Analytical Cutting Force Model Research Articles

Development of a predictive analytical cutting force and torque model for flat bottom drilling of metals using mechanistic approach

By far a large scale of industrial components is being manufactured from metallic materials. Most of these components possess holes in order to fulfill design and application requirements, such as assembly of screws, pins or passing channels for fluids. Depending on the utilized manufacturing method and positioning of these components during machining processes, these holes are being drilled even in vertical or inclined orientations with respect to the jig and fixturing systems. In vertical drilling of the flat surfaces conventional or indexable inserted drill are the commonly used tools. However, these types of tools do not demonstrate sufficient performance on the surfaces drilled holes due to the occurred run-out, vibrations when being used in inclined features. Therefore, flat bottom drills have been developed in order to be used for curved or inclined surfaces. Thus, optimization of the tool and components design requires a deeper knowledge on the cutting forces and torques when using flat bottom drills. In this study, a predictive analytical cutting force model is developed for flat bottom drills for both vertical and inclined plunging using mechanistic approach in Matlab. The model is established on the distributed elementally cutting along the tool radius considering both rake and relief faces based upon the orthogonal and oblique cut principles. Accordingly, the performance of the developed model for different cutting tools with various geometries and machining parameters have been evaluated and verified with experimental results of flat bottom drilling of brass alloy.

An analytical cutting force model for elliptical vibration texturing of nano-grating surfaces

Although the direct texturing processes using dynamic cutting depth modulation have been widely demonstrated for generating micro/nano-structured surfaces, the material shearing removal dominates the surface topography generation that inevitably inhibits the machining feasibility of high-aspect textures. This paper proposes a novel nano-grating generation mechanism governed by the combined effect of shearing-based material removal and compressive forming-based deformation in elliptical vibration texturing. A newly dynamic cutting force model is established to reveal its transient cutting mechanics that incorporating the process elastic rebounding behaviors and essential local cutting characteristics in three deformation zones. The model fully considers the complex transient shear angle variation, friction reversal phenomenon on tool-chip interface as well as the unique flank-waviness interaction. A series of texturing experiments are delicately designed to modulate the contribution of material shearing removal and flank compressive forming on nano-grating generation mechanism. The measured dynamic cutting force show good agreements with the simulated results, based on which the model accuracy and main process assumptions are well validated. Furthermore, the relationship between the cutting force characteristics and nano-grating topography is analyzed to guide the optimal elliptical trajectory designs for simultaneously achieving high-quality nano-gratings and smaller dynamic cutting forces. The outcomes of this paper not only lay the scientific foundations for machining capability extension of direct texturing processes, but also contribute to the understandings of combined surface generation mechanisms of other intermittent cutting processes in nano-scale domain.

Generic Cutting Force Modeling with Comprehensively Considering Tool Edge Radius, Tool Flank Wear and Tool Runout in Micro-End Milling.

Accurate cutting force prediction is crucial in improving machining precision and surface quality in the micro-milling process, in which tool wear and runout are essential factors. A generic analytic cutting force model considering the effect of tool edge radius on tool flank wear and tool runout in the micro-end milling process is proposed. Based on the analytic modeling of the cutting part of the cutting edge in the end face of the micro-end mill bottom, the actual radius model of the worn tool is established, considering the tool edge radius and tool flank wear. The tool edge radius, tool wear, tool runout, trochoidal trajectories of the current cutting edge, and all cutting edges in the previous cycle are comprehensively considered in the instantaneous uncut chip thickness calculation and the cutter-workpiece engagement determination. The cutting force coefficient model including tool wear is established. A series of milling experiments are performed to verify the accuracy and effectiveness of the proposed cutting force model. The results show that the predicted cutting forces are in good agreement with the experimental cutting forces, and it is necessary to consider tool wear in the micro-milling force modeling. The results indicate that tool wear has a significant influence on the cutting forces and cutting force coefficients in the three directions, and the influences of tool wear on the axial cutting force and axial force coefficient are the largest, respectively. The proposed cutting force model can contribute to real-time machining process monitoring, cutting parameters optimization and ensuring machining quality.

