The deformation of material leads to severe thermal-mechanical effects during metal cutting with chamfered insert. The high cutting temperature on the contact face results in the wear of the insert which is a critical issue. However, there is still a lack of a comprehensive understanding of thermal-mechanical effects, especially with respect to the presence of the tool flank wear. To address this, an analytical thermal-mechanical model is developed in this paper for the prediction of the temperature distribution with a worn insert based on a modified slip-line field approach. Firstly, an analytical slip-line field model is introduced based on material plasticity and ploughing theory considering the tool flank wear. The structure of the slip-line field model, especially at the dead metal zone and the flank zone, is modified to reveal the material flow mechanism. Then, heat sources, including primary heat source, secondary heat source, tertiary heat source and fourth heat source, are clarified to explain the heat generation phenomenon in the cutting process. In addition, a cutting temperature field model is developed to show the effect of tertiary heat source based on the imaginary heat source theory. Finally, the slip-line field geometry and temperature distribution are extracted from two-dimensional finite element simulation to verify the proposed model. And orthogonal experiments are carried out for measuring the maximum cutting temperature. The good agreement of predicted results, simulated results, and experimental results verifies the accuracy of the proposed model.
Research Article
Thermal-mechanical model for machining with chamfered insert considering tool flank wear
https://doi.org/10.21203/rs.3.rs-1719730/v1
This work is licensed under a CC BY 4.0 License
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Chamfered insert
Slip-line field
Temperature prediction
Flank wear
Metal cutting is a process that the chip is separated from the workpiece through the movement of the tool and the workpiece, which includes complex physical phenomena such as elastic and plastic deformation, shearing and extrusion. The slip-line field (SLF) is widely used in the machining field, considering the micro-edge effect due to high-precision and high-quality machining requirements [1].
Merchant [2] examined the application of SLF in metal cutting studies. The study tested the SLF of a single shear plane and showed that the method was an effective tool for simulating chip formation, cutting temperature, cutting force, stress, and strain in cutting process. Previously, SLF for machining was mainly developed as sharp edge tool. Researchers clarified the great importance of chamfered inserts in the machining process especially on the aspects of excellent edge strength and enhanced tool life. More recently, a number of studies had explored the thermal-mechanical behavior in the cutting process with chamfered insert. Fang and Wu [3] established the SLF for machining with a chamfered insert and investigated the influence of the cutting speed on cutting force. Force ratios of three aluminum alloys were calculated by the proposed model and the findings were close to experimental results. Ren and Altintas [4] investigated the influence of chamfer features and cutting speed on forces with an analytic model. The proposed model was designed to determine the suitable chamfer features, resulting in a more precise outcome due to lower cutting forces. Weng et al. [5] developed a novel model to describe the influence of various chamfer edge types on cutting forces. Zhou et al. [6] studied the effect of chamfer angle on tool wear in the superfinishing hard turning with PCBN cutting tools. In summary, the above research deeply explored the influence of chamfered tool edge on cutting performance and provided a reference for edge preparation. In addition to cutting performance, friction and stress-strain effect of cutting process are also evaluated. Karpat and Ozel [7] employed an analytical model to explore the dead metal zone (DMZ) and the friction factor at the secondary deformation zone when cutting with a chamfered insert. Zhang et al. [8] used digital image technology to analyze the kinematic field when cutting with CBN chamfered insert and AISI 4140, then explored the strain rate, velocity and SLF during the cutting process. However, there is less research on the working condition of worn chamfered inserts, especially on the modeling of cutting temperature.
Cutting temperature is an important physical quantity to evaluate the cutting process. Edge micro-geometry has been claimed as a crucial factor for the temperature on the machined surface [9, 10]. There are a lot of detailed studies focusing on the importance of cutting temperature in metal cutting. Komanduri and Hou [11] presented a semi-infinite medium oblique band heat source approach to predict the cutting temperature. They published a set of thermal models for the cutting process, which provided a solid basis for further studies. More specifically, their models were based on sharp edge tools, which were easy to break. Karpat and Özel [12] extended Komanduri’s research and focused on predicting temperature in the high speed cutting condition with chamfered inserts. In general, the material shear flow stress is the most important factor to be considered when estimating cutting force. Karpat’s study, on the other hand, offered a creative way for determining cutting force without directly measuring the material shear flow stress. Based on previous studies, Hu et al. [13] presented a modified 3-D analytical model for predicting cutting temperature, which shows the applicability of SLF method in three-dimensional field. Aydin [14] dealt with the temperature distribution when cutting with a sharp tool by an analytical model based on Oxley’s machining theory. Wang et al. [15] got precise temperature distribution during cryogenic machining by the established thermal model based on the imaginary heat source approach. Wu et al. [16] proposed a novel temperature predicted method for end milling, which is analyzed in temperature increase phase and temperature decrease phase. Experimental and simulated methods are also used in the study of cutting temperature. Saini et al. [17] carried out an experimental study and discussed the effect of cutting parameters on tool tip temperature during dry turning with AISI 4340. Natasha et al. [18] used simulated and experimental technology to compare the difference in temperature distribution and chip formation between the cryogenic and dry environment during turning with AISI 4340. Results illustrated that turning with liquid nitrogen cooling could effectively reduce the cutting temperature, and the highest temperature was always on the rake face.
