Modeling of workpiece temperature suppression in high-speed dry milling of UD-CF/PEEK considering heat partition and jet heat transfer

Abstract

High-performance carbon fiber-reinforced polyether-ether-ketone (CF/PEEK) has been gradually applied in aerospace and automobile applications because of its high strength-to-weight ratio and impact resistance. The dry-machining requirement tends to cause the cutting temperature to surpass the glass transition temperature (T_g), leading to poor surface quality, which is the bottleneck for dry milling of CF/PEEK. Temperature suppression has become an important breakthrough in the feasibility of high-speed dry (HSD) milling of CF/PEEK. However, heat partitioning and jet heat transfer mechanisms pose strong challenges for temperature suppression analytical modeling. To address this gap, an innovative temperature suppression analytical model based on heat partitioning and jet heat transfer mechanisms is first developed for suppressing workpiece temperature via the first-time implementation of an air jet cooling process in the HSD milling of UD-CF/PEEK. Then, verification experiments of the HSD milling of UD-CF/PEEK with four fiber orientations are performed for dry and air jet cooling conditions. The chip morphologies are characterized to reveal the formation mechanism and heat-carrying capacity of the chip. The milling force model can obtain the force coefficients and the total cutting heat. The workpiece temperature increase model is validated to elucidate the machined surface temperature evolution and heat partition characteristics. On this basis, an analytical model is verified to predict the workpiece temperature of air jet cooling HSD milled with UD-CF/PEEK with a prediction accuracy greater than 90%. Compared with those under dry conditions, the machined surface temperatures for the four fiber orientations decreased by 30%–50% and were suppressed within the T_g range under air jet cooling conditions, resulting in better surface quality. This work describes a feasible process for the HSD milling of CF/PEEK.

Graphical abstract

Keywords

thermoplastic CF/PEEK / high-speed dry milling / chip formation / heat partition / jet heat transfer / temperature suppression

1 Introduction

Carbon fiber-reinforced polymer composites (CFRPs) feature high specific strength/stiffness, good resistance to impact and corrosion, and superior design flexibility [1] and are used in high-end manufacturing applications such as automobiles, aircraft, and rockets. Recently, carbon fiber-reinforced thermoplastics (CFRTPs) have attracted widespread interest from manufacturing and academic communities for replacing thermoset CFRPs in high-end manufacturing applications because of their high fracture toughness and impact resistance, good resistance to heat and humidity, few preservation conditions, short molding cycles, recyclability, and reparability [2,3]. Carbon fiber-reinforced polyether-ether-ketone (CF/PEEK) is a typical CFRTP with excellent fracture toughness, corrosion and impact resistance, thermal stability (T_g = 143 °C, melting point = 343 °C, and heat distortion temperature = 330 °C), and biocompatibility [4,5]. Although CFRTP structural parts are manufactured using the near-net-shape forming technique, the milling process remains an essential machining technique for satisfying the requirements of geometrical accuracy and surface quality [6]. The poor wettability of the fiber-PEEK interface can lead to its failure in wet environments [7]. Therefore, dry cutting remains the preferred machining condition used in the secondary CFRTP manufacturing sector. However, the cutting temperature tends to exceed the matrix temperture T_g, causing the softened matrix to provide inadequate support for the fibers [8]. Severe thermal damage, such as matrix loss, fiber debonding/fracturing, delamination, and cavities, can cause poor surface quality and affect the overall strength and performance of the components [9]. Therefore, high cutting temperatures pose an essential challenge for surface quality in dry milling processes.

Currently, cutting temperature has become an important issue in CFRTP machining quality. Wang et al. [1] investigated the cutting mechanisms in thermoset CF/epoxy and thermoplastic CF/PEEK to determine that both cutting mechanisms depend mainly on fiber orientation. Compared with CF/epoxy, thermoplastic PEEK matrix features high damage tolerance, leading to differences in damage and chip formation. For CF/PEEK, short cracks and long chips are produced for the 0° and 45° fiber orientations, splintered chips and few subsurface damages are produced for the 135° fiber orientation, and lumpy chips are produced for the 90° fiber orientation. Ge et al. [10] studied the drilling performance of CF/epoxy and thermoplastic CF/polyether-ketone-ketone (PEKK) materials. The analysis showed that CF/epoxy involves fiber–matrix brittle fracture-dominated material removal, resulting in the formation of powdery chips adhering to the machined surface. However, CF/PEKK, which has excellent ductility, involves matrix plastic deformation-dominated material removal, generating continuous chips and a matrix smearing phenomenon. Compared with CF/epoxy, CF/PEKK features a machining temperature exceeding the T_g and larger heat-affected zones, especially in high-speed cutting. Wen et al. [11] conducted grinding experiments on CF/PEEK and CF/epoxy. The conclusion showed that the grinding temperature is slightly greater for CF/PEEK than for CF/epoxy, but the surface quality is significantly better for CF/PEEK than for CF/epoxy, owing to the high ductility of CF/PEEK. Moreover, the surface roughness and heat distribution are primarily influenced by the fiber orientation. Xu et al. [3] found that the machined surface morphology and dimensional accuracy are better for CF/PEEK than for CF/PI in drilling CF/PEEK and CF/PI. Ge et al. [12] investigated the CF/PEKK cutting mechanism by controlling the workpiece temperature (23 °C, 100 °C < T_g, and T_g < 200 °C). When the workpiece temperature increases and exceeds the T_g, the changes in the material removal mechanism are strongly related to the significant reductions in the matrix strength, matrix–fiber bonding strength, and fracture toughness, and the surface roughness and machining damage increase rapidly due to severe thermal damage. In addition, 0°, 45°, and 90° CF/PEKK produce continuous chips, while 135° CF/PEKK generates lumpy chips. Cao et al. [13] confirmed the feasibility of high-speed dry (HSD) milling of CF/PEEK according to the cutting temperature and surface integrity. Nevertheless, machined surfaces are prone to significant matrix smearing in high-speed cutting. According to the temperature sensitivity of the thermoplastic matrix [14], the cutting temperature should be controlled within the T_g range to suppress the sudden decrease in the mechanical properties of the CFRTP due to the softened matrix [15]. Liu et al. [16] constrained the machining temperatures within the T_g range to optimize the cutting temperature, surface roughness, and material removal rate of CF/PEEK HSD milling. The results indicated that optimal process parameters can limit machining temperatures and improve machining efficiency. However, process optimization relies on many experiments, and optimal parameters are sensitive to changes in fiber orientation, leading to poor commonality. Overall, these studies provide some insights into the effect of the ductility and temperature sensitivity of thermoplastic matrices on CFRTP machining, but the active suppression of cutting temperature in the dry milling of CF/PEEK materials needs to be explored in depth.

Some auxiliary cooling processes have attempted to control the workpiece temperature in CFRP milling. Kumar and Gururaja [17] investigated the surface quality of milled uni-directional (UD)-CFRP using cryogenic liquid nitrogen and drying processes. The cutting temperature in dry milling is higher than the T_g, leading to severe surface defects, including dust particles, matrix loss, fiber fracture, interface debonding, and cavities. Under cryogenic conditions, the cutting temperature is suppressed within the T_g, resulting in improved surface quality with less matrix loss, fiber fracture, and pull-out. Given the extreme sensitivity of CFRPs to cutting temperatures, matrix hardened by cryogenic machining conditions can reduce toughness and increase matrix strength [18], affecting matrix-controlled deformation behavior [19]. Therefore, the cutting temperature suppressed by an appropriate cooling process can effectively improve the CFRP machinability. Gao et al. [20] explored the machinability of UD-CFRP milling by using cryogenic liquid nitrogen with temperatures ranging from −196 to 20 °C. For the 0° fiber orientation, the surface roughness slightly decreases as the machining temperature decreases from 20 to −160 °C due to the increased fiber–matrix bonding strength. However, liquid nitrogen at −196 °C penetrates the finished surface to weaken the fiber–matrix bonding strength, resulting in increased surface roughness. For the 135° and 90° fiber orientations, the matrix brittleness and interlayer thermal stresses increase as the machining temperature decreases from 0 to −196 °C, resulting in a higher surface roughness. Thus, the effect mechanism of cryogenic liquid nitrogen on the machining quality of anisotropic CFRPs is highly complex, leading to poor adaptability of the process parameters for cryogenic liquid nitrogen cooling processes. Furthermore, the temperature sensitivity of CFRPs is reflected not only by the high temperature that deteriorates CFRP machinability but also by the extremely low temperature that may worsen CFRP machinability. In addition to cryogenic gases, minimum quantity lubrication (MQL) has been used to suppress the cutting temperature in CFRP machining [21,22]. Zhang and Zhang [23] conducted CFRP up/downmilling experiments under dry, fluid, cryogenic CO₂, MQL, and nanoparticle-enhanced MQL conditions. The results show that upmilling is favorable for improving the machinability of high-speed cutting CFRPs. In addition to dry cutting, the other four machining processes reduce the surface roughness and cutting temperature. Zou et al. [24,25] discovered that the fundamental reason for surface quality improvement in cryogenic cutting is to avoid material property degradation caused by high cutting temperatures. When water/oil-based cooling media are utilized for cool CFRP milling, the matrices are susceptible to physical expansion and chemical variability [26], which hinders the performance of CFRP materials. Therefore, fluids, oils, and even MQL are not recommended for CFRP machining. Currently, the air-cooling process has been used for drilling CFRPs because of its low cost and high environmental friendliness [27]. The cutting temperatures are also well suppressed to obtain good hole-making quality. In general, medium-cooling milling CFRPs remain in the process exploration stage, while the air-cooling process and heat transfer mechanism used in CF/PEEK dry milling are rarely reported.