An analytical cutting force model of quasi-intermittent vibration assisted swing cutting based on predictive machining theory

Quasi-intermittent vibration assisted swing (QVASC) method was aimed to improve the cutting machinability of difficult-to-machine materials. Inherited the intermittent cutting characteristics of the elliptical vibration cutting (EVC) technology, this method reduces the impact of residual height on the machined surface quality. But there is still a lack of in-depth research on cutting force modeling of QVASC. Based on the conventional cutting force model, a cutting force prediction model in QVASC processing, which considers the time-variable characteristics of QVASC, adopts the non-equidistant shear zone model and regards the workpiece material properties, tool geometry, and cutting conditions as the input data are proposed in this paper. Using the micro-element method, the proposed model decomposed the cutting edge to calculate the cutting force and the cutting force value by superimposing them. It finally predicts the chip flow angle. Experimental results show that when the cutting velocity increases, the average cutting force and the Z -direction increases by 20%, the average cutting force and the Y direction decreases by 17%. The average cutting force along X direction remains unchanged; the depth of cutting became larger. Besides, the average cutting force X decreased by 18%, Y decreased 21%, and Z increased by 13%. As the feed rate increases, the X direction is increased by 26%, and the Z direction is reduced by 22%, while the cutting force in the Y direction is unchanged. After comparing and verifying the measured value and the predicted value, the minimum error of the prediction model reaches 4.01%, which validates the force model of QVACS.

Analytical modeling of micro-milling operations on biocompatible Ti6Al4V titanium alloy

Among the biocompatible materials, Ti6Al4V titanium alloy is widely spread due to its properties, such as corrosion and fatigue resistance combined with low density. Ti6Al4V can be processed by Additive Manufacturing technologies, such as Power Bed Fusion (PBF). The biomedical applications require good surface finishing to ensure biocompatibility with tissues and organs. Machining is an adequate process to ensure low final roughness of components. The necessity to realize miniaturized features implicates the usage of micro mills with diameter lower than one millimeter. It implicates several issues, such as size effects, higher than expected cutting forces, rapid tool wear which can be addressed by experimental tests and process modeling. This work reports the results of micro-milling performed on additively manufactured samples in Ti6Al4V. PBF process was utilized to manufacture the samples by employing laser source (PBF-LB). The machining center was equipped with a loadcell to acquire cutting force signal. An analytical cutting force model was calibrated on the experimental data with the purpose of predicting loads on the tool by considering ploughing- and shearing- regimes. Specific machining tests were performed to calculate the Minimum Uncut Chip Thickness (MUCT) and to calibrate the unknow parameters of the model, while further tests allowed to verify the reliability of the model about the cutting force prediction. The elaboration of the cutting force data was performed by an iterative methodology based on the Particle Swarm Optimization (PSO) algorithm.

Modeling and estimation of cutting forces in ball helical milling process

Milling forces play an important role in the milling process and are generally calculated by the mechanistic or numerical methods; reliable model of cutting forces is very important for the simulation of milling process, which has big scientific significance to further improve machining quality. Ball helical milling technology is used to make holes based on the cutting principle of helical milling using ball end cutter, and due to the influence of spherical surface machining characteristic, the modeling of cutting force in ball helical milling is difficult. Therefore, the main purpose of this paper is to establish an analytical cutting force model in the ball helical milling process. Considering cutting characteristics in the axial feed, the kinematics of ball helical milling is first presented, then the chip thickness distribution in different directions along the cutting edges is predicted. Furthermore, based on the characteristics of helical milling technology and geometry shape of ball end cutter and the classical mechanical cutting force model, through the study on the ball-end milling mechanics, a new relatively accurate theoretical cutting force model is established. At the same time, cutting force coefficients are identified through instantaneous force method according to the Ti-alloy experimental research result. Finally, higher simulation precision of cutting force model in ball helical milling process is received.

Dynamic reaction of machine tools to transient cutting conditions

Transient machining conditions often occur during the milling process, especially when complex toolpath layouts are deployed. Although modern CAM-aided toolpath generation algorithms aim at keeping the cutter engagement conditions as constant as possible and avoid sudden changes, this can not always be ensured. These transients are accompanied by temporary peak excursions in cutting forces and changing dynamic content of the excitation forces. This may have the potential to excite unwanted vibrations in the machining process and even may initiate chatter. Using a virtual process simulation environment it is possible to predict resultant dynamic forces along a complete NC tool path with high time and angular resolution and gain insights into the dynamics of transient events during machining operations. This simulation environment has the capability to use an analytical cutting force model, which spares extensive testing and parameter identification beforehand. Besides, well known empirical cutting formulations can be used as well. The results of the dynamic force prediction is compared against experimental results for different toolpath layouts and the dynamic behavior of the machine tool under cutting conditions will be discussed.

