An examination of the fundamental mechanics of cutting force coefficients

In metal cutting, the cutting force is the key factor affecting the machined surface, and is also important in determining reasonable cutting parameters. The research and construction of cutting force prediction models therefore has a great practical value. The accuracy of cutting force prediction largely depends on the cutting force coefficients of the material. In the average cutting force model, cutting force coefficients are considered to be constant. This study makes use of experiments to investigate the cutting force coefficients in the average cutting force model, with a view to accurately identifying cutting force coefficients and verifying that they are related only to the tool–workpiece material couple and the tool geometrical parameters, and are not affected by milling parameters. To this end, the paper first examines the theory behind identifying cutting force coefficients in the average cutting force model. Based on this theory, a series of slot-milling experiments are performed to measure the milling forces, fixing spindle speeds and radial/axial depths of cutting, and linearly varying the feed per tooth. The tangential milling force coefficient and the radial milling force coefficient are then calculated by linearly fitting the experimental data. The obtained results show that altering the milling parameters does not change the milling force coefficients for the selected tool/workpiece material combination.     

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.     

Prediction of cutting force for self-propelled rotary tool using artificial neural networks

In this paper, a cutting force model for self-propelled rotary tool (SPRT) cutting force prediction using artificial neural networks (ANN) has been introduced. The basis of this approach is to train and test the ANN model with cutting force samples of SPRT, from which their neurons relations are gradually extracted out. Then, ANN cutting force model is achieved by obtaining all weights for each layer. The inputs to the model consist of cutting velocity V, feed rate f, depth of cut a_p and tool inclination angle λ, while the outputs are composed of thrust force F_x, radial force F_y and main cutting force F_z. It significantly reduces the complexity of modeling for SPRT cutting force, and employs non-structure operator parameters more conveniently. Considering the disadvantages of back propagation (BP) such as the convergence to local minima in the error space, developments have been achieved by applying hybrid of genetic algorithm (GA) and BP algorithm hence improve the performance of the ANN model. Validity and efficiency of the model were verified through a variety of SPRT cutting samples from our experiment tested in the cutting force model. The performance of the hybrid of GA–BP cutting force model is fairly satisfactory.     

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.     

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.     

Estimating cutting force from rotating and stationary feed motor currents on a milling machine

The feed motor current of a machine tool contains substantial information about the machining state. The current has been used as a measure of cutting forces in much previous research; however, this indirect measurement of the cutting forces was feasible only in a low frequency range up to about 60 Hz when milling machining. In this paper, the bandwidth of the current sensor was expanded to 130 Hz. The unusual current behavior between 45 and 60 Hz was examined and analyzed. It is necessary to estimate the cross-feed directional cutting force that is normal to a machined surface, since it directly affects the error of that surface. However, because of the undesired behavior of the stationary motor current, difficulties are encountered when using it to estimate the cutting state. An empirical approach was used to resolve this problem. As a result, we show that the current is related to the infinitesimal rotations of the motor, and it is this that causes the undesired behavior of the current. Subsequently, a relationship between the current of the stationary feed motor and the cutting force normal to machined surface was identified with an error of less than 20%.     

Modeling micro-end-milling operations. Part I: analytical cutting force model

A new analytical cutting force model is proposed for micro-end-milling operations. The model calculates the chip thickness by considering the trajectory of the tool tip while the tool rotates and moves ahead continuously. The proposed approach allows the calculation of the cutting forces to be done accurately in typical micro-end-milling operations with very aggressively selected feed per tooth to tool radius (f_t/r) ratio. The difference of the simulated cutting forces between the proposed and conventional models can be experienced when f_t/r is larger than 0.1. The estimated cutting force profile of the proposed model had good agreement with the experimental data.     

Bandsawing. Part I: cutting force model including effects of positional errors, tool dynamics and wear

This article presents a mechanical cutting force model for bandsawing. The model describes the variation in cutting force between individual teeth and relates it to initial positional errors, tool dynamics and edge wear. Bandsawing is a multi-tooth cutting process, and the terminology of the cutting action is discussed and compared with other cutting processes. It will also be shown that the setting pattern and the preset feed govern the cutting data.     

Real-time determination of cutting force coefficients without cutting geometry restriction

The determination of the cutting force coefficients is a critical point in the case of using the mechanistic cutting force model for predicting the forces during milling processes. The main reason is that the computations require a series of experiments with special geometrical conditions, and the validity of the results is limited. In this paper a cutting force predicting method, based on the mechanistic cutting force model will be introduced, together with an algorithm for determining the cutting force coefficients in the course of a single experiment without restrictions in regard to the cutting geometry. Besides the fact that the proposed method lifts the geometrical restrictions of the previously published solutions, it makes it possible to calculate the coefficients just when they are needed for force prediction right at the machining process, to avoid the problem of the limited validity of the coefficients. In this case the real-time measuring of the cutting forces is needed, while the forthcoming forces can be predicted with an appropriate look-forward algorithm, which is also presented.     

Estimation of cutting forces in micromilling through the determination of specific cutting pressures

In this paper a new model for the estimation of cutting forces in micromilling based on specific cutting pressure is presented. The proposed model includes three parameters which allow to control the entry of the cutter in the workpiece and which consider also the errors in the radial position of the cutting edges of the tool.

Due to the difficulties presented in the manufacturing of the micromilling tools, manufacturing errors frequently appear. These are errors in the radial and angular position of the cutting edge and have significant influence in the estimation of the instantaneous cutting force in micromilling.

The accuracy of the estimated parameters of the cutting force expression plays a major role in the resulting cutting force. For this reason, the influence of the fitting of the specific cutting pressure is analyzed.

