Cutting Force Coefficients Research Articles

Mechanistic modelling of dynamic cutting forces in micro end milling of Zr-based bulk metallic glass

This paper presents the mechanistic modelling of dynamic cutting forces in micro end milling using cutting force coefficients determined empirically from the average cutting forces in the ploughing and shearing dominant regimes. The influence of the cutting tool edge radius and the effects of ploughing, elastic recovery, overlapping tooth engagement of the cutting tool etc. are considered in the cutting force model. The ploughing forces are modelled as proportional to the interactive area between the rounded cutting edge and the work material. The proposed model is compared with the results of several micro milling experiments with Zr-based bulk metallic glass. The study reveals that the radial ploughing coefficient is larger than the tangential ploughing coefficient. However, the tangential cutting coefficient is found to be larger than the radial cutting coefficient. The developed model is found to predict the cutting forces fairly well under different micro cutting conditions.

Mechanistic modelling of dynamic cutting forces in micro end milling of Zr-based bulk metallic glass

This paper presents the mechanistic modelling of dynamic cutting forces in micro end milling using cutting force coefficients determined empirically from the average cutting forces in the ploughing and shearing dominant regimes. The influence of the cutting tool edge radius and the effects of ploughing, elastic recovery, overlapping tooth engagement of the cutting tool etc. are considered in the cutting force model. The ploughing forces are modelled as proportional to the interactive area between the rounded cutting edge and the work material. The proposed model is compared with the results of several micro milling experiments with Zr-based bulk metallic glass. The study reveals that the radial ploughing coefficient is larger than the tangential ploughing coefficient. However, the tangential cutting coefficient is found to be larger than the radial cutting coefficient. The developed model is found to predict the cutting forces fairly well under different micro cutting conditions.

Prediction of Stability Lobe Diagrams in High-Speed Milling by Operational Modal Analysis

Self-excited regenerative vibration or chatter limits the primary requirements like productivity, surface finish and dimensional accuracy of high-speed machining. It is the most critical factor that severely affects the tool-life and life of the machine tool. Out of several methods followed for suppressing and avoiding chatter, machining conditions chosen with stability lobe diagram is the most reliable way. Stability lobe diagrams are typically generated by knowing specific cutting force coefficients and tool point frequency response functions (FRFs). Inaccurate use of tool point FRFs significantly affects the stable regions of stability lobe diagrams. As tool-point FRFs are influenced by gyroscopic effect, centrifugal force, thermal change in bearing dynamics, etc. during machining, it is important to consider the effect of these factors on tool point FRFs in order to generate accurate stability lobe diagrams. The present work covers a new approach for estimating tool point FRFs during machining operations, employing cutting tool vibration signals. For measuring the vibration at the tip of end mill at different spindle speeds, a non-contact laser vibrometer is used. In order to remove the tooth pass frequency and its harmonics from the measured signals, a comb filter is employed. The filtered signal is subjected to Operational Modal Analysis (OMA) in order to derive tool point FRFs. With the estimated FRFs at different spindle speeds, the stability lobe diagrams are drawn for high-speed milling machine. Comparative study of stability lobe diagrams, drawn with static modal analysis and Operational Modal Analysis, have shown that the cutting conditions chosen from stability lobe diagram derived with OMA, are found to be more realistic for avoiding chatter during high-speed milling applications.

