Analytical prediction of chatter stability in ball end milling with tool inclination

The paper presents an analytical method to predict chatter stability in ball end milling with tool inclination. The chatter stability limits in ball end milling without the tool inclination have been predicted in the previous study by deriving directional milling force coefficients and then solving a simple quadratic equation. However, the tool is generally inclined and not perpendicular to the cut surface in practice. Therefore, a new method is developed to compute the directional milling force coefficients considering the tool inclination. It is confirmed that the chatter stability predicted by the proposed method agrees well with the experiments.     

Influence of tool inclination on brittle fracture in glass cutting with ball end mills

Glass milling is discussed with influences of tool inclination on brittle fracture. Cutting tests are performed to observe surfaces in the up-cut and the down-cut processes with a ball end mill inclined in the feed direction of the cutter. Brittle fracture occurs in the down-cut process at high feed rates. Then the machined surfaces in cutting with the ball end mills tilted in the vertical plane with respect to the feed direction are associated with those of the up-cut and the down-cut processes. The cutting forces are also measured to discuss brittle fracture with the change of the undeformed chip thickness. The scratches on the surface finished with the tilted ball end mill are shown in an analytical model with a notched edge shape. The maximum feed rates at which brittle fracture does not occur are shown with the tool inclination in the cutting tests.     

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.     

Predictive cutting force model in complex-shaped end milling based on minimum cutting energy

A force model is presented to predict the cutting forces and the chip flow directions in cuttings with complex-shaped end mills such as ball end mills and roughing end mills. Three-dimensional chip flow in milling is interpreted as a piling up of the orthogonal cuttings in the planes containing the cutting velocities and the chip flow velocities. Because the cutting thickness changes with the rotation angle of the edge in the milling process, the surface profile machined by the previous edge inclines with respect to the cutting direction. The chip flow model is made using the orthogonal cutting data with taking into account the inclination of the pre-machined surface. The chip flow direction is determined so as to minimize the cutting energy, which is the sum of the shear energy on the shear plane and the friction energy on the rake face. Then, the cutting force is predicted for the chip flow model at the minimum cutting energy. The predicted chip flow direction changes not only with the local edge inclination but also with the cutting energy consumed in the shear plane cutting model. The cutting processes with a ball end mill and a roughing end mill are simulated to verify the predicted cutting forces in comparison with the measured cutting forces.     

Prediction of chatter in NC machining based on a dynamic cutting force model for ball end milling

Ball end milling is one of the most widely used cutting processes in the automotive, aerospace, die/mold, and machine parts industries, and the chatter generated under unsuitable cutting conditions is an extremely serious problem as it causes excessive tool wear, noise, tool breakage, and deterioration of the surface quality. Due to the critical nature of detecting and preventing chatter, we propose a dynamic cutting force model for ball end milling that can precisely predict the cutting force for both stable and unstable cutting states because our uncut chip thickness model considers the back-side cutting effect in unstable cutting states. Furthermore, the dynamic cutting force model considers both tool runout and the penetration effect to improve the accuracy of its predictions. We developed software for calculating the cutting configuration and predicting the dynamic cutting force in general NC machining as well as single-path cutting. The chatter in ball end milling can be detected from the calculated cutting forces and their frequency spectra. A comparison of the predicted and measured cutting forces demonstrated that the proposed method provides accurate results.     

On the dynamics of ball end milling: modeling of cutting forces and stability analysis