Impact of different tool trajectories on the kinetic characteristics of the cutting process

Simulation models are increasingly used lately to analyze machining conditions during process design. The knowledge of resultant cutting forces along the tool trajectory provides essential information in order to optimize the tool path layout. An analytical cutting force model implemented in a process simulation environment allows to predict resultant forces along a complete NC tool path without the need for extensive testing and parameter identification beforehand. Instead, tool geometry, cutting parameters, material data and friction parameters are the only input parameters needed. The model is presented and simulation and experimental results for different tool trajectories are compared against each other.

Analytical force modelling for micro milling additively fabricated Inconel 625

In recent years, miniaturization of components has been concerned with several industrial fields including aerospace, energy, and electronics. This phenomenon resulted in increasing demand of micro-components with complex shape and high strength, often in high-temperature environment. Nickel-based superalloys such as Inconel 625 are a class of material suitable to aforementioned applications and can be successfully processed with Additive Manufacturing (AM). Moreover, micro-milling can be employed to manufacture micro-scale features on the additively fabricated parts or to achieve better surface finishes, as required for high-precision mechanical assemblies. In micro machining, it is possible to notice a lack of scientific study focusses on the material removal behavior of difficulty-to-cut alloys produced via Additive Manufacturing. This paper describes an analytical cutting force model suitable also for AM’d parts which considers the presence of ploughing- and shearing- dominated cutting regimes. A refinement procedure of the cutting force model was defined and applied by performing an experimental work on Inconel 625 samples fabricated by LaserCUSING™. A search algorithm was employed to develop an iterative methodology to determine the unknown cutting force model parameters. The model was successfully utilized to predict how the cutting force is affected as the process parameters change.

Analytical modelling and experimental validation of micro-ball-end milling forces with progressive tool flank wear

In this paper, an analytical model for estimating the micro-ball-end milling forces is presented based on experimental investigation of progressive tool flank wear. The wear form and wear mechanism of the micro-ball-end mill are revealed through a series of micro-ball-end milling experiments. The effecting laws of cutting parameters such as feed per tooth, cutting speed, and inclined angle on tool flank wear are investigated. The experimental results indicate that the progressive tool flank wear has significant influence on cutting force in micro-milling of NAK80 steel. To assure the prediction accuracy of micro-ball-end milling force, an analytical methodology is presented to estimate cutting forces which considers not only the shearing force resulted from chip formation but also ploughing and rubbing force resulted by combined elastic contact and plastic flow at enlarged flank wear land. To verify the validity of the developed analytical model, a series of experiments are carried out on high-precision machine by using micro-ball-end mill with different flank wear lands. The comparisons of theoretical and experimental cutting forces indicate that the developed model can provide acceptable predicted accuracy. The proposed analytical cutting force model could be employed to monitor progressive tool flank wear land width in micro-ball-end milling of complex surface in future work.

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.

An analytical cutting force model for plunge milling of Ti6Al4V considering cutter runout

As one of the most efficient machining methods, plunge milling has gained more attention as a promising cutting process. This strategy is often used for roughing and semi-roughing processes for the more vibration free than other cutting operations. The motivation of this paper is that the cutting forces in plunge milling differ from that in side milling for the complex cutting condition and tool geometry. In this work, a systematic and analytical cutting force prediction model considering cutter runout for plunge milling is proposed. The detailed analysis of cutting geometry is important for modeling. The precise uncut width is calculated with consideration of the cutting step. In addition, the real-time uncut chip thickness of different inserts is calculated with consideration of the effect of cutter runout. The deduced cutting force model based on the predictive model can be used in various cutting conditions in the plunge milling process. Plunge milling tests with various cutting steps are carried out to verify the proposed model with the quantitative analysis of the results. The results indicate that the simulated results show quite good agreements with the measured cutting forces, which proves the correctness and accuracy of the proposed model.