Identification and analysis of cutting force coefficients in the helical milling process

Identification and analysis of cutting force coefficients in the helical milling process

Semi-analytic modelling of cutting forces in micro ball-end milling of NAK80 steel with wear-varying cutting edge and associated nonlinear process characteristics

Cutting edge of miniature ball-end mill is one of decisive importance for the machining performance by affecting the thermal and mechanical load in cutting process. In this paper, a semi-analytic model is proposed to estimate the cutting forces in micro ball-end milling of NAK80 steel considering wear-varying cutting edge and the associated nonlinear process characteristics. The wear-varying cutting edge geometry under the different wear stage is obtained by 3D optical profilometer. The measured results indicate that cutting edge of miniature ball-end mill under the different wear stage includes not only the enlarged cutting edge radius but also the extended flank wear land, which can be described by a combination of edge radius and flank wear land width. The influence laws of the edge radius and flank wear land width on tangential and feed force coefficients are investigated, and the enlarged edge radius and extended flank wear land under different wear stage could be separated from each other by utilizing the cutting force coefficients data based on their different sensitivity on cutting forces. A semi-analytic method is developed to predict the shearing/plowing/friction forces in primary and tertiary shear zones based on classical oblique cutting and slip-line field model. The nonlinear tool-chip friction behavior with the phenomenon that the ratio of tool-chip contact length to uncut chip thickness and friction factor nonlinearly change with the ratio of uncut chip thickness to edge radius are investigated and employed to estimate rake/shear/friction angles, and the nonlinear strain gradient plasticity effect with the fact that effective strain gradient is affected by not only rake angle and shear angle, but also primary shear zone thickness that obviously increases with reduce of the ratio of uncut chip thickness to edge radius are considered to estimate the shear flow stress. The nonlinear behavior derived from the tool-chip/workpiece friction and material constitutive affects the contribution level of size effect on cutting forces in micro ball-end milling. Finally, to calibrate and validate the effectiveness of the proposed cutting forces model, a set of micro ball-end milling of NAK80 steel experiments are performed on a three axis ultra-precision machine by using same solid carbide tool with wear-varying cutting edge under different wear stage. The comparisons between the predicted and measured results show that the proposed model can provide higher accuracy and better understanding for micro ball-end milling of NAK80 steel.

Cutting Force Estimation Considering the Specific Cutting Force Constant

Few studies have been conducted regarding theoretical turning force modelling while considering cutting constant. In this paper , a new cutting force modelling technique was suggested which considers the specific cutting force coefficients for turning. The specific cutting force is the multiplication of the cutting force coefficient and uncut chip thickness . This parameter was used for experimental modelling and prediction of theoretical cutting force. These coefficients, which can be obtained by fitting measured average forces in several conditions, were used for the formulation of three theoretical cutting forces for turning. The cutting force mechanism was verified in this research and its results were compared with each of the experimental and theoretical forces. The deviation of force was incurred by a small amount in this model and the predicted force considering feed rate , nose radius , and radial depth shows a physical behavior in main force , normal force, and feeding force, respectively. Therefore, this modelling technique can be used to effectively predict three turning forces with different tool geometries considering cutting force coefficients.

Identification of Polynomial Cutting Coefficients for a Dual-Mechanism Ball-end Milling Force Model

Background: Calibration of cutting coefficients is the key content in modeling a mechanistic cutting force model. Generally, in modeling cutting force for ball end milling, the tangent, radial and binormal cutting force coefficients are each considered as a polynomial, respectively. This fact is due to the dependency between the cutting force coefficients and the cutting edge inclination angle which is variable in ball-end mills. Objective: This paper presents an approach to determine the polynomial cutting force coefficients. Methods: In this approach, the cutting force coefficients are expressed as explicit linear equations about the average slotting forces. After analysis of the least square regression method which is utilized in the cutting coefficients evaluation, the principle of cutting parameters choice in calibration experiment and the relationship between the order of polynomial and the number of experiments are presented. Besides, a lot of patents on identification of polynomial cutting coefficients for milling force model were studied. Results: Finally, a series of semi-slotting verification cutting tests were arranged, the measured force agrees well with the predicted force, which demonstrates the effectiveness of this approach. Conclusion: Based on the calibration method proposed in this paper, the cutting coefficients can be determined through (m+2) slotting experiments for m-degree shearing coefficients polynomial theoretically.

