Specific Cutting Force Coefficients Research Articles

Physical model-based tool wear and breakage monitoring in milling process

Tool wear and breakage is one of the biggest obstacles for developing the unattended CNC machining. Especially when cutting the difficult-to-machining materials, the tool wear will be more rapid and the tool breakage becomes more frequent, which makes an effective tool wear and breakage monitoring very urgent. In the paper, a physical model-based tool wear and breakage monitoring method is proposed. Firstly, a physical model of milling force with the influence of cutter runout and tool wear is established. The spindle box vibration and cutting torque of spindle drive system induced by milling force have been clarified theoretically. Then, through the measurements of milling force, spindle box vibration and driving current, a tool wear monitoring method by extracting the comprehensive feature from the seven-channel specific cutting force coefficients (SCFCs) has been presented. In the method, a multi-parameter decoupling identification procedure for the cutter runout, tooth wear loss and respective SCFCs has been clarified. The force homogenization effect of multi-tooth with tool wear is found. Moreover, an efficient tool breakage monitoring method is further put forward, which incorporates the amplitude ratios of multi-channel data to form an indicator for judging the occurrence of tool damage. The generation mechanism of the sudden distortion on signal waveform resulting from tool breakage is also explained. Finally, long-time milling experiments with multiple groups of machining parameters have been carried out on the general and heavy-cutting machine tools to verify the validity of the proposed method. The verification results indicate that the tool wear and breakage monitoring method can well estimate the cutting status of cutter. The study can provide a useful research basis for the potential industrial application of tool wear and breakage monitoring technology.

Prediction of stability boundaries in milling by considering the variation of dynamic parameters and specific cutting force coefficients

In the present work, stability lobe diagrams for high speed milling are generated by the application of Operational Modal Analysis (OMA) technique during machining operation at different spindle speeds. The vibration signals are acquired by laser vibrometer during milling operation. To make the vibration signals feasible for OMA, a new approach is proposed to excite the milling cutter by white noise excitation. Specific cutting force coefficients are also estimated at different spindle speeds. The effect of variation of spindle speed on the dynamic parameters and specific cutting force coefficients is considered in the present work. With the application of the estimated specific cutting force coefficients and dynamic parameters, stability lobe diagrams are drawn at different spindle speeds. A comparative study of stability lobe diagrams, generated at different spindle speeds is also performed and the accuracy of these diagrams is presented.

Cutting force model for power skiving of internal gear

Abstract In recent years, power skiving has been rapidly promoted as a highly efficient machining method for internal gears. Many researches have been performed to improve the machining accuracy and tool life. In the present study, a simulation model for the cutting area and cutting forces was developed with the aim of improving the machining accuracy and tool life in the power skiving process. During the power skiving of internal gears, the cutting direction, chip thickness, and effective rake angle have a complex relationship with the relative motion of the tool and workpiece. First, the cutting area and uncut chip thickness during the skiving process were analyzed by performing a simulation of the interference of a discretized cutting tool edge and workpiece surface. Then, a two-dimensional oblique cutting model was applied to cutting edge elements. The cutting forces for the edge elements were expressed using the cutting direction, uncut chip thickness, effective rake angle, and specific cutting force coefficients, which represent the characteristics of the cutting forces of the workpiece material. A method to identify the cutting force coefficients according to the effects of the change in the effective rake angle was proposed on the basis of time-averaged cutting forces measured via cutting tests with power skiving tool which has multiple cutting edges. An optimization method was used to minimize the error of the measured and simulated cutting forces when the radial depth of cut and the feed rate were varied. Finally cutting tests were performed in which the radial depth of cut was changed, and the simulated forces were compared with the measured values. The analytical cutting forces obtained using the proposed method exhibited good agreement with the experimental results with an error of 15 %.

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.

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.

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.