Research on cutting temperature models for dry machining CFRPs is gradually emerging. Wang et al. [28] used K-type thermocouples to measure cutting temperatures in CFRP milling and interpreted the temperature variation for different fiber orientations by the solid heat conduction model and anisotropic thermal conductivity. The fiber axial direction is the best for heat dissipation, resulting in the highest cutting temperature of 45° and the lowest cutting temperature of 135°. Wang et al. [29] developed a heat partition analytical model for CFRP orthogonal cutting by using tool heat transfer and Hertzian contact theory. The results showed that fiber orientation has a considerable impact on heat partitioning, and heat partitioning is much greater for workpieces than for tools, in which the workpiece and chip are treated as a unit. Liu et al. [30] constructed a workpiece temperature analytical model for the helical milling of CFRPs according to the heat source superposition method. On the basis of the reverse heat transfer principle, the conjugate gradient method combined with the measured temperatures can be utilized to predict workpiece heat partitioning and heat flow. Liu et al. [31] presented a workpiece temperature analytical model to clarify the thermal mechanism of the HSD milling of CFRTPs. An appropriate increase in the feed rate and cutting width can also reduce the cutting temperature during high-speed cutting. However, the heat partitioning mechanism in the cutting zone has not been explored to determine the cutting temperature suppression potential. To date, research on the active temperature suppression mechanism of CFRTP machining is limited, especially for the use of the HSD milling process.

This study develops a novel temperature suppression analytical model based on heat partition and jet heat transfer mechanisms for suppressing machined surface temperature by integrating air jet cooling into the HSD milling of UD-CF/PEEK, filling the gap in workpiece temperature suppression modeling of CF/PEEK machining. First, the heat partitions under dry and air jet cooling conditions are analyzed based on the continuous chip morphology. Cutting force modeling is utilized to estimate the total cutting heat according to the assumption that all the mechanical work is transformed into heat. A workpiece temperature increase model based on fiber orientations is constructed to derive workpiece heat flow via the conjugate gradient algorithm, and the machined surface temperature and chip carrying heat are obtained. An air jet heat transfer model is developed to calculate the air carrying heat. Then, verification experiments on the dry milling of UD-CF/PEEK under different fiber orientations and process parameters are conducted to analyze the chip characteristics, machined surface temperature evolution and heat partitioning characteristics. Finally, the analytical model is validated to reveal the feasible temperature suppression mechanism of the air jet cooling process used in the HSD milling of UD-CF/PEEK. This work provides theoretical and technical guidance for regulating the jet parameters of cryogenic jet cooling processes and suppressing the cutting temperature in CFRTP machining.

2 Workpiece temperature suppression model in UD-CF/PEEK HSD milling

The thermoplastic matrix has a determinant influence on the chip morphology in the HSD milling of CF/PEEK, which directly affects the heat partition in the cutting zone. Therefore, on the basis of chip morphological characteristics, the heat partitioning mechanism in the cutting zone needs to be analyzed under dry and air jet cooling conditions. Then, the heat-carrying capacities of the workpiece, chip and tool can be determined according to the cutting force model and the workpiece temperature increase model of the HSD milling of CF/PEEK. Moreover, combined with the air jet heat transfer mechanism, a workpiece temperature suppression model for the HSD milling of CF/PEEK can be established.

2.1 Heat partition analysis for dry and air jet cooling conditions

Owing to the high ductility of the thermoplastic matrix [10], CFRTP chips feature continuous ribbons or lumps in dry machining instead of powdered chips for thermoset composites [11]. Fig.1(a) shows that the continuous chips fly away from the cutting zone during UD-CF/PEEK HSD milling, meaning that the chips can carry a portion of the total cutting heat. The cutting heat can be transferred instantly into the workpiece, cutting tool, and chip during dry cutting (Fig.1(b)). Hypothetically, all mechanical work can be translated to cutting heat, similar to previous studies [29,30]. The total cutting heat Q_total can be expressed as follows:

Fig.1 Analysis of chips and heat partition during UD-CF/PEEK HSD milling: (a) formed chips and (b) heat partitions under dry and air jet cooling conditions. PCD: polycrystalline diamond.

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(1)$Q_{\text{total}}=W=Q_{\text{chip}}+Q_{\text{tool}}+Q_{\text{CF/PEEK}},$

where W is the total mechanical work, W =F_t∙v_c. Here, v_c and F_t denote the cutting speed and tangential cutting force, respectively. Q_chip, Q_CF/PEEK, and Q_tool are the heats transmitted to the chip, workpiece, and cutting tool under dry conditions, respectively.

The cutting partitions are the ratios of the heats transmitted to the chip, cutting tool, and workpiece vs. total cutting heat, characterizing the heat transfer of the cutting zone:

(2)$\left[\begin{array}{c}{R}_{\text{chip}}\\ R_{\text{tool}}\\ R_{\text{CF/PEEK}}\end{array}\right]=\frac{1}{Q_{\text{total}}}\left[\begin{array}{c}{Q}_{\text{chip}}\\ Q_{\text{tool}}\\ Q_{\text{CF/PEEK}}\end{array}\right],$

where R_tool, R_CF/PEEK, and R_chip are the heat partitions of the cutting tool, workpiece, and chip, respectively. Note that R_tool + R_CF/PEEK + R_chip = 1.

Heat dissipation from the machined surface is achieved by applying additional heat flux in air jet cooling milling (Fig.1(b)). Therefore, the workpiece heat under dry conditions can be redistributed between the workpiece and the jet air:

(3)$Q_{\text{CF/PEEK}}=Q_{\text{CF/PEEK}}^{\text{res}}+Q_{\text{air}},$

where $Q_{\text{CF/PEEK}}^{\text{res}}$ and Q_air are the heat carried by the workpiece and air under air jet cooling conditions, respectively. Therefore, the heat partitions of the workpiece and air can be calculated by

(4)$\left[\begin{array}{c}{R}_{\text{CF/PEEK}}^{\text{res}}\\ R_{\text{air}}\end{array}\right]=\frac{1}{Q_{\text{CF/PEEK}}}\left[\begin{array}{c}{Q}_{\text{CF/PEEK}}^{\text{res}}\\ Q_{\text{air}}\end{array}\right],$

where $R_{\text{CF/PEEK}}^{\text{res}}+R_{\text{air}}=1$.

Under air jet cooling conditions, the ratio of the workpiece carrying heat to the total cutting heat $R_{\text{CF/PEEK}}^{\text{res,t}}$ is calculated by

(5)$R_{\text{CF/PEEK}}^{\text{res,t}}=Q_{\text{CF/PEEK}}^{\text{res}}/\phantom{Q_{\text{CF/PEEK}}^{\text{res}}{Q}_{\text{total}}}{Q}_{\text{total}}=R_{\text{CF/PEEK}}^{\text{res}}{R}_{\text{CF/PEEK}}.$

2.2 Mechanical work from milling force modeling

Fig.1(a) shows the fiber orientation, which characterizes the angle between the direction of the cutting speed turning counterclockwise to the fiber axis when cutting UD-CF/PEEK. According to Ref. [32], given the high ratio of the milling tool diameter to the cutting width, the fiber orientation is simplified as a constant during the milling process. On the basis of Fig.2, the cutting force model for the HSD milling of UD-CF/PEEK can be modeled as follows [33]:

Fig.2 Cutting force analysis for UD-CF/PEEK HSD milling. PCD: polycrystalline diamond.

