Field-assisted machining of difficult-to-machine materials

In Pre-LAC process, the laser source directly radiates the surface to be cut, achieving the softening effect of the workpiece by heating to an evaluated temperature, and the machine tool completes the cutting motion to achieve ultra-precision machining of DMMs. As a result, the heat softens the shear zone of the workpiece, making it easier to separate the cutting chips from the substrate. The distance between the laser and the tool has a direct impact on the machining effect. Scholars have applied Pre-LAC technology to the processing of DMMs such as silicon nitride [81], ZrO₂ ceramics [82], and fused silica glass [73]. The softening effect of laser radiation decreases the yield strength of the material, increases the ductility, and improves the surface quality of the DMMs [8]. Song et al [73] found that the workpiece processed with Pre-LAC had fewer surface defects, such as cracks and grooves, and exhibited improved surface quality and cutting performance compared to those cut with ordinary cutting (OC), as shown in figure 5(a). A commercial laser system called ILPAC, developed by Innolite GmbH Co., has been successful in achieving improved machining quality of silicon [83], as shown in figure 5(b). In the cutting experiment, to achieve a better laser softening effect, the distance between the laser and the tool was fixed to 0.5 mm. Compared with CM, the surface roughness of LAC can be reduced by up to 90.05%. However, cutting fluid is prohibited during Pre-LAC as it can interfere with the laser beam path and cause refraction issues. Additionally, the separation of the heating and cutting regions causes a large thermal affected area.

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Conversely, the In-LAC method has gained widespread usage because it circumvents the disadvantages described above. Micro-LAM Co. developed a commercial OPTIMUS T1 system [20, 84–86]. The OPTIMUS T1 system, as shown in figure 5(c), has been successful in achieving the optical machining of silicon with a surface roughness of 1.05 nm in Ra [87]. Additionally, germanium can retain surface roughness of less than 2 nm RMS using In-LAC method [85]. Mohammadi et al [84] conducted taper cutting experiments on silicon and observed that utilizing the In-LAC could effectively eliminate the radial spokes caused by crystal orientation effects. This, in turn, led to a significant enhancement in the surface quality of the workpiece. Ke et al [80, 88] used a self-developed In-LAC system to study the machining performance of silicon. They discovered that In-LAC can greatly enhance the material's flexibility and workability [89], and the DBT depth of silicon was raised by 364% compared with OC. Using similar experimental methods, the crucial DoC of fused silica was raised from 82.06 nm to 324.03 nm, which resulted in the development of a smooth surface with a Sa of 19.4 nm with laser assistance [90]. Huang et al [91] shown that the laser thermal effect induced by In-LAC influences nitrided mold steel's mechanical properties, in which the nano-hardness and elastic modulus are decreased by 41% and 20% at 400 °C, respectively. Based on the Taguchi method, an experimental investigation was conducted to determine the optimal finish quality for WC, achieving a surface with 3.06 nm in Sa [92]. However, the high laser power used during In-LAC has the potential to cause local graphitization on the diamond tool [93]. You and Fang [94] introduced a novel In-LAC method, known as high effective laser assisted turning (HE-LAT), which involves refracting the laser beam at the rake face and cutting edge, and total reflection at the flank face, as shown in figure 5(d). Experimental results demonstrated that HE-LAT can eliminate surface fluctuations, and prevent diamond local graphitization by using lower laser power.

DMMs are difficult to process at room temperature, mainly because the ultimate yield strength is greater than the fracture strength, resulting in uneven plastic deformation. This problem can be eliminated by heating the material to its thermoplastic stage [96]. Dislocations facilitate the ductile deformation of brittle materials when the temperature is above the ductile-to-brittle transition temperature [72]. Considering that the bonding forces among atoms and grains in the material will diminish at elevated temperatures, the laser radiation induced thermal field will remarkably improve the material machinability. Many researchers have reported that there is a sharp decline in the hardness of DMMs as the temperature increases, as shown in figure 6 [97].

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For most DMMs, the fracture toughness experiences a significant rise when the material reaches the brittle to ductile transition temperature. Additionally, heating can improve ductile machinability by lowering tensile strength and increasing fracture toughness [98]. It is observed that all DMMs undergo a transition from ductile to brittle mode during nano-scratching as the DoC increases [99]. The critical depth of the transition from the ductile mode to the brittle mode is called the critical ductile-brittle transition (DBT) depth. When the DoC exceeds the critical depth for machining DMMs, material removal is accomplished through the propagation and intersection of cracks [100, 101]. The critical DBT depth can be estimated by the empirical formula as follows [102]:

$$\begin{align}\begin{array}{*{20}{c}} {{d_{\text{c}}} = \,b\left( {\frac{E}{H}} \right)\,{{\left( {\frac{{{K_{{\text{IC}}}}}}{H}} \right)}^{\text{2}}}} \end{array}\end{align} \tag{ 1 }$$

where b is a constant that depends on the tool geometry, E is the Young's modulus, H represents the hardness, K_IC is fracture toughness. Obviously, increasing K_IC and decreasing H will significantly increase the DBT depth, improving the plasticity of the material. Experimental research has confirmed that laser heating could enhance the DBT depth during diamond cutting [22, 80, 91]. In this way, the material removal rate can be improved significantly.

Cutting temperature plays an important role in the surface finish quality and tool life of LAC. If the workpiece temperature is too low, the material is not softened sufficiently, leading to poor machined surface quality and serious tool wear. Furthermore, elevated cutting temperatures can lead to the graphitization of the diamond tool and subsurface damage on the workpiece [103]. Therefore, controlling the temperature distribution precisely is one of the key technologies of LAC. Ravindra [104] utilized liquid temperature lacquers to measure the temperature during LAC of silicon. Nonetheless, the measurement accuracy may be compromised by the exceedingly low tool speed. Due to the spatial resolution limitation of current thermal instruments, it is not feasible to accurately measure the temperature field of the heat-affected zone at the nanoscale [105]. As a result, developing a precise thermal simulation model using analytical methods or finite element methods is an excellent approach to calculating the thermal field in LAC.

Analytic method considers laser energy input, radiation, convection, cutting heat, and natural convection, as illustrated in figure 7 [106, 107]. The heat conduction differential equation can be expressed by [108]:

$$\begin{align} \rho {c_p}\omega \frac{{\partial h}}{{\partial \emptyset }} + \rho {c_p}{V_z}\frac{{\partial h}}{{\partial z}} + \rho {c_p}\frac{{\partial T}}{{\partial t}} &= \frac{1}{r}\frac{\partial }{{\partial z}}\left[ {rk\frac{{\partial T}}{{\partial r}}} \right] + \frac{1}{{{r^2}}}\frac{\partial }{{\partial \emptyset }}\left[ {k\frac{{\partial T}}{{\partial \emptyset }}} \right] \nonumber\\ & \quad + \frac{\partial }{{\partial z}}\left[ {k\frac{{\partial T}}{{\partial z}}} \right] + Q \end{align} \tag{ 2 }$$

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where $h$ refers to the enthalpy in ${\text{J}}\cdot{\text{k}}{{\text{g}}^{ - 1}}$. $Q$ is the volumetric energy addition in ${\text{w}}\cdot{{\text{m}}^{ - 3}}$. $\omega$ is the rotational speed in ${\text{rad}}\cdot{{\text{s}}^{ - 1}}$. $\rho ,{\text{ }}{c_p},{\text{ }}k$ refer to materials' density, specific heat, and thermal conductivity, respectively. And $r$, $\emptyset$, and $z$ are cylindrical coordinates.