General Modeling and Calibration Method for Cutting Force Prediction With Flat-End Cutter

A general calibration method of cutter runout and specific cutting force coefficients (SCFCs) for flat-end cutter is proposed in this paper, and a high accuracy of cutting force prediction during peripheral milling is established. In the paper, the cutter runout, the bottom-edge cutting effect, and the actual feedrate with limitation during large tool path curvature are concerned comprehensively. First, based on the trochoid motion, a tooth trajectory model is built up and an analytical instantaneous uncut chip thickness (IUCT) model is put forward for describing the cutter/workpiece engagement (CWE). Second, a noncontact identification method for cutter runout including offset and inclination is given, which constructs an objective function by using the cutting radius relative variation between adjacent teeth, and identifies through a numerical optimization method. Thirdly, with consideration of bottom-edge cutting effect, the paper details a three-step calibration procedure for SCFCs based on an enhanced thin-plate milling experiment. Finally, a series of milling tests are performed to verify the effectiveness of the proposed method. The results show that the approach is suitable for both constant and nonconstant pitch cutter, and the generalization has been proved. Moreover, the paper points out that the cutter runout has a strong spindle speed-dependent effect, the milling force in cutter axis direction exists a switch-direction phenomenon, and the actual feedrate will be limited by large tool path curvature. All of them should be considered for obtaining an accurate milling force prediction.

Accurate and fast measurement of specific cutting force coefficients changing with spindle speed

Prediction of cutting forces is essential to simulate dynamic effects of the milling process, and optimize process parameters to reduce detrimental vibrations. Cutting forces are conventionally modeled by assuming a dependence on uncut chip thickness using dedicated coefficients, to be experimentally identified. These coefficients are proven to vary significantly with spindle speed, causing the need of a time-consuming experimental phase to achieve an accurate simulation of cutting forces in a wide range of spindle speeds. This paper presents a method to efficiently identify the specific cutting force coefficients in the entire speed range by a single milling test, in which spindle speed is ramped-up. During the test, the forces signals are acquired and then processed to identify the speed-varying cutting force coefficients. The method was applied to the identification of Aluminum 6082-T4 coefficients in a wide range of speeds and results were validated through traditional approach, proving the efficiency and effectiveness of the proposed technique. In addition, an application of the obtained coefficients to chatter prediction is presented and validated through chatter tests.

Analysis of cutting force coefficients in high-speed ball end milling at varying rotational speeds

ABSTRACTIn high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool failure, tool deflection, machine tool chatter, vibration, etc. Thus, an accurate prediction of cutting forces before actual machining is essential for a good insight into the process to produce good quality machined parts. In this article, an attempt has been made to determine specific cutting force coefficients in ball end milling based on a linear mechanistic model at a higher range of rotational speeds. The force coefficients have been determined based on average cutting force. Cutting force in one revolution of the cutter was recorded to avoid the cutter run-out condition (radial). Milling experiments have been conducted on aluminum alloy of grade Al2014-T6 at different spindle speeds and feeds. Thus, the dependence of specific cutting force coefficients on cutting speeds has been studied and analyzed. It is found that specific cutting force coefficients change with change in rotational speed while keeping other cutting parameters unchanged. Hence, simulated cutting forces at higher range of rotational speed might have considerable errors if specific cutting force coefficients evaluated at lower rotational speed are used. The specific cutting force coefficients obtained analytically have been validated through experiments.

Analysis of rotational speed variations on cutting force coefficients in high-speed ball end milling

In high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool deflection, tool failure, machine tool chatter and vibration, etc. Thus, an accurate prediction of cutting forces prior to actual machining is very much essential for a good insight into the process to produce good quality machined parts. In ball end milling, the cutting forces are proportional to the chip cross-sectional area and constant of proportionalities are referred as cutting force coefficients and they depend on many factors, like cutter geometry, cutting conditions, tool material and workpiece material properties. However, determining these specific cutting force coefficients in ball end milling process is not at all straightforward; rather it is fairly complex. Machining with higher cutting speed affects the chip formation mechanisms and finally causes a significant change in the cutting force coefficients. In the present study, the effect of rotational speeds has been investigated on the cutting force coefficients. A series of experiments have been performed at higher rotational speed. It has been found that the cutting force coefficients are influenced by rotational speed significantly. The results are also verified using experiments.