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(6)$\left[\begin{array}{c}{F}_x\left({\varphi }_j\right)\\ F_y\left({\varphi }_j\right)\end{array}\right]=\left[\begin{array}{cc}\cos {\varphi }_j& \sin {\varphi }_j\\ -\sin {\varphi }_j& \cos {\varphi }_j\end{array}\right]\left[\begin{array}{c}{F}_{\text{t}}\left({\varphi }_j\right)\\ F_{\text{r}}\left({\varphi }_j\right)\end{array}\right],$

(7)$\left[\begin{array}{c}{F}_{\text{t}}\left({\varphi }_j\right)\\ F_{\text{r}}\left({\varphi }_j\right)\end{array}\right]=g\left({\varphi }_j\right)\left[\begin{array}{c}{\displaystyle \sum _{k=1}^N{K}_{\text{tc}}\cdot h_{\text{c}}\left({\varphi }_j\right)a_{\text{p}}}\\ {\displaystyle \sum _{k=1}^N{K}_{\text{rc}}\cdot h_{\text{c}}\left({\varphi }_j\right)a_{\text{p}}}\end{array}\right],$

where F_x and F_y denote the measured milling forces for the x-axis and y-axis of the coordinate system denoted by oxyz, respectively; F_t and F_r denote the tangential and radial milling forces, respectively; ${\varphi }_j$ denotes the instantaneous contact angle for the jth tooth, and its maximum is ${\varphi }_{\text{c}}=\arccos \left(\left(R-a_{\text{e}}\right)R^{-1}\right)$, where R denotes the tool radius; $g\left({\varphi }_j\right)$is the discriminant coefficient for the contact state of the jth tooth with the workpiece, when ${\varphi }_j\in \left[0,{\varphi }_{\text{c}}\right]$, $g\left({\varphi }_j\right)=1$; otherwise, $g\left({\varphi }_j\right)=0$; and the coefficients K_tc and K_rc represent the tangential and radial shear effects of the milling force, respectively. The uncut chip thickness is calculated by $h\left({\varphi }_j\right)=f_{\text{z}}\sin {\varphi }_j$. a_p is the cutting depth. N denotes the number of cutting cutters.

According to the average cutting force method [30], the force coefficients are determined using the experimentally measured cutting force. The average tangential force is used to simplify the calculation of the instantaneous tangential force so that the total mechanical work is deduced as follows:

(8)$W=v_{\text{c}}\overline{F_{\text{t}}\left({\varphi }_j\right)}=v_{\text{c}}\left[{\displaystyle \sum _{j=1}^{N}g\left({\varphi }_j\right)K_{\text{tc}}\cdot \overline{h({\varphi }_j)}\cdot a_{\text{p}}}\right]=v_{\text{c}}{K}_{\text{tc}}\overline{h}{a}_{\text{p}},$

where $\overline{h({\varphi }_j)}$ is the average uncut chip thickness, and $\overline{h({\varphi }_j)}=\overline{h}={\displaystyle \frac{1}{{\varphi }_{\text{c}}}}{\int }_0^{{\varphi }_{\text{c}}}{f}_{\text{z}}\sin \varphi \text{d}\varphi$.

2.3 Determination of the heat carried by the UD-CF/PEEK workpiece

2.3.1 Fiber orientation-based modeling of the increase in workpiece temperature

For UD-CF/PEEK dry milling, the workpiece heat source can be modeled as a moving arc-surface heat source, which moves along the insulation boundary on a semi-infinite anisotropic solid (Fig.3). According to Ref. [34], the heat flow on the arc surface is positively correlated with the instantaneous uncut thickness, which is given as follows:

Fig.3 Heat source analysis for UD-CF/PEEK HSD milling: (a) tool-workpiece position relationship and (b) superposition of the workpiece heat source.

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(9)$\left[\begin{array}{c}q\left(\varphi \right)\\ q_{\text{avg}}\end{array}\right]=q_{\text{max}}\left[\begin{array}{c}{\displaystyle \frac{\sin \varphi }{\sin {\varphi }_{\text{c}}}}\\ {\displaystyle \frac{1-\cos {\varphi }_{\text{c}}}{{\varphi }_{\text{c}}\sin {\varphi }_{\text{c}}}}\end{array}\right],$

where $q\left(\varphi \right)$, q_avg, and q_max are the instantaneous, average, and maximum heat flows, respectively. In addition, given the 0° axial rake angle on the cutter, the heat flow is uniformly distributed in the cutting depth direction.

According to the moving heat source idea [35], a point heat source function is a prerequisite for obtaining the heat source function of complex geometry. First, the heat source function of any point S with instantaneous heat release can be derived for the insulation boundary as follows [36]:

(10)$\begin{array}{rl}\mathrm{\Delta }T& \left(X,Y,Z,t\right)=\frac{q\left(\varphi \right)\sqrt{\rho c}}{4\sqrt{{\text{π}}^3{k}_1{k}_2{k}_3{t}^3}}\\ & \cdot \text{exp}\left\{-\frac{\rho c}{4t}\left[\frac{{\left(X-X_S\right)}^2}{k_1}+\frac{{\left(Y-Y_S\right)}^2}{k_2}+\frac{{\left(Z-Z_S\right)}^2}{k_3}\right]\right\},\end{array}$

where t is the observation moment of the temperature increase; k₁, k₂, and k₃ denote the dominant thermal conductivities corresponding to the X-axis, Y-axis, and Z-axis of the workpiece coordinate system OXYZ for the UD-CF/PEEK material (Fig.3(a)); and c and ρ denote the specific heat capacity and density of the material, respectively. Therefore, the actual temperature induced by the point heat source is $T\left(X,Y,Z,t\right)=\mathrm{\Delta }T\left(X,Y,Z,t\right)+T_{\text{a}}$ at an environment temperature of T_a = 20 °C.

Then, according to the principle of temperature field superposition [37], the heat source function of the arc surface is obtained by superimposing the heat source function of numerous points from the direction of the cutting depth and circular arc (Fig.3(b)). Finally, the heat source function of the moving arc surface is obtained by superimposing the duration of the heat release for the heat source function of the arc surface. For the 0° and 90° fiber orientations, the fiber axis is orthogonal or parallel to the OXYZ axes. The temperature increase function of the workpiece heat source can be directly derived as follows [31]:

(11)$\begin{array}{rl}\mathrm{\Delta }{T}_{\text{c}}& \left(X,Y,Z,t\right)={\int }_0^{{\varphi }_{\text{c}}}{\int }_0^{a_{\text{p}}}{\int }_0^t\mathrm{\Delta }T\left(X,Y,Z,t-\tau \right)\text{d}\tau \text{d}ZR\text{d}\varphi \\ =& \frac{q_{max}R}{4\text{π}\sqrt{k_1{k}_2}}{\int }_0^{{\varphi }_{\text{c}}}{\int }_0^t\frac{\sin \varphi }{\sin {\varphi }_{\text{c}}\left(t-\tau \right)}\\ & \cdot \exp \left\{-\frac{\rho c}{4\left(t-\tau \right)}\left[\frac{{\left(X-v_{\text{f}}\tau -R\sin \varphi \right)}^2}{k_1}+\frac{{\left(Y-R\cos \varphi \right)}^2}{k_2}\right]\right\}\\ & \cdot \left[\text{erf}\left(\frac{Z}{\sqrt{4a_3\left(t-\tau \right)}}\right)-\text{erf}\left(\frac{Z-a_{\text{p}}}{\sqrt{4a_3\left(t-\tau \right)}}\right)\right]\text{d}\tau \text{d}\varphi ,\end{array}$

where τ is the moment when heat begins to be released, v_f denotes the feedrate during cutting, a₃ denotes the thermal diffusivity corresponding to k₃, and $a_3=k_3\cdot$ $(\rho c{)}^{-1}$. The error function erf is defined as $\text{erf}\left(p\right)=$ ${\displaystyle \frac{2}{\sqrt{\text{π}}}}{\int }_0^p{\text{e}}^{-u^2}\text{d}u$.

For the 45° and 135° fiber orientations, the fiber axis is not orthogonal or parallel to the Y-axis or X-axis in the OXYZ (Fig.3(b)). Therefore, the auxiliary coordinates OX₁Y₁Z₁ and ox₁y₁z₁ are established to make their axes vertical or parallel to the fiber axis. The coordinate points in OXYZ and oxyz can be converted to the coordinate points in the coordinate OX₁Y₁Z₁ as follows:

(12)$\left[\begin{array}{c}{X}_1\\ Y_1\\ Z_1\end{array}\right]=\left[\begin{array}{ccc}\cos \alpha & \sin \alpha & 0\\ -\sin \alpha & \cos \alpha & 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right],$

(13)$\left[\begin{array}{c}{X}_1\\ Y_1\\ Z_1\\ 1\end{array}\right]=\left[\begin{array}{cccc}\cos \alpha & \sin \alpha & 0& v_{\text{f}}\tau \cos \alpha \\ -\sin \alpha & \cos \alpha & 0& -v_{\text{f}}\tau \sin \alpha \\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ \mathit{\text{z}}\\ 1\end{array}\right],$

where α describes the angular relationship between OXYZ and OX₁Y₁Z₁, and α = 45°.