The thermal energy input resulting from laser irradiation on the workpiece can be calculated by equation (3). q_H, q_conv, and q_rad represent the absorbed laser energy, thermal convention, and radiation, respectively

$$\begin{align}\begin{array}{*{20}{c}} {k\frac{{\partial T}}{{\partial r}} = {q_H} - {q_{{\text{conv}}}} - {q_{{\text{rad}}}}} \end{array}.\end{align} \tag{ 3 }$$

The absorbed laser energy with a Gaussian distribution is given by equation (4), in which α, P, R represent the absorption ration, laser power and laser spot radius

$$\begin{align}\begin{array}{*{20}{c}} {{q_H} = \alpha \frac{{2P}}{{\pi {R^2}}}{e^{ - \frac{{2{r^2}}}{{{R^2}}}}}} \end{array}.\end{align} \tag{ 4 }$$

Thermal convection can be described by equation (5) where ${h_l}$ is the heat transfer coefficient

$$\begin{align}\begin{array}{*{20}{c}} {{q_{{\text{conv}}}} = {h_l}\left( {T - {T_0}} \right)} \end{array}.\end{align} \tag{ 5 }$$

The radiation heat transfer between the surface and ambient air is calculated using equation (6) where $\sigma$ is Boltzmann's constant, and $\varepsilon$ is emissivity of material

$$\begin{align}\begin{array}{*{20}{c}} {{q_{{\text{rad}}}} = \varepsilon \sigma \left( {{T^{\,4}} - {T_0}^4} \right)} \end{array}.\end{align} \tag{ 6 }$$

Rozzi et al [108] compared predicted surface temperature histories with measurements to verify the accuracy of the thermal model, which provides the basis for the parameters selection during LAC of nitride silicon. However, due to the complicated factors influenced the machining process, the accuracy of analytic method is not high enough.

The finite element analysis technique shows great potential in accurately calculating the temperature distribution during the LAC process, by considering the intricate boundary conditions and the thermal initial state. You et al [92] calculated the temperature distribution induced by laser heating, and applied this information to guide laser power selection for In-LAC of WC. Lin et al [90] developed a model to predict the temperature distribution of fused silica during laser heating, which was demonstrated to have high accuracy through temperature measurement with thermocouples. The findings indicated that the laser beam center had the highest temperature, which decreased rapidly with distance from the center of the beam. Ren et al [109] established a three-dimensional thermal model for Pre-LAC of fused silica. As shown in figures 8(a) and (b), the temperature in the cutting zone of the workpiece reaches 1490 K during Pre-LAC, while the temperature at the tool nose reaches 510 K. The temperature field during In-LAC found that there is a small influence area on the workpiece surface, with the majority of heat distributed in a semicircular region on the subsurface, as shown in figures 8(c) and (d) [80]. Compared to the temperature field produced during Pre-LAC, the heat affected zone is smaller and the temperature is higher due to the smaller diameter of the laser spot during In-LAC.

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The high temperature produced by laser irradiation during LAC improves the ductile machinability of DMMs. Macroscopically, the effect of the laser changes the material removal mechanisms from brittle fracture to ductile removal. Microscopically, laser irradiation might cause phase transition, which affects surface generation and subsurface deformation during LAC. Due to the large material removal scale of pre-LAC, the material removal mechanism at a microscopic scale is rarely discussed by scholars, and the cutting mechanism during In-LAC is discussed through systematic numerical analysis and experimental investigation [110].

Hydrostatic pressure and shear stress are created during diamond cutting, which facilitate a high-pressure phase transformation [111, 112]. The high-pressure phase exhibits excellent properties of electroconductivity and machinability due to a microstructural modification [113]. During the LAC process, the high-pressure phase transformation affects the formation of lattice structure in the chip and the machined surface. Molecular dynamics (MD) simulation and cross-sectional TEM observations found that laser assistance changes the transformation path of silicon, and the amorphous Si was directly generated from the Si-I rather than from the Si-II. The newly created amorphous Si experiences partial recrystallization and is converted into metastable Si-III and Si-XII phases through laser annealing [20]. The various pathways of phase transformation routes indicate that the material removal mechanism is dependent on temperature. Furthermore, the dislocation activity was increased by a factor of ∼8 × 10¹⁴ with laser assistance, which enhances the plastic deformability of the material, contributing to the rise of the critical DBT depth and the reduction of the subsurface damage [22, 80]. Liu et al [89] studied the subsurface damage evolution of single crystal silicon at elevated temperature by MD simulation and diamond cutting experiments, and found that as the cutting temperature increased, the shear resistance of the amorphous layer decreased and the self-lubricating effect of the amorphous layer became more prominent. This outcome is beneficial in suppressing the formation of subsurface damage, as shown in figure 9.

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As mentioned forward, the temperature field under different laser powers varies a lot, which influences the material removal mechanism. You et al [93, 94] found that the cutting shear band with grain slippage consistently occurs along the grain boundary due to the high toughness during diamond cutting of polycrystalline WC. When employing low laser powers in LAC, grain strength is weakened effectively due to the thermal effect, resulting in the formation of straight shear bands and improved grain refinement. Conversely, higher laser powers used in polycrystalline material removal predominantly exhibit extrusion without any discernible shear band and pure amorphous cutting chips. The difference of the surface generation process influences the subsurface damage. With laser assistance, the dense crystal defects in the affected layer of the machined WC caused by the severe grain deformation and stress release decrease, and the thickness decreases from ∼227.9 nm to ∼17.8 nm.

LAC is a highly effective approach to achieving superior machining quality on DMMs. The quality of machining is evaluated and optimized by assessing surface integrity, cutting force, tool life, and material removal rate, as summarized in table 2. The effectiveness of laser assistance is mainly from two perspectives: laser absorption rate and laser power. The workpiece material is required to have a certain absorption rate of the laser, and the critical temperature of the material softening modification is ensured by controlling the laser power. Future research on LAC can be carried out as follows: (1) exploring the tool wear inhibition mechanism through numerical simulation and molecular dynamics simulation. (2) Establishing a high precision temperature control model based on online laser absorptivity measurement. (3) Developing a LAC system that is easy to operate and more integrated, promoting its industrial application.

In one-dimensional (1D) UVC, ultrasonic vibration can be introduced separately to the cutting tool in the cutting direction [118], feed direction [126], and radial direction [127] according to the vibration direction; the principle schematic is depicted in figures 11(a)–(c) [128]. Skelton [16] proposed a linear vibration cutting technique, which involves machining with an assisted vibration having a linear motion in the nominal cutting direction. They found that applying a constant frequency ultrasonic vibration can significantly reduce the cutting force and temperature, improve tool life and machined surface quality. Zhou et al [114] designed a classical 1D linear UVC device. And the groove cutting experiments were applied to investigate the effect of tool vibration on the DBT of glass. The groove cutting experiments were performed in glass to study the impact of tool vibration on the DBT of glass. The results showed that the critical DoC was about 1.5 μm.