Determining cutting force coefficients from instantaneous cutting forces in ball end milling

The precise prediction of cutting forces helps in improving the machining performances. This involves the modelling of cutting force components in tangential, radial and axial directions and determination of respective specific cutting force coefficients. In the present work, an improved method of identification of specific cutting force coefficient is proposed for ball end milling cutter using semi-mechanistic force model. The cutter is discretised into a finite number of axial discs along the axis of the cutter. Using the geometry of ball end milling cutter, true uncut chip thickness is modelled based on the trochoidal trajectory of a cutting edge element. Specific cutting force coefficients have been determined through inverse method. Also, a fourth order polynomial curve fitting method has been employed to establish a mathematical relationship between the said coefficients and axial depth of cuts. Several experiments have been carried out at different feed rate and axial depth of cut to determine the specific cutting force coefficients based on the proposed identification method. Validation results show good agreement between predicted and experimental results. Compared to conventional identification model, the specific force coefficient identification process discussed in the present paper is fast, convenient and accurate.

An accurate prediction method of cutting forces in 5-axis flank milling of sculptured surface

The instantaneous uncut chip thickness and entry/exit angle of cutter/workpiece engagement continuously vary with tool path and workpiece geometry in 5-axis flank milling of sculptured surface, which results in the obvious time-varying characteristic for consecutive cutting forces. An accurate prediction method for cutting force in 5-axis flank milling of sculptured surface is proposed in this paper. Comprehensively considering curved tool path and actual tool motion process with cutter runout (offset and inclination) effects, an accurate representation model for instantaneous uncut chip thickness during cutter/workpiece engaging in 5-axis flank milling is presented firstly, which can reach a higher accuracy and efficiency with the aid of linear iteration process than the methods published. Then, based on the thin plate milling experiments, an efficient calibration procedure for cutter runout parameters and specific cutting force coefficients is given and further verified in practice. Finally, a series of validation experiments are conducted under different cutting conditions, and the results reveal that there is a very good agreement between the experimental and simulation data both in shape and magnitude and prove the effectiveness and accuracy of the proposed method.

A new method for cutting force prediction in peripheral milling of complex curved surface

The instantaneous uncut chip thickness and entry/exit angle of tool/workpiece engagement vary with tool path, workpiece geometry and cutting parameters in peripheral milling of complex curved surface, leading to the strong time-varying characteristic for instantaneous cutting forces. A new method for cutting force prediction in peripheral milling of complex curved surface is proposed in this paper. Considering the tool path, cutter runout, tool type(constant/nonconstant pitch cutter) and tool actual motion, a representation model of instantaneous uncut chip thickness and entry/exit angle of tool/ workpiece engagement is established firstly, which can reach better accuracy than the traditional models. Then, an approach for identifying of cutter runout parameters and calibrating of specific cutting force coefficients is presented. Finally, peripheral milling experiments are carried out with two types of tool, and the results indicate that the predicted cutting forces are highly consistent with the experimental values in the aspect of variation tendency and amplitude.

Specific cutting force and cutting condition interaction modeling for round insert face milling operation

Face milling by round insert is currently one of the most common processes for roughing, semi-finishing, and finishing machining operations. Proper estimation and analysis of the round insert cutting forces play an important role in the process optimization. This paper presents a new method for identifying specific cutting force coefficients (SCFCs) for full immersion face milling with round inserts. At the first step, an inverse method is proposed to solve the mechanistic force model equations by non-dominated sorting genetic algorithm II (NSGA-II) which is one of the powerful multi-objective optimization methods. In addition, the artificial neural network (ANN) models are developed to predict the SCFCs in non-experimented conditions. Mean absolute percentage error values for the proposed ANN are between 1.7 and 10.1 % for training and testing which are satisfactory. In order to evaluate the efficiency of NSGA-II and ANN models, extensive experimental cutting force results are compared with those obtained with the proposed algorithm. The good accordance in the entire time of cutting edge engagement shows the validity of the developed methodology. Moreover, the interactions of cutting parameters, i.e., cutting speed, feed per tooth, and depth of cut (DOC) on variations of tangential and radial shearing coefficients (ktc, krc) of specific cutting force are thoroughly investigated. The results show that in addition to cutting conditions, the cutting edge geometry of round insert has a significant influence on ktc and krc variations.

Extracting Specific Cutting Force Coefficients in Micro Drilling with Tool Edge Radius Effects<sup> </sup>

This article introduces a methodology for extracting specific cutting force coefficients by performing micro drilling experiments with tool edge radius effect.Tool edge radius mainly affects the effective rake angle that varies according to undeformed chip thickness. Ploughing effect is also considered for undeformed chip thickness lower than the minimum chip thickness. In this work specific normal and frictional cutting coefficients for both ploughing and shearing are determined from mechanistic approach of fitting experimental specific thrust forces of the micro drilling process. The variations of these cutting coefficients with respect to cutting speedand feed are presented. Finally these coefficients have been applied to the mechanistic model to predict thrust force in micro drilling. The predicted thrust force values at different feed show good agreement with the experimental results.