According to Eq. (13), the point P(X,Y,Z) in OXYZ can be transformed into P(X₁,Y₁,Z₁) in OX₁Y₁Z₁. Moreover, according to Eq. (14), any point on the workpiece heat source can be converted from the coordinate S(X_S,Y_S,Z_S) in OXYZ to the coordinate $S(R\sin (\varphi +\alpha )+v_{\text{f}}\tau \cos \alpha ,$ $R\cos (\varphi +\alpha )-v_{\text{f}}\tau \sin \alpha ,Z_{\text{1}S})$ in OX₁Y₁Z₁. Similarly, the temperature increase function of the workpiece heat source for the 45° and 135° fiber orientations is derived as follows [31]:

(14)$\begin{array}{rl}\mathrm{\Delta }{T}_{\mathrm{c}}& \left(X_1,Y_1,Z_1,t\right)=\frac{q_{max}R}{4\text{π}\sqrt{k_1{k}_2}}{\int }_0^{{\varphi }_{\mathrm{c}}}{\int }_0^t\frac{\sin \varphi }{\sin {\varphi }_{\mathrm{c}}\left(t-\tau \right)}\\ & \cdot \exp \{-\frac{\rho c}{4\left(t-\tau \right)}[\frac{{\left(X_1-R\sin (\varphi +\alpha )-v_{\mathrm{f}}\tau \cos \alpha \right)}^2}{k_1}\\ & +\frac{{\left(Y_1-R\cos (\varphi +\alpha )+v_{\mathrm{f}}\tau \sin \alpha \right)}^2}{k_2}]\}\\ & \cdot \left[\mathrm{e}\mathrm{r}\mathrm{f}\left(\frac{Z_1}{\sqrt{4a_3\left(t-\tau \right)}}\right)-\mathrm{e}\mathrm{r}\mathrm{f}\left(\frac{Z_1-a_{\mathrm{p}}}{\sqrt{4a_3\left(t-\tau \right)}}\right)\right]\mathrm{d}\tau \mathrm{d}\varphi ,\end{array}$

where k_v and k_p represent the thermal conductivities perpendicular and parallel to the fiber orientation in UD-CF/PEEK, respectively. According to the position relationship between the workpiece coordinate axes and fiber orientation, k₁, k₂, and k₃ are substituted by the two thermal conductivities to calculate the increase in the workpiece temperature. Furthermore, the two dominant thermal conductivities perpendicular to the fiber orientation are equal.

2.3.2 Conjugate gradient algorithm for workpiece heat flow

According to the reverse heat conduction principle [38], the heat flow on the workpiece heat source can be solved by combining the temperature increase model and the measured temperature. Therefore, the objective function of the heat flow is an error function constructed by minimizing the sum of the squared errors between the measured temperatures and the model-predicted temperatures, shown as follows:

(15)$minf\left(q_{max}\right)=min\sum _{i=1}^I{\left[\left(T_i^{\text{m}}-T_{\text{a}}\right)-\mathrm{\Delta }{T}_i^{\text{e}}\left(q_{max}\right)\right]}^2,$

where I denotes the amount of temperature measured using a thermocouple, $T_i^{\text{m}}$ is the ith temperature in the measured temperature sequence, and $\mathrm{\Delta }{T}_i^{\text{e}}\left(q_{max}\right)$ is the corresponding temperature increase estimated by the workpiece temperature increase model.

The numerical method can be used to estimate the nonlinear parameter, namely, the heat flow described in Eq. 15. The conjugate gradient algorithm [30], which has excellent stability and convergence, is a simple and efficient iterative optimization method for solving such nonlinear parameter estimation problems. Therefore, the conjugate gradient algorithm is suitable for determining workpiece heat flow. The core optimization process in the conjugate gradient algorithm can be expressed as follows [30]:

(16)$q_{max}^{K+1}=q_{max}^K+S^K{d}^K,$

(17)$d^K=-\mathrm{\nabla }f\left(q_{max}^K\right)+C^K{d}^{K-1},$

where K denotes the total number of iterations. The new conjugate gradient descent d^K describes the linear combination between the previous descent d^K−1 and the new gradient descent $\mathrm{\nabla }f\left(q_{max}^K\right)$.

Meanwhile, the new gradient $\mathrm{\nabla }f\left(q_{max}^K\right)$ can be calculated as follows:

(18)$\mathrm{\nabla }f\left(q_{max}^K\right)=2\sum _{i=1}^I\frac{\mathrm{\partial }\mathrm{\Delta }{T}_i^{\text{e}}\left(q_{max}^K\right)}{\mathrm{\partial }{q}_{max}^K}\left[\mathrm{\Delta }{T}_i^{\text{e}}\left(q_{max}^K\right)-T_i^{\text{m}}+T_{\text{a}}\right].$

The Fletcher–Reeves conjugate coefficient C^K is taken as follows:

(19)$C^K=\{\begin{array}{cc}0,& K=0,\\ {\left[{\displaystyle \frac{\mathrm{\nabla }f\left(q_{max}^K\right)}{\mathrm{\nabla }f\left(q_{max}^{K-1}\right)}}\right]}^2,& K⩾1.\end{array}$

The search step S^K is utilized as follows:

(20)$S^K=\frac{-{\displaystyle \sum _{i=1}^I\left[{\displaystyle \frac{\mathrm{\partial }\mathrm{\Delta }{T}_i^{\text{e}}\left(q_{max}^K\right)}{\mathrm{\partial }{q}_{max}^K}}{d}^K\right]\left[\mathrm{\Delta }{T}_i^{\text{e}}\left(q_{max}^K\right)-T_i^{\text{m}}+T_{\text{a}}\right]}}{{\displaystyle \sum _{i=1}^I{\left[{\displaystyle \frac{\mathrm{\partial }\mathrm{\Delta }{T}_i^{\text{e}}\left(q_{max}^K\right)}{\mathrm{\partial }{q}_{max}^K}}{d}^K\right]}^2}}.$

Therefore, according to Eqs. (10) and (16), the workpiece carrying heat can be derived by the workpiece heat flow as follows:

(21)$Q_{\text{CF/PEEK}}=q_{\text{avg}}\left(a_{\text{p}}{\varphi }_{\text{c}}R\right).$

2.4 Estimation of chip carrying heat

During UD-CF/PEEK dry milling, the heat-carrying chip can be utilized to analyze the heat partitioning of the chip. Given the small uncut cutting thickness, the average chip temperature is assumed to be the maximum temperature on the machined surface [29]. Hence, the heat carried by the flying chips is estimated as follows:

(22)$Q_{\text{chip}}=\rho v_{\text{c}}\overline{h}{a}_{\text{p}}\overline{c}\left(T_{max}^{\text{surf}}-T_{\text{a}}\right),$

where $T_{\text{max}}^{\text{surf}}$ is the maximum temperature of the machined surface calculated by the workpiece temperature increase model, and $\overline{c}$ is the average specific heat capacity of the workpiece material.

2.5 Jet heat transfer modeling for air jet cooling

Air is readily available from the environment without the need for a complex preparation process, exhibiting the advantages of low cost and good environmental friendliness. Moreover, the air is easily compressed and conveyed. Therefore, compressed air may be used as the ideal jet medium to realize the air jet cooling process. In the dry milling of CF/PEEK, the air jet not only enhances the convective heat transfer of the workpiece heat source but also accelerates the discharge of chips. According to the jet heat transfer rule [39], the jet air carrying heat can be derived as follows:

(23)$Q_{\text{air}}=h_{\text{air}}{a}_{\text{p}}{l}_{\text{c}}\left(T_{\text{max}}^{\text{surf}}-T_{\text{air}}\right),$

where h_air is the convective coefficient of jet-air heat transfer, l_c = R∙ϕ_c denotes the arc length in the workpiece heat source, and T_air denotes the jet-air temperature.

The convective coefficient characterizing the heat exchange capacity of the jet air on the heat source is expressed as follows [40]:

(24)$h_{\text{air}}=k_{\text{air}}\cdot \text{Nu}\cdot l^{-1},$

where k_air denotes the air thermal conductivity, l denotes the heat transfer width of the cutting zone, and Nu is the Nusselt number.

Nu may be derived from the Prandtl number Pr and Reynolds number Re as follows [41]:

(25)$\left[\begin{array}{c}\text{Nu}\\ \mathrm{R}\mathrm{e}\\ Pr\end{array}\right]=\left[\begin{array}{c}0.906{\mathrm{R}\mathrm{e}}^{1/\phantom{12}2}{Pr}^{1/\phantom{13}3}\\ {\rho }_{\text{air}}{v}_{\text{air}}l/{\mu }_{\text{air}}\\ c_{\text{air}}{\mu }_{\text{air}}/k_{\text{air}}\end{array}\right],$

where ρ_air, c_air, and μ_air are the density, specific heat at constant pressure, and dynamic viscosity of air, respectively. ν_air is the air velocity at the nozzle outlet.