The flank wear phenomenon often occurs gradually during machining. As tool flank wear intensifies, the cutting temperature increases and the tool life decreases. Huang and Liang [19] derived the distribution of the average temperature along the flank-workpiece contact interface. Cui et al. [20] reported the cutting temperature in milling while taking flank wear into account, which can properly forecast the temperature of a fresh or worn tool. Xiong et al. [21] brought up an analytical predicted model to forecast the temperature in milling by a worn bottom edge with the consideration of the effect of heating time. Cutting temperature has always been a hot topic in cutting research. However, there is little temperature model for cutting with a worn chamfered insert, and details of this cutting condition are not clear yet.
The focus of this study is to predict the cutting temperature when cutting with the flank-wear chamfered insert. Firstly, a modified SLF considering tool flank wear effect is proposed based on plasticity theory, which reveals the material flow mechanism during the cutting process, especially at the tertiary deformation zone. Secondly, a novel iterative method is introduced to the proposed SLF aiming at determining the intensity of all the heat sources. Additionally, a temperature field model is suggested based on imaginary heat source theory, indicating the temperature increase by four heat sources and their imaginary heat sources when cutting with worn chamfered insert. Finally, 2-D finite element (FE) simulations and dry turning experiments of AISI 4340 steel with a worn chamfered insert are used to validate the developed models. A satisfactory agreement is reached between the predictions, simulations and measurement.
This paper is divided into five sections. Section 1 introduces a wide range of published SLF in various working conditions. A modified SLF is proposed in section 2, which explains the hypothetical SLF in cutting process. Also, an iterative strategy for calculating cutting force and geometry of SLF is developed by employing the modified SLF. In section 3, a temperature distribution predicted model is proposed. 2-D FE simulations and orthogonal cutting experiments are utilized to validate this temperature prediction approach in section 4. The prediction results, simulation results, and experimental results reveal satisfying consistency. The last section presents conclusions.
2.1 Modified SLF
Based on the plastic deformation theory, the SLF is potentially helpful for investigating both cutting forces and chip formation in metal cutting operation. Since the SLF is an analytical model, this method may have discrepancies such as being less intensive in computation and time-consuming compared to numerical methods such as FE simulation.
As shown in Fig. 1, modified SLF and hodograph are given for orthogonal cutting with a worn chamfered insert. The model deals with the situation that the chamfered length lAB is smaller than uncut chip thickness h, and the chamfered face is completely covered by the formed chip.
The modified SLF mainly includes the following regions. ACDEFGHIJ is the primary deformation zone. In this shear and plastic deformation zone, the material changes to the chip from the bulk where shear and plastic deformation mainly occur. Especially, the DEF area is called the pre-flow zone while ρ is called prow angle. DMZ is the triangle-like region ABC with a curved edge BC highlighted in Fig. 1, and often recognized as a stable rigid body before the contact face. Point C is the separation point, and part of the material flows upward along with the DMZ-tool interface and leaves the surface of the workpiece, the other part of the material flows along the DMZ bottom and forms a machined surface finally. The main slip-line field DBC is a fan area regulated by the slip-line angle θ. The shear velocity converts to the chip velocity in this region. The friction factor angle ξ4 controls the right-triangle region BML in which the sliding contact occurs [22]. Similarly, AJK is the tertiary deformation zone. Dimension of this region is mainly regulated by the friction factor angle ξ1 since it is right-triangle.
The local shear flow stresses on interfaces can be calculated by
$$\left\{ {\begin{array}{*{20}{c}} {{\tau _{AK}}=k\cos \left( {2{\xi _1}} \right)} \\ {{\tau _{AB}}=k\cos \left( {2{\xi _2}} \right)} \\ {{\tau _{BL}}=k\cos \left( {2{\xi _4}} \right)} \end{array}} \right.$$
1
The value of the material shear flow stress k depends on strain, strain rate and temperature. It is worth noticing that the friction factor angle ξ2 is assumed to be zero, which means τAB equals k.
Considering the continuity of the speed in the shear plane, the rising height of the vertex D keeps consistent with the rising height of the DMZ-workpiece interface. That means the height from unprocessed surface to point D should equal the height from machined surface to point C. The prow angle can be expressed by the following formula [23].
$$\rho ={\sin ^{ - 1}}\left( {\frac{{{l_{AC}}\sin \left( \beta \right)}}{{\sqrt 2 {l_{AK}}\sin \left( {{\xi _1}} \right)}}} \right)$$
2
where lAK is the tool flank wear length. lAC is the length of the DMZ bottom side. β is the angle between the DMZ bottom side and the cutting speed direction.
