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.     

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.     

约束应力对AD95陶瓷动态硬度的影响

以商用AD95氧化铝陶瓷为研究对象,在不同约束应力下测试材料的动态、静态压痕硬度,同时观察动态、静态压痕的形貌照片以及压痕横截面照片.研究结果表明,AD95陶瓷的动态压痕硬度高于静态,且随着约束应力提高二者均不断增大;约束应力越大,动态硬度提高越明显.因为高应变率条件下的惯性效应和约束应力的耦合作用,使裂纹扩展严重滞后,材料变形抗力大幅提高,动态硬度迅速增加.     

Modelling the cutting edge radius size effect for force prediction in micro milling

This paper presents a theoretical model for cutting force prediction in micro milling, taking into account the cutting edge radius size effect, the tool run out and the deviation of the chip flow angle from the inclination angle. A parameterization according to the uncut chip thickness to cutting edge radius ratio is used for the parameters involved in the force calculation. The model was verified by means of cutting force measurements in micro milling. The results show good agreement between predicted and measured forces. It is also demonstrated that the use of the Stabler's rule is a reasonable approximation and that micro end mill run out is effectively compensated by the deflections induced by the cutting forces.     

Analytical modeling and experimental validation of micro end-milling cutting forces considering edge radius and material strengthening effects

This paper presents a novel micro end-milling cutting forces prediction methodology including the edge radius, material strengthening, varying sliding friction coefficient and run-out together. A new iterative algorithm is proposed to evaluate the effective rake angle, shear angle and friction angle, which takes into account the effects of edge radius as well as varying sliding friction coefficient. A modified Johnson–Cook constitutive model is introduced to estimate the shear flow stress. This model considers not only the strain-hardening, strain-rate and temperature but also the material strengthening. Furthermore, a generalized algorithm is presented to calculate uncut chip thickness considering run-out. The cutting forces model is calibrated and validated by NAK80 steel, and the relevant micro slot end-milling experiments are carried out on a 3-axis ultra-precision micro-milling machine. The comparison of the predicted and measured cutting forces shows that the proposed model can provide very accurate predicted results. Finally, the effects of material strengthening, edge radius and cutting speed on the cutting forces are investigated by the proposed model and some conclusions are given as follows: (1) the material strengthening behavior has significant effect on micro end-milling process at the micron level. (2) Cutting forces predicted increase with the increase of edge radius. (3) Considering varying sliding friction coefficient can enhance the sensitivity of the predicted cutting forces to cutting speed.     

Nano-precision measurement of diamond tool edge radius for wafer fabrication

In this paper, a non-destructive nano-precision measurement method for diamond tool cutting edge radius is presented. The basis of the method is that the profile of a tool cutting edge can be copied by indenting the tool cutting edge into the surface of a selected material, and that the copy of the profile can be measured at nano-precision level using AFM. The selected material elastic error compensation coefficient has to be determined to cancel out the effect of elastic spring-back. Copper was selected as the indentation piece material due to its (1) high rigidity and high density, (2) large Young’s modulus and (3) low yield strength. The elastic error compensation coefficient for the copper material is determined through the indentation of a tungsten carbide tool edge on the copper surface. By comparing the actual tool edge radius measured using scanning electron microscope (SEM) on the sectional view of the tungsten carbide tool with the one measured from the copied profile of the tool edge on the copper surface, the coefficient is obtained. Three diamond tool edge radii were obtained using the proposed method. Analysis is given for the accuracy of the proposed method, showing that as far as the error elastic compensation coefficient is consistent with the copper material used, the only source of errors with the measurement will come from the device for measuring the indented profile on the surface.     

Modelling and analysis of micro scale milling considering size effect, micro cutter edge radius and minimum chip thickness

This paper presents mechanisms studies of micro scale milling operation focusing on its characteristics, size effect, micro cutter edge radius and minimum chip thickness. Firstly, a modified Johnson–Cook constitutive equation is formulated to model the material strengthening behaviours at micron level using strain gradient plasticity. A finite element model for micro scale orthogonal machining process is developed considering the material strengthening behaviours, micro cutter edge radius and fracture behaviour of the work material. Then, an analytical micro scale milling force model is developed based on the FE simulations using the cutting principles and the slip-line theory. Extensive experiments of OFHC copper micro scale milling using 0.1 mm diameter micro tool were performed with miniaturized machine tool, and good agreements were achieved between the predicted and the experimental results. Finally, chip formation and size effect of micro scale milling are investigated using the proposed model, and the effects of material strengthening behaviours and minimum chip thickness are discussed as well. Some research findings can be drawn: (1) from the chip formation studies, minimum chip thickness is proposed to be 0.25 times of cutter edge radius for OFHC copper when rake angle is 10° and the cutting edge radius is 2 μm; (2) material strengthening behaviours are found to be the main cause of the size effect of micro scale machining, and the proposed constitutive equation can be used to explain it accurately. (3) That the specific shear energy increases greatly when the uncut chip thickness is smaller than minimum chip thickness is due to the ploughing phenomenon and the accumulation of the actual chip thickness.     

