Experimental studies of cutting force variation in face milling

The purpose of this paper is to present a developed cutting force model for multi-toothed cutting processes, including a complete set of parameters influencing the cutting force variation that has been shown to occur in face milling, and to analyse to what extent these parameters influence the total cutting force variation for a selected tool geometry. The scope is to model and analyse the cutting forces for each individual tooth on the tool, to be able to draw conclusions about how the cutting action for an individual tooth is affected by its neighbours.A previously developed cutting force model for multi-toothed cutting processes is supplemented with three new parameters; eccentricity of the spindle, continuous cutting edge deterioration and load inflicted tool deflection influencing the cutting force variation. A previously developed milling force sensor is used to experimentally analyse the cutting force variation, and to give input to the cutting force simulation performed with the developed cutting force model.The experimental results from the case studied in this paper show that there are mainly three factors influencing the cutting force variation for a tool with new inserts. Radial and axial cutting edge position causes approximately 50% of the force variation for the case studied in this paper. Approximately 40% arises from eccentricity and the remaining 10% is the result of spindle deflection during machining. The experimental results presented in this paper show a new type of cutting force diagrams where the force variation for each individual tooth when two cutting edges are engaged in the workpiece at the same time. The wear studies performed shows a redistribution of the individual main cutting forces dependent on the wear propagation for each tooth.     

Accurate 3-D cutting force prediction using cutting condition independent coefficients in end milling

The instantaneous uncut chip thickness and specific cutting forces have a significant effect on predictions of cutting force. This paper presents a systematic method for determining the coefficients in a three-dimensional mechanistic cutting force model—the cutting force coefficients (two specific cutting forces, chip flow angle) and runout parameters. Some existing models have taken the approach that the cutting force coefficients vary as a function of cutting conditions or cutter rotation angle. This paper, however, considers that the coefficients are affected only by the uncut chip thickness. The instantaneous uncut chip thickness is estimated by following the movement of the position of the center of a cutter. To consider the size effect, the present method derives the relationship between the re-scaled uncut chip thickness and the normal specific cutting force, K_n with respect to the cutter rotation angle, while the other two coefficients—frictional specific cutting force, K_f and chip flow angle, θ_c—remain constant. Subsequently, all the coefficients can be obtained, irrespective of cutting conditions. The proposed method was verified experimentally for a wide range of cutting conditions, and gave significantly better predictions of cutting forces.     

Cutting force estimation in sculptured surface milling

Cutting force milling models developed up to now are mostly used for planar milling using end-mills. Only a reduced number of models applying ball-end mills have been developed. Furthermore these models usually only consider horizontal surface machining, even though the main application of ball-end mills is sculptured surface machining. This article proposes a model that is able to estimate the cutting forces in inclined surfaces machined both up-milling and down-milling. For this purpose a semi-mechanistic model has been developed that calculates the cutting forces based on a set of coefficients which depend on the material, the tool, the cutting conditions, the machining direction and the slope of the surface.A coordinate transformation has been included in order to consider the slope milling case with different cutting directions.The model has been tested on two materials, an aluminum alloy Al7075-T6 and a 52 HRC tool steel AISI H13. Validation tests have been carried out on inclined planes using different slopes and different machining directions.The results provide errors below 10% in most of the cases and both the value and shape of the predicted forces adjust the measured cutting force.     

Analytical predictions and experimental validation of cutting force ratio, chip thickness, and chip back-flow angle in restricted contact machining using the universal slip-line model

This paper presents analytical predictions and experimental validation of a recently developed universal slip-line model for machining with restricted contact cut-away tools. Three important machining parameters, i.e. the cutting force ratio, chip thickness, and chip back-flow angle, are predicted on the basis of: (1) the universal slip-line model; (2) a maximum value principle for determining the state of stresses in the plastic region in restricted contact machining; (3) Dewhurst and Collins’ matrix technique for numerically solving slip-line problems; and (4) Powell’s algorithm for non-linear optimizations. All predictions are based on purely theoretical calculations with no experimental/empirical data as input. The extensive comparisons between theory and experiments show a reasonable agreement. Major new research findings from this study include: (1) the applicable ranges of an extreme friction slip-line model and of Johnson’s and Usui and Hoshi’s slip-line models; and (2) the general rule of the variation of tool–chip friction conditions. Tool–chip contact in machining with restricted contact cut-away tools is categorized into three broad cases. A theoretical method is also presented in the paper to distinguish different tool–chip contact cases in practical machining situations.     