The shear angle ϕ can be given as
$$\phi =\frac{\pi }{4} - \rho$$
3
δ 1 and δ2 is the fan angle of region CGH and AIJ.
$${\delta _1}=\phi - \beta$$
4
$${\delta _2}=\beta +{\xi _1} - \alpha$$
5
θ is the slip-line angle.
$$\theta =\phi - {\xi _4}$$
6
l CD is equal to the length of the shear plane, which is given as
$${l_{CD}}=\frac{{h - {l_{AK}}\sin \left( \alpha \right)}}{{\sin \left( \phi \right)}}$$
7
t ch represents chip thickness which can be calculated by
$${t_{ch}}={l_{CD}}\cos \left( {{\xi _4}} \right)$$
8
l BL stands for the length of tool-chip contact interface and is defined by
$${l_{BL}}={t_{ch}}\left( {\tan \left( {\frac{\pi }{4} - {\xi _4}} \right)+\tan \left( {{\xi _4}} \right)} \right)$$
9
Lengths and angles of the SLF follow a strict geometric relationship. Thus, all these expressions can be derived from four initial inputs, namely ξ1, ξ4, lAC and β.
The force experienced by the tool during the cutting process includes cutting force and thrust force. The DMZ stagnating before the chamfered face is modeled as a stable rigid body and regarded as a part of the tool when analyzing the contact force [24]. The total force in cutting can be divided into four parts in this situation. The first part locates at the flank-workpiece interface, which decomposes into two component forces (i.e., F2 in tangential direction and N2 in normal direction). The second part is at the DMZ-workpiece interface. Two-component forces characterize it as F2 in the tangential direction and N2 in the normal. The third part (arc BC) is the sticking zone. The component force N3 represents the simplified resultant force, ignoring the tangential force. The fourth part (line BL) is the sliding zone where the contact force is composed of N4 and F4.
Specifically, expressions are as follows.
$$\left\{ {\begin{array}{*{20}{l}} {{F_{_{1}}}=kw\cos \left( {2{\xi _1}} \right){l_{AK}}} \\ {{N_1}=kw\left( {1+2{\delta _1}+2{\delta _2}+\sin \left( {2{\xi _1}} \right)} \right){l_{AK}}} \\ {{F_2}=kw{l_{AC}}} \\ {\begin{array}{*{20}{l}} {{N_2}=kw\left( {1+2{\delta _1}} \right){l_{AC}}} \\ {{N_3}=kw\left( {1+2{\xi _4}} \right){l_{BC}}} \\ {{F_4}=kw\cos \left( {2{\xi _4}} \right){l_{BL}}} \\ {{N_4}=kw\left( {1+\sin \left( {2{\xi _4}} \right)} \right){l_{BL}}} \end{array}} \end{array}} \right.$$
10
Therefore, Fc and Ft can be determined through following matrix.
$$\left[ {\begin{array}{*{20}{c}} {{F_c}} \\ {{F_t}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {\cos \left( \alpha \right)}&{\begin{array}{*{20}{c}} {\sin \left( \alpha \right)}&{\cos \left( \beta \right)}&{\sin \left( \beta \right)}&{\begin{array}{*{20}{c}} {\cos \left( {\phi - \frac{\theta }{2}} \right)}&{ - \sin \left( {{\gamma _2}} \right)}&{\cos \left( {{\gamma _2}} \right)} \end{array}} \end{array}} \\ { - \sin \left( \alpha \right)}&{\begin{array}{*{20}{c}} {\cos \left( \alpha \right)}&{ - \sin \left( \beta \right)}&{\cos \left( \beta \right)}&{\begin{array}{*{20}{c}} { - \sin \left( {\phi - \frac{\theta }{2}} \right)}&{\cos \left( {{\gamma _2}} \right)}&{\sin \left( {{\gamma _2}} \right)} \end{array}} \end{array}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {{F_1}} \\ {{N_1}} \end{array}} \\ {{F_2}} \\ {{N_2}} \end{array}} \\ {{N_3}} \\ {{F_4}} \\ {{N_4}} \end{array}} \right]$$
11
2.2 Developed iterative methodology
In this section, the SLF geometry can be determined using an iterative method with the measured data. Specifically, a series of orthogonal experiments are carried out to get the initial input data, namely the Fc, Ft, and t. They are placed into the iterative system and then the most suitable SLF geometry can be computed. The realization of the iteration method mainly relies on the tolerance ΔD, which represents the deviation of the prediction and measurement.
$$\Delta D=\sqrt {{{\left( {\frac{{{F_{cp}}}}{{{F_{tp}}}} - \frac{{{F_{cm}}}}{{{F_{tm}}}}} \right)}^2}+{{\left( {\frac{{{t_{cp}}}}{h} - \frac{{{t_{cm}}}}{h}} \right)}^2}}$$
12
Details of the iterative process can be found in Fig. 3. With the given cutting condition, ξ1, ξ4, β, and lAC are selected as the initial input combination. A set of SLF geometry can be calculated by the previously derived formulations. It is necessary to compare the value of ΔD and the initial tolerance (0.5) to verify whether the current output SLF geometry is the most perfect combination matched with the cutting condition well.