Influence of asymmetric cutting edge roundings on surface topography

For finishing operations in machining, hardened steel hard turning can compete with grinding operations by means of accuracy and productivity. In the past research focussed on the effect of process parameters and tool macro geometry on the resulting surface roughness. Recent investigations show, that the cutting edge micro geometry is an important factor to influence surface quality. The knowledge generated by new methods displays the importance of asymmetric cutting edge roundings on cutting forces, chip formation and tool life. It is known, that chip formation also affects the resulting surface quality. Therefore, this paper investigates the effect of asymmetric cutting edge roundings on the resulting surface roughness in hard turning of roller bearing inner rings. Cutting tests with differently shaped cutting edges and two different feed values are conducted. The resulting surface roughness is measured. The consequent surface quality is explained by geometric coherences between uncut chip thickness and stresses along the cutting edge and the effect of material side flow. It is found, that the cutting edge geometry and the resulting stress distribution around the cutting edge affects the generated surface quality.     

Angle and frequency domain force models for a roughing end mill with a sinusoidal edge profile

This paper presents analytical force models for a cylindrical roughing end mill with a sinusoidal edge profile in both the angle and frequency domains. Starting from a general expression for the chip thickness model, it is shown that under normal feed conditions, there exists only one cutting point at any axial position for an N-flute roughing end mill with its chip thickness N times that of a regular end mill, while the effective axial depth of cut is only 1/Nth that of a regular end mill. Based on the chip load model, the analytical force model is subsequently established through convolution integration of the elemental cutting function with the cutting edge geometry function in the angular domain, followed by Fourier analysis to obtain the frequency domain force model. Distinctive features of the milling forces for a roughing end mill are illustrated and compared with a regular end mill in the frequency as well as in the angular domain. The effects of the geometric parameters of a roughing end mill on the chip load distribution and on the features of milling force are discussed. The force models in both the frequency and angular domains are finally verified through milling experiments.     

Analytical stability lobes including nonlinear process damping effect on machining chatter

Indentation of the tool edge and flank face into workpiece surface undulations has been recognized in the literature as the main source of process damping. This damping affects the process stability at low cutting speed greatly. Numerical simulations have allowed integrating the nonlinear indentation force into machining chatter models. It is shown in this paper that the indentation force requires very high discretization resolution for accurate numerical simulation. The objective of the current work is to develop the stability lobes analytically taking into account the effect of nonlinear process damping. The developed lobes could be established for different amplitudes of vibration. This is a departure from the traditional notion that the stability lobes represent a single boundary between fully stable and fully unstable cutting conditions. Plunge turning is utilized in the current work to illustrate the procedure of establishing the lobes analytically. Experimental cutting tests were conducted at three feedrates for sharp and worn tools and the results agreed well with the analytically established lobes.     

Upper bound analysis of oblique cutting with nose radius tools

A generalized upper bound model for calculating the chip flow angle in oblique cutting using flat-faced nose radius tools is described. The projection of the uncut chip area on the rake face is divided into a number of elements parallel to an assumed chip flow direction. The length of each of these elements is used to find the length of the corresponding element on the shear surface using the ratio of the shear velocity to the chip velocity. The area of each element is found as the cross product of the length and its width along the cutting edge. Summing up the area of the elements along the shear surface, the total shear surface area is obtained. The friction area is calculated using the similarity between orthogonal and oblique cutting in the ‘equivalent’ plane that includes both the cutting velocity and chip velocity. The cutting power is obtained by summing the shear power and the friction power. The actual chip flow angle and chip velocity are obtained by minimizing the cutting power with respect to both these variables. The shape of the curved shear surface, the chip cross section and the cutting force obtained from this model are presented.     