Effect of Progressive Tool Wear on the Evolution of the Dynamic Stability Limits in High-Speed Micromilling of Ti-6Al-4V

Abstract Micromilling can fabricate complex features in a wide range of engineering materials with an excellent finish but the limited flexural stiffness of the micro-end mill can result in catastrophic tool failure. This issue can be overcome by using high rotational speeds. Note that the combination of high rotational speeds and low flexural stiffness can induce process instability which is aggravated by the accelerated wear of the micro-tools at high speeds, specifically, for Ti-alloys. The effect of progressive tool wear on the stability has been investigated in micromilling of Ti-6Al-4V. For incorporating tool wear, the cutting force coefficients are modeled as a function of initial and instantaneous cutting edge radius (CER) and feed per tooth. The initial CER of the micro-tool is considered due to the inherent variability in the tool grinding process. A significant increase (85–114%) in the instantaneous CER is observed with an increase in the length of cut. A 2DOF time-domain model based on semi-discretization method has been used to characterize the evolution of stability limits with an increase in the length of cut. The progressive tool wear affects the stability limits along with the initial CER and the feed per tooth. At higher speeds (90,000–110,000 rpm), the effect of progressive tool wear is pronounced and the stability limits reduce by ∼30% in that range.

Identification of Cutting Force Coefficients in Different Cutting Edges of Ball-End Milling Cutter

Identification of Cutting Force Coefficients in Different Cutting Edges of Ball-End Milling Cutter

Extraction of surface curvatures from tool path data and prediction of cutting forces in the finish milling of sculptured surfaces

To achieve higher accuracy in the prediction of cutting forces in finish milling process of sculptured parts, the curvatures of in-process workpiece surface are necessary to be taken into consideration in the calculation of cutter-workpiece engagement boundaries. These curvatures, however, are not readily available in tool path data, as the main existing source of geometrical information of the process. In this paper, first, a new straightforward algorithm is proposed to extract the principal curvatures and principal directions of the in-process workpiece surface from ball-end finish milling tool path data. These quantities, then, are employed to calculate the boundaries of engagement between the tool and workpiece geometries. In the next step, the cutting forces acting on a helical ball-end tool are formulated utilizing mechanistic approach and with the inclusion of radial run-out effect. By minimizing the square error between the predicted and experimentally measured cutting forces, the cutting force coefficients and radial run-out parameters are identified. Finally, the validity of the proposed force model is demonstrated by comparing the simulated forces with experimental measurements. The performed simulations show that the model can well capture the variation of milling forces along curved tool paths resulting from the variation of surface curvatures. Furthermore, it is shown that depending on the machining tolerance used in the tool path generation step, saw-tooth-like fluctuations may appear in the time history of milling forces originating from the approximation of curved paths by single steps (straight lines). All of the geometrical input parameters of the proposed force model are extracted from tool path data and hence it is quite flexible to be integrated into process modeling/optimization systems.

Influence of cutting parameters on force coefficients and stability in plunge milling

Fixed dynamometer is often used to collect cutting force data in plunge milling. The cutting force test signal is distorted because of the dynamic characteristics of the test system consisting of the workpiece and the dynamometer. Then the accuracy of cutting force coefficients based on experimental data analysis is affected. The inverse filtering technique is utilized to compensate for the measurement signal dynamically and verified by experiments. The influence of cutting parameters on cutting force coefficients is investigated by means of the nonlinear instantaneous milling force method. The results demonstrate that the cutting force coefficient has a nonlinear relationship with the feed per tooth and the spindle speed. An improved semi-discrete method is proposed for the machining feature of the plunge milling and utilized to predict the stability of the plunge milling. The measurement signal is analyzed by using the nonlinear method such as phase plane and Poincare section; the accuracy of the prediction of the stability lobe diagram is verified. The results demonstrate that the stability boundary of instantaneous cutting force coefficients is higher than that of the average cutting force coefficients. The research results provide theoretical guidance for the optimization of cutting parameters in the actual machining process.