Modelling of frictional chatter in metal cutting

A new model of cutting process is developed in order to simplify modelling and gain a further insight into the mechanics of frictional chatter. It is based on the well known Rayleigh oscillator generating self-excited oscillations and has been applied to the shaping/planning operation. The new approach which takes into account also the forces acting on the tool flank is compared with the one developed by Wiercigroch and Krivtsov [1]. The results obtained here are alike to a certain degree but some of them show some different trends. Nonlinear dynamic behaviour is examined by bifurcation diagrams with cutting velocity and specific cutting force coefficient as the bifurcation parameters. The effect of the the tool stiffness variation in the directions parallel and perpendicular to the workpiece has been investigated. Some practical results unveiling stabilizing effects of the friction force on the tool flank have been shown.

비절삭저항 상수 변화에 따른 절삭력 분석

ABSTRACT Considering the run-out effect and cutting force coefficients, the cutting force profile of half immersion end-milling was analyzed in detail. The effects of three specific cutting-force coefficients and three edge-force coefficientsare verified. Through a detailed investigation, it is proved that the radial cutting force coefficients and arethe major factors which increase the cutting forces Fx and Fy in end-milling. However, the axial cutting force coefficients have no influence on the force Fx and Fy changes in end-milling. Also, the analyzed end-milling force model shows good consistency with the actual measured force with regard to Fx and Fy. Thus, this model can be used for the prediction ofthe force history in end-milling with run-out,and it incurs a different force history with different start and exit immersion anglesas well as holding effects. Key Words : Force modelling(절삭력모델링), Immersion angle(물림각), Run-out(런아웃), Cutting force coefficient(절 삭력상수), Edge force coefficient(모서리절삭력상수)

Analytical modelling of slot milling exit burr size

A computational model was recently proposed by authors to approximate the tangential cutting force and consequently predict the thickness of the exit up milling side burr. To calculate the cutting force, the specific cutting force coefficient with respect to material properties was used. The model was sensitive to material yield strength and few cutting and tool geometrical parameters. However, the effects of cutting speed, tool coating, and tool rake angle on burr size were neglected. Other phenomena that could affect the burr size such as friction and abrasion were not taken into account either. Therefore, in the current work, a mechanistic force model is incorporated to propose a burr size prediction algorithm. The tangential and radial forces are calculated based on using specific cutting force coefficients in each direction. Furthermore, using the new approach, the burr size is predicated and the effects of a broad range of cutting parameters on burr size and friction angle are evaluated. Experimental values of burr size correlated well with prediction. It was found that the cutting speed has negligible effects on force and burr size. Lower friction angle was recorded when using larger feed per tooth. Consequently, thinner exit up milling side burr was obtained under high friction angle.

Chatter Stability Prediction in Milling Using Speed-varying Cutting Force Coefficients

Chatter prediction accuracy is significantly affected by reliability of data entry, i.e., cutting force coefficients and frequency response, both influenced by spindle speed. The evaluation of specific cutting force coefficients in High-Speed Milling (HSM) is challenging due to the frequency bandwidth of commercial force sensors. In this paper specific cutting coefficients have been identified at different spindle speeds: dynamometer signals have been compensated thanks to an improved technique based on Kalman filter estimator. The obtained speed-varying force coefficients have been used to improve the reliability of stability lobe diagrams for HSM, as proven by experimental tests.

An enhanced method for cutting force estimation in peripheral milling

A new model for cutting force estimation is presented in this paper. It is based on the specific cutting force coefficient, which is defined as a function of chip thickness. The distinguishing feature of the proposed cutting force model is the use of average chip thickness for cutting force calculation on each position of the cutting tool, in such a way that only one iteration is needed on every angular position of the tool. This model is based on the actual workpiece–tool interaction which provides information about the real position of the cutting edge. It provides an alternative to other studies in scientific literature commonly based on numerical integrations. With this model, it is possible to estimate the cutting forces not only under steady-state conditions but also under variable machining conditions of axial and radial depth of cut.