According to the Hill overstress theory, the iterative operation has a boundary constraint, which states that the area between the stress line and the rigid line must be within an accepted level to avoid overstress. This range is deduced with [25]
$$- 1+2\cos (\eta - \frac{\pi }{4}) \leqslant \frac{{{P_D}}}{k} \leqslant 1+2(\eta - \frac{\pi }{4})$$
13
where 𝜂 represents the deflection angle and ranges from 𝜋/4 to 3𝜋/4. PD is the hydrostatic stress at point D and can be given as
$${P_D}=k(1+2\theta +2\delta )$$
14
With the help of the test results in cutting experiments, the curves that indicate the variation between ξ1, ξ4, β, lAC and tool flank wear can be fitted. The proposed iterative calculation method based on the SLF offers a novel idea for calculating the material shear flow stress k. In addition, the SLF geometry and the local shear flow stresses on each interface can be yielded, which can be employed to solve the thermal issue of chamfered inserts during cutting.
3.1 Multi heat sources
The heat generated during metal cutting is generally considered to be generated by the shear deformation of the material and the friction behavior between tool and workpiece [26]. However, there is a slight difference and challenge while cutting with worn chamfered inserts because the DMZ and the flank wear land complicate the thermal distribution and material flow [27]. It is necessary to gain a complete explanation of the thermal generation in this kind of cutting condition.
As shown in Fig. 4, the heat sources of the cutting process with worn chamfered insert mainly include four sections. The primary heat source (PHS) is produced during the shear deformation process (line DC). The secondary heat source (SHS) represented by BL is generated by the friction between the chip and rake face (line LB). The tertiary heat source (THS) is generated by the friction in flank-workpiece interface (line AK). The fourth heat source (FHS) includes the AC and AB sections. The AC section mainly accounts for the shearing and squeezing. Two sides of the AB section are the DMZ and the tool. Both the speeds of the two sides are close to zero. They are approximately keeping relatively static without friction, which means no heat is generated there in principle. The temperature rise in the tool is mostly from SHS, while PHS also contributes to the temperature increase. The AB section heat source, which is called induced heat source, is exactly regarded as the influence of the PHS on the temperature rise in the tool side.
Different heat sources have the same features of being modeled within semi-infinite mediums on different sides [28]. However, as designed, the modeling of each is various. Specifically, the PHS is regarded as a uniform moving oblique band heat source on the chip side while the SHS is regarded as a non-uniform moving band heat source. On the tool side, all heat sources are modeled as non-uniform static rectangular heat sources. On workpiece side, both PHS and FHS are modeled as uniform moving oblique band source, while THS is solely modeled as non-uniform moving heat source.
According to the geometric relationship of the hodograph proposed in Fig. 1, the velocity expressions of each region can be written as follows
$$\left\{ {\begin{array}{*{20}{l}} {{V_{CD}}={V_{cu}}{\text{cos}}\phi {\text{+}}{{\text{V}}_{cu}}{\text{sin}}\phi \tan \left( {{\xi _4}} \right)} \\ {{V_{ch}}=\frac{{{V_{cu}}\sin \phi }}{{\cos \left( {{\xi _4}} \right)}}} \\ {{V_{AC}}=\frac{{{V_{cu}}\sin \rho }}{{\sin \left( {\rho +\phi - {\delta _1}} \right)}}} \\ {{V_{AK}}=\frac{{{V_{cu}}\sin \left( {{\xi _1} - \alpha } \right)}}{{\sin \left( {{\xi _1}} \right)}}} \end{array}} \right.$$
15
In this way, the intensities of each heat source are defined by the following expressions.
