Model for surface topography prediction in peripheral milling considering tool vibration

This paper presents a model for the prediction of surface topography in peripheral milling operations taking into account that the tool vibrates during the cutting process. The model includes the effect of tool vibrations in the equations of the cutting edge paths, which are transformed into equivalent polynomial equations and solved for discrete positions along the feed direction by applying a standard root finder. Through this procedure, surface topography generation is simplified with respect to other models in literature. The model allows the topography, the roughness values and the form errors of the milled surface to be predicted. Cutting test results show good agreement with model predictions.     

An analytical force model with shearing and ploughing mechanisms for end milling

An analytical force model with both shearing and ploughing mechanisms is established for the end milling processes. The elemental forces are defined as the linear combination of shearing and ploughing forces in six cutting constants. The analytical model for the total milling forces in the angular and frequency domain are derived by convolution approach and Fourier transform respectively and are expressed as the superposition of the shearing force component and ploughing force component. This dual-mechanism model is analyzed and discussed in the frequency domain and compared with the lumped shear model. An expression is derived for identifying the cutting constants of the dual-mechanism model from the average milling forces. Explicit inclusion of ploughing force in the model is shown to result in better predictive accuracy and yields a linear force model with constant cutting coefficients. Experiments verify the accuracy and the frequency analysis of the dual-mechanism model and show that cutting constants for the dual-mechanism model are fairly independent of chip thickness.     

An in-process surface recognition system based on neural networks in end milling cutting operations

An in-process based surface recognition system to predict the surface roughness of machined parts in the end milling process was developed in this research to assure product quality and increase production rate by predicting the surface finish parameters in real time. In this system, an accelerometer and a proximity sensor are employed as in-process surface recognition sensors during cutting to collect the vibration and rotation data, respectively. Using spindle speed, feed rate, depth of cut, and the vibration average per revolution (VAPR) as four input neurons, an artificial neural networks (ANN) model based on backpropagation was developed to predict the output neuron-surface roughness R_a values. The experimental results show that the proposed ANN surface recognition model has a high accuracy rate (96–99%) for predicting surface roughness under a variety of combinations of cutting conditions. This system is also economical, efficient, and able to be implemented to achieve the goal of in-process surface recognition by retrieving the weightings (which were generated from training and testing by the artificial neural networks), predicting the surface roughness R_a values while the part is being machined, and giving feedback to the operators when the necessary action has to be taken.     

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.     

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.     

Toolpath selection based on the minimum deflection cutting forces in the programming of complex surfaces milling

In this paper, a new methodology for the selection of the milling toolpaths on complex surfaces that minimize dimensional errors due to tool defection is presented. In this way, an improvement on the accuracy of milled surfaces is achieved. The methodology can be applied to both three and five axes milling. In the three axes case, it is based on the calculation of the minimum cutting force component that is related with the tool deflection. This component has been previously defined as that perpendicular to the tool axis and contained on the plane defined by the tool axis and the normal vector to the workpiece surface.Cutting forces are calculated for each 15° sense on the tangent plane to the milled surface, in a grid of control points defined by the user, both for dowmilling and upmilling. With this information there are two possibilities. First, select a general toolpath direction that minimizes the mean value of the tool deflection force on the surface, and bearing this in mind, the CAM operator can produce a CNC program which leads to an accuracy improvement. The second option is the selection of different milling directions at each control point. Joining these points, the minimum force lines are defined on the workpiece surface. These can be used as the master guides for the toolpath programming of a complete surface.In the case of five axes milling, the approach is different, because in this case the tool-axis orientation with respect to the workpiece surface may be changed using the two rotary axes. Therefore, for each workpiece area both tool-axis orientation and machining direction can be selected to keep tool deflection force below a threshold value.Some case studies of both techniques and in-deep discussion of results are presented. Applying this approach, in three axes milling dimensional errors fall down from 30 μm to below 4 μm. In five axes milling errors can be kept below 15 μm in most of the cases.     

Theoretical modelling and simulation of cutting forces in face milling with cutter runout

A new approach to theoretical modelling and simulation of cutting forces in face milling is presented. Based on a predictive machining theory, the action of a milling cutter is modeled as the simultaneous actions of a number of single-point cutting tools. The milling forces are predicted from the workpiece material properties, cutter parameters, tooth geometry, cutting conditions and types of milling. The properties of the workpiece material are considered as functions of strain, strain-rate and temperature in the cutting region. It takes into account the effect of the intermittent contact between each milling tooth and the workpiece on the temperature in the cutting region. It also takes into account the effect of cutter runout on the undeformed chip thickness. Milling experiments have been conducted to verify the proposed model. Good agreements between the experimental and simulated results are presented.     

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 statistical modeling of surface roughness in high-speed flat end milling

Surface roughness is one of the most important requirements in machining process. The surface roughness value is a result of the tool wear. When tool wear increase, the surface roughness also increases. The determination of the sufficient cutting parameters is a very important process obtained by means of both minimum surface roughness values and long tool life. The statistical models were developed to predict the surface roughness.This paper presents the development of a statistical model for surface roughness estimation in a high-speed flat end milling process under wet cutting conditions, using machining variables such as spindle speed, feed rate, depth of cut, and step over. First- and second-order models were developed using experimental results of a rotatable central composite design, and assessed by means of various statistical tests. The highest coefficient of correlation (R_adj²) (88%) was obtained with a 10-parameter second-order model. Meanwhile, a time trend was observed in residual values between model predictions and experimental data, reflecting the probable effect of the tool wear on surface roughness. Thus, in order to enhance the estimation capability of the model, another independent variable was included into the model to account for the effect of the tool wear, and the total operating time of the tool was selected as the most suitable variable for this purpose. By inserting this new variable as a linear term into the model, R_adj² was increased to 94% and a good fit was observed between the model predictions and supplementary experimental data.In this study, it was observed that, the order of significance of the main variables is as X₅>X₃>X₄>X₁>X₂ (total machining time, depth of cut, step over, spindle speed and feed rate, respectively).     