铣削力建模与计算机仿真

本文综合分析了切削过程中刀具几何参数对端铣铣削力的影响，对铣削力模型进行了修正，建立了适合端铣铣削力计算机仿真的铣削力模型。并对仿真结果与实际测试曲线进行了比较。     

Indirect cutting force measurement in multi-axis simultaneous NC milling processes

There have been many research works for the indirect cutting force measurement in machining process, which deal with the case of one-axis cutting process. In multi-axis cutting process, the main difficulties to estimate the cutting forces occur when the feed direction is reversed. This paper presents the indirect cutting force measurement method in contour NC milling processes by using current signals of servo motors. A Kalman filter disturbance observer and an artificial neural network (ANN) system are suggested. A Kalman filter disturbance observer is implemented by using the dynamic model of the feed drive servo system, and each of the external load torques to the x and y-axis servo motors of a horizontal machining center is estimated. An ANN system is also implemented with a training set of experimental cutting data to measure cutting force indirectly. The input variables of the ANN system are the motor currents and the feedrates of x and y-axis servo motors, and output variable is the cutting force of each axis. A series of experimental works on the circular interpolated contour milling process with the path of a complete circle has been performed. It is concluded that by comparing the Kalman filter disturbance observer and the ANN system with a dynamometer measuring cutting force directly, the ANN system has a better performance.     

Feedrate scheduling for indexable end milling process based on an improved cutting force model

In CNC machining, an optimal process plan is needed for higher productivity and machining performance. This paper proposes a mechanistic cutting force model to perform feedrate scheduling that is useful in process planning for indexable end milling. Indexable end mills, which consist of inserts and a cutter body, have been widely used in the roughing of parts in the mold industry. The geometry and distribution of inserts compose a discontinuous cutting edge on the cutter body, and tool geometry of indexable end mill varies with axial position due to the geometry and distribution of inserts. Thus, an algorithm that calculates tool geometry data at an arbitrary axial position was developed. The developed cutting force model uses cutting-condition-independent cutting force coefficients and considers run out, cutter deflection, geometry variation and size effect for accurate cutting force prediction. Through feedrate scheduling, NC code is optimized to regulate cutting forces at given reference force. Experiments with general NC codes show the effectiveness of feedrate scheduling in process planning.     

The estimation of cutting forces and specific force coefficients during finishing ball end milling of inclined surfaces

The majority of cutting force models applied for the ball end milling process includes only the influence of cutting parameters (e.g. feedrate, depth of cut, cutting speed) and estimates forces on the basis of coefficients calibrated during slot milling. Furthermore, the radial run out phenomenon is predominantly not considered in these models. However this approach can induce excessive force estimation errors, especially during finishing ball end milling of sculptured surfaces. In addition, most of cutting force models is formulated for the ball end milling process with axial depths of cut exceeding 0.5 mm and thus, they are not oriented directly to the finishing processes. Therefore, this paper proposes an accurate cutting force model applied for the finishing ball end milling, which includes also the influence of surface inclination and cutter's run out. As part of this work the new method of specific force coefficients calibration has been also developed. This approach is based on the calibration during ball end milling with various surface inclinations and the application of instantaneous force signals as an input data. Furthermore, the analysis of specific force coefficients in function of feed per tooth, cutting speed and surface inclination angle was also presented. In order to determine geometrical elements of cut precisely, the radial run out was considered in equations applied for the calculation of sectional area of cut and active length of cutting edge. Research revealed that cutter's run out and surface inclination angle have significant influence on the cutting forces, both in the quantitative and qualitative aspect. The formulated model enables cutting force estimation in the wide range of cutting parameters, assuring relative error's values below 16%. Furthermore, the consideration of cutter's radial run out phenomenon in the developed model enables the reduction of model's relative error by the 7% in relation to the model excluding radial run out.     

Prediction of cutting force distribution and its influence on dimensional accuracy in peripheral milling

Cutting force has a significant influence on the dimensional accuracy due to tool and workpiece deflection in peripheral milling. In this paper, the authors present an improved theoretical dynamic cutting force model for peripheral milling, which includes the size effect of undeformed chip thickness, the influence of the effective rake angle and the chip flow angle. The cutting force coefficients in the model were calibrated with the cutting forces measured by Yucesan [18] in tests on a titanium alloy, and the model was proved to be more accurate than the previous models. Based on the model, a few case studies are presented to investigate the cutting force distribution in cutting tests of the titanium alloy. The simulation results indicate that the cutting force distribution in the cut-in process has a significant influence on the dimensional accuracy of the finished part. Suggestions about how to select the cutter and the cutting parameters were given to get an ideal cutting force distribution, so as to reduce the machining error, meanwhile keeping a high productivity.     

