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.     

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.     

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.     

Identification of shearing and ploughing cutting constants from average forces in ball-end milling

This paper presents an analytical model for the direct identification of global shearing and ploughing cutting constants from measured average cutting forces in ball-end milling. This model is based on the linear decomposition of elemental local cutting forces into a shearing component and a ploughing component. Then, a convolution integral approach is used to obtain the average cutting forces leading to a concise and explicit expression for the global shearing and ploughing cutting constants in terms of axial depth of cut, cutter radius and average milling forces. The model is verified by comparisons with an existing force model of variable cutting coefficients. Cutting constants are identified through milling experiments and the prediction of cutting forces from identified cutting constants coincides with the experimental measurements. A model for identifying the lumped shearing constants is obtained as a subset of the presented dual mechanism model. Experimental results indicate that a model with dual-mechanism cutting constants predicts the ball-end milling forces with better accuracy than the lumped force model.     

A cutting force model for finishing processes using helical end mills with significant runout

Analytical cutting force models play an important role in a wide array of simulation approaches of milling processes. The accuracy of the simulated processes directly depends on the predictive power of the applied cutting force model, which may vary under specific circumstances. End milling processes with small radial cutting depths, e.g. finishing processes, are particularly problematic. In this case, the tool runout, which is usually neglected in established cutting force models, can become quite significant. Within this article, well-known cutting force models are implemented for runout-prone finishing processes and modified by integrating additional parameters. A method is presented for how these additional runout parameters can be efficiently determined alongside commonly used cutting coefficients. For this purpose, a large number of milling experiments have been performed where the cutting forces were directly measured using a stationary dynamometer. The measured cutting forces were compared with the simulated cutting forces to verify and assess the modified model. By using the presented model and calibration method, cutting forces can be accurately predicted even for small radial cutting depths and significant tool runout.     

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.     

Radial immersion angle estimation using cutting force and predetermined cutting force ratio in face milling

Radial immersion ratio is an important factor to determine the threshold for tool conditioning monitoring and automatic force regulation in face milling. In this paper, a method of on-line estimation of the radial immersion angle using cutting force is presented. When a tooth finishes sweeping, a sudden drop of cutting force occurs. This force drop is equal to the cutting force that acts on a single tooth at the swept angle of cut and can be obtained from the cutting force signal in feed and cross-feed directions. The ratio of cutting forces in feed and cross-feed directions acting on the single tooth at the immersion angle is a function of the immersion angle and the ratio of radial-to-tangential cutting force. In this study, it is found that the ratio of radial-to-tangential cutting force is not affected by cutting conditions and axial rake angle. Therefore, the ratio of radial-to-tangential cutting force determined by just one preliminary experiment can be used regardless of the cutting conditions for a given tool and workpiece material. Using the measured cutting force during machining and a predetermined ratio, the radial immersion ratio is estimated in the process. Various experiments show that the radial immersion ratio and instantaneous ratio of the radial to tangential direction cutting force can be estimated very well by the proposed method.     

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.     

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.     

Practical implementation of cutting force model for step drill using 3D CAD data

As an extension of the cutting force model, which was developed by analyzing the forces on rake and relief face, a practical method of cutting force model is suggested. By a calibration test, cutting coefficients are determined, including the information on tool geometry, work material and cutting conditions such as cutting speed and feed rate. As inputs for the force model, normal rake angle and normal relief angle were obtained by a new method from the measured angles using a 3D CAD machine. This practical force model can be applied for machining CFRP successfully, which was proved from the experiments.     

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.     

Evaluation of cutting force uncertainty components in turning

A procedure is proposed for the evaluation of those uncertainty components of a single cutting force measurement in turning that are related to the contributions of the dynamometer calibration and the cutting process itself. Based on an empirical model including errors from both sources, the uncertainty for a single measurement of cutting force is presented, and expressions for the expected uncertainty vs. cutting parameters are proposed. This approach gives the possibility of evaluating cutting force uncertainty components in turning, for a defined range of cutting parameters, based on few experiments.     