$$\left\{ {\begin{array}{*{20}{l}} {{Q_1}={\tau _{CD}}{V_{CD}}=k\left( {{V_{cu}}\cos \left( \phi \right)\tan \left( {{\xi _4}} \right)} \right)} \\ {{Q_2}={\tau _{BL}}{V_{ch}}=k\cos \left( {2{\xi _4}} \right)\frac{{{V_{cu}}\sin \left( \phi \right)}}{{\cos \left( {{\xi _4}} \right)}}} \\ {{Q_3}={\tau _{AK}}{V_{AK}}=k\cos \left( {2{\xi _1}} \right)\frac{{{V_{cu}}\sin \left( {{\xi _1} - \alpha } \right)}}{{\sin \left( {{\xi _1}} \right)}}} \\ {{Q_4}={\tau _{AC}}{V_{AC}}=k\frac{{{V_{cu}}\sin \left( \rho \right)}}{{{\text{sin}}\left( {\rho +\phi - {\delta _1}} \right)}}} \end{array}} \right.$$
16
3.2 Temperature rise model
Figure 5 shows temperature rise by the heat sources and imaginary heat sources at the workpiece. Point P in the figure is that point whose temperature is to be calculated. The expression for the temperature rises in the workpiece during the cutting process is derived as
$${T_w}=\left\{ {\begin{array}{*{20}{l}} {\frac{{{Q_1}}}{{2\pi {\lambda _w}}}\int_{0}^{{{l_{CD}}}} {{e^{\left[ {x - \left( {{x_D}+{l_i}\cos \left( \phi \right)} \right)} \right]\frac{{{V_{cu}}}}{{2{a_w}}}}}} \left[ {{K_0}\left( {\frac{{{V_{cu}}{R_1}}}{{2{a_w}}}} \right)+{K_0}\left( {\frac{{{V_{cu}}{{R^{\prime}}_1}}}{{2{a_w}}}} \right)} \right]d{l_i}} \\ {+\frac{{{S_m}{Q_4}}}{{2\pi {\lambda _w}}}\int_{0}^{{{l_{AC}}}} {{e^{\left[ {x - \left( {{x_C}+{l_i}\cos \left( \beta \right)} \right)} \right]\frac{{{V_{cu}}}}{{2{a_w}}}}}} \left[ {{K_0}\left( {\frac{{{V_{cu}}{R_2}}}{{2{a_w}}}} \right)+{K_0}\left( {\frac{{{V_{cu}}{{R^{\prime}}_2}}}{{2{a_w}}}} \right)} \right]d{l_i}} \\ {+\frac{{B_{3}^{{wp}}{Q_3}}}{{\pi {\lambda _w}}}\int_{0}^{{{l_{AK}}}} {{e^{\left[ {x - \left( {{x_A}+{l_i}\cos \left( \alpha \right)} \right)} \right]\frac{{{V_{cu}}}}{{2{a_w}}}}}} \left[ {{K_0}\left( {\frac{{{V_{cu}}{R_3}}}{{2{a_w}}}} \right)+{K_0}\left( {\frac{{{V_{cu}}{{R^{\prime}}_3}}}{{2{a_w}}}} \right)} \right]d{l_i}} \end{array}} \right.$$
17
where K0 represents the modified Bessel function of the second kind. The meaning of Sm just mentioned is the partition of the FHS to the work piece part, which is valued 0.2 according to Karpat and Özel [12].
The influence that heat sources and imaginary heat sources rise temperature on the chip is shown in Fig. 6. The chip temperature rises during the cutting process can be deduced with
$${T_c}=\left\{ {\begin{array}{*{20}{l}} {\frac{{{Q_1}}}{{2\pi {\lambda _w}}}\int_{0}^{{{l_{CD}}}} {{e^{ - \left[ {\left( {y - {y_D}} \right)+{l_i}\sin \left( \phi \right)} \right]\frac{{{V_{cu}}}}{{2{a_w}}}}}} \left[ {{K_0}\left( {\frac{{{V_{cu}}{R_4}}}{{2{a_w}}}} \right)+{K_0}\left( {\frac{{{V_{cu}}{{R^{\prime}}_4}}}{{2{a_w}}}} \right)} \right]d{l_i}} \\ {+\frac{{{S_m}{Q_4}}}{{2\pi {\lambda _w}}}\int_{0}^{{{l_{AC}}}} {{e^{ - \left[ {\left( {y - {y_D}} \right)+{l_{CD}}\sin \left( \phi \right)+{l_i}\sin \left( \beta \right)} \right]\frac{{{V_{cu}}}}{{2{a_w}}}}}} \left[ {{K_0}\left( {\frac{{{V_{cu}}{R_5}}}{{2{a_w}}}} \right)+{K_0}\left( {\frac{{{V_{cu}}{{R^{\prime}}_5}}}{{2{a_w}}}} \right)} \right]d{l_i}} \\ {+\frac{{B_{1}^{{chip}}\left( {1 - {S_m}} \right){Q_4}}}{{\pi {\lambda _w}}}\int_{0}^{{{l_{AB}}}} {{e^{ - \left[ {\left( {y - {y_A}} \right) - {l_i}\cos \left( {{\gamma _1}} \right)} \right]\frac{{{V_{cu}}}}{{2{a_w}}}}}} \left[ {{K_0}\left( {\frac{{{V_{cu}}{R_6}}}{{2{a_w}}}} \right)+{K_0}\left( {\frac{{{V_{cu}}{{R^{\prime}}_6}}}{{2{a_w}}}} \right)} \right]d{l_i}} \\ {+\frac{{B_{2}^{{chip}}{Q_2}}}{{\pi {\lambda _w}}}\int_{0}^{{{l_{BL}}}} {{e^{ - \left[ {\left( {y - {y_B}} \right) - {l_i}} \right]\frac{{{V_{cu}}}}{{2{a_w}}}}}} \left[ {{K_0}\left( {\frac{{{V_{cu}}{R_7}}}{{2{a_w}}}} \right)+{K_0}\left( {\frac{{{V_{cu}}{{R^{\prime}}_7}}}{{2{a_w}}}} \right)} \right]d{l_i}} \end{array}} \right.$$