Cutting force prediction of sculptured surface ball-end milling using Z-map

The cutting force in ball-end milling of sculptured surfaces is calculated. In sculptured surface machining, a simple method to determine the cutter contact area is necessary since cutting geometry is complicated and cutter contact area changes continuously. In this study, the cutter contact area is determined from the Z-map of the surface geometry and current cutter location. To determine cutting edge element engagement, the cutting edge elements are projected onto the cutter plane normal to the Z-axis and compared with the cutter contact area obtained from the Z-map. Cutting forces acting on the engaged cutting edge elements are calculated using an empirical method. Empirical cutting mechanism parameters are set as functions of cutting edge element position angle in order to consider the cutting action variation along the cutting edge. The relationship between undeformed chip geometry and the cutter feed inclination angle is also analyzed. The resultant cutting force is calculated by numerical integration of cutting forces acting on the engaged cutting edge elements. A series of experiments were performed to verify the proposed cutting force estimation model. It is shown that the proposed method predicts cutting force effectively for any geometry including sculptured surfaces with cusp marks and a hole.     

In-process prediction of cutting depths in end milling

In geometric adaptive control systems for the end milling process, the surface error is usually predicted from the cutting force owing to the close relationship between them, and the easiness of its measurement. Knowledge of the cutting depth improves the effectiveness of this approach, since different cutting depths result in different surface errors even if the measured cutting forces are the same. This work suggests an algorithm for estimating the cutting depth based on the pattern of cutting force. The cutting force pattern, rather than its magnitude, better reflects the change of the cutting depth, because while the magnitude is influenced by several cutting parameters, the pattern is affected mainly by the cutting depth. The proposed algorithm can be applied to extensive cutting circumstances, such as presence of tool wear, change of work material hardness, etc.     

Simplified and efficient calibration of a mechanistic cutting force model for ball-end milling

Accurate evaluation of the empirical coefficients of a mechanistic cutting force model is critical to the reliability of the predicted cutting forces. This paper presents a simplified and efficient method to determine the cutting force coefficients of a ball-end milling model. The unique feature of this new method is that only a single half-slot cut is to be performed to calibrate the empirical force coefficients that are valid over a wide range of cutting conditions. The instantaneous cutting forces are used with the established helical cutting edge profile on the ball-end mill. The half-slot calibration cut enables successive determination of the lumped discrete values of the varying cutting mechanics parameters along the cutter axis whereas the size effect parameters are determined from the known variation of undeformed chip thickness with cutter rotation. The effectiveness of the present method in determining the cutting force coefficients has been demonstrated experimentally with a series of verification test cuts.     

TWEM, a method based on cutting forces—monitoring tool wear in face milling

One of the most important objectives in manufacturing is the intelligent machining system. To come to such a solution, the tool wear has to be determined on-line during the cutting process on unmanned machining systems. This contribution discusses the results experimentally obtained in face milling with a new rotating dynamometer. The paper introduces the concept of tool wear indicators which can be determined by simple analysis of the feature parameters of cutting force signals. The disturbance of the cutting force signals obtained by using the rotating dynamometer can be solved by applying tool wear indicators such as Normalized Cutting Force indicator (NCF) and Torque-Force Distance indicator (TFD). The Method for Tool Wear Estimation—TWEM is proposed.     

One-step-ahead prediction of flank wear using cutting force

Tool wear prediction plays an important role in the tip geometry compensation during precision machining. The purpose of this study is to develop a reliable method to predict flank wear during a turning process. The force ratio and increment values are applied to predict one-step-ahead flank wear. The results of this paper show that using force ratios, flank wear can be predicted to within 8 and 11.9%, and also using force increment, flank wear can be predicted to within 10.3% of the actual wear for various turning conditions.     

Prediction of chatter stability for multiple-delay milling system under different cutting force models

This paper systematically studies the stability lobe prediction methods for the milling process with multiple delays, which are often induced by cutter runout. Emphasis is put on how to effectively incorporate the instantaneous cutting force model into the prediction procedure of stability lobes. Two original methods are proposed based on the vibration time history of the cutter motion, which is numerically obtained by time domain simulation. A comparison study is made with the existing method taken from the literature and experimental verifications are also carried out to validate both methods.In this study, two different instantaneous cutting force models together with the constant cutting force model are considered in the calculation of the cutting force coefficients during the simulation. The effects of different cutting force models on stability lobes, their consistencies and limitations are highlighted. At the same time, cutting force coefficients calibrated from three tests with different feeds per tooth are also considered in order to show the influences of cutting force coefficient's accuracy. It is found that both types of cutting force models and the calibration accuracy of the cutting force coefficients have great influences on the reliability of the stability lobes.     