A model for cutting forces generated during machining with self-propelled rotary tools

In this paper, a force model for self-propelled rotary tool is presented. Conventional oblique cutting force predictions were reviewed and extended to predict the cutting forces generated during machining with the self-propelled rotary tools. The model presented is based on Oxley's analysis and was verified by cutting tests using a typical self-propelled tool. Good agreement was obtained between the predicted and the experimentally measured forces under a wide range of cutting conditions. The effect of different cutting conditions on the friction coefficient along the chip/tool interface and tool rake face normal force were also presented and discussed.     

The measurement of parasitic forces in orthogonal cutting

Not all the forces measured during a cutting operation contribute to chip formation. Some fraction of the forces are parasitic forces such as ploughing or flank forces, which make no contribution to the chip formation process. It its desirable to measure these forces so that the mechanics of the cutting process can be interpreted correctly. However, a possibly more important reason is that parasitic forces are known to increase with worn tools. Thus if the parasitic force can be measured directly, or extracted from the overall measured forces it may be useful for in-process tool condition monitoring provided appropriate calibration of the relationship between the parasitic force and cutting tool dullness has been performed.A method for measuring the parasitic forces in orthogonal cutting is proposed and shown to permit calculating workpiece material properties which are consistent with those measured using other techniques. Another technique for evaluating parasitic forces which was previously shown to yield inaccurate results for zinc was re-evaluated for Delrin® and again resulted in incorrect results.     

Improved modelling of cutting force coefficients in peripheral milling

Titanium is one of the most widely used metals in the aircraft and turbine manufacturing industries. Accurate prediction of cutting forces is important in controlling the dimensional accuracy of thin walled aerospace components. In this paper, a general three-dimensional mechanistic model for peripheral milling processes is presented. The effects of chip thickness, rake angle and cutting geometry on chip flow, rake face friction and pressure, and cutting forces are analyzed. A set of closed form expressions with experimentally estimated cutting force factors are presented for the prediction of cutting forces. The model is verified experimentally in the peripheral milling of a titanium alloy. For a given set of cutting conditions and tool geometry, the model predicts the cutting forces accurately for the chip thickness and rake angle ranges tested.     

Modeling of turning process cutting forces for grooved tools

A mechanistic modeling approach to predicting cutting forces for grooved tools in turning has been developed. The model assumes the existence of an equivalent orthogonal cutting operation for any oblique operation. The effects of tool nose radius and chip flow have been incorporated by defining a set of equivalent groove parameters. Two calibration methods have been presented for the model. A variety of commercial grooved inserts were chosen to validate the model. The workpiece material used was AISI 1018 steel. The force predictions from the model were found in good agreement with the measured forces. The effects of cutting conditions and groove parameters on the cutting forces and their implication in designing grooved tools were also determined.     

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.     

On cutting parameters selection for plunge milling of heat-resistant-super-alloys based on precise cutting geometry

In plunge milling operation the tool is fed in the direction of the spindle axis which has the highest structural rigidity, leading to the excess high cutting efficiency. Plunge milling operation is one of the most effective methods and widely used for mass material removal in rough/semi-rough process while machining high strength steel and heat-resistant-super-alloys. Cutting parameters selection plays great role in plunge milling process since the cutting force as well as the milling stability lobe is sensitive to the machining parameters. However, the intensive studies of this issue are insufficient by researchers and engineers. In this paper a new cutting model is developed to predict the plunge milling force based on the more precise plunge milling geometry. In this model, the step of cut as well as radial cutting width is taken into account for chip thickness calculation. Frequency domain method is employed to estimate the stability of the machining process. Based on the prediction of the cutting force and milling stability, we present a strategy to optimize the cutting parameters of plunge milling process. Cutting tests of heat-resistant-super-alloys with double inserts are conducted to validate the developed cutting force and cutting parameters optimization models.     

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.     

A model for thread milling cutting forces

This paper presents a mechanistic model for prediction of the thread milling forces. The mechanics of cutting for thread milling is analyzed similar to the end milling process but with modified cutting edge geometry. The chip thickness and cutting force models are developed considering the unique geometry of the tool. The model has been calibrated for 6061 Aluminum and validated. The effects of tool and thread geometry have been studied using the model.