18
Figure 7 depicts the influence that heat sources and imaginary heat sources rise temperature on the tool side. The tool temperature rises during the cutting process is obtained by
$${T_t}=\left\{ {\begin{array}{*{20}{l}} {\frac{{B_{3}^{{tool}}{Q_3}}}{{2\pi {\lambda _t}}}\int_{0}^{{{l_{AK}}}} {\int_{{ - \frac{w}{2}}}^{{\frac{w}{2}}} {\left( {\frac{1}{{{R_8}}}+\frac{1}{{{{R^{\prime}}_8}}}} \right)} } d{l_i}d{z_i}} \\ {+\frac{{B_{1}^{{tool}}\left( {1 - {S_m}} \right){Q_4}}}{{2\pi {\lambda _t}}}\int_{0}^{{{l_{AB}}}} {\int_{{ - \frac{w}{2}}}^{{\frac{w}{2}}} {\left( {\frac{1}{{{R_9}}}+\frac{1}{{{{R^{\prime}}_9}}}} \right)} } d{l_i}d{z_i}} \\ {+\frac{{B_{2}^{{tool}}{Q_2}}}{{2\pi {\lambda _t}}}\int_{0}^{{{l_{BL}}}} {\int_{{ - \frac{w}{2}}}^{{\frac{w}{2}}} {\left( {\frac{1}{{{R_{10}}}}+\frac{1}{{{{R^{\prime}}_{10}}}}} \right)} } d{l_i}d{z_i}} \end{array}} \right.$$
19
Especially, \(B_{1}^{{chip}}\) represents the heat distribution fraction that the FHS distributes to the chip at chamfered face. \(B_{2}^{{chip}}\) illustrates the heat distribution fraction that the SHS distributes to the chip at the rake face. \(B_{3}^{{wp}}\) is the heat distribution fraction that the THS distributes to the workpiece at flank wear zone. \(B_{1}^{{tool}}\) represents the heat distribution fraction that the FHS distributes to the tool at chamfered face. \(B_{2}^{{tool}}\) illustrates the heat distribution fraction that the SHS distributes to the tool at the rake face. \(B_{3}^{{tool}}\) represents the heat distribution fraction that the THS distributes to the tool at the flank wear zone. These fractions are both nonlinear and can be described as
$$\left\{ {\begin{array}{*{20}{l}} {\begin{array}{*{20}{l}} {B_{1}^{{chip}}=\left( {{B_{c1}} - \Delta {B_1}} \right)+2\Delta {B_1}{{\left( {\frac{{{l_i}}}{{{l_{AB}}}}} \right)}^{{m_1}}}+{C_1}\Delta {B_1}{{\left( {\frac{{{l_i}}}{{{l_{AB}}}}} \right)}^{{k_1}}}} \\ {B_{2}^{{chip}}=\left( {{B_{c2}} - \Delta {B_2}} \right)+2\Delta {B_2}{{\left( {\frac{{{l_i}}}{{{l_{BL}}}}} \right)}^{{m_2}}}+{C_2}\Delta {B_2}{{\left( {\frac{{{l_i}}}{{{l_{BL}}}}} \right)}^{{k_2}}}} \\ {B_{3}^{{wp}}=\left( {{B_{c3}} - \Delta {B_3}} \right)+2\Delta {B_3}{{\left( {\frac{{{l_i}}}{{{l_{AK}}}}} \right)}^{{m_3}}}+{C_3}\Delta {B_3}{{\left( {\frac{{{l_i}}}{{{l_{AK}}}}} \right)}^{{k_3}}}} \end{array}} \\ {B_{1}^{{tool}}=\left( {{B_{t1}}+\Delta {B_1}} \right) - 2\Delta {B_1}{{\left( {\frac{{{l_i}}}{{{l_{AB}}}}} \right)}^{{m_1}}} - {C_1}\Delta {B_1}{{\left( {\frac{{{l_i}}}{{{l_{AB}}}}} \right)}^{{k_1}}}} \\ {B_{2}^{{tool}}=\left( {{B_{t2}}+\Delta {B_2}} \right) - 2\Delta {B_2}{{\left( {\frac{{{l_i}}}{{{l_{BL}}}}} \right)}^{{m_2}}} - {C_2}\Delta {B_2}{{\left( {\frac{{{l_i}}}{{{l_{BL}}}}} \right)}^{{k_2}}}} \\ {B_{3}^{{tool}}=\left( {{B_{t3}}+\Delta {B_3}} \right) - 2\Delta {B_3}{{\left( {\frac{{{l_i}}}{{{l_{AK}}}}} \right)}^{{m_3}}} - {C_3}\Delta {B_3}{{\left( {\frac{{{l_i}}}{{{l_{AK}}}}} \right)}^{{k_3}}}} \end{array}} \right.$$
20
Since the temperature expression has been derived, the cutting temperature at any position can be calculated easily. At the same time, the cutting temperature field as well as the highest temperature peak can be drawn.
4.1 Validation of SLF considering flank wear
The cutting thickness is much smaller than the width of cut in the simulation. In the cutting width direction, the strain state and flow direction of the chips at each point on the cutting edge are roughly the same. After reasonable simplifications and assumptions, the dry machining model was finally simplified into a simpler plane-strain orthogonal cutting model.
