation of edge force with respect to edge geometry is studied through Finite Element Method (FEM) simulations. The modified force prediction model is established by introducing a factor S to describe the trend of edge effect with respect to the ratio of chamfer length to UCT. Finally, a modified force prediction model is presented and the constants in the model can be calibrated through a Particle Swarm Optimization (PSO)-based algorithm. Experiments of orthogonal cutting AISI304 with different chamfered carbide inserts are performed to validate the correctness and feasibility of the proposed model. The experimental results show that this model is effective in predicting the cutting force components under the condition of different edge preparations and cutting parameters.

Identification of optimal machining parameters in trochoidal milling of Inconel 718 for minimal force and tool wear and investigation of corresponding effects on machining affected zone depth

Increasing the productivity and efficiency of milling practices is of high importance with the rapidly changing global economy. To this end researchers have turned to alternative milling toolpaths, such as trochoidal milling, which has been shown to increase tool life with a corresponding reduction in machining time for some applications. To better understand the trochoidal milling process and optimize it for manufacturing scenarios, the modeling of cutting forces must be investigated; semi-mechanistic methods are the focus of this work. The basis for this type of force modeling lies in uncut chip thickness modeling combined with cutting force coefficients and edge force coefficients. With a novel uncut chip thickness model proposed by the authors in a previous work, this investigation looks to understand the dependence of the model coefficients as they relate to trochoidal path parameters along with machining outputs such as maximum cutting force and tool wear. Furthermore, the machining parameters are investigated as to how they relate to the improvement of tool life and cutting force utilizing the Taguchi method, where optimal parameters are found for minimum tool wear and cutting forces. The effects of the trochoidal path on the subsurface of the machined samples as they relate to the machining affected zone, are also investigated in both the radial and axial directions. It is found that tool wear increases the depth of the machining affected zone as does increasing chip thickness.

Modeling of Cutting Forces with a Serrated End Mill

The paper presents a mechanistic cutting force model of serrated end mill to predict cutting forces. Geometric model of serrated end mill is established, which covers variable helix end mill geometries. In this model, the serration of helical cutting flutes is expressed spatially and the wave of serration is defined to be a sine wave. The spatial vector is applied to define chip thickness so as to enhance the spatial expressiveness of the model, which is perpendicular to the curvature of each flute. Each helical flute is scatted into a series of infinitesimal cutting edges. The infinitesimal cutting forces depend on three cutting force coefficients and three edge force coefficients in the tangential, radial, and axial directions at every cutting element. By integrating the infinitesimal cutting forces along each cutting edge, the milling forces with serrated end mill can be predicted. The model feasibility of the serrated end mill is verified by comparing the predicted and measured cutting forces. Moreover, the model is also verified such that it can also predict cutting forces with other types of end mills, such as variable helix serrated end mill, variable helix end mill, and regular end mill.

Modeling of cutting force coefficients in cylindrical turning process based on power measurement

The cutting force is an important physical quantity in metal cutting, and the cutting force coefficients are the basis for establishing the cutting force model. In this paper, the relation between the cutting power and the cutting force coefficients is established. A cutting power model was established with a linear relationship between the spindle power and material removal rate (MRR). The power-based model of the main cutting force coefficients is proposed by extracting the linear equation coefficients of the power-MRR function. The power-based model of feed force coefficients is established as a quadratic polynomial equation between the motor power of the feed axis and feed rate. And the cutting force coefficients and the edge force coefficients of feed force are expressed respectively by the two orders of coefficients of the equation. The thrust force coefficients are indirectly calculated from the relation between tangential cutting force and thrust force with friction angle of tool-chip. The power-based models were verified by a series of cutting tests regarding material properties, cutting parameters, and axial directions. The results show that the cutting force coefficients obtained by measuring the cutting power have good correspondence with that identified by dynamometer.

Development and experimental validation of a mechanistic model of cutting forces in micro- ball end milling of full slots

ABSTRACTIn the present work, a mechanistic model of cutting forces is developed with a novel approach to arrive at the cutting edge geometry as well as the cutting mechanics. The geometry of cutting elements derived and verified using a virtual tool generated in CAD environment is considered. The cutting and edge force coefficients at every discrete point on the cutting edge of micro-ball end mill are established in a novel way from the basic metal cutting principles and fundamental properties of materials, considering edge radius and material strengthening effects. Further, measured edge radius is used in the model. Full slot micro-ball end milling experiments are conducted on a high-precision high-speed machining center using a 0.4 mm diameter tungsten carbide tool and cutting forces are measured using a high-sensitive piezo-electric dynamometer. It is established that the predicted as well as experimental cutting forces are higher at very low uncut chip thickness in comparison with the cutting edge radius in micro-ball end milling also. Amplitudes of cutting forces and instantaneous values with incremental rotation of the tool are compared with predicted values over two revolutions for validation of proposed model.