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Zhou et al [116] also investigated the machinability of steel alloys with UVC and the results showed that the cutting force, surface finish, and tool life were improved compared with OC. Muhammad et al [117] carried out titanium alloy with ultrasonically assisted turning and found enhancements in both the surface roughness of the machined workpiece and the generation of chips. Zhang et al [118] studied the machinability of Ni-base superalloy by UVC. And the experimental results showed that the surface roughness and subsurface damage were reduced to Sa 4.815 nm and 0.190 μm from 60 nm and 2.27 μm, respectively. However, the 1D UVC has shortcomings in that the tool edge would scratch the machined surface and suffer from severe alternating stress, which impairs surface quality and tool life in the process of separation [129].

To address the problems of 1D UVC, Shamoto and Moriwaki [19, 29] proposed the two-dimensional (2D) EVC technology which vibrating direction including parallel to cutting direction and cutting depth direction. The two dimensional elliptical vibrator device can be classified to resonant [130] and non-resonant [131], as shown in figures 11(d) and (e).

The resonant vibration device demands precise positioning of the tool (or workpiece), and the resonance frequency of the transducer must align with the working frequency [129]. Moriwak and Shamoto [132] proposed the first EVC device in the ultrasonic frequency in 1995, as shown in figure 11(d-i). The device is mainly composed of a square beam and two symmetrical cylindrical rods. Two pairs of piezoelectric plates are symmetrically arranged on the four sides of the square beam to drive the whole device to produce first-order bending in two perpendicular directions. The standing wave nodes of the square beam are selected as the supporting position, the tool tip is fixed on the edge of the cylindrical rod and generates the locus of vibration when the vibrator is working. Cutting experiments of oxygen free copper were conducted to verify the performance of the device. The results found that the cutting force of EVC is significantly decreased and the cutting thickness is thinner than that of OC. Shamoto and Moriwaki [29] developed the above elliptical device in 1999. The square beam is replaced by a six-prism beam, and the original cylindrical rod is instead by a stepped cylindrical rod (see figure 11(d-ii)). The piezoelectric plates are attached to the two sides of the six-prism beam, and the device works in two mutually perpendicular third-order bending vibration resonance modes. The fixed supporting point of the device must be selected at the node position of the bending vibration mode of the device to avoid the supporting structure affecting the bending mode of the transducer. The improved EVC device has been realized ultraprecision cutting hardened steel successfully. Suzuki et al [119, 133] cooperated with Taga Electric Co. to develop the latest EVC device, as shown in figure 11(d-iii). A bolt clamped Langevin type transducer (BLT) is used to actuate the device, which consists of PZT actuators sandwiched between metal cylindrical parts. Meanwhile, the device with a compact structure works in the composite mode of second-order longitudinal vibration (cutting depth direction) and fifth-order bending vibration (cutting speed direction). The elliptical vibration track is located in the direction of DoC and cutting speed which is convenient for tool installing and cutting experiments. The working frequency and amplitude of this device are 38 kHz–42 kHz and 0–4 μm_p-p. However, the manufacturing and assembling of this device is difficult, which needs additional dedicated controllers to decouple the longitudinal-bending vibration modes in the two perpendicular directions and achieve modal degeneracy of these two vibration modes [134].

Guo and Ehmann [135] designed a tertiary motion generator by combining two longitudinal vibration modes, as shown in figure 11(d-iv). The device is composed of two sandwich-type longitudinal ultrasonic transducers crossed at 60° and coupled in the output by a flexible hinge, which can realize the tool's high-frequency elliptical vibrating with 28 kHz on the plane formed by its normal line and tangent line. The device has generated micro/meso-scale features successfully, while the coupling performance of two-direction vibration is poor, resulting in serious energy loss, and the considerable size of structure will limit its industrial application. As for the non-resonant UVC system, it operates at a frequency lower than the system's initial natural frequency [11]. Within them, Wang et al [131] designed an ultrafast 2D non-resonant cutting tool to fabricate the micro-structure surface, as shown in figure 11(e). The tool trajectory measurement experiments were carried out to evaluate the device performance. Tests were conducted at both low (200 Hz) and high (5.5 kHz) frequencies. The results showed a favorable agreement with the designed and measured trajectories. Furthermore, the effect of elliptical inclination angle on ductile cutting was analyzed, and it was found that the inclination angle of 135° is the most suitable for ductile cutting.

Based on the above innovative two-dimensional elliptical cutting vibration device, lots of scholars have carried out cutting experiments. Suzuki et al [119] used the resonant EVC device to machine tungsten alloy molds. Throughout a cutting distance of 50 m, the maximum surface roughness was maintained below 100 nm Rz. Tan et al [120] applied the EVC technology in cutting Ti-6Al-4V. The experiments indicated that the tool wear was obviously restrained and the surface quality was significantly improved when the finished surface was less than 30 nm. Zhang et al [122] studied the single crystal silicon machining in ductile by adopting the EVC technology. The grooving experiments demonstrated that the nominal DBT depth in EVC is more than 12 times higher than that in OC. Zhang et al [123] studied the machinability of CaF₂ by EVC. The results demonstrated that the critical DoC for the DBT is increased by 42 times compared with that for OC. Zhang et al [121] carried out a fundamental study on the ductile machining of tungsten carbide. The results showed that the finished surface roughness is lower than 4 nm by EVC in ductile mode machining. 2D UVC has achieved micron/nano-scale surface microstructure machining of DMMs.

The three-dimensional (3D) UVC system was proposed based on the research of two dimensional EVC. Zhang and Song [136] proposed a novel ultrasonic EVC mechanism with decoupled 3D and fabricated a prototype device. And the vibration characteristics test experimental results showed that the performance of the innovative 3D EVC mechanism is satisfactory. Kurniawan et al [124] developed a sandwiched piezoelectric actuator-based holder for a resonant 3D ultrasonic elliptical vibration tool (UEVT). The 3D-UEVT produced a peak-to-peak amplitude of about 0.8 μm in two bending directions and a range of 0.3 μm to 0.5 μm in the longitudinal direction, as shown in figure 11(f-i). And the microgroove pattern experiments of AISI 1045 carbon steel were carried out. The results showed the novel 3D ultrasonic vibration tool holder has lesser cutting force and surface roughness compared with OC. Kurniawan et al [137] designed a 3D-UEVT holder based on coupled resonant modes, as shown in figure 11(f-ii). And the amplitude in the x-, y- and z-axis directions is approximately reached to 0.42 μm, 0.5 μm, and 0.6 μm at a resonant frequency, respectively. Shamoto et al [33] proposed the 3 DOF ultrasonic vibration tool technology to machine hardened die steel. And this method can achieve the machining of sculptured mirror surfaces on hardened die steel. So far, the primary focus of the 3D UVC has been on the device's structural design and output stability, while the exploration of surface microstructure processing applications is gradually gaining attention [129].