Influence of radial and axial runouts on surface roughness in face milling with round insert cutting tools

In face milling processes, the surface quality of the machined part depends on many factors, including feed, cutting tool geometry and tool errors. In this work, a numerical model for predicting the surface profile and surface roughness as a function of these factors is presented, incorporating a random values generation algorithm that makes it possible to determine the variation in surface roughness from the values that can be adopted by tool errors. This work is focused on round insert cutting tools and the influence of tool errors such as radial and axial runouts. The results that correspond to a number of teeth equal to 4, insert diameter of 12 mm, depth of cut of 0.5 mm, cutting speed of 120 m/min and feed of 0.4–1.4 mm/rev are analysed. Milling experiments are made to verify the validity of the model and the discrepancies between the experimental and theoretical surface profiles are assumed to be a consequence of different factors such as the variation in undeformed chip thickness along the surface profile.     

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.     

Influence of machining cycle of horizontal milling on the quality of cutting force measurement for the cutting tool wear monitoring

The cutting tools are today used a lot by industry and they are expensive, so it was interesting to optimize their use, by developing a predictive method of their wear, particularly, the flank wear V _b . For this task, the flank tool wear was measured in off-line using a binocular microscope, whereas, the cutting forces are recorded by means of a dynamometer (Kistler 9255B). The acquired signatures are analyzed during the milling operation throughout the tool life. In this paper, we are interested in the extraction of the appropriate indicators which characterize the tool wear by temporal and frequential analyses of the cutting force signals; and highlighting the influence of the clamp holes and the machining cycle to the quality of the measurements.     

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.     

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.     

Experimental study of surface roughness in slot end milling AL2014-T6

The aim of this work was to analyze the influence of cutting condition and tool geometry on surface roughness when slot end milling AL2014-T6. The parameters considered were the cutting speed, feed, depth of cut, concavity and axial relief angles of the end cutting edge of the end mill. Surface roughness models for both dry cutting and coolant conditions were built using the response surface methodology (RSM) and the experimental results. The results showed that the dry-cut roughness was reduced by applying cutting fluid. The significant factors affecting the dry-cut model were the cutting speed, feed, concavity and axial relief angles; while for the coolant model, they were the feed and concavity angle. Surface roughness generally increases with the increase of feed, concavity and axial relief angles, while concavity angle is more than 2.5°.     

Influence of feed, eccentricity and helix angle on topography obtained in side milling processes

Influence of feed, eccentricity and helix angle on surface roughness is presented for side milling operations with cylindrical tools. A model was developed to predict surface topography as well as different roughness parameters. Roughness topography was obtained for one specific tool having grinding errors and eccentricity, for different helix angles.It was found that, as feed increases the number of cutting edge marks on the workpiece’s surface per revolution maintains or increases. As grinding errors and eccentricity increase, the number of cutting edge marks tends to decrease. Regarding helix angle, it was observed that roughness profile does not change along the workpiece’s height if no helix angle is considered. When helix angle is considered and the tool has both high eccentricity and high runout due to grinding errors, roughness heterogeneity bands are observed. The bands’ pattern is repeated along each helix pitch. The higher the helix angle, the narrower the roughness heterogeneity bands become.     

A three-dimensional analytical cutting force model for micro end milling operation

In the present day manufacturing arena one of the most important fields of interest lies in the manufacturing of miniaturized components. End milling with fine-grained carbide micro end mills could be an efficient and economical means for medium and small lot production of micro components. Analysis of the cutting force in micro end milling plays a vital role in characterizing the cutting process, in estimating the tool life and in optimizing the process. A new approach to analytical three-dimensional cutting force modeling has been introduced in this paper. The model determines the theoretical chip area at any specific angular position of the tool cutting edge by considering the geometry of the path of the cutting edge and relates this with tangential cutting force. A greater proportion of the helix face of the cutter participating in the cutting process differs the cutting force profile in micro end milling operations a bit from that in conventional end milling operations. This is because of the reason that the depth-of-cut to tool diameter ratio is much higher in micro end milling than the conventional one. The analytical cutting force expressions developed in this model have been simulated for a set of cutting conditions and are found to be well in harmony with experimental results.     

A study on the effects of vibrations on the surface finish using a surface topography simulation model for turning

In this paper, a surface topography simulation model is established to simulate the surface finish profile generated after a turning operation. The surface topography simulation model incorporates the effects of the relative motion between the cutting tool and the workpiece with the effects of tool geometry to simulate the resultant surface geometry. It is experimentally shown that the surface topography simulation model can properly simulate the surface profile generated by turning operations. The surface topography simulation model is used to study the effects of vibrations on the surface finish profile. It is found that the vibration frequency ratio is a more important vibration parameter than the vibration frequency on the characterization of the surface finish profile. The vibration frequency ratio is the ratio between the vibration frequency and the spindle rotational speed.     

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.     

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.