This paper presents a dynamic force model and a stability analysis for ball end milling. The concept of the equivalent orthogonal cutting conditions, applied to modeling of the mechanics of ball end milling, is extended to include the dynamics of cutting forces. The tool is divided into very thin slices and the cutting force applied to each slice is calculated and summed for all the teeth engaged. To calculate the instantaneous chip thickness of each tooth slice, the method of regenerative chip load calculation which accounts for the effects of both the surface undulations and the instantaneous deflection is used. To include the effect of the interference of the flank face of the tool with the finished surface of the work, the plowing force is also considered in the developed model. Experimental cutting forces are obtained using a five-axis milling machine with a rotary dynamometer. The developed dynamic model is capable of generating force and torque patterns with very good agreement with the experimental data. Stability of the ball end milling in the semi-finishing operation of die cavities is also studied in this paper. The tangential and radial forces predicted by the method of equivalent orthogonal condition are fitted by the equations F_t = K_t(Z)bh_av and F_r = K_r(Z)F_t, where b is the depth of cut and h_av is the average chip thickness along the cutting edge and Z is the tool axis coordinate. The polynomial functions K_t(Z) and K_r(Z) are the cutting force constants. The interdependency of the axial and radial depths of cut in ball end milling results in an iterative solution of the characteristic equation for the critical width of cut and spindle speed. In addition, due to different cutting characteristics of the cutting edge at different heights of the ball nose, stability lobes are represented by surfaces. Comparison of the time domain simulation for the shoulder removal process in die cavity machining with the analytical predictions shows that the proposed method is capable of accurate prediction of the stability lobes.     

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.     

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

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

The prediction of cutting forces in end milling with application to cornering cuts

This paper presents the development, verification, and implementation of a mechanistic model for the force system in end milling. This model is based on chip load, cut geometry, and the relationship between cutting forces and chip load. A model building procedure based on experimentally obtained average forces is presented and both instantaneous and average force system characteristics are described as a function of cut geometry and feed rate. A computer program developed to implement the mechanistic model provides tabular and graphical outputs which show force distributions as functions of the axial depth of cut and rotation of the cutter. Force characteristics during concerning cuts are predicted by the model and verified via a set of cornering cut experiments typical of aerospace machining operations. Force characteristics in cornering are examined as a function of axial depth of cut and feedrate.     

High speed ball nose end milling of γ-TiAl alloys

Following a brief review on the development and intended application of γ-TiAl for aeroengine components, the paper details statistically designed machinability experiments involving high speed ball end milling in order to benchmark 4th generation alloy Ti–45Al–8Nb–0.2C against Ti–45Al–2Mn–2Nb +0.8%vol. TiB_2, which has been the prime focus of machinability evaluation and associated publications. Testing utilised 8 mm diameter, solid WC, AlTiN coated ball nose end cutters in a factorial design and involved measurement of cutting temperatures and workpiece surface roughness in addition to tool life and cutting forces. The trials established alloy Ti–45Al–8Nb–0.2C as providing a ∼25% increase in tool life based on a maximum flank wear criteria of 300 μm. On average, alloy Ti–45Al–2Mn–2Nb +0.8%vol. TiB₂ had a surface roughness Ra of ∼0.1 μm higher than Ti–45Al–8Nb–0.2C with values <0.6 μm Ra possible. Maximum cutting temperatures for Ti–45A–8Nb–0.2C measured using infra red pyrometry were ∼250 °C at a cutting speed of 160 m/min for a new tool, rising to ∼430 °C at a cutting speed of 340 m/min with a tool that had 300 μm of flank wear. For both γ-TiAl alloys, fracture/pullout was observed on every milled surface that was assessed and varied from a few microns to a few millimeters depending on test operating levels, within general, higher cutting speeds and tool flank wear levels causing an increased level of damage.     

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.     

Closed form formulation of cutting forces for ball and flat end mills

In this paper, a set of basis functions for the calculation of cutting forces in milling are introduced. It is shown that the cutting force at any tool position can be determined by the linear combination of the force basis functions. The method is based on the projection of the chip load area onto the reference coordinate planes. Due to the analytical integration of the cutting forces along the cutter edge, the developed closed form equations provide a fast means of calculating the cutting forces. The validity of the method is experimentally verified for both flat and ball end mills.     

Prediction of cutting forces in helical end milling fiber reinforced polymers

Machining of fiber reinforced composites is an important activity in the integration of these advanced materials into engineering applications. Machining damage due to excessive cutting forces may result in rejecting the composite components at the last stages of their production cycle. Therefore, the ability to predict the cutting forces is essential for selecting process parameters that would result in minimum machining damage. This work utilizes mechanistic modeling techniques for simulating the cutting of carbon fiber-reinforced polymers (CFRP) with a helical end mill. A methodology is developed for predicting the cutting forces by transforming specific cutting energies from orthogonal cutting to oblique cutting. It is shown that the method developed is capable of predicting the cutting forces in helical end milling of unidirectional and multidirectional composites and over the entire range of fiber orientations from 0° to 180°. This is a significant improvement over previous models that were only capable of addressing orthogonal cutting and/or a limited range of fiber orientations. Model predictions were compared with experimental data and were found to be in good agreement in cutting unidirectional laminate, but with lesser agreement in the case of a multidirectional laminate.     