As shown in figure 12(a), in the UVC process, the tool only executes cutting in the time segment t_a –t_b , while it is in the uncut state at other times during one vibration period. The main characteristic of 1D UVC is intermittent cutting, which changes the OC process. Nath and Rahman [138] proposed the tool-workpiece contact ratio r to analyze this property. The intermittent cutting characteristics are described as follows:

$$\begin{align}& {v_c} + 2A\pi f\text{cos} 2\pi f{t_b} = 0\end{align} \tag{ 7 }$$

$$\begin{align}& A\text{sin} 2\pi f\left( {T + {t_a}} \right) - A\text{sin} 2\pi f{t_b} = {v_c}\left( {T + {t_a} - {t_b}} \right)\end{align} \tag{ 8 }$$

$$\begin{align}& r = \frac{{{t_b} - {t_a}}}{T}\end{align} \tag{ 9 }$$

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Combining equations (7)–(9), the final equation is obtained as follows:

$$\begin{align}{v_c}\left( {1 - r} \right) = 2Af\text{sin} \pi r{\text{cos}}\left[ {{\text{co}}{{\text{s}}^{ - 1}}\left( { - \frac{{{v_c}}}{{2\pi Af}}} \right) - \pi r} \right],\;2\pi Af > {v_c}\end{align} \tag{ 10 }$$

where ${v_c}$ is nominal cutting speed. f (i.e. vibration period, T = 1/f) is frequency and A is vibration amplitude. ${T_a}$ is the time of initial tool-workpiece contact. ${T_b}$ is the time of initial separation of tool and workpiece.

It is worth noting that there are actual upper and lower limits of cutting speed to ensure the effectiveness of vibration cutting [129]. When the horizontal speed ratio (HSR = v_c/2πAf) is less than 1, UVC is satisfied, otherwise it is OC (i.e. HSR > 1). Moreover, thanks to the existence of separation phenomenon in each vibration period, the cutting zone can be effectively cooled by air and cutting fluid, which makes the thermochemical wear of the tool to be suppressed. The ultra-precision machining of DMMs, such as ferrous metals, can be achieved by applying UVC technology [7].

In the 2D UVC process, the tool oscillates at an angular frequency $\omega$ with vibration amplitude A of the cutting direction and amplitude B of the depth of cut direction. During the process of material removal in a cycle, the cutting path of the tool tip starts at point A, reaches the lowest point M of the trajectory, passes through the point D (i.e. initial contact between rake face and chip) and the friction reversal point E, finally separates the chip at the point F, accordingly in figure 12(b). In order to accurately clarify the tool trajectory, the displacement function of tool tip relative to workpiece in Cartesian coordinates can be described as follows:

$$\begin{align}x\left( t \right) = A{\text{ sin}}\left( {\omega t} \right) - {v_c}t\end{align} \tag{ 11 }$$

$$\begin{align}y\left( t \right) = B{\text{ sin}}\left( {\omega t + \varphi } \right).\end{align} \tag{ 12 }$$

Then, the velocity function of the tool tip can be obtained by deriving the time variable, as shown in equations (13) and (14):

$$\begin{align}{v_x}\left( t \right) = \frac{{dx\left( t \right)}}{{dt}} = \omega A{\text{ cos}}\left( {\omega t} \right) - {v_c}\end{align} \tag{ 13 }$$

$$\begin{align}{v_y}\left( t \right) = \frac{{dy\left( t \right)}}{{dt}} = \omega B{\text{ cos}}\left( {\omega t + \varphi } \right)\end{align} \tag{ 14 }$$

where ${v_x}\left( t \right)$ and ${v_y}\left( t \right)$ represent the velocity of the nominal cutting direction and the depth of cut direction, respectively. ${v_c}$ is the cutting speed. $\varphi$ is the phase shift. HSR directly affects the shape and thickness of undeformed chips. With the increase of HSR, the overlap of tool paths gradually decreases and the duty cycle gradually increases. If the HSR is greater than 0.32 and the cutting depth is greater than the vibration amplitude B, the tool will never break contact with the workpiece and the 2D UVC will no longer be effective [129].

Blake and Scattergood [139] found that when TOC_t is less than a critical value (d_c), the ductile-regime cutting can be achieved. Hence, it is critical to clarify the change of TOC_t in 2D UVC. Zhang et al [140] proposed that TOC_t represents the y-axis distance between the cutting edge and the surface remaining from the previous cutting cycle, and analyzed its numerical changes by the following equations:

$$\begin{align}TO{C_t} = \left\{ \begin{array}{*{20}{ll}} {{\text{ }}0} & {t < {t_A},{\text{ }}t \unicode{x2A7E} {t_F}} \\ {y\left( {{t_p}} \right) - y\left( t \right)} & {{t_A} \unicode{x2A7D} t < {t_D}} \\ {{a_p} - \left[ {y\left( t \right) + B} \right]} & {{t_D} \unicode{x2A7D} t < {t_F}} \end{array}\right.\end{align} \tag{ 15 }$$

$$\begin{align}\frac{{x\left( t \right) - x\left( {{t_p}} \right)}}{{y\left( t \right) - y\left( {{t_p}} \right)}} = \text{tan} \gamma ,{\text{ }}0 < \left( {t - {t_p}} \right) < \frac{{2\pi }}{\omega }\end{align} \tag{ 16 }$$

where y is the displacement function of the tool tip along the y-axis. a_p is the nominal cutting depth. t_p is the time at which the tool tip passed point P during the previous cutting cycle. $\gamma$ is the tool rake angle.

It is evident that the value of TOC_t undergoes continuous variation and is consistently less than ${a_p}$ because of the overlapping cutting cycles. Hence, the cutting force becomes smaller because of the lesser material removal volume. Nath et al [141] found that the ductile machining of brittle materials can be achieved if the maximum value of TOC_t (TOC_tmax) is not greater than the d_c. TOC_tmax plays a critical role in the ductile-regime cutting of DMMs. Furthermore, Liu et al [142] investigated the variation of TOC_tmax during one cycle. t_i was the time that TOC_t reached the maximum value. When b> a_p, TOC_tmax would be slowly increasing with increasing a_p . Continue to enlarge a_p, t_i would be a constant t_D dependent on the UVC system while TOC_tmax increased quickly, as depicted in the figure 12(c).

To further examine the impact of TOC_t on the material removal mechanism, simulations were conducted to explore the nanoscale processing of 2D UVC on DMMs. Dai et al [143] utilized molecular dynamics simulations to investigate the subsurface quality and material removal of monocrystalline silicon during UVC processing. The simulation results indicated that UVC processing tends to induce ductile-mode cutting in silicon, which has a beneficial impact on tool longevity. However, it can also result in higher subsurface temperatures. Liu et al [144, 145] modified the classical molecular dynamics model to investigate the material removal mechanism in UVC of monocrystalline silicon. A single vibration cycle was described through an increment of the tool vibration amplitude and nominal depth of cut. The results indicated that within a single vibration cycle, the primary mechanism of material removal transitions from extrusion to shear, see figure 13. Tensile stress is the main cause of subsurface damage in the shear stage. Furthermore, increasing the radius of the cutting edge, decreasing the velocity ratio of the nominal cutting and DOC direction, and increasing the amplitude of the cutting direction will delay the extrusion-shear transition.

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As illustrated in figure 14(a), there is the trajectory of the tool tip in 3D UVC. During one cycle, the tool starts to cut the workpiece at point t₀, reaches the bottom point t₁ in the y direction, where the velocity of the tool tip is zero. Finally, it is separated from the workpiece at the point t₂. Then, the tool jump into the next cycle at point t₃ [146].