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.

A 3-D instantaneous cutting force prediction model of indexable disc milling cutter for manufacturing blisk-tunnels considering run-out

This paper proposed a three-dimensional (3-D) instantaneous cutting force (ICF) forecasting model for an indexable disc milling cutter considering cutter run-out. For milling blisk-tunnels, the indexable disc milling cutter must rotates about Y-axis at a certain angle; therefore, the cutting force in Z-direction is related to tangential, radial, and axial components, which have a large influence on processing precision and stability. Herein, a systematic method is presented to effectively determine the 3-D instantaneous cutting force coefficients (ICFCS) through only several calibration experiments. It was found that the distribution laws of the ICFCS match exponent functions of instantaneous uncut chip thickness (IUCT). Experiments were carried out to validate the 3-D cutting force model, it turns out that the presented model can successfully and precisely predict the 3-D ICF of an indexable disc milling cutter under a variety of processing parameters.

Plane surface milling force prediction with fillet end milling cutter under pre-determined inclination angle

Fillet end milling is widely used in mould, aerospace, shipping manufacture and other fields. As one of the important parameter in milling machining, milling force is related to machining efficiency and quality, as well as tool wear, but it is difficult to predict. Aiming at fillet end milling under a pre-determined inclination angle, considering cutter run-out, this paper presents a cutting force coefficients identification model related to chip thickness and axial position angle, and then achieve milling force prediction. A parametric relationship among feed direction, cutter axis and to-be-machined surface are established, and then, the analytic expression of previous swept surface, to-be-machined surface and cutter envelope surface is derived. Boundary curves of cutter workpiece engagement (CWE) are established based on spatial surface intersection analytically. The criterion of the cutter edge element involved in cutting is proposed. Judging element along the cutter edge one by one, whereafter the algorithm of in-cut-cutting edge (ICCE) is proposed. Combining mechanical force model with chip thickness considering feed direction and cutter run-out, a milling force prediction model is established. Based on the method of undetermined coefficients, combining average instantaneous measured force, coefficients corresponding to axial position angle and chip thickness are solved. Further instantaneous peak measured force is used to obtain cutter run-out parameters. Simulation and experiments show that CWE agrees well with that of experiment and ICCE is consistent well with that of simulation. Milling force experiments of different machining parameters show the milling force coefficients and run-out parameters can be applied to fillet end milling under pre-determined inclination angle well.

Improved dynamic cutting force model with complex coefficients at orthogonal turning

Self-excited vibration (chatter) is determined by the relation between the vibrating system and the cutting process. In current theories, the dynamic cutting force model in a form suggested by Tlusty and Polacek in the 1950s is still used. However, this model oversimplifies the dynamic cutting process by trying to express all processes using a single cutting force coefficient. Measurement results presented in this article clearly show that such simplification of the cutting process is unacceptable. This work follows upon the original measurement method by Tlusty and Polacek using controlled tool vibration. The method was intended to research the cutting process dynamics. However, the original Tlusty and Polacek method ignored the impact of the length of the workpiece surface wave. The original method is innovatively developed by taking into account the impact of the chatter frequency. The new method allows to better understand the processes occurring during dynamic cutting. As opposed to the original method, current advanced measurement equipment allows for more precise examination of the cutting process in dependence on the chatter frequency. The article shows that results obtained by the new method can be utilized for modeling the cutting force with greater precision in order to better predict the cutting process stability.