Influence of the cutting edge rounding on the chip formation process: Part 1. Investigation of material flow, process forces, and cutting temperature

In order to meet the ever-increasing demand for high quality and low cost products, machining processes with geometrically defined cutting edges such as high speed cutting, or hard turning are being used. Due to the fact that cutting is accomplished through a physical interaction between the cutting edge and the workpiece, the characteristics of the cutting edge itself play a key role in influencing the machining process, which determines the product quality and the tool life. As a result, cutting edge design has attracted the focus of many researchers, and crucial improvements have been achieved. Rounded cutting edges have been found to improve the tool life, and the product quality. However, to better understand the impact of prepared cutting edges on the aspects of the machining processes, and to produce tailored cutting edges for specific load profiles, further investigation on the influence of the cutting edge design on the machining processes needs to be carried out. In this study, the effect of symmetrically and asymmetrically rounded cutting edge on the material in the vicinity of the cutting edge has been investigated using finite element simulation techniques. The results obtained from this investigation show that process forces and material flow under the flank face are mainly influenced by the micro-geometry S_??. However, the magnitude and the location of maximum nodal temperature are influenced by S_?? as well as S_??.     

Modelling the effects of tool-edge radius on residual stresses when orthogonal cutting AISI 316L

Tool-edge geometry has significant effects on the cutting process, as it affects cutting forces, stresses, temperatures, deformation zone, and surface integrity. An Arbitrary-Lagrangian–Eulerian (A.L.E.) finite element model is presented here to simulate the effects of cutting-edge radius on residual stresses (R.S.) when orthogonal dry cutting austenitic stainless steel AISI 316L with continuous chip formation. Four radii were simulated starting with a sharp edge, with a finite radius, and up to a value equal to the uncut chip thickness. Residual stress profiles started with surface tensile stresses then turned to be compressive at about 140 μm from the surface; the same trend was found experimentally. Larger edge radius induced higher R.S. in both the tensile and compressive regions, while it had almost no effect on the thickness of tensile layer and pushed the maximum compressive stresses deeper into the workpiece. A stagnation zone was clearly observed when using non-sharp tools and its size increased with edge radius. The distance between the stagnation-zone tip and the machined surface increased with edge radius, which explained the increase in material plastic deformation, and compressive R.S. when using larger edge radius. Workpiece temperatures increased with edge radius; this is attributed to the increase in friction heat generation as the contact area between the tool edge and workpiece increases. Consequently, higher tensile R.S. were induced in the near-surface layer. The low thermal conductivity of AISI 316L restricted the effect of friction heat to the near-surface layer; therefore, the thickness of tensile layer was not affected.     

The edge force components in oblique cutting

It is shown that in an oblique cutting operation two of the edge force components can be derived on the basis of the hypotheses: (a) that there exists an equivalent orthogonal cutting operation which is such that the depth of the layer of workpiece material which is extruded below the cutting edge in oblique cutting, h, is equal to that which would be extruded below the cutting edge in this equivalent orthogonal cutting operation, and (b) the area of contact between the flank face and the extruded layer in oblique cutting is that which would exist in the equivalent orthogonal cutting operation.By applying these hypotheses, expression for the edge force component acting normal to the generated surface, F_v′, and that acting along the cutting speed direction, F_c′, are derived and are verified using empirical cutting data. It has not proved possible to formulate a model from which the edge force component acting along the cutting edge direction, F₂′, can be deduced. However, on the basis of conjecture, a simple-minded argument is advanced which leads to an expression for F₂′. This expression is verified using empirical force data.     

Generalized modeling of chip geometry and cutting forces in multi-point thread turning

A generalized mechanics model of multi-point thread turning operations is presented. The cross section of the chip is determined from the thread profiles of the current and previous teeth as well as the infeed settings of the tool. The chip is discretized along the cutting edge, and the cutting force coefficients are evaluated for each element considering the varying effective oblique cutting angles and chip thickness. The nonlinear Kienzle force model is used to account for the effect of edge radius at low chip thickness values. Total cutting forces are obtained by resolving the elemental forces in the insert coordinate system, and integrating them along the engaged teeth. The experimentally validated generalized mechanics model can be used to predict the chip and cutting load distributions for multi-point inserts with custom thread profiles and infeed plans. The model can be used for both process planning and insert design.     

受限解空间下粗粒度正则化的熔池边缘自适应检测方法

边缘检测是熔池图像处理的关键步骤. 鉴于熔池区域弧光变化剧烈,依赖人为设置阈值的边缘检测方法难以适应弧光的动态变化过程,文中提出了一种基于深度学习的熔池边缘提取模式. 首先对原始熔池图像进行像素级标注和数据增广以构建数据集;其次结合先验知识提出了一种受限解空间下的粗粒度正则化方法(coarse grained regularization method in restricted solution space, CGRRSS)以增强边缘特征;最后从定量和定性两方面将所提方法与传统方法进行了对比. 结果表明,所提方法对边缘点的召回率较高,所获熔池边缘更连续且对伪边缘具有更好的抑制作用. 单幅图像检测时间6.2 ms,可满足在线监测需求.     