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There are three different vibration amplitudes of three perpendicular directions during the 3D UVC process. Similar to the motion analysis of the 2D UVC process, the tool tip path with the vibration can be depicted as:

$$\begin{align}x\left( t \right) & = A\text{cos} \left( {\omega t} \right) - {v_c}t{\text{cos}}i\end{align} \tag{ 17 }$$

$$\begin{align}y\left( t \right) & = B\text{cos} \left( {\omega t + {\varphi _y}} \right)\end{align} \tag{ 18 }$$

$$\begin{align}z\left( t \right) & = C\text{cos} \left( {\omega t + {\varphi _z}} \right) + {v_c}t{\text{cos}}i.\end{align} \tag{ 19 }$$

The Cartesian coordinates of the relative tool and workpiece position along the nominal cutting, thrust, and feeding directions are represented by x, y, and z, respectively. The vibration amplitudes in the x, y, and z directions are denoted by A, B, and C, respectively. Time is represented by t and angular frequency by ω. The inclination angle is indicated by i, while the phase shifts of the vibrations in the y and z directions are represented by ${\varphi _y}$ and ${\varphi _z}$, respectively.

Although the vibration trajectory becomes complicated, the cutting force will become smaller due to the newly added vibration direction. Compared to the orthogonal 2D UVC locus, 3D UVC also includes the oblique 2D UVC locus, as shown in figure 14(b). Due to the oblique cutting characteristic, the chip is pulled laterally, thereby decreasing the frictional thrust component that hinders the flow of the chip. In summary, not only is the friction between the tool and the chip reduced or reversed, but the thrust component is also further reduced in the 3D UVC process [33, 147].

In summary, with the change of machining mode, the contact mode between the tool and the workpiece during intermittent machining also changes. Compared to OC, UVC technology could significantly decrease cutting force, diminish tool wear, and enhance the surface machining precision of the workpiece. Nowadays, the UVC system has made a great deal of achievements. The advanced ultra-precise manufacturing companies, German Son-x, German Innolite, and Japanese Taga company have produced commercial products of UTS-2, ILSonic, and EL-50Σ, respectively. The 2D UVC has achieved micron/nano-scale surface microstructure machining of DMMs. The 3D UVC technology mainly concentrates on the structural design and output stability of the device, while research on the application of surface microstructure processing is gradually being explored. Meanwhile, attention should be given to future work on UVC technology: (1) in-depth research on the mechanism of high-precision surface formation, especially the influence of material deformation and tool impact on machining quality, (2) improving the UVC system stability, which can be conducted long time stable working, (3) increasing the vibration frequency and amplitude of the UVC system, which is beneficial to improve the machining efficiency for industrial applications.

Enhancing cutting tools has consistently been a crucial research subject in the whole mechanical manufacturing industry. Enhancing the wear resistance and cutting performance of cutting tools is critical in determining processing efficiency, surface quality, and component cost. High-speed steel material continues to be a vital component in the mechanical manufacturing industry due to its exceptional comprehensive performance in strength, toughness, and processing capacity. Therefore, the early magnetization treatment of tool materials is mainly concentrated on high-speed steel tools. Muju and a Ghosh [18] conducted a study on MFAC cutting steel alloys. By calculating the tool wear gain coefficient under the magnetic field, they found that the wear gain coefficient was positively correlated, and the magnetic field was conducive to reducing the wear of high-speed steel tool. Xu and Liu [149] found that magnetization treatment of high-speed steel tool can improve its durability 1.5–3.0 times, under certain circumstances, tool life can be increased by 4–6 times. Li and Mu [150] magnetized the high-speed steel tool by low frequency pulse magnetization, and discovered that the mechanical property of the magnetized tool material was improved. Magnetization can reduce the residual stress of the tool, thereby improving the durability of the tool. To further study the magnetic field on the tool to extend the life of the reasons, El Mansori et al [12] wound a 6 mm diameter DC coil outside the tool, the magnetic field intensity can be controlled by adjusting the current intensity, as shown in figure 15(a). It is found that the magnetic field can enhance the durability of cutting tools during the cutting process. Under the excitation of a high magnetic field, the mean width of the pits on the tool surface decreases by about 50% and the maximum depth decreases by about 75%.

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Dehghani et al [151] designed an L-arm device for the MFAC of steel alloy. The L-arm device connects the tool to the workpiece, forming a closed-loop circuit that provides a consistently stable magnetic field for magnetizing the workpiece, as shown in figure 15(b). The findings from the experiment indicate that the wear of the tool flank is reduced by 94% after applying the magnetic field. Therefore, the current research results can show that MFAC can indeed improve the tool life. Magnetized tools can effectively inhibit tool wear and improve workpiece machining quality, but it is difficult to assess the influence of magnetic field on improving cutting performance. Meanwhile, it cannot be applied to non-magnetic cutting tools like diamond tools, so the application range is limited.

In addition to the magnetization treatment of the tool, some scholars have also studied the magnetization treating workpiece during the machining process. El Mansori et al [152] studied the surface plastic deformation of MFAC steel alloys. It was discovered that as the magnetic field strength increased, the thickness of the second deformation zone increased, and the serrated degree of chips was greatly reduced. Subsequently, they also found that the utilization of the magnetic field improved the machinability of the workpiece material, altered the shear angle, shear strain, and cutting thickness ratio, and affected the contact condition between the tool and chip, and increased the tool life by 2–3 times [153]. In recent years, magnetic fields have been integrated into the ultra-precision diamond cutting process by some researchers to reduce the material swelling impact on the surface of machined titanium alloys. Yip and To [35, 154–158] installed two permanent magnets with a magnetic field intensity of 0.02 T on the machine tool. During cutting operations, the titanium alloy workpiece rotates within a magnetic field that is produced by the installation of two permanent magnets, as shown in figure 15(c). Under the influence of the magnetic field, there was a significant improvement in the surface quality of the workpiece. The accuracy of DoC, width, and radius of the cutting groove reached satisfactory over 98%. Compared with OC, the bottom surface roughness decreases from 36.58 nm to 15 nm [35]. There are many beneficial effects by introducing a magnetic field. The eddy current damping generated by the magnetic field not only dissipates the vibration energy at the tool tip but also decreases the cutting heat at the interface between the tool and titanium [158]. As a result, the negative impact on surface quality caused by brittle deformation is significantly reduced, leading to an improved surface quality in both the ductile and brittle deformation zones [155]. Moreover, the thermal conductivity of titanium alloy is low, which means that the high temperature at the processing interface makes the material melt, and the average grain diameter reduction rate is 20.3%, the grains of titanium alloy surface are effectively refined to improve the machining properties of titanium alloy [156]. The primary wear mechanism during cutting of titanium alloy is adhesive tool wear. With the assistance of a magnetic field, the adhesive wear of the tool is reduced and the maximum flank wear width is decreased by 23% [154].