The Johnson-Cook model, which is ideal for describing the material viscoplasticity and hardening characteristics that changed with the temperature at large strain rates condition, is adopted in this study. It is very suitable for the cutting process simulation. The constitutive equation expression is shown in Eq. (21). Johnson-Cook model parameters of AISI 4340 are shown in Table 1.
$$\bar {\sigma }=\left( {A+B{{\bar {\varepsilon }}^n}} \right)\left[ {1+C\ln \left( {\frac{{\dot {\bar {\varepsilon }}}}{{{{\dot {\bar {\varepsilon }}}_0}}}} \right)} \right]\left( {1 - {{\frac{{T - {T_r}}}{{{T_m} - {T_r}}}}^m}} \right)$$
21
| A/MPa | B/MPa | C | m | n | Tm/K |
|---|---|---|---|---|---|
| 792 | 510 | 0.014 | 1.03 | 0.26 | 1520 |
During the machining process, the chips flow along the tool rake face and squeeze the rake face, and friction phenomenon is highly complicated. Therefore, the use of a reasonable friction model can make the simulation results more realistic and reliable. A modified coulomb friction model is adopted in this article. It can be defined by
$${\tau _f}=\left\{ {\begin{array}{*{20}{l}} {\begin{array}{*{20}{c}} {{\tau _{\hbox{max} }},}&{\mu {\sigma _n} \geqslant {\tau _{\hbox{max} }}} \end{array}} \\ {\begin{array}{*{20}{c}} {\mu {\sigma _n},}&{\mu {\sigma _n}<{\tau _{\hbox{max} }}} \end{array}} \end{array}} \right.$$
22
In this formula, τf represents the friction stress, τmax represents the limiting shearing stess, µ represents the friction coefficient, and σn represents the normal stress. \(\mu {\sigma _n} \geqslant {\tau _{\hbox{max} }}\) represents the stick friction area, \(\mu {\sigma _n}<{\tau _{\hbox{max} }}\) represents the sliding friction area.
FE simulation is used for the validation of the proposed model. The tool material is cemented carbide, and the workpiece material is AISI 4340. Their physical properties are shown in Table 2. The variant of test is flank wear length, and four groups of different values (lAK) are set. An initial rake angle of 0° was used for all test groups. The width of cut was uniformly defined as 2.5 mm, and the cutting speed was maintained at 75 m/min. Simulated length of cut is 5 mm. It is assumed that the tool is rigid in the simulation.
Figure 8 demonstrates the cutting simulation result (lAK = 0.15 mm) with respect to the material flow direction and DMZ geometry. The regions have been divided into five sections according to the proposed SLF in this figure. The boundary of each part of the SLF roughly fits with the boundary of each region of the simulated velocity field. Furthermore, the material velocity in the triangle-like area before the chamfer face is close to the workpiece area. The phenomenon that material trapped underneath the chamfered face is also observed in some research [30, 31] and this triangle-like area is called DMZ.
The SLF corresponding to various flank wear lengths is obtained in Fig. 9. By comparison, it is evident that the SLF geometry is closely related to the flank wear length, especially the friction factor angle ξ1 of the tertiary deformation zone near the flank wear face. In the 2-D FE simulation, the SLF geometry is extracted with the help of FE simulation software. The cutting force and chip thickness obtained from the orthogonal cutting experiment are put into the iterative calculation system introduced earlier. Finally, the geometric parameters of the SLF corresponding to the cutting experiments can be output using the MATLAB program.
The comparison of predicted and simulated results is demonstrated in Fig. 10. The influence of flank wear on the length of the DMZ bottom edge and the rising angle of the DMZ bottom edge is slight. The friction factor angle of the tertiary deformation zone ξ1 changes linearly with the flank wear length lAK. By fitting the discrete experimental group data, a more accurate functional relationship expression between ξ1 and lAK can be obtained, as shown in Fig. 11. With the help of these functional relations, the SLF geometry of any wear condition can be calculated.
4.2 Validation of temperature distribution with simulation
Figure 12 depicts the comparison results from simulation method and proposed model. The model prediction results and the simulation results have some similar features. There are two prominent temperature centers both of them. For the rake face, the maximum temperature exists near the apex of the chamfered face, and the value is 847°C. For the flank face, the maximum temperature appears far away from the tool tip with a value of 834°C. The simulated temperature field is slightly different than the predicted one.
A series of points are extracted along the contact path K-A-B-J to obtain the temperature distribution at the tool-workpiece interface, chamfered face, and tool-chip interface. The temperature curve with the extracted distance is displayed in Fig. 13 and the predicted and simulated profiles show the same trend. The temperature increases and then decreases from the tool tip to the tool-chip interface. The temperature increases first and then falls from the tool tip to the tool-workpiece interface. The average temperature of the contact surface in the predicted result is 798°C, while that is 757°C in the simulated result. The maximum predicted error with the value of 10.2% appears at point K, and the average error of the value is 7.1%.
The predicted result and simulated result on chip are illustrated in Fig. 14. It is indicated that the peak temperature occurs at the contact boundary, and the position of highest temperature corresponds to the location of peak temperature on tool side.