A unified analytical cutting force model for variable helix end mills

The paper proposes a unified analytical cutting force model based on a predictive machining theory for variable helix end mill considering cutter runout. The variable helix end mill is divided into a set of differential oblique elements along the axial direction. The cutting process of oblique element is based on the non-equidistant shear zone model and the equivalent plane method. The cutting forces of oblique element are modeled by shearing force components due to shearing at the shear zone and edge force components due to rubbing in the tertiary zone. In the primary shear zone, a modified Johnson-Cook model is introduced to account for the material size effect affected by varying instantaneous uncut chip thickness (IUCT) during milling process. In the tertiary zone, edge radius and the partial effective rake angle are included in the analytical model in order to take into account the rubbing effect precisely. The total instantaneous cutting forces are obtained by summing up the cutting forces acting oblique elements on all flutes. The unified analytical cutting force model is verified by experimental data using four different types of end mills, and a good agreement of the predicted and measured cutting forces shows that the proposed model is valid for variable helix end mills.

Cutting deflection control of the blade based on real-time feedrate scheduling in open modular architecture CNC system

Machining accuracy of thin-walled parts which have low-rigidity is greatly influenced by cutting deflection in flank milling. In this paper, cutting deflection of aero-engine blade during processing is controlled within a required dimensional accuracy based on the strategy of real-time feedrate scheduling which is integrated into an open modular architecture CNC system (OMACS) of five-axis milling machine. The maximum deflection position of blade is determined through combining analytical cutting force model in flank milling and finite element analysis (FEA)-based transient dynamic analysis. Then, the numerical model of blade deflection is established to obtain the numerical relationship among feedrate, cutting force, and blade deflection, which is usually used to get optimized cutting force and feedrate by setting allowable value of blade deflection. To implement blade deflection control during machining, a real-time control strategy of feedrate scheduling based on nonlinear root-finding algorithm of Brent-Dekker and principle of feedrate smooth transition is developed and integrated into OMACS which has functions of real-time cutting force signal processing and real-time feedrate adjustment. Experimental results show that blade deflection is effectively controlled by proposed strategies, machining accuracy, and efficiency are improved.

Analytical Force Modeling of Fixed Abrasive Diamond Wire Saw Machining With Application to SiC Monocrystal Wafer Processing

Free abrasive diamond wire saw machining is often used to cut hard and brittle materials, especially for wafers in the semiconductor and optoelectronics industries. Wire saws, both free and fixed abrasive, have excellent flexibility, as compared to inner circular saws, outer saws, and ribbon saws, as they produce a narrower kerf, lower cutting forces, and less material waste. However, fixed abrasive wire saw machining is being considered more and more due to its potential for increased productivity and the fact that it is more environmentally friendly as it does not use special coolants that must be carefully disposed. The cutting forces generated during the wire saw process strongly affect the quality of the produced parts. However, the relationship between these forces and the process parameters has only been explored qualitatively. Based on analyzing the forces generated from the chip formation and friction of a single abrasive, this study derives an analytical cutting force model for the wire saw machining process. The analytical model explains qualitative observations seen in the literature describing the relationship between the cutting forces and the wafer feed rate, wire velocity, and contact length between the wire and wafer. Extensive experimental work is conducted to validate the analytical force model. Silicon carbide (SiC) monocrystal, which is employed extensively in the fields of microelectronics and optoelectronics and is known to be particularly challenging to process due to its extremely high hardness and brittleness, is used as the material in these experimental studies. The results show that the analytical force model can predict the cutting forces when wire saw machining SiC monocrystal wafers with average errors between the experimental and predicted normal and tangential forces of 9.98% and 12.1%, respectively.

Cutting force prediction in end milling of curved surfaces based on oblique cutting model

To obtain a superior machined surface quality, predicting cutting force is important for planning and optimizing cutting process before actual machining. This paper established a novel analytical cutting force model for end milling of curved surfaces. Taking the variation of cutter geometry into account, cutting force coefficients were characterized by physical parameters, e.g., the normal friction angle, the normal shear angle, the chip flow angle, and the shear stress. Based on an oblique cutting model, a mathematical relationship of the physical parameters was obtained by the minimum energy principle. A Newton iterative algorithm was utilized to solve the established non-linear equations for calibrating the cutting force coefficients. Taken the variable radial depths of cut into account, a vector method was derived to calculate the equivalent feed rates and the entry/exit angles. After calibrating the cutting force coefficients with performing straight milling tests, two typical curved surfaces were investigated. The one was a circular curved surface with constant radial depth of cut, while the other was a Bezier curved surface with variable radial depth of cut. The predicted cutting forces were compared with experimental results, and a good correlation was obtained.