Wu et al [159] introduced a magnetic field in the process of diamond cutting single crystal copper. The findings indicate that the magnetic field influences the metal cutting process by altering the cutting force, chip morphology, and surface finish. In comparison to OC, MFAC leads to an elevation in the induced Lorentz force, whilst the cutting force ratio and friction coefficient of the rake face are diminished by 16%. Additionally, the tribological behavior of the tool-chip contact interface is enhanced. Guo et al [160] attributed this process to the magneto-plastic effect, due to the application of magnetic fields, the plasticity of metals will undergo a significant alteration. Subsequently, they conducted experiments on CaF₂ [161]. The micro deformation test under a weak magnetic field of 0.02 T confirmed the impact of magneto-plasticity on CaF₂. Under the influence of the magnetic field, the surface stacking effect was weakened by 10–15 nm, and the dislocation density was about 30% lower than that without magnetic field, and the fracture toughness increased by 53.8%. Micro-cutting tests along the CaF₂ (111) plane with different crystal orientations show that magneto-plasticity contributes to an increase in the DBT of the machined surface. The DBT depth is increased from 512 nm to 664–806 nm when cutting along the crystal direction $[11\bar 2]$. Xiao et al [162] conducted the MFAC experiments on nickel-based superalloys. The experimental results indicate that the application of a magnetic field leads to an improved chip morphology in comparison to OC. The cutting force oscillations (F_c, F_a , and F_f ) are markedly reduced by 90%, 88%, and 78%, respectively. The Ra surface roughness value increases from 23 nm to 13 nm, while the P-V value of the fan-shaped region of the machined surface undergoes a 49% reduction.

During the OC process, the workpiece is affixed to the spindle and rotates at a predetermined speed. Vibration is an inevitable occurrence that can cause the tool tip and workpiece to deviate from their intended motion trajectory, resulting in undesired effects [164]. After the introduction of the magnetic field, as shown in figure 16(a), the workpiece rotates at a specific velocity within the magnetic field. There will be countless 'wires'cutting the magnetic induction line inside the workpiece, which will produce Lorentz force and make the workpiece in motion become a damping mechanism. The greatest role of the damping effect is to increase the difficulty of vibration of the workpiece, so the kinetic energy of the workpiece is converted into heat energy loss [165]. By reducing the vibration effect of the workpiece, the relative motion error between the tool and the workpiece is significantly decreased, which guarantees the precision of the machined surface [158]. Simultaneously, the relevant literature indicates that enhancing the strength of the magnetic field can enhance the damping effect and decrease the passive vibration during the cutting process.

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Numerous experimental investigations have demonstrated that the magnetic field utilized during cutting can considerably increase the thermal conductivity of the material. Currently, there exist two primary perspectives regarding the impact of magnetic fields on the temperature of the machining process. The first is based on the magnetic cooling effect, the magnetic domain direction confusion occurs in the demagnetization process, which absorbs a lot of heat [148]; the other is the explanation of the magnetic field heat conduction chain. This explanation is based on the phenomenon that the thermal conductivity of magnetic nanofluids in the magnetic field is significantly enhanced [166], while titanium alloy is a paramagnetic material, and a similar phenomenon can occur with titanium alloy [156]. These workpieces belong to metals or their alloys, and there are many magnetic particles inside these materials. These magnetic particles will become magnetized when exposed to a magnetic field. The particular manifestation is that these magnetic particles will align their own magnetic dipole moment with the direction of the magnetic field, thus forming a thermally conductive linear chain [35, 157]. These linear chains can promote the loss of heat generated by processing.

In the MFAC process, the workpiece will undergo changes in material properties while under the influence of the magnetic field. From the perspective of metallographic structure, the grain size in the workpiece will change, and the magnetic field will refine the grain of the workpiece, thereby improving the surface microhardness. The enhancement of thermal conductivity inhibits the formation of accumulation edges and can also promote the refinement of workpiece grains [156]. Considering the tribological properties of the material, the application of an external magnetic field will cause the crystal's multi-domain configuration to transition to a single-domain configuration, reducing the diffusion activation energy, thereby increasing the dislocation motion inside the workpiece [12]. After the material surface accumulates defects, the wear effect is improved. From the perspective of the internal stress of the material, the magnetic treatment attributes to a rise in the dislocation activity of the workpiece, the dislocation's mobility is improved, and the material's plasticity is enhanced [167]. After the plastic softening of the material, the internal residual stress is eliminated. From the perspective of magneto-plastic effect and electron spin, there are often some lattice defects in the workpiece. These defects may also exist in non-singlet form or possess a low enough number of non-singlet states in the ground state, thus allowing them to interact with the external magnetic field [161]. When subject to a magnetic field, the free radical pair located between the dislocation and the stopper underwent a transition from a singlet state to a triplet state with minimal binding energy, as shown in figure 16(b). As a result, the dislocation is no longer bound by its spin-related forces, leading to the phenomenon of magneto-plasticity.

In summary, MFAC is a kind of FAC method that integrates materials, electromagnetic, heat transfer, and other disciplines. Compared with OC, the magnetic field can create eddy currents on the subsurface of the workpiece, which will produce damping effects during the cutting process. This damping effect can reduce workpiece surface corrugations and surface roughness caused by tip related vibration. Besides, the magnetic field can enhance the thermal conductivity between the tool and workpiece, thereby preventing localized high temperatures in the machining zone. Furthermore, the magnetic field has the ability to refine the grain structure of the workpiece material, enhance dislocation movement within the material, and induce magneto-plastic effects, ultimately enhancing the material machinability and prolonging the tool life. The key to magnetic field assistance is the effectiveness of magnetic field application on the workpiece material. In addition, the application of appropriate magnetic field intensity is the focus of ensuring the magnetic field assistance effect. The following future work on the MFAC should be noticed: (1) the mechanism of material removal under magnetic-thermal-mechanical coupling needs further elucidation. (2) The machined materials are limited by their principle, so it is necessary to expand the machining range of magnetized and non-magnetized DMMs. (3) The magnetization effect and stability of machining area need to be further improved by developing a controllable method for high-density magnetic energy accumulation.

The concept of LMP first appeared in the 1980s [24], and was initially applied to the surface treatment of fused silica. It eliminates microcracks and improves the energy threshold by laser melting. But in fact, the technology of improving surface quality by laser melting has appeared earlier [193]. After decades of development, LMP has been widely applied in the surface treatment of metals [194, 195], alloys [196, 197], glasses [198–200], ceramics [201], and other materials (table 5), and has become a new polishing technology and shine in semiconductor, optoelectronics, aerospace and other fields [202–204]. Depending on the initial roughness and spatial wavelength, different kinds of lasers should be selected for polishing.

In the continuous wave laser polishing (CWLP) (figure 27(a)), lasers with powers of 100–300 W scan the material surface at velocities of 10–200 s·cm⁻² [221] to form a continuous melted layer along the scanning direction, usually with a depth of 20–100 μm [195]. With the movement of laser beams, new molten materials are continuously added and solidified on the opposite side of the molten pool. The melting process is only influenced by the laser power, spot diameter, and scanning velocity. Because of the flexibility of laser, it has unique advantages in polishing free surface. Ostholt et al [206] used a continuous wave laser to polish the freedom surface of an optical mold, and the roughness was reduced from 1.7 μm to 0.4 μm. Temmler et al [195] found that laser is helpful to grain refinement and hardness enhancement, and obtained the surface of tool steel with Ra = 50 nm. The improvement of the material's tensile strength and ductility after laser polishing was also found in further research [207]. CWLP is usually used to process rough surfaces with macro scale spatial wavelength and large-sized workpieces, such as selective laser melting parts [209, 222], it may not be suitable for micro scale element or structure [220].