The temperature field on workpiece side obtained from the proposed model and simulated technology is given in Fig. 15. The prediction results show that the highest temperature appears at the position 0.05mm away from the point K at flank-workpiece interface with the value of 831°C, which is close to the simulation results. The value and location of the maximum temperature on the workpiece side correspond to that on the tool side both in prediction result and simulation result.
4.3 Validation of temperature fields with cutting tests
In this section, the orthogonal cutting experiments are used to verify the correctness of the proposed models, as shown in Fig. 16. The triangular insert, whose flank face is specially ground to a specific flank wear land from conventional chamfered insert for simulating the wear state in production, is mounted on the tool holder whose rake angle is adjusted to 0 degree. The workpiece is processed with a piece, and its dimension is 50×20×2.5 mm. Kistler 9257B dynamometer is employed to acquire the cutting forces, and FAST M200 thermal camera is utilized to measure the temperatures. As shown in Fig. 17, the tool edge micro-geometry is observed by Alicona Infinite Focus SL. In this paper, the tool material is cemented carbide, and the workpiece material is AISI 4340. The physical properties of these two materials are shown in Table 2.
| Property | AISI 4340 steel [32] | Carbide insert [33] |
|---|---|---|
| Density (kg/m3) | 7850 | 15000 |
| Poisson’s ratio | 0.3 | 0.2 |
| Elastic modulus (GPa) | 208 | 800 |
| Hardness (HRC) | - | 90.1 (HRA) |
| Thermal diffusivity (cm2/s) | 0.1188 | 0.1511 |
| Thermal conductivity (W/m∙K) | 44.5 | 46 |
| Specific capacity (J/kg∙K) | 477 | 203 |
During cutting experiments, the cutting speed keeping constant was 75 m/min and the width of cut was kept at 2.5 mm. Three levels (0.09 mm, 0.14 mm, 0.16 mm) of flank wear length were utilized to verify the proposed model. A comparison of the measured and simulated cutting and thrust forces is given in Fig. 18(a). Fc and Ft extracted by simulation are close to the measured result, which further shows the correctness of the simulated cutting model. It is also observed that the Fc slightly rise as the flank wear length increase, while the Ft sharply rise with the increase of the flank wear length. The reason could be the rise of flank wear length enhances the friction and extrusion effect. Figure 18(b) demonstrates the comparison of the predicted and measured maximum temperature, and result shows that the cutting temperature increases as the flank wear length increases. This is caused by the material flow behavior beneath the flank wear land. When the flank wear phenomenon is inconspicuous, the material flows along with the flank wear land and quickly leaves this area. When the flank wear length increases, the friction effect boosts, and the cutting temperature increases.
In this research, a thermal-mechanical model is presented for predicting the cutting temperature in machining with worn chamfered insert considering tool flank wear effect. Predicted SLF geometry and temperature are close to those obtained by FE simulation and measurement, which validates the accuracy of the predicted model. The main conclusions of this investigation can be drawn:
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A modified SLF model for turning with worn insert considering tool flank wear is proposed based on material flow mechanism. The model mainly includes five regions, including the primary deformation zone, the DMZ, the main SLF, the secondary deformation zone, and the tertiary deformation zone. This model reveals the material flow behavior nearby DMZ and flank wear area.
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An iterative method is proposed to estimate the SLF geometry and the material flow stress with the proposed SLF model. It is found that SLF geometry keeps stable with the varying flank wear length, while the friction factor angle of the tertiary deformation zone changes linearly with the flank wear length.
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A modified thermal model is developed based on the imaginary heat source theory with the consideration of the tool flank wear effect. The intensities and distribution of PHS, SHS, THS, and FHS are determined with the thermal-mechanical model, then the temperature fields on the chip side, workpiece side, and tool side are obtained.
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Orthogonal turning tests of AISI 4340 steel with a worn insert have been carried out. Temperatures acquired from the experiments and the numerical simulations are compared with the predicted results. The comparison results demonstrate that the predicted temperature is in good agreement with the measured result. The results show that the maximum cutting temperature increases as the flank wear length increases.
The work done in this paper is to establish a two-dimensional thermal-mechanical model to predict the cutting temperature. This work can be extended to three-dimensional level, and three-dimensional thermal-mechanical analytical modeling is becoming a hot and difficult point in metal cutting research. Subsequently, based on the existing analytical thermal model, the cutting width is taken into account to obtain a more comprehensive thermal predicted method for oblique cutting with the consideration of the flank wear effect.
Funding
This work was supported by the National Natural Science Foundation of China (52175482), and the State Key Laboratory of Digital Manufacturing Equipment and Technology (DMETKF2021005).
Competing Interests
The authors have no relevant financial or non-financial interests to disclose.
Author Contributions
Kejia Zhuang: supervision, original idea, manuscript writing. Xin Yao: manuscript writing, data collection. Cheng Hu: original idea, manuscript writing. Lingli Zou: data collection. Fengtian Lin: data collection. Chaoqun Wu: reviewing and editing.
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