Development of a virtual machining system, part 1: approximation of the size effect for cutting force prediction

In this three-part paper, components of a virtual machining system for evaluating and optimizing cutting performance in -axis NC machining are presented. Part 1 describes a new method of calculating cutting-condition-independent coefficient and its application to the prediction of cutting forces over a wide range of cutting conditions. The prediction of the surface form error and transient cutting simulations, described in Parts 2 and 3, respectively, can be effectively performed based on the cutting force model with the improved size effect model that is presented in Part 1.

The relationship between the instantaneous uncut chip thickness and the cutting coefficients is calculated by following the movement of the center position of the cutter, which varies with nominal feed, cutter deflection and runout. The salient feature of the presented method is that it determines the cutting-condition-independent coefficients using experimental data processed for one cutting condition. The direct application of instantaneous cutting coefficient with size effects provides more accurate predictions of the cutting forces. A systematic comparison of the predicted and measured cutting forces over a wide range of cutting conditions confirms the validity of the proposed mechanistic cutting force and size effect models.     

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.     

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.     

Numerical simulation and prediction of cutting forces in five-axis milling processes with cutter run-out

Radial cutter runout is a common issue in milling processes and has a direct effect on milling stability due to variations of resulting chip load and forces. This paper presents a new method to effectively model and predict the instantaneous cutting forces in 5-axis milling processes with radial cutter runout based on tool motion analysis. First, the undeformed chip thickness model taking runout effect into account is established under continuous change of cutter axis orientation by means of the sweep traces of cutter edges. Second, the engaged cutting edge is determined and cutting coefficients are subsequently calibrated. Finally, the method of identifying runout parameters from the measured cutting forces is proposed, and mechanistic method is then applied to predict the cutting force. Since this method is completely based on the relative motion analysis of tool-part, it can reduce the prediction errors of cutting forces effectively and is suitable for generic rotation cutters. Several validation examples are given under different cutting conditions to prove its effectiveness and accuracy. The results reveal that the developed method can predict the cutter forces with a high accuracy and has the ability to be used in simulations and optimizations of five-axis machining.     

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.     

Phase width analysis of cutting forces considering bottom edge cutting and cutter runout calibration in flat end milling of titanium alloy

This paper is concerned with the combined cutting effects of both flank and bottom edges based on a systematic study of the cutting force in flat end milling of the titanium alloy. Besides the flank edge, the bottom edge of the cutter is also found to be an important factor influencing the cutting force distributions and can lead to uniform phase widths for non-zero cutting forces even under considerable cutter runout. One such phenomenon of uniform phase width induced by the bottom edge for the cutting force is deeply revealed. To do this, the models for characterizing the cutting force coefficients related to both edges are established based on the measured instantaneous cutting forces, and cutter runout is considered in the computation of process geometry parameters such as cutter/workpiece engagements and instantaneous uncut chip geometry parameters. Novel algorithms for identifying the cutter runout parameters and the bottom uncut chip width are also developed. Results definitely show that the flank cutting force coefficients can be treated as constants and that size effect obviously exists in the bottom cutting force coefficients that can be characterized by a power function of the bottom uncut chip width.The proposed model is validated through a comparative study with the existing model and experiments. From the outcomes of the current work, it is clearly seen that the prediction of cutting forces for titanium alloy can resort to the proposed model instead of traditional ones.     

An experimental method for studies of intermittent cutting at small cutting depths

Most devices for metal cutting experiments are designed to simulate continuous cutting at relatively large cutting depths. However, there is also a need for techniques to study the more complex situations prevailing in other important cutting operations like milling, sawing, hobbing, shaper cutting and grinding. These operations are characterized as being intermittent and having a relatively small and varying cutting depth per edge. In order to supply an experimental set-up for basic studies of chip formation and cutting forces under these conditions a new method for single stroke, single edge metal cutting has been developed.

The experiments are performed in a modified Charpy pendulum which offers force measurement and accurate selection of cutting speed and feed in the ranges typical of many intermittent cutting operations. The equipment is also provided with an excellent quick-stop mechanism to aid in chip formation studies.

The test method is described in detail and examples of metallographical and scanning electron microscopical studies of quick-stopped samples as well as registrations of specific thrust and cutting forces are presented.     

New procedures for calibration of instantaneous cutting force coefficients and cutter runout parameters in peripheral milling

In this paper, new procedures are proposed to calibrate the instantaneous cutting force coefficients and the cutter runout parameters for peripheral milling. By combining with optimization algorithm, i.e., the Nelder–Mead simplex method, detailed calibration schemes are derived for a mechanistic cutting force model in which the cutting force coefficients are described as the exponential functions of the instantaneous uncut chip thickness. Three different cutter runout models are considered in the calculation of instantaneous uncut chip thickness. Only one or two tests are required to perform the calibration. Experimental verifications are also conducted to validate the proposed procedures, and the results show that they are efficient and reliable. To see the effect of different runout models on milling process, comparisons among the predicted results under a wide range of cutting parameters are made to study the consistency and limitations of different models. It is found that the radial cutter runout model is a recommendable one for cutting force modelling.     

Intermittent metal cutting at small cutting depths—2. Cutting forces

Cutting forces in intermittent metal cutting at small cutting depths were investigated by single edge experiments. Single cutting strokes were performed in a modified Charpy pendulum tester which offers cutting and thrust force measurement and accurate selection of cutting speed and feed in ranges typical for many intermittent high speed steel (HSS) tool operations.