Stability analysis of machine-tool vibrations in the frequency domain

The identification of the stability lobes for machine-tool vibrations via frequency domain methods is presented using the example of interrupted turning process with round inserts. An analytic cutting force model for round inserts is derived, where the directional factors depend nonlinear and non-homogeneous on the depth of cut. Vibrations in tangential, normal and axial direction are taken into account. In particular, tangential vibrations in cutting speed direction lead to a state-dependent delay. Thus, the model is characterized by periodic excitation due to interrupted cutting and state-dependent delays due to tangential vibrations. The application of the multifrequency solution for the stability analysis of such non-autonomous systems with state-dependent delays is presented.

Study of cutting force in ultra-precision raster milling of V-groove

Cutting force plays an important role in the design of cutting plans, setting of cutting conditions, inspection of tool wear, and prediction of machined surface topography. As no previous research has focused on cutting force in ultra-precision raster milling (UPRM), this paper presents a theoretical and experimental study on cutting force modeling in UPRM of V-groove. An analytic cutting force model is established to predict the cutting force components both in the feed direction and thrust direction, and a dynamic model is developed to simulate the free vibration signal induced by the cutting force pulse. The effects of cutting parameters in UPRM are studied, including the depth of cut and feed rate, and a group of experiments conducted to verify the simulation results. The simulation and experimental results show that cutting force in UPRM is figured as a force pulse followed by a free vibration signal induced by the force pulse and that the amplitudes of cutting force in both feed direction and thrust direction increase with the growing depth of cut and feed rate.

Prediction of Cutting Forces in Mill-Grinding SiCp/Al Composites

In this study, an analytical cutting force model has been presented for mill-grinding SiCp/Al composites. In this model, except the chip formation force and frictional force components, debonding and particle fracture force components are considered in modeling the total force. The energy theory of particle fracture and Griffith theory of fracture were applied in developing the debonding and particle fracture force components during mill-grinding SiCp/Al composites. Results of verification experiments for the developed cutting force model reveal that the mean forecast error of this developed cutting force model is less than 8% excluding few experimental values which deviate far from the corresponding theoretical model values, and has acceptable agreement with the experimental values under different machining conditions.

3D mechanical modeling of soil orthogonal cutting under a single reamer cutter based on Drucker–Prager criterion

Reamers have been the major implement used to enlarge the hole size in reaming stage of horizontal directional drilling (HDD). The choice of its available structural design becomes critical to maximize the rate of penetration and minimize the tripping time, thereby decreasing the cost of operations and the risk of experiencing stability problems. Moreover, because the duration period of a HDD project is largely dependent on the reaming stage, it is crucial to study the reaming efficiency by use of the appropriate operating conditions (cutting angle and depth). In the paper, the reaming efficiency of reamer is analyzed based on the development of a 3D analytical cutting force model of soil orthogonal cutting under a single reamer cutter. Focusing on the soil orthogonal cutting mechanism under a single reamer cutter, the interaction and friction between soil and cutter and the shear action of 3D shear zone are comprehensively considered, consequently the mechanical properties are given. Based on these analyses and using the Drucker–Prager criterion given a weight to the intermediate principal stress, the analytical models are proposed. In addition, this paper presents 3D FEM simulations for the analysis of soil orthogonal cutting under a single reamer cutter. The subject has been covered in two parts. Part one deals with the verification of the analytical cutting force model, the other focuses on the assessment and selection of the criterions of shear angle. The analytical cutting force model presented provides the capability to evaluate cutter loading for utilization of a single cutter with different rake angles to cut soils, and to plot the effect of change in the rake angle. Finally, the optimum rake angle of single reamer cutter was obtained. The results of this analysis can be integrated to study reamer performance. It can also provide a guideline to the application and design of the reamer assembly for various soils.