A mechanistic prediction model of instantaneous cutting forces in drilling of carbon fiber-reinforced polymer

Drilling of carbon fiber-reinforced polymer (CFRP) is one indispensable machining operation to produce holes for final assembly of structural parts. Excessive cutting forces during drilling processes will lead to machining defects, such as fiber breakage, burrs, micro cracks, and plies delamination within laminate. This paper aims to simulate the variation of instantaneous cutting forces in CFRP drilling considering the influences of fiber orientation, machining parameters, and tool geometries. The cutting edges are split into infinitesimal elements; the instantaneous cutting forces are obtained by the accumulation of elemental forces exerted on all engaged elements. The overall cutting forces are the combination of forces contributed by the cutting lips and chisel edge using different machining mechanisms; oblique cutting and mechanistic modeling approaches are applied to the cutting lips while the principle of contact mechanics is adopted for the chisel edge. An integrated artificial neural network (ANN) and genetic algorithm (GA), ANN-GA is developed especially for predicting the specific cutting force coefficients, which are functions of the fiber orientation and can account for the variation of cutting forces. Meanwhile, the change of geometrical parameters along the cutting lips is analyzed, and the effects of fiber orientation and tool geometries are integrated in the model. Results showed the proposed model is able to predict the instantaneous cutting forces in CFPR drilling. Model predictions agree well with experimental data and are beneficial for optimizing the machining processes of CFRP composite laminates.

Overhang length effect during micro-milling of Inconel 718 superalloy

The accuracy of machining force relies on the accuracy of the cutting force coefficients which are determined by calibration experiments and are related to cutting tool–workpiece material couple. To this end, a mechanistic model was established to anticipate machining forces that occurred during micro-milling under different tool overhang lengths. This study assumed that the cutting force coefficients varied with the tool overhang length, and this assumption was proved by some micro-milling experiments. Force coefficients were computed by linearly fitting the experimental force data. In the current work, also wear on tool and burr formation were observed as functions of feed per tooth and overhang length. The overhang length of 15 and 20 mm significantly reduced the diameter of the micro-tool as compared to the overhang length of 10 mm. The obtained results showed that cutting forces and top burr width increased with the increasing overhang length. It was also found that the values of cutting and edge coefficients differed with the overhang length.

The identification of the cutting force coefficients for ball-end finish milling

The identification of the cutting force coefficients for ball-end is mostly studied by slotting or half slotting experiments with a large cutting depth. However, in the high-speed finish milling of hard-to-cut materials, such as titanium alloy and high temperature alloy, a small cutting depth is generally adopted in order to ensure machining quality, and its axial depth is less than 0.5 mm. During the cutting process, the single tooth cutting state is always maintained and the cutter-tip point is not involved in cutting. Therefore, the cutting force coefficients identified by slotting or half slotting experiments may not be accurate in the finish milling. Accordingly, this paper proposes a method to identify the force coefficients of ball-end based on the single tooth average cutting force. In order to avoid the cutter-tip point being involved in cutting, oblique cutting experiments are used in this paper, and the cutter engagement area is obtained when the cutter is inclined. Based on the instantaneous cutting force model of ball-end, an identification model of single tooth average force coefficients is established. Compared with the average force coefficients model of the traditional whole cycle, the root mean square error of the established model in this paper is relatively small. Especially for the high-speed cutting, the error is less than 15% of the traditional method.

Influence of supercritical CO2 cooling on tool wear and cutting forces in the milling of Ti-6Al-4V

Ti-6Al-4V is known as a difficult-to-machine alloy due to its low thermal conductivity which limits the material’s machinability causing rapid tool wear. Supercritical CO2 is an environmentally friendly alternative cooling technique that can improve the machinability of Ti-6Al-4V enabling higher productivity. This study investigates the variation in tool life and cutting force coefficients when milling Ti-6Al-4V with scCO2, scCO2 combined with minimum quantity lubrication and flood coolant. Results from cutting trials carried out at 60 m/min have shown that when the chip load is controlled, substantial improvement in tool life can be obtained with scCO2+MQL compared to flood coolant with no significant change in cutting force coefficients. However, it has been found that the capabilities of scCO2 are limited outside the practical speed and feed range resulting in no additional benefit in tool life and sharp increase in cutting force coefficients due to higher thermal gradient and excessive tool wear.

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.