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In contrast to CWLP, the melting process of pulsed laser polishing (PLP) is discrete (figure 27(b)). Due to the extremely tiny beam diameter (<100 μm [214]) and tens of microseconds pulse duration [200], the existence time of laser formed micron molten pool (molten depth less than 6 μm [223]) is very short, and the fused material has solidified before the forming of next molten pool. For the spatial wavelength of initial surface roughness δ< 80 μm, CWLP has little effect [188], while PLP can further reduce the roughness to nano-scale [205]. Xiao et al [220] successfully eliminated the rainbow pattern on monocrystalline silicon by nanosecond pulsed laser, as shown in figure 28, which was produced by ultraprecision cutting, and reduced the roughness to 0.6 nm. Porosity can be reduced by laser melting, and Li et al [217] found that shrinkage cavities, pores, and microcracks in the heat affected zone of IN 718 superalloy was disappeared after PLP.

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It is worth mentioning that although PLP can reduce the surface roughness to nano-scale, it does not mean that pulse is necessarily better than continuous wave, because PLP has almost no improvement in rough surface with δ > 80 μm. Therefore, it is particularly important to select the appropriate laser according to the specific conditions of the initial surface [188]. Generally, CWLP is SOM [208, 209, 211], accompanied by high frequency ripple. Interestingly, pulse laser has a very good polishing effect on high-frequency roughness, which naturally leads to dual-beam polishing technology [223]. The CW laser can be first used to remove the low frequency roughness. Followed by PLP, high frequency ripple introduced by SOM can be removed. Micro end milled Ti6Al4V with a surface roughness Sa of (172 ± 25) nm is polished to (47 ± 5) nm by this strategy. This process can also be refined into three laser beams [224]. Previous research has proved that proper SOM can lead to lower roughness compared with SSM, because properly increasing the melting pool duration is contributed to the full flattening of the melt bulk. As a result, dual-beam polishing technologies were developed to increase the duration of the molten pool [225, 226].

The LMP equipment is simple in structure and flexible in operation, and laser beam can be guided to the processing surface through optical fibers and mirrors (figure 29(a)) because of its long-distance transmission characteristics. The velocity and trajectory of the laser spot are controlled by the galvanometer (figure 29(b)), which can be set up by a computer together with the laser power and frequency. Laser system can be attached with displacement table, chamber, etc to form an independent polishing system (figure 29(c)), or integrated with machining equipment (robots, machine tools, etc) to satisfy various polishing requirements (figure 29(d)).

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For the micro scale melting pool in LMP, the surface flattening is mainly caused by surface tension and thermocapillary flow. Fluid tends to flow to the direction of high surface tension, i.e. thermocapillary or Marangoni flow [227, 228]. Temperature gradient is formed between the center and the edge of the molten pool because of the Gaussian energy distribution of laser beam. According to the positive and negative of the temperature gradient of surface tension ($\partial \gamma /\partial T$), the flow from edge to center or the opposite can occur [193, 229]. For most metal materials $\partial \gamma /\partial T < 0$, which is why the boundary ripple occurs during SOM. But there are exceptions, $\partial ^{\prime}\gamma /\partial T^{\prime} = 0$ at 2283 K for stainless steel, leading to center bulge or boundary ripple under different energy intensities [230].

The molten surface with roughness features, which owns higher surface tension because of their large curvature, oscillates as stationary capillary wave driven by surface tension and damps out due to the viscosity of molten bulk, forming a smoother surface. Therefore, two polishing regimes can be distinguished: thermocapillary regime and capillary regime, depending on the dominant drive, stationary capillary wave oscillations or Marangoni flow, as shown in figure 30.

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The LMP process is mainly determined by three factors: surface material properties, original surface topography, and laser energy fluence. In order to fully utilize the advantages of laser polishing, a relatively smooth surface will be prepared. The auxiliary gas, according to the material properties, can provide a more suitable environment for LMP [194, 197, 213]. The control of laser parameters is the most convenient and expeditious, so the precise control of energy density determines the quality of polishing. The energy density can be simply expressed as

$$\begin{align}I = \frac{{Pt}}{S}\end{align} \tag{ 20 }$$

where I is energy density, P is laser power, t is laser irritation duration per unit time and S is scanning area per unit time. The control of laser power can be implemented in the mode [212, 231], size [190, 214, 232, 233] and distribution [196]. Continuous laser can be modulated into pulse laser by Q-switch or mode locking [212]. Power has a positive contribution to the depth and diameter of the molten pool [234, 235]. As mentioned above, increasing power can observe the transition from SSM to SOM [190, 191], and the effect of Marangoni flow will gradually become obvious [229].

For continuous laser, the working time t is the unit time, and S= vtD, where v is the scanning velocity, and D is the beam diameter (1/e²). As for pulsed laser, t can be written as τ/f, where τ is pulse width, f frequency. The scanning area of each pulse can be expressed as πD²/4, while S is related to the overlap rate between pulses, which can be expressed as

$$\begin{align}{O_\tau } & = \frac{{D - v/f}}{D}\end{align} \tag{ 21 }$$

$$\begin{align}{O_n} & = \frac{{D - p}}{D}\end{align} \tag{ 22 }$$

where ${O_\tau }$ is the overlap rate of the scanning direction, ${O_n}$ is the overlap rate perpendicular to the scanning direction, and D can be simply adjusted by the defocusing amount. Therebefore, S and t are not variables that can be considered separately in pulse laser polishing, and scanning area per unit time S/t considering pulse width, frequency, laser diameter, scanning velocity and pitch can be separated from the equation (20). Phefferkorn et al [223, 229, 232] systematically explored the effect of pulse width on surface topography, and found that long pulse width can form larger molten pool, which can reduce low-frequency roughness better. Because of the longer duration of larger molten pool, if the laser frequency is further increased until the pulse interval is less than molten pool duration, the continuous melting process will become a quasi-continuous melting process [205]. Laser diameter decreases with the increase of defocus amount [203, 235, 236]. When focus energy intensity is too much, a certain amount of defocusing will greatly help to reduce the surface roughness. Xiao et al [220] got a monocrystalline silicon surface with a surface roughness Sa as low as 0.6 nm by defocusing 0.8 mm. Better choices of scanning velocity [199, 211, 218, 237] and scanning pitch [237] can not only obtain smaller surface roughness, but also improve the surface quality. The highest hardness of 316 l stainless steel could be obtained after three passes with 100 mm·s⁻¹ scanning velocity [207].

MAF is a flexible processing method that is not limited by the size and shape of the workpiece. It was originally developed as a machining process in the Soviet Union in the 1930s, but it was not further developed until after the 1960s [241]. In recent years, researchers have gradually designed MAFs in various forms such as cylinders, planes, and curved surfaces. Shinmura et al [28] performed the cylindrical MAF to finish the Si₃N₄ ceramic rod with a diameter of 2 mm. The workpiece is held between the N pole and the S pole of the magnet, and the working gap between the workpiece and the magnet is filled with magnetic abrasives. The abrasive abrasives form a flexible magnetic abrasive brush (FMAB) under the action of a magnetic field, which acts as a multi-point cutting tool. Surface roughness Ra increased from 0.45 μm to 0.04 μm after processing. Chang et al [242] conducted an experimental study on SKD11 by using the cylindrical MAF (see figure 32(a)), and the surface roughness Ra was increased from 0.25 μm to 0.05 μm after finishing. Yamaguchi and Shinmura [243] reported internal finishing of alumina ceramic components using a working rotary system. Four small permanent magnetic poles are evenly arranged on the circular yoke to generate the magnetic field required to attract iron particles to gather on the inner surface of the tube. As the tube rotates at high speed, the abrasives in the mixture perform micro-cut the inner surface of the tube. After processing, the surface roughness of alumina ceramics decreased to Ra 0.02 μm, and the residual stress was significantly reduced. Kim et al [244] used MAF to finish the planar workpiece of aluminum matrix composite. A plane MAF consists of a single permanent magnet that generates a gradient magnetic field and achieves material removal by regulating rotational and translational motion. After 60 min of processing, the surface roughness reaches Ra 0.35 μm.