An analytical force prediction model for turning operation by round insert considering edge effect

As a common type of ceramic inserts, the round inserts with high hardness and super high wear resistance are now widely used in high efficiency machining of some key components of aviation industry and nuclear industry. Cutting forces have an important effect on the surface quality of key components and tool life of inserts in machining process. However, the lack of understanding on the complex geometry and detailed description of uncut chip thickness (UCT) restrict the cutting force prediction of round inserts. In this paper, an analytical model for cutting force prediction of round inserts based on the precise cutting geometry is presented. First, a new geometric method for the cutting edge discretization of ceramic round insert in high speed turning is proposed. Different from the previous methods, the discretization of cutting edge in this research is performed on the rake face rather than the reference plane, which makes the prediction more accurate for the reason that the projection of tool edge is ellipse on the reference plane. Second, the shear flow stress in the primary deformed area, used to estimate the cutting force coefficients, is calculated based on the unequal division shear zone model. Then, a new prediction model considering shear flow stress and chamfer length is developed in edge force coefficients forecasting and is verified by the simulation of finite elements method (FEM). Finally, a series of cutting experiments are implemented to verify the feasibility of the proposed analytical model for cutting force prediction of round inserts. It indicates that the forecast results are in good agreement with the measured cutting forces, which proves the correctness and accuracy of the model.

Effects of geometric parameters of wavy-edge bull-nose helical end-mill on cutting force prediction in end-milling of Inconel 718 under MQL cooling strategy

This paper presents the results of the development of a mechanistic cutting force prediction model for wavy-edge, bull-nose, helical endmill (WEBNHE), which was validated and used to investigate the effects of the geometric parameters of the WEBNHE on the predicted cutting force components and the resultant cutting force. The mechanistic cutting force prediction model was validated by conducting end-milling experiments on Inconel 718 and incorporating the effect of the Minimum Quantity Lubrication (MQL) cooling strategy through experimentally identified six cutting force and edge force coefficients. The geometric parameters investigated in this research were: the wavelength, wave magnitude, axial shift of the linear part, and the helix angle of the wavy cutting edges. These parameters were varied one at a time, and the cutting force components for each variation were predicted using the mechanistic cutting force prediction model. The results show that the predicted and measured cutting force components were in good agreement in magnitude and shape. The cutting force components generated from the end-milling under the MQL cooling strategy were lower than under the emulsion cooling strategy. The magnitudes and shapes of the predicted cutting force components and the resultant cutting force of the WEBNHE were unique (asymmetric) in magnitude and shape compared to those of standard, bull-nose, helical endmill (SBNHE) due to the uniqueness of the wavy-cutting edge geometry.The results also show that the predicted cutting force component in the feed direction Fy is the largest and the most affected by the geometric parameters, followed by Fx. However, Fz is insignificantly affected. It was also observed that the maximum magnitudes and ranges of the cutting force component in the feed direction Fy and the resultant cutting force FR increased with an increase in the wave magnitude and decrease with increase of the wavelength, axial shift, and the helix angle. The wavy cutting edge spends more time in the cutting zone than the standard, helical, cutting edge; this extra time affects the frequency content of the cutting force signals generated by the endmill and improves the end-milling dynamics. Additionally, the distribution of the cutting forces on the wavy cutting edges was not equal due to the asymmetric cutting edge geometry.

Modeling and Simulation of Cutting Forces in Side Milling

In order to acquire high machining quality and minimum machining time, cutting forces are usually modeled to understand the milling process, simulate or predict cutting forces, and optimize the machining parameters. In this paper, side milling tests were conducted on superalloy Inconel 718 with a solid carbide end mill, and the cutting forces vs. cutting time were measured. The average cutting forces were extracted from the measured instantaneous cutting forces under different feed rates of experiments, and the components of the shear forces and edge forces were determined by using the linear regression of the experimental data. The cutting force coefficients, including shear force coefficients and edge force coefficients, were identified. In addition, the algorithms of the mathematical model were implemented in Matlab. The predicted cutting forces were in good agreement with the experimentally measured forces, and the validation of the cutting force model was demonstrated.

Development of a mechanistic cutting force model for wavy-edge bull-nose helical end-milling of inconel 718 under emulsion cooling strategy

This paper presents the results of the development of a mechanistic cutting force model to predict cutting forces in high-speed end-milling of Inconel 718 using a wavy-edge, bull-nose, helical endmill (which hereafter will be abbreviated as WEBNHE). The model incorporates the effects of emulsion cooling strategy into the mechanistic cutting force model through the experimental determination of six specific cutting force and edge force coefficients. The cutting force is predicted as three components (Fx, Fy, and Fz) and the resultant cutting force FR. The mechanistic cutting force model depends on a mathematical model to represent the geometry of this endmill, which is also developed in this research. The mechanistic model also depends on three cutting force coefficients in the tangential, radial, and axial directions (ktc, krc, kac, respectively), and on three edge force coefficients (kte, kre, kae), also in the tangential, radial, and axial directions. These coefficients are determined experimentally in a separate work in which “emulsion” was applied as the cooling strategy. MATLAB codes were developed and used to simulate the developed mathematical and mechanistic cutting force models. Finally, to validate the mechanistic cutting force model, machining experiments were conducted and real cutting force components were measured and compared with the predicted cutting force components. The predicted values agree fairly well with the experimentally measured values in both magnitude and shape. The percentage of the prediction error for the highest peak force magnitudes at 93 rpm were 11.38%, –0.46%, and 11% for the Fx, Fy, and Fz components respectively, while the percentage prediction error for the lowest cutting force magnitudes are 15.25%, 17.84%, and 10% for Fx, Fy, and Fz components respectively. The developed mechanistic cutting force model can be used to investigate the effect of tool geometry and machining parameters on cutting forces, machining power, machine tool vibration, and to simulate the end-milling process to improve machinability and productivity, and also to understand more fully the end-milling process using WEBNHE.