Determination of the chip geometry, cutting force and roughness in free form surfaces finishing milling, with ball end tools

CAD/CAM systems offer various possibilities for finishing milling of parts such as dies and moulds, turbine blades and other high quality components, but most of them do not take into account the surface topomorphy expected, which is significantly affected, among others, by the milling kinematics and the contact conditions between the tool and the workpiece. In order to predict the workpiece roughness in multiaxis finishing milling with ball end tools, the computer supported milling simulation algorithm ‘ ’ was developed. By means of this algorithm, considering the individual movements of the cutting tool and of the workpiece due to the milling kinematics, the undeformed chip geometry, the cutting force components, the tool deflections and the final surface topomorphy expected are determined. Numerous investigations concerning the parameters mentioned above, with various workpiece materials have been carried out in order to determine the correlation of the experimental results with the corresponding calculated ones with the aid of the algorithm. Moreover the algorithm validity was extensively evaluated in milling of free form surfaces of large hydroturbine blades. The convergence between the experimental and the related calculated surface topomorphies by means of the computer program was found out to be satisfactory. Thus, the prediction of appropriate cutting conditions and milling kinematics to fulfill surface topomorphy requirements was enabled.     

A chatter free calibration method for determining cutter runout and cutting force coefficients in ball-end milling

The accuracy of cutting force coefficients plays an important role in predicting reliable cutting force, stability lobes as well as surface location error in ball-end milling. In order to avoid chatter risk of the traditional calibration test with an entire-ball-immersed cutting depth, a cylindrical surface milling method is proposed to calibrate the cutting force coefficients with the characteristics of low cutting depth and varying lead angle. A dual-cubic-polynomial function is also presented to describe the non-uniform cutting force coefficients of the ball part cutting edge and the nonlinear chip size effect on cutting force. The variation of the maximum chip thickness versus the lead angle is established with the consideration of cutter runout. According to the dependence of chip thickness on lead angle, a runout identification method is introduced by seeking the critical lead angle at which one of the cutter flutes is just thoroughly out of cut. Then, a lumped equivalent method is adopted for the low cutting depth condition so that the dual-cubic-polynomial model can be calibrated for the chip size effect and the cutting force coefficients respectively. The accuracy of the proposed calibration method has been validated experimentally with a series of milling tests. The stability examinations indicate that the proposed method has an evident chatter-free advantage, compared with that of varying cutting depth method.     

Prediction of cutting forces in milling of circular corner profiles

This paper proposes an approach to predict the cutting forces in peripheral milling of circular corner profiles in which varying radial depth of cut is encountered. The geometric relationship between an end mill and the corner profile is investigated and a mathematical model is presented to describe the different phases of the cutter/workpiece contact. The milling process for circular corner is discretized into a series of steady-state cutting processes, each with different radial depth of cut determined by the instantaneous position of the end mill relative to the workpiece. A time domain analytical model of cutting forces for the steady-state machining conditions is introduced to each segmented process for the cutting force prediction. The predicted cutting forces can be calculated in terms of tool/workpiece geometry, cutting parameters and workpirece material property, as well as the relative position of the tool to workpiece. Experiments are conducted and the measured forces are compared to the predictions for the verification of the proposed method.     

Modelling the cutting edge radius size effect for force prediction in micro milling

This paper presents a theoretical model for cutting force prediction in micro milling, taking into account the cutting edge radius size effect, the tool run out and the deviation of the chip flow angle from the inclination angle. A parameterization according to the uncut chip thickness to cutting edge radius ratio is used for the parameters involved in the force calculation. The model was verified by means of cutting force measurements in micro milling. The results show good agreement between predicted and measured forces. It is also demonstrated that the use of the Stabler's rule is a reasonable approximation and that micro end mill run out is effectively compensated by the deflections induced by the cutting forces.     

An in-depth analysis of the synchronization between the measured and predicted cutting forces for developing instantaneous milling force model

This paper proposes an analytical approach to synchronize the measured and predicted cutting forces for calibrating instantaneous cutting force coefficients that vary with the instantaneous uncut chip thickness in general end milling. Essential issues such as the synchronization criterion, phase determination of measured cutting forces, specification of calibration experiments and related cutting parameters are highlighted both theoretically and numerically to ensure the calibration accuracy. A closed-form criterion is established to select cutting parameters ensuring the single tooth engagement. Numerical cutting simulations and experimental test results are compared to validate the proposed approach.