The new mechanistic force model determines the instantaneous cutting force coefficients using experimental data processed for one cutter revolution. The model has been validated through experimental tests over a wide range of cutting conditions. The results obtained show good agreement between the predicted and measured cutting forces.     

Cutting force prediction in ball end milling of sculptured surface with Z-level contouring tool path

This paper presents an approach to predict cutting force in 3-axis ball end milling of sculptured surface with Z-level contouring tool path. The variable feed turning angle is proposed to denote the angular position of feed direction within tool axis perpendicular plane. In order to precisely describe the variation of feed turning angle and cutter engagement, the whole process of sculptured surface milling is discretized at intervals of feed per tooth along tool path. Each segmented process is considered as a small steady-state cutting. For each segmented cutting, the feed turning angle is determined according to the position of its start/end points, and the cutter engagement is obtained using a new efficient Z-map method. Both the chip thickness model and cutting force model for steady-state machining are improved for involving the effect of varying feed turning angle and cutter engagement in sculptured surface machining. In validation experiment, a practical 3-axis ball end milling of sculptured surface with Z-level contouring tool path is operated. Comparisons of the predicted cutting forces and the measurements show the reliability of the proposed approach.     

Investigation of the effect of rake angle on main cutting force

This paper presents a study of comparison of empirical and experimental results for main cutting force during machining rotational parts by unworn cutting tools. A dynamometer was designed and produced for measuring the forces. Two strain gauges were placed at the correct position on the machine tool and cutting tool at the design stage. Correct gauge positioning sensed displacements of the tool caused by cutting forces. AISI 1040 was used as the workpiece material. Main cutting force (F_c) was measured for eight different rake angles changing from negative to positive values at five different cutting speeds. The depth of cut and feed rate were kept throughout the experiments. Empirical results according to Kienzle approach were compared with experimental results. Main cutting force was observed to have a decreasing trend as the rake angle increased from negative to positive values. The deviation between empirical approach and experiments was in the order of 10–15%.     

PCBN刀具高速铣削TC4钛合金切削性能与工艺参数优化研究

针对钛合金TC4(Ti-6Al-4V)的加工特性,采用PCBN刀具,基于单因素试验,研究高速铣削条件下工艺参数对切削力、切削振动等的影响规律,提出综合考虑切削力、切削振动、表面粗糙度的工艺参数优选方法。研究表明:切削力和切削振动随切削速度v和每齿进给量f_z的增大呈现一定的波动,随径向切深a_e和轴向切深a_p的增大而增大,切削振动受切削力影响较为显著。考虑切削性能,以材料切除率为优化目标,以切削力、切削振动和表面粗糙度等为约束条件,建立工艺参数优选模型,可得到不同约束条件下工艺参数的优选组合。     

Simulation of the main cutting force in Crankshaft turn broaching

The measurement of the cutting forces of a turn-broaching machine is very complex due to the relative movement between workpiece and tool. In this work the cutting forces were simulated through the modeling of the process kinematics and by applying the Kienzle equation. A new experimental approach was proposed to determine the cutting forces using a conventional CNC turning machine tool. Through a series of experiments, the model has been calibrated. A comparison between the numerical and experimental results showed a similar trend. The effect of maximum cutting depth, workpiece diameter, cutting edge inclination angle, and feed rate on the main cutting force has been studied.     

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.     

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.     

Mechanistic cutting force model in band sawing

In order to establish a mechanistic model of cutting force, specific cutting pressure was first obtained through cutting experiments. The band sawing process is similar to milling in that it involves multi-point cutting, so it is not an easy matter to evaluate specific cutting pressure. This was achieved by making the thickness of workpiece smaller than one pitch of the saw tooth, analogous to fly cutting in the face milling process. Then the cutting force was predicted by analysing the geometric shape of a saw tooth. The tooth shape used was the raker set style that is generally used in band sawing. A set of teeth comprises three teeth, ranked as left, straight, and right. The mechanistic model developed in the research considered the shape of each tooth in a set. The predicted cutting forces coincided well with those measured in the validation experiment. Therefore, the predicted cutting forces in band sawing can be used for the adaptive control of saw-engaging feed rate in band sawing.     

工艺参数对单晶硅超精密加工切削力的影响

为了了解单晶硅超精密车削过程中不同切削参数及刀具前角对切削力的影响,利用单晶金刚石车刀对单晶硅进行单因素变量超精密车削试验。试验结果表明:进给量f和切削深度a_p对X、Y、Z方向的切削力F均有增大的趋势;而在切削速度v_c增加时,各方向的F逐渐减小;切削前角减小时,切削力反而增大。通过各因素对切削力F的变化幅值可以得到,对F影响较大的参数为a_p及f。选取最佳组合参数对单晶硅进行超精密切削试验,得到极为光滑的表面。     

Milling force prediction using a dynamic shear length model

Modelling of cutting forces in milling is often needed in machining automation. In this paper, a new method for the determination of the cutting forces in face milling is presented, which applies a predictive machining theory originally developed for orthogonal cutting to milling operations, with a dynamic shear length model developed and incorporated. The proposed dynamic shear length model is developed based on the analysis for the true tooth trajectories of a milling cutter, taking into account of the characteristic wavy surface effects in milling. The prediction for the cutting forces is carried out at each step of the angular increment of cutter rotation from input data of fundamental workpiece material properties, tool geometry and cutting conditions. Cutting forces at a cutter tooth can be predicted once the shear angle, shear length, shear plane area, and the shear flow stress along the shear length have been determined. The milling force prediction using the dynamic shear length model is verified through milling experimental tests. The sensitivity of the difference between the static and dynamic shear length models with respect to the feed per tooth and the cutter diameter is discussed.     

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.