The cutting performance of a number of double rake HSS edges, with primary rake angles ranging from +20° (“parrot bill”) to −60°, all with a preground 0.1 mm flank length were tested in two steel grades (one plain carbon and one austenitic stainless). Some of the edge geometries were tested also in TiN coated condition. The relative performance of the different edges was investigated with respect to specific cutting and thrust forces. The influence of cutting length and depth, edge micro geometry, TiN coating and cutting speed is discussed specifically.

Among the most important observations were:

• The cutting and thrust forces at a fixed cutting depth may change significantly during the short (25–30 mm) cuts.

• The chamfer formed by a double rake geometry with negative primary angle increases the forces.

• For these chamfered tools the forces increase linearly with the projected flank length. TiN coating increases rather than reduces the forces during these short cuts.

The relationships between the varied parameters and chip formation phenomena like dead zone formation, chip curl and surface finish were presented in part 1 of this paper.     

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.     

Cutting force model for multi-toothed cutting processes and force measuring equipment for face milling

This article presents a mechanical cutting force model for multi-tooth cutting processes, where initial position errors in radial and axial direction, eccentricity and edge wear are taken into account. The cutting forces are presented for each individual cutting edge, and in a system of coordinates where one axis is parallel to the cutting speed vector at any instant. The process parameter cutting resistance, C_r is derived from the measured main cutting force F_M. C_r should be regarded as a parameter since it is always increasing with decreasing values of theoretical chip thickness h₁. A new way of measuring cutting forces in multi-tooth cutting processes is also presented. Eight cutting force components are measured on the tool close to each of the four cutting edges. The aroused signals are filtered, amplified, A/D-converted and put together in a serial stream for transmission through a hollow spindle via a fibre optic cable. The signals are sent from the rotating spindle to the frame of the machine over an air gap with Light Emitting Diodes. They are then demultiplexed, D/A-converted, and stored in a PC-based eight channel oscilloscope. With this measurement equipment it is possible to directly measure the cutting forces acting on each individual cutting edge.     

Development of micro milling force model and cutting parameter optimization

Taking the minimum chip thickness effect,cutter deflection,and spindle run-out into account,a micro milling force model and a method to determine the optimal micro milling parameters were developed.The micro milling force model was derived as a function of the cutting coefficients and the instantaneous projected cutting area that was determined based on the machining parameters and the rotation trajectory of the cutter edges.When an allowable micro cutter deflection is defined,the maximum allowable cutting force can be determined.The optimal machining parameters can then be computed based on the cutting force model for better machining efficiency and accuracy.To verify the proposed cutting force model and the method to determine the optimal cutting parameters,micro-milling experiments were conducted,and the results show the feasibility and effectiveness of the model and method.     

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.     

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.     

Efficient calibration of instantaneous cutting force coefficients and runout parameters for general end mills

This paper aims at developing a unified approach to identify the cutting force coefficients together with the cutter runout parameters for general end mills such as cylindrical, ball, bull nose ones, etc. The cutting forces that are modeled using the instantaneous cutting force coefficients are analyzed and separated into two terms: a nominal component independent of the runout and a perturbation component induced by the runout. The nominal component enables the calibration of the instantaneous cutting force coefficients whereas the runout parameters are determined from the perturbation component. The validity of the present method is demonstrated with simulation and experimented data.     

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.     

Systematic study on cutting force modelling methods for peripheral milling

This paper systematically studies the cutting force modelling methods in peripheral milling process in the presence of cutter runout. Emphasis is put on how to efficiently calibrate the cutting force coefficients and cutter runout. Mathematical derivations and implementation procedures are carried out based on the measured cutting force or its harmonics from Fourier transformation. Five methods are presented in detail. In the first three methods the cutting force coefficients are assumed to be constants whereas in the last two they are taken as functions of instantaneous uncut chip thickness. The first method and the fifth one are taken from literatures for comparison. The second, the third and the fourth methods are original contributions, which are carried out with optimization ideas. The second method proceeds using the first and Nkth harmonic forces as the source signal while the third and the fourth are derived based on the measured cutting forces and its first harmonics. The engagement of the cutter with the workpiece is considered in these three new calibration procedures without the requirement of a prior knowledge of the actual cutter runout. Comparisons among the calibrated results from different methods are made to study the limitations and consistency of the presented methods. Experiments are also conducted to show the prediction ability of all methods.     

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.     

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.     

A unified instantaneous cutting force model for flat end mills with variable geometries

A new and unified instantaneous cutting force model is developed to predict cutting forces for flat end mills with variable geometries. This model can routinely and efficiently determine the cutting properties such as shear stress, shear and normal friction angles (SSSNFAs) involved in the cutting force coefficients by means of only a few milling tests rather than existing abundant orthogonal turning tests. Novel algorithms are developed to characterize these properties using following steps: transformation of cutting forces measured in Cartesian coordinate system into a local system on the normal plane, establishment of explicit equations to bridge SSSNFAs and the transformed cutting forces, determination of SSSNFAs by solving the equations and fitting SSSNFAs as functions of process geometries. Results definitely show that shear stress can be treated as a constant whereas shear and normal friction angles should be characterized by Weibull functions of instantaneous uncut chip thickness. Experiments verify that the proposed unified model is effective to predict the cutting forces in flat end milling in spite of cutter geometries and cutting conditions.