Fig.4 illustrates the implementation process of the workpiece temperature suppression model in UD-CF/PEEK HSD milling. First, the total cutting heat is calculated using the milling force model with the average cutting force method. Then, the workpiece temperature increase model is employed to determine the workpiece carrying heat and machined surface temperature according to the conjugate gradient algorithm. Furthermore, the heat carried by the chip and the heat carried by the cutting tool are determined to obtain the heat partition of the workpiece under dry conditions. On this basis, the jet heat transfer model is used to calculate the air carrying heat and the residual workpiece heat partition. Finally, the machined surface temperature under jet air cooling conditions can be predicted using the workpiece temperature increase model. Therefore, the workpiece temperature suppression model is developed by integrating jet heat transfer, heat partitioning, and the temperature increase model. The air jet cooling process can be used to suppress the machined surface temperature in the HSD milling of CF/PEEK. Moreover, the developed temperature suppression model describes the physical relationships among the air jet parameters, cutting process parameters, and workpiece temperature. According to the expected workpiece temperature and given cutting process parameters, the workpiece temperature suppression model may be used to obtain suitable air jet parameters to accurately guide workpiece temperature suppression.

Fig.4 Calculation flow of the temperature suppression model in the HSD milling of CF/PEEK via air jet cooling.

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3 Experimental methods

As depicted by the model presented above, the chip morphology, workpiece temperature, and heat partition characteristics of the HSD milling of CF/PEEK need to be elucidated first, and then the verification experiments of the air jet cooling HSD milling process of CF/PEEK are conducted. According to previous studies on CFRTP machining [10,31], fiber orientation, cutting speed, and feed per tooth are important factors affecting workpiece temperature and chip morphology.

Therefore, three cutting speeds, two feeds per tooth, and four fiber orientations were used in the HSD milling experiments of CF/PEEK under dry and air jet cooling conditions to validate the developed temperature suppression model (Tab.1). Three replicate experiments were performed for each set of process parameters to ensure the reliability and reproducibility of the experimental data. The CF/PEEK material was composed of thermoplastic carbon fiber T700 (Toray, Japan) and thermoplastic PEEK (Junhua Peek, China) (Tab.2). The milling tool was equipped with 6 insert cutters (polycrystalline diamond, Type APKT1604, China) with axial and radial rake angles of 0° and tool radii of 50 mm. The experiments were performed by a machining center (BV8H, Bochl Machine Tool, China) (Fig.5(a)). For the air jet cooling process, the air compressor first generates high-pressure air, and a pressure regulating valve is used to regulate and monitor the air pressure. Then, an air flow meter is used to monitor the compressed air flow, and finally, the compressed air passes through the nozzle to form jet air (Fig.5(b) and Fig.5(d)). The obtained jet parameters of compressed air are shown in Tab.3. In addition, a Kistler 9257B dynamometer system with a sampling rate of 100 kHz was used to measure the cutting force. The workpiece temperatures were recorded using a 500 Hz sampling rate by K-type thermocouples (Omega, USA) and a data acquisition board (OM-DAQ-USB-2401, Omega, USA) for good responsiveness and accuracy [42] (Fig.5(a)). A thermocouple was arranged at a cutting length of 30 mm to capture the increase in the workpiece temperature under steady-state conditions, and the thermocouple measurement depth was a half cutting depth of 1.5 mm, leading to a high workpiece temperature (Fig.5(c)). Thermal conduction silicone grease was used to fill the space between the thermocouple and the workpiece. Accurate temperature measurements of the width d_m and macroscopic morphology of the chip were acquired using an ultradepth microscope (LECIA-DVM6, Germany). Field-emission scanning electron microscopy (SEM; ZEISS-EVO 25, German) was utilized to observe the microstructures of the chip and machined surface. A laser confocal microscope (Olympus LEXT OLS4000, Japan) was used to determine the surface roughness.

Tab.1 Milling conditions for UD-CF/PEEK dry milling

Cutting speed, vc/(m∙min−1)	Feed per tooth, fz/(mm∙z−1)	Fiber orientation, θ/(° )	Cutting width, ae/mm	Cutting depth, ap/mm	Cutting condition
250,1000,1500	0.07	0,45,90,135	0.8	3	Dry
1500	0.12	0,45,90,135	0.8	3	Dry
1500	0.07	0,45,90,135	0.8	3	Air-jet cooling

Tab.2 Air parameters for air jet cooling conditions

Air parameter	Value	Unit
Density	1.185	kg/m3
Specific heat capacity	1011	J/(kg∙K)
Thermal conductivity	0.02489	W/(m.K)
Dynamic viscosity	1.7995E−5	Pa.s
Jet speed	313	m/s
Nozzle outlet diameter	2	mm
Total pressure	0.5	MPa
Flow rate	80	L/min
Jet distance	30	mm

Tab.3 Performance parameters of the UD-CF/PEEK workpiece [31]

Performance parameter	Value	Unit
Carbon fiber mass content	66	%
Density	1580	kg/m3
Tensile strength	2200	MPa
Tensile modulus	130	GPa
Bending strength	2000	MPa
Bending modulus	116	GPa
Compression strength	1200	MPa
Compression modulus	120	GPa
In-plane shear strength	78	MPa
Heat deflection temperature	332	°C
Glass transition temperature	143	°C

Fig.5 Experimental methods for HSD milling of UD-CF/PEEK under dry and air jet cooling conditions: (a) experimental site, (b) cutting zone setup, (c) thermocouple measurement method, and (d) air jet method. PCD: polycrystalline diamond.

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4 Results and discussion

According to the experimental results, the chip morphological characteristics need to be analyzed to prove the heat-carrying capacity and heat partition mechanism of the chips. For the calculation of the total cutting heat, the cutting force coefficients are determined by validating the milling force model. The workpiece temperature increase model needs to be validated to predict machined surface temperature, and the workpiece temperature evolution for different process parameters and fiber orientations is used to analyze the heat partition characteristics of the workpiece, chip and tool under dry conditions. On this basis, the air jet cooling and milling process of a CF/PEEK HSD and its workpiece temperature suppression model can be validated.

4.1 Chip formation

The macroscopic morphologies of the chips after the HSD milling of CF/PEEK were first analyzed for different milling parameters to verify the chip morphological characteristics and heat partition capacity (Fig.6). In general, CF/PEEK chips mainly feature a continuous morphology instead of the powder-like chips of thermoset CFRPs [29]. This observation is primarily attributed to the good ductility of thermoplastic PEEK, which has superior fracture stress [43]. The 0°, 45°, and 90° chips show continuous ribbon or lump shapes. However, the 135° chips feature fine lump shapes because severe fiber bending fracture and interlaminar crack extension tend to form small chips [44]. At the same f_z = 0.07 mm/z, as v_c increases from 250 to 1500 m/min, the chip size increases slightly at 0°, while the chip size decreases at 45°, 90°, and 135°. When f_z increases from 0.07 to 0.12 mm/z at v_c = 1500 m/min, the chip sizes at 0°, 45°, and 90° increase slightly, while the chip size at 135° is essentially unchanged. Therefore, the fiber orientation has a critical influence on the UD-CF/PEEK chip size, followed by the machining parameters. CF/PEEK chips of certain sizes fly away from the cutting zone instead of adhering to the machined surface. Moreover, part of the cutting heat can be carried away by the chips, demonstrating the heat-carrying capacity of the chips.

Fig.6 Chip macromorphology for the dry milling of UD-CF/PEEK by using different cutting parameters: (a1–a4) vc = 250 m/min and fz = 0.07 mm/z, (b1–b4) vc = 1500 m/min and fz = 0.07 mm/z, and (c1–c4) vc = 250 m/min and fz = 0.07 mm/z.

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The macrostructural features of the chip morphologies for the HSD milling of UD-CF/PEEK are shown in Fig.7. The 0° chips have a long and short continuous shape (Fig.7(a)). The long chips have a significant curl shape and slight fold structure, meaning that long and thin chips with low stiffness are susceptible to overall and localized plastic deformation. However, long continuous chips tend to fracture into short lump shapes under tool compression. Compared with the 0° chip, the 45° chips have a more remarkable fold structure (Fig.7(b)). For the 0° fiber orientation, the chip flow direction is almost parallel to the fiber axis, and the plastic deformation of the chip is limited by the fibers. However, the local stiffness of the chip length direction of 45° is lower than that of 0° because of the acute angle between the 45° fiber orientation and the chip flow direction. Fig.7(c) shows that the 90° chips possess a severe fold structure and net structure. For the 90° fiber orientation, the fiber fracture plane is vertical to the fiber axis [12], and the 90° chips are severely squeezed by the tool front face, leading to severe plastic deformation and loss of fiber and matrix. Fig.7(d) shows that the 135° chips exhibit a net structure with severe fiber and matrix loss. For the 135° fiber orientation, severe fiber–matrix debonding, crack extension and fiber bending fracture can result in crushed chips [1]. The cutting temperatures soften the thermoplastic matrix to withstand high plastic deformation [45], resulting in chips with the ability to maintain a continuous morphology. Therefore, the CF/PEEK chip morphology depends on the fiber orientation and thermoplastic matrix ductility.