The effects of chamfered and honed tool edge geometry in machining of three aluminum alloys

The effects of tool edge geometry in machining have received much attention in recent years due to a variety of emerging machining techniques, such as finish hard turning and micro-machining. In these techniques, the uncut chip thickness is often on the same order of magnitude as tool edge dimension. This paper presents and analyses the results of our recent experimental and theoretical study on the effects of tool edge geometry in machining. Both chamfered and honed tools are investigated covering a wide range of cutting speed and feed rate conditions. The three aluminum alloys 7075-T6, 6061-T6, and 2024-T351 are selected as work materials for particular research purposes. The cutting force, the thrust force, the ratio of the cutting force to the thrust force, and the chip thickness are measured. The similarities and differences in machining with a chamfered tool and with a honed tool are compared. A new slip-line model of chip formation for machining with a chamfered tool is proposed. Good agreement has been reached between the predicted and experimental results. The effects of different aluminum alloys and cutting speeds on the cutting forces, especially on the thrust force, are also studied.     

Cutting edge rounding: An innovative tool wear criterion in drilling CFRP composite laminates

An evenly and smoothly distributed abrasion wear, observed along the entire cutting edge of an uncoated carbide drill bit in drilling CFRPs, is due to the highly abrasive nature of the carbon fibres. A very few researchers have only quoted this wear mode as being responsible for giving rise to the rounding of the cutting edge, or its bluntness. However, this wear feature has seldom been investigated, unlike the conventional flank wear in practice. This paper offers a new approach in unveiling and introducing the cutting edge rounding (CER) – a latent wear characteristic as a measure of sharpness/bluntness – of uncoated cemented carbide tools during drilling CFRP composite laminates. Four different types of drills (conventional and specialised) were tested to assess the applicability and relevance of this new wear feature. Mechanical loads (drilling thrust and torque) were recorded, and the hole entry and exit delamination were quantified. For the utilised tools, the accruing magnitude of CER was also recorded, in parallel with studying their conventional flank wear. Very appreciable correlations between the CER and the drilling loads, and also the quantitative delamination results are observed. Results reveal that this new wear type develops almost similarly for the selected tools and is practically independent of their respective conventional flank wear patterns. Moreover, a distinct, non-zero magnitude of the CER for a very fresh tool state may provide researchers with some lucid information in further studying the results during wear tests, more emphatically. The CER correlations with quantitative delamination results are noticed quite comparable to those of the conventional flank wear via statistical linear regression analyses.     

Performance of cryogenically treated WC drill using tool wear measurements on the cutting edge and hole surface topography when drilling CFRP

Drilling CFRP poses major challenges from the perspective of rapid tool wear and poor hole quality, with the development of higher strength fibers further accentuating these problems. Cryogenic treatment is one way of increasing tool hardness thereby improving tool life and hole quality through longer retention of cutting edge sharpness. In this study, tool wear is monitored by measuring flank wear, cutting edge flatting (CEF), peak flatting (PF) and cutting edge surface roughness (CESR). While flank wear is unable to distinguish the better performance of the cryo-treated drill from the untreated drill, the other wear parameters are able to account for the better hole quality (exit delamination) produced by this drill. CEF and PF are direct measures of the extent of cutting edge blunting unlike flank wear which measures wear along the flank due to rubbing. Fiber pullout is the primary reason for deterioration in surface finish and Rz and Rv are better measures than Ra in estimating surface quality.     

Development of freeform grinding methods for complex drill flank surfaces and cutting edge contours

This paper details the development of an innovative freeform grinding method that enables the generation of complex drill flank surfaces and cutting edge contours that are non-quadratic model based. This method allows a direct and independent design of drill cutting angle distributions—normal rake angle (γ_n) and relief angle (α_f). Mathematical formulations were first developed for γ_n and α_f in terms of drill geometric parameters such as helix angle, flute contour, and cutting edge contour. The developed freeform grinding methods enhance the flexibility of the grinding process by enabling the production of drills with convex and concave flank surfaces and complex cutting edge contours with standard wheel sets, eliminating the need to manufacture specially designed form grinding wheels.