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In addition, based on the MAF principle, the researchers found that additional ultrasonic vibrations can be used to obtain a perfectly quality workpiece surface. Yin and Shinmura [32] proposed a vertical vibration-assisted magnetic abrasive finishing (VMAF) technique, in which the workpiece was vibrated in the vertical direction. The relative motion between the FMAB and the workpiece, consisting of vertical vibration and rotation, can generate pulse pressure acting on the abrasive particles to achieve efficient micro-removal of materials. They applied this method to the finishing of stainless steel and found that the vibration-assisted deburring time was reduced by 40% compared with no vibration, and the initial surface of 2.5 μm Ry pre-polish was improved to 0.45 μm Ry after four passes of polishing. Further, Guo et al [245] proposed a vibration-assisted magnetic abrasive polishing (VAMAP) method, which could polish micro-featured surfaces. The surface roughness Ra increased from 166.9 nm to 25.4 nm and from 2.23 μm to 0.32 μm when the rectangular microstructure and the miniature V-grooves were polished, respectively. And the profile of microstructures was well maintained. However, this technique is limited to nonmagnetic or micromagnetic materials with straight microfeatures. On this basis, Guo et al [36] presented a new localized VAMAP method, as shown in figure 32(b). It can be used to polish curved microfeatures, and the workpiece material can be ferromagnetic. This method uses loose abrasives to achieve nanoscale surface roughness and damage-free surface while maintaining the morphology of the microfeatures. Using this method to polish the Fresnel-type structure, the surface roughness Ra was reduced from the initial value of 10.4 nm to 7.7 nm.

At present, there are various types of MRF devices, such as groove type [25], wheel type [25], belt type [246, 247], disk type [248, 249], cluster type [250, 251], ball head type [252, 253], etc, which are suitable for surface processing of various types and sizes, such as plane, concave, convex, inner surface, etc. The diameter of the polished workpiece is mostly more than 100 mm or even 1 m. The research status and characteristics comparison of MRF devices are shown in table 6.

The MRF technology was first proposed by William Kordonski, who developed the first MRF device in 1990s [25]. However, the first groove type MRF device is limited to polishing convex surfaces. William Kordonski creatively proposed a wheel type MRF device, as shown in figure 33(a) [25]. In the device, an electromagnet was used at the polishing tool to excite the gradient magnetic field, and the MRL was injected at the front end of the polishing tool. When the polishing tool rotates, it drives the MRL into the polishing area with magnetic field distribution. According to the rheological characteristics of the MRL, the MRL hardens rapidly and can be used to polish the workpiece surface. Kim et al [254] carried out research based on wheel type MRF device, and adjusted the distribution position of the polishing wheel and workpiece from vertical direction to horizontal direction. Four kinds of alumina abrasive polishing solutions with different compositions and proportions were prepared to study the surface topography and roughness obtained under different processing parameter settings such as electric current and wheel velocity. After optimizing the process parameters, it was found that the surface roughness of BK7 glass could be reduced to 3.8 nm. Yin et al [248, 249] explored the material removal rate under the influence of permanent magnet configurations by using a disc type MRF device, as depicted in figure 33(b). Permanent magnets of different configurations are placed under the polishing disc and form a gradient magnetic field distribution. The configured MRL fills the gap between the workpiece surface to be polished and the underneath of the polishing disc. A porous pad is used at the bottom of the polishing disc to increase the friction between the MRL and the disc, and the MRL is adsorbed to form a polishing die for processing. They obtained the results that the surface roughness of zirconia ceramic decreased from the original value of about 100 nm to less than 20 nm.

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Pan and Yan [250] expanded the disk magnetorheological field excited by a single permanent magnet to the cluster magnetorheological field distributed around the circumference of multiple permanent magnets, realizing the plane polishing of three kinds of hard and brittle material substrates with a diameter of about 100 mm. On this basis, they further improved the experimental device and developed a dynamic magnetic field cluster MRF device [251], as shown in figure 33(c). The deflection movement occurs in a small local range, forming a dynamic magnetic field. This method is conducive to achieving the self-sharpening of polishing particles in MRF, and obtaining a stable material removal function. In the device of literature [250], the position of the permanent magnet is fixed, so a static gradient magnetic field distribution is formed. In the device of literature [251], the permanent magnet is no longer in a fixed position, and a partial sway motion occurs in a small range, to form a dynamic magnetic field. In the annular array of permanent magnets under the polishing disc, the permanent magnets are embedded on the small eccentric shaft. The main shaft of the polishing disc rotates around the fixed axis, and the eccentric main shaft rotates to drive the eccentric rotation of the deflection disc, thus driving the small eccentric shaft and the embedded permanent magnet to rotate together. Since the spatial position of the rotating main shaft of the polishing disc and the rotating main shaft of the permanent magnet is offset, a dynamic magnetic field is formed. This method is conducive to achieving the self-sharpening of polishing particles in MRF, and obtaining a stable material removal function. The device is used to polish the single crystal silicon plane. After 5 h, the surface roughness is reduced from the initial 480 nm to 3.3 nm, and an ultra-smooth surface is obtained.

Compared with the disk type and cluster type MRF devices that are only suitable for processing plane workpieces, the oblique axis type and ball head type MRF devices are more flexible and suitable for processing complex surfaces. Yin et al [255] used an oblique axis MRF device to polish the stainless steel workpiece surface. When the MRL moves between strong and weak magnetic fields, it can realize fast switching between liquid and solid like states. After polishing, the surface roughness decreases from the original 450 nm to 20 nm. Singh et al [252] used a MRF device to polish the inner surface of cylindrical gray cast iron. After 90 min processing time, the surface roughness Ra, Rq, and Rz values decreased by 77.44%, 70.16% and 72.16% respectively. In addition, Zhang et al [256] introduced axial ultrasonic vibration into the MRF polishing head, and proposed an ultrasound-assisted magnetorheological polishing (UAMRF) method, which could further improve the MRR of MRF when applied to K9 glass. The MRR was about 3.1 times that of traditional MRF, and the surface roughness reached 4 nm. Zhai et al [257] used Fe₃O₄/SiO₂ core-shell abrasives for UAMRF of sapphire wafers, which can achieve large MRR (1.974 μm·h⁻¹) and low surface roughness Ra (0.442 nm). Another innovative idea of MRF is to introduce electrochemical action into the MRF process. Yan et al [258] proposed an electrochemical MRF (EC-MRF) technique combining a controlled electrochemical method and MRF. They took gallium nitride as the research object, controlled the surface processing quality by adjusting the etching potential difference, achieved a 113% increase in MRR compared to traditional MRF, and reduced the surface roughness from Ra 6.5 nm to Ra 0.9 nm.