Fig.7 Chip morphological characteristics for different fiber orientations (vc = 1500 m/min, fz = 0.07 mm/z): (a) 0° fiber orientation, (b) 45° fiber orientation, (c) 90° fiber orientation, and (d) 135° fiber orientation.

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The chip micromorphology for different fiber orientations revealed the mechanism of chip formation (Fig.8). In the SEM micrograph, the highlighted white spots indicate a clustered PEEK matrix because of the weak electrical conductivity of PEEK. A long continuous ribbon chip of 0° is characterized by many regular fractured fiber segments, in which the fiber axes are parallel to the length of the chip (Fig.8(a)). With the advanced compression action of the cutting edge, carbon fiber debonding and peel-off can occur, and the fibers are eventually bent to break. This scenario reflects that chip formation at 0° is dominated by fiber–matrix interface debonding and fiber bending fracture. Moreover, the long continuous 45° ribbon chip features significant fiber–matrix interface separation, leading to the formation of many extruded fiber bundles (Fig.8(b)). A plausible explanation is that fibers are cut off by the shearing and compression advance action of the cutting edge, and fiber bundles are prone to sliding by the extrusion of the rake face, which facilitates chip flow formation. Therefore, chip formation at 45° is dominated by fiber shearing fracture and fiber–matrix interface separation. A short continuous ribbon chip of 90° holds many deflected fiber bundles (Fig.8(c)). For the 90° fiber orientation, the tool rake face parallel to the fiber orientation compresses the fibers, resulting in the fiber fracture plane being perpendicular to the fiber orientation. Under these conditions, the chips could not easily flow out from the fiber–matrix interface, causing severe extrusion deformation of the fiber bundles. Thus, chip formation at 90° is based on fiber extrusion fracture. Moreover, the cracked ribbon chip at 135° features significant cracks and cavities (Fig.8(d)). Meanwhile, the cracked chip exposes many fractured fiber segments. The fibers are severely bent under the compression and extrusion advance action of the tool rake face, and severe fiber–matrix debonding and crack extension develop, ultimately leading to significant fiber fractures and chip cracks. Therefore, chip formation at 135° is dominated by severe fiber bending fracture. In addition, the micromorphology of the chip has obvious matrix smearing characteristics for the four fiber orientations, while the matrix effectively wraps the fractured fibers to maintain continuous chips. This scenario indicates the high ductility of the PEEK matrix in the dry milling of CF/PEEK.

Fig.8 Chip micromorphology for different fiber orientations in the HSD milling of UD-CF/PEEK (vc = 1500 m/min, fz = 0.07 mm/z): (a) 0° fiber orientation, (b) 45° fiber orientation, (c) 90° fiber orientation, and (d) 135° fiber orientation.

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4.2 Cutting force coefficients

For subsequent calculations of the total cutting heat, the average cutting force method can first be used to obtain reliable cutting force coefficients, after which the milling force model can be validated. The slight variations in the fiber orientation have a negligible influence on the force coefficients because of the small cutting widths relative to the large tool diameters used in the dry milling of CFRPs [46]. The HSD milling of CF/PEEK involves periodic single-tooth cutting. The maximum single-tooth cutting duration is a force cycle $t_{\text{f}}=60/\left(nN\right)$, where n denotes the spindle rotation speed. The effective cutting duration in a cycle is calculated as $\mathrm{\Delta }t=30\arccos [(R-a_{\text{e}})/R](n\text{π})$. Therefore, the force cycle t_f can be recognized from the time-series data of measuring the milling force to extract the effective cutting force corresponding to $\mathrm{\Delta }t$. Then, the force coefficients in Eq. (8) are calibrated by the average cutting force method. Finally, the force coefficients are taken as average force coefficients corresponding to three force cycles. Then, the prediction performance of the milling force model is visualized (Fig.9). The HSD milling of 135° UD-CF/PEEK is taken as an example to illustrate that the force model forecasts the milling force to sufficiently match the measured force. For all experiments, the absolute percentage error in the force model is less than 10%, which is acceptable for total mechanical work estimation.

Fig.9 Measured and predicted forces for the effective cutting cycle (θ = 135°, vc = 1500 m/min, fz = 0.12 mm/z): (a) x-axis cutting force Fx and (b) y-axis cutting force Fy.

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Fig.10 shows the force coefficients of the HSD milling of UD-CF/PEEK under different fiber orientations, cutting speeds and feeds per tooth. K_tc shows a regular fluctuation variation with increasing fiber orientation (Fig.10(a)), which is consistent with Refs. [47,48]. According to Ref. [49], fiber rebound has a remarkable impact on F_r. As the fiber orientation increases from 0° to 90°, the variations in K_rc are small, which signifies that the fiber rebound strengths are close for the same cutting depth (Fig.10(b)). However, the dramatic decrease in K_rc at 135° indicates that the fiber rebound effect on the cutting edge is significantly reduced, which is attributed to the concave machined surface at 135° [12]. Therefore, the force coefficients have significant fiber orientation-dominated anisotropy. Moreover, increasing cutting speed leads to a gradual decrease in K_tc and K_rc, implying a decrease in the cutting force and specific cutting energy, which is consistent with past findings [50]. As f_z increases from 0.07 to 0.12 mm/z, K_tc and K_rc increase because of the increasing uncut chip thickness, in accordance with Ref. [51].

Fig.10 Force coefficients of UD-CF/PEEK HSD milling: (a) tangential force coefficient Ktc and (b) radial tangential force coefficient Krc.

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4.3 Machined surface temperature considering the UD-CF/PEEK temperature sensitivity

According to Fig.4, the suppression model for workpieces with increasing temperature needs to be validated for calculating the machined surface temperature and subsequently determining the chip heat-carrying capacity. The CFRP thermal performance (k_v, k_p, and c) should be quantitatively characterized as a function of temperature, describing the change in thermal conductivity under different cutting temperatures, to improve the accuracy of the established temperature increase model. CFRP materials exhibit significant temperature sensitivity during the cutting process because the low glass transition temperature of the resin matrix is easily exceeded by the cutting temperature, resulting in variations in the thermal properties of the CFRP [52]. In addition, the thermal conductivity parallel to the fiber orientation k_p is much greater than that perpendicular to the fiber orientation k_v [28], implying that the thermal conductivity features significant anisotropy. Compared with conventional thermoset CFRPs, thermoplastic CFRPs/PEEKs have higher cutting temperatures and lower glass transition temperatures [11], resulting in greater temperature sensitivity. Therefore, the thermal performances in UD-CF/PEEK need to be determined, which are expressed as follows [31]:

(26)$\left[\begin{array}{c}{k}_{\text{v}}\\ k_{\text{p}}\\ c\end{array}\right]=\left[\begin{array}{c}-4.25\times {10}^{-6}\cdot T^2+1.8927\times {10}^{-3}\cdot T+0.6603\\ -3.9355\times {10}^{-5}\cdot T^2+2.0821\times {10}^{-2}\cdot T+4.3625\\ -4.9458\times {10}^{-3}\cdot T^2+3.9095\cdot T+721.0392\end{array}\right].$

According to the workpiece temperature increase model and measured temperatures, the heat flow can be calculated to predict the workpiece temperature under dry conditions. The accuracy of the workpiece temperature increase model is characterized using the percentage error E_p and root mean square error E_RMS [53,54], which are obtained by

(27)$\left[\begin{array}{c}{E}_{\text{p}}\\ E_{\text{RMS}}\end{array}\right]=\sqrt{\frac{1}{I}\sum _{i=1}^I{\left(T_i^{\text{m}}-T_i^{\text{p}}\right)}^2}\left[\begin{array}{c}{\left(T_{max}^{\text{m}}\right)}^{-1}\\ 1\end{array}\right],$

where $T_{\text{max}}^{\text{m}}$ is the maximum temperature measured by the thermocouple.

Tab.4 shows the measured and predicted temperatures of the experiments under dry conditions. When the E_RMS is less than 8 °C, the E_p is less than 6%, which demonstrates that the temperature increase model possesses an acceptable prediction precision under dry conditions.