Virtual compensation of deflection errors in ball end milling of flexible blades

The deflections of highly flexible turbine blades and slender end mills lead to tolerance violations during milling. This paper presents a digital simulation and compensation model for blade machining operations. Stiffness of the blade at the cutting zone is updated as the metal is removed without re-meshing using a computationally efficient sub-structuring technique. The cutter–workpiece engagement is evaluated by considering the deformations of both end mill and the blade under the cutting loads. The estimated deformations are compensated by modifying the tool path coordinates. The model has been experimentally verified in ball-end milling of a blade whose dimensional errors have been reduced from ～70 μm to ～10 μm.     

Cutting force modeling for flat end milling including bottom edge cutting effect

This study proposes a novel mechanistic cutting force model for flat end milling. The prominent feature of this model lies in that the overall cutting forces contributed by both the flank edge and the bottom edge cuttings are simultaneously taken into consideration. In the model formulation, to reflect the size effect in flank cutting, the flank cutting force coefficients are treated as an exponent function of instantaneous uncut chip thickness and are identified by nonlinear least-square algorithm. With the help of the calibrated flank cutting force coefficients, the bottom cutting force coefficients are instantaneously calibrated by the force component that is obtained by subtracting the flank force component from the total measured force. It is shown that the bottom cutting force coefficients can be treated as constants. The validity of the proposed cutting force model is also experimentally demonstrated over a relatively wide range of cutting conditions. It turns out that the bottom edge cutting has a remarkable effect on total cutting forces, when the axial depth of cut is relatively small.     

高能球磨制备超细TiH_2粉研究

利用氢化钛的氢脆性,在室温下通过高能球磨制备超细氢化钛粉。研究不同球磨条件对粉末粒度和形貌的影响,并对制备的粉末进行了扫描电镜分析。结果表明,球磨时间对粉末粒度的影响很大,粉末粒度在球磨初期迅速减小,球磨2min粉末迅速细化,粒度约为5μm~10μm。粒度为40μm的氢化钛粉,用庚烷保护湿磨30min时粒度达到1μm以下,球磨60min即可制得粒度为0.1μm的超细氢化钛粉。     

Evaluation of cutter orientations in high-speed ball end milling of cantilever-shaped thin plate

This work was carried out in order to evaluate machinability in high-speed ball end milling of thin cantilever-shaped aluminum plate, and the effect of tool path, tool angle on geometric accuracy and surface integrity. The experiments were performed at tilt angles 0°, 15°, 45° of workpieces using four cutter orientations (horizontal outward, horizontal inward, vertical outward, vertical inward). Workpiece deflection, surface profile and machined surface have been measured. The results show that when machining cantilever-shaped thin plate, the best cutting strategy is vertical outward at a workpiece tilt angle of 45°.     

高能球磨法制备金属微粉的研究

对几种典型粉体Fe粉，Ni粉，Al粉进行系列球磨试验。用扫描电镜测其粒度，得到铁粉球磨时间与粒径的关系曲线，着重讨论了铁粉粒度随时间变化的3个阶段：粉末粒度迅速变化，缓慢变化和不变阶段，对高能球磨法制备超细微粉的过程制具有一定意义。     

An improved cutting force and surface topography prediction model in end milling

During the milling operation, the cutting forces will induce vibration on the cutting tool, the workpiece, and the fixtures, which will affect the surface integrity of the final part and consequently the product's quality. In this paper, a generic and improved model is introduced to simultaneously predict the conventional cutting forces along with 3D surface topography during side milling operation. The model incorporates the effects of tool runout, tool deflection, system dynamics, flank face wear, and the tool tilting on the surface roughness. An improved technique to calculate the instantaneous chip thickness is also presented. The model predictions on cutting forces and surface roughness and topography agreed well with experimental results.