Tab.4 Measured and predicted temperatures under dry conditions

No.	vc/(m∙min−1)	fz/(mm∙z−1)	θ/(° )	dm/mm	$T_{max}^{\text{m}}$/°C	$T_{max}^{\text{p}}$/°C	ERMS/°C	Ep/%
1	250	0.07	0	0.175	117	113	1.93	1.98
2	250	0.07	45	0.191	172	176	7.88	5.18
3	250	0.07	90	0.202	134	133	6.57	5.75
4	250	0.07	135	0.184	105	108	4.29	5.04
5	1000	0.07	0	0.180	138	128	2.74	2.33
6	1000	0.07	45	0.216	214	224	3.63	1.87
7	1000	0.07	90	0.214	187	179	4.25	2.56
8	1000	0.07	135	0.192	142	135	2.17	1.79
9	1500	0.07	0	0.243	89	83	1.60	2.32
10	1500	0.07	45	0.247	168	165	3.93	2.66
11	1500	0.07	90	0.172	142	133	1.83	1.51
12	1500	0.07	135	0.211	95	97	2.02	2.69
13	1500	0.12	0	0.195	64	61	1.01	2.32
14	1500	0.12	45	0.242	118	119	2.12	2.15
15	1500	0.12	90	0.281	106	112	1.71	1.98
16	1500	0.12	135	0.157	94	92	1.39	1.88

Fig.11(a) shows the predicted temperatures, which agree well with the measured temperatures in which the No. 10 experiment is used as an example. Furthermore, the machined surface temperature (d_m = 0 mm) significantly exceeds the subsurface temperature (d_m = 0.247 mm), which indicates a high temperature gradient in the finished surface layer, attributed to the low thermal conductivity in CF/PEEK. Fig.11(b) shows the maximum machined surface temperatures $T_{\text{max}}^{\text{surf}}$ in UD-CF/PEEK dry milling. $T_{\text{max}}^{\text{surf}}$ first increases and then decreases with increasing fiber orientation. Overall, the $T_{\text{max}}^{\text{surf}}$ of 45° is the largest, while the $T_{\text{max}}^{\text{surf}}$ of 135° is the smallest, which matches Ref. [28]. The machined surface temperature depends mainly on the workpiece carrying heat and the heat dissipation under different fiber orientations. According to Eq. (26), the heat dissipation in the cutting zone is fastest along the fiber orientation. On this basis, combined with the heat dissipation zone analysis of Ref. [28], the heat dissipation capability becomes progressively better as the fiber orientation increases in the HSD milling of UD-CF/PEEK. The workpiece carrying heat for different fiber orientations is shown in Fig.12(b). Therefore, taking 45° as an example, researchers can easily understand that the 45° with the almost maximum workpiece carrying heat and the worst heat dissipation capacity has the highest machined surface temperatures. In addition, $T_{\text{max}}^{\text{surf}}$ first increases and then decreases with increasing v_c, which is similar to what occurs in metal machining [38]. $T_{\text{max}}^{\text{surf}}$ tends to decrease with increasing f_z because the increase in the moving speed of the heat source strongly decreases the heat conduction time. Nevertheless, the $T_{\text{max}}^{\text{surf}}$ of 45° exceeds the T_g of CF/PEEK, which explains the difficulty in effectively limiting the machined surface temperature within the T_g in HSD dry milling of CF/PEEK by increasing f_z. Therefore, the machined surface temperatures are influenced mainly by the fiber orientation, followed by the cutting speed and feed per tooth.

Fig.11 Workpiece temperature for UD-CF/PEEK dry milling: (a) temperature increase curves for different dm values (in the No. 10 experiment) and (b) maximum machined surface temperature $T_{\text{max}}^{\text{surf}}$ at dm = 0 mm.

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Fig.12 Heat partition analysis for UD-CF/PEEK HSD milling: (a) total cutting heat Qtotal, (b) workpiece carrying heat QCF/PEEK, (c) chips carrying heat Qchip, and (d) heat partition ratio.

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4.4 Heat partitions for the workpiece, chip, and tool

The heat partitions of the workpiece, chip, and tool are obtained first in the HSD milling of CF/PEEK according to Fig.4 to analyze the cutting heat partition characteristics under dry conditions (Fig.12). The total cutting heat Q_total fluctuates with increasing fiber orientation (Fig.12(a)), which is consistent with K_tc in Fig.10(a). The Q_total also reaches a maximum at 90°, which agrees with Ref. [55]. Increasing v_c or f_z results in a gradual increase in Q_total. As the fiber orientation increases, the heat transferred into the workpiece Q_CF/PEEK first increases and then decreases (Fig.12(b)). The Q_CF/PEEK is obviously larger for the 45° and 90° orientations than for the 0° and 135° orientations. Given that k_p is much larger than k_v, the fiber axis is the best direction for cutting heat dissipation. The fiber axis at 0° is parallel to the machined surface, resulting in heat accumulation on the machined surface layer, which is unfavorable for heat dissipation. The 135° fiber direction can produce a cratered surface to reduce the tool-workpiece contact length, which is undesirable for heat transfer [29]. In addition, the Q_CF/PEEK in high-speed milling is much larger than that in low-speed milling, and the Q_CF/PEEK under different cutting parameters is closer in high-speed cutting. Increasing v_c or f_z can enhance the heat transferred into the chips Q_chip (Fig.12(c)). The Q_chip in high-speed milling is obviously greater than that in low-speed milling. As the fiber direction increases, Q_chip first increases and then decreases on the basis of the chip temperature assumption. Moreover, the workpiece heat partition R_CF/PEEK is much smaller than the tool heat partition R_tool and the chip heat partition R_chip (Fig.12(d)). The RCFs/PEEKs at 45° and 135° are larger than those at 0° and 90°. The R_CF/PEEK at 45° is also the largest, but the R_CF/PEEK at 0° is the smallest. Under the same fiber orientation, increasing v_c or f_z causes faster heat source movement and shorter heat transfer times, and the R_CF/PEEK decreases. Moreover, as the cutting speed increases, R_tool first decreases and then increases, while R_chip first increases and then decreases. An increase in f_z results in an increase in R_tool and a decrease in R_chip. As a result, the Q_CF/PEEK is much less than the Q_chip and Q_tool in the dry milling of CF/PEEK. For thermoplastic CF/PEEK, continuous chips with good heat-carrying capacity facilitate a reduction in the amount of heat carried by the workpiece.

4.5 Verification of the workpiece temperature suppression model

On the basis of the analysis of the workpiece temperature and heat partition presented above, air jet cooling HSD milling of CF/PEEK was first designed and executed to suppress the machined surface temperature. Furthermore, the proposed workpiece temperature suppression model is validated; thus, the workpiece temperature and machined surface quality are comparatively analyzed under dry and air jet cooling conditions.

4.5.1 Workpiece temperature suppression

The machined surface temperature must be effectively suppressed. Here, the process feasibility of air jet cooling during HSD milling of UD-CF/PEEK and its temperature suppression model need to be verified. On the basis of Fig.4, the workpiece heat flow and heat partition under air jet cooling conditions can be determined to predict the machined surface temperature. Validation experiments for the air jet cooling HSD milling of CF/PEEK were designed (Tab.5). A feed per tooth of 0.07 mm/z instead of 0.12 mm/z was used to demonstrate the workpiece temperature suppression effect for the air jet cooling process. Tab.5 also shows the maximum measured temperatures $T_{\text{max}}^{\text{m}}$ and maximum predicted temperatures $T_{\text{max}}^{\text{p}}$ for the measuring point and the maximum machined surface temperatures $T_{\text{max}}^{\text{surf}}$ (d_m = 0 mm). For the temperature curve, the E_RMS is lower than 4 °C, and the E_p is lower than 7%, which means that the workpiece temperature increase model can accurately describe the temperature variation under air jet cooling conditions.

Tab.5 Measured and predicted temperatures under air jet cooling conditions

No.	vc/(m∙min−1)	fz/(mm∙z−1)	θ/(° )	dm/mm	$T_{\text{max}}^{\text{m}}$/°C	$T_{\text{max}}^{\text{p}}$/°C	ERMS/°C	Ep/%	$T_{\text{max}}^{\text{surf}}$/°C
17	1500	0.07	0	0.186	49	48	1.77	6.140	66
18	1500	0.07	45	0.182	108	111	2.06	2.350	133
19	1500	0.07	90	0.249	91	93	3.51	4.950	110
20	1500	0.07	135	0.295	57	54	1.74	4.756	67

According to the jet parameters designed by the temperature suppression model, the jet-air convection heat transfer coefficient is calculated to be 1683.74 W/(m²∙K) using Eqs. (24) and (25). Then, on the basis of the calculation process shown in Fig.4, the temperature suppression model is used to directly predict workpiece temperatures under air jet cooling conditions, and machined surface temperatures and heat partitions are obtained (Fig.13). As the fiber orientation increases, the $R_{\text{CF/PEEK}}^{\text{res}}$ first increases and then decreases (Fig.13(a)). The $R_{\text{CF/PEEK}}^{\text{res}}$ at 90° is the largest and is close to 80%, while the $R_{\text{CF/PEEK}}^{\text{res}}$ values at 0° and 135° are small and close to 50%. This illustrates that the jet air can remove 20% to 50% of the heat from the workpiece heat source based on Eq. (4), resulting in less $R_{\text{CF/PEEK}}^{\text{res,t}}$ for air jet cooling conditions than for dry conditions. For identical cutting parameters, the $T_{\text{max}}^{\text{surf}}$ for the air jet cooling condition is significantly lower than that for the dry condition (Fig.13(b)). Furthermore, under different fiber orientations, $T_{\text{max}}^{\text{surf}}$ decreases by approximately 30% to 50% under air jet cooling conditions, which is noticeably lower than the decrease in T_g. This proves that the air jet cooling process is effective in suppressing workpiece temperatures in CF/PEEK HSD milling. Furthermore, the machined surface temperature simulated by the temperature suppression model agrees well with that derived from the experimental temperature, and the percentage errors of this model are less than 10%. This proves the validity and accuracy of the workpiece temperature suppression model for air jet cooling HSD milling of CF/PEEK. Furthermore, on the basis of this model, the expected $T_{\text{max}}^{\text{surf}}$ can be used to regulate the temperature and flow rate of the jet medium. Then, the workpiece temperature of the dry machining CFRTP can be actively controlled via a medium-jet cooling process.

Fig.13 Workpiece temperature analysis for air jet cooling HSD milling: (a) heat partition ratio on the workpiece and (b) machined surface temperatures $T_{\text{max}}^{\text{surf}}$ (in experiments Nos. 9–12 and Nos. 17–20).

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4.5.2 Machined surface quality

The three-dimensional topography and surface roughness of the finished surface were further analyzed to evaluate the machining quality under air jet cooling conditions (Fig.14). At 0°, the carbon fibers are well embedded in the PEEK matrix on the finished surface. The machined surface under air jet cooling conditions features slight fiber fracture, fiber pullout and matrix clustering (Fig.14(b1)). However, the machined surface under dry conditions exhibits significant matrix clustering due to the high $T_{\text{max}}^{\text{surf}}$ close to the T_g (Fig.14(a1) and Fig.13(b)). Therefore, a high cutting temperature softens the PEEK matrix, and the matrix flows viscously and aggregates into clusters during dry cutting. At 45°, the matrix smearing covers almost all the fractured fiber surfaces, which is attributed to the high ductility of the PEEK matrix. Under air jet cooling conditions, the surface topography displays smooth and uniform matrix smearing, and few fiber segments are attached to the surface (Fig.14(b2)). Nevertheless, the machined surface under dry conditions features cavities and flake-shaped matrix smearing (Fig.14(a2)). A cutting temperature of 45° (>T_g) significantly softens the PEEK matrix (Fig.13(b)) and reduces the fiber–matrix bonding strength in the machined surface layer, leading to fiber bending fracture below the machined surface. At 90°, the matrix smearing covers almost all the fiber fracture surfaces. Under air jet cooling conditions, a slight matrix cluster appears on the machined surface (Fig.14(b3)), probably due to tool plowing. However, under dry conditions, the machined surface develops fiber segments embedded in the finished surface, severe matrix clusters, and small cavities (Fig.14(a3)). A high cutting temperature (>T_g) softens the matrix (Fig.13(b)), resulting in fiber fracture under the machined surface, and the fiber segments are pressed into the machined surface under tool action. For 135°, the surface morphology exhibits a large cavity for dry and air jet colling conditions (Fig.14(a4) and (b4)). $T_{\text{max}}^{\text{surf}}$ at 135° is obviously lower than T_g (Fig.13(b)). Therefore, the machined surface formation depends on the 135° fiber orientation-dominated material removal mechanism. The removal of this material results in severe fiber bending fracture as the tool rake face advances, leading to a cavity created by fiber fracture beneath the finished surface. In addition, slight matrix clusters appear on the finished surface under dry conditions.

Fig.14 Machined surface topography and roughness for different fiber orientations: (a1–a4) dry condition, (b1–b4) air jet cooling condition, and (c) three-dimensional surface roughness Sa (vc = 1500 m/min, fz = 0.07 mm/z).

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According to Refs. [12,56], the three-dimensional surface roughness S_a, namely, the arithmetic mean deviation of the surface profile, can be calculated to quantitatively characterize the surface quality of dry and air jet cooling CF/PEEK milling (Fig.14(c)). S_a is taken as the average of three separate S_a for the same machined surface. In general, S_a for air jet cooling and milling is clearly lower than that for dry milling, which is consistent with the analysis of the surface topography. Compared with those under dry conditions, the significant decreases in the S_a of 45° and 90° and the slight decreases in the S_a of 0° and 135° under air jet cooling conditions are attributed to smooth surfaces with low damage under lower $T_{\text{max}}^{\text{surf}}$ within T_g. In particular, the machined surface temperature at 45 °C is much higher than the T_g under dry conditions, while it is effectively suppressed within T_g using the air jet cooling process. The surface roughness also improved significantly. In addition, the S_a of the 135° orientation is the highest among all fiber orientations, mainly due to the large cavity caused by the 135° fiber orientation effect. A significantly decreased cutting temperature of 0° is effective in suppressing surface damage, but the surface roughness decreases less, mainly due to the fiber stripping and bending fracture modes at 0°. On the one hand, the surface roughness depends strongly on the material removal mechanisms for different fiber orientations. On the other hand, workpiece temperature suppression below T_g plays an important role in improving surface roughness for different fiber orientations. The low workpiece temperature safeguards the matrix strength to provide effective support and restraint for the fibers and reduce surface defect formation. Therefore, the air jet cooling process can be utilized to actively suppress the workpiece surface temperature within T_g to improve the surface quality.

5 Conclusions

This study proposes an innovative temperature suppression analytical model considering heat partitioning and jet heat transfer for suppressing workpiece temperature via the first-time implementation of an air jet cooling process in the HSD milling of UD-CF/PEEK. Then, the chip characteristics, machined surface temperature evolution and heat partitioning characteristics in the HSD milling of UD-CF/PEEK were analyzed. The analytical model is verified based on the air jet cooling of the HSD milling of UD-CF/PEEK. This work describes a feasible process for the HSD milling of CF/PEEK. The main findings are listed below:

I. The morphological characteristics, formation mechanism and heat-carrying capacity of the chips in the HSD milling of UD-CF/PEEK were revealed. For the four fiber orientations, the chips feature a continuous ribbon morphology with matrix smearing characteristics, which is mainly attributed to the high ductility of the thermoplastic PEEK matrix. Furthermore, the chip structure characteristics and formation mechanism depend primarily on the fiber orientation. As a result, the chips can fly away from the cutting zone, thus carrying part of the cutting heat.

II. Under different fiber orientations and process parameters, the milling force model is calibrated to obtain the force coefficients, with a prediction error below 10%. Hence, the force coefficients are acceptable for exploring the total cutting heat. In addition, the force coefficients have significant fiber orientation-dominated anisotropy. For the same fiber orientation, increasing the cutting speed or decreasing the feed per tooth can decrease the force coefficients.

III. The surface temperature evolution and heat partitioning characteristics of the machined surfaces of UD-CF/PEEK were elucidated via HSD milling. With different fiber orientations and process parameters, the temperature increase model is validated to predict the workpiece temperature, with an E_RMS of 8 °C and an E_p below 6%, in which the thermal conductivity and specific heat capacity are quantitatively characterized as polynomial functions of temperature. The predicted temperatures indicate that the machined surface features a high temperature gradient, which is attributed to the low thermal conductivity of CF/PEEK. Moreover, the machined surface temperature first increases and then decreases with increasing fiber orientation, in which 45° is the maximum because of the near-maximum workpiece carrying heat and the worst heat dissipation capacity. Appropriately increasing the feed per tooth can reduce the machined surface temperature in the HSD milling of UD-CF/PEEK, which hinders the effective temperature suppression within the T_g, especially in the 45° fiber orientation. Moreover, the heat partitions are calculated to reveal that the heat partition of the workpiece is much smaller than that of the tool and chip for different fiber orientations, illustrating that the chip exhibits good heat-carrying capacity. The workpiece heat partition at 45° is the largest, while that at 0° is the smallest.

IV. With experimental verification under four fiber orientations, the workpiece temperature suppression model is verified to forecast the machined surface temperature in air jet cooling HSD milling of CF/PEEK, with a prediction accuracy exceeding 90%, where the jet-air heat transfer coefficient is 1683.74 W/(m²∙K). Under air jet cooling conditions, the jet air can remove 20%–50% of the workpiece heat under dry conditions, and the machined surface temperature is significantly reduced by 30%–50% and suppressed within the T_g. Finally, the machined surface morphology and surface roughness indicate that the machined surface quality is significantly improved using the air jet cooling process because of the guaranteed matrix strength achieved by actively suppressing the workpiece temperature. Therefore, the feasibility of air jet cooling HSD milling of CF/PEEK is proven.

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Acknowledgements

This work was supported by the National Key Research and Development Program of China (Grant No. 2022YFB3206700), the Fundamental Research Funds for the Central Universities, China (Grant No. 2023CDJYXTD-003), and the Natural Science Foundation of Chongqing, China (Grant No. 2022NSCQ-MSX2038).

Conflict of Interest

The authors declare that they have no conflict of interest.

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