High-speed grinding: from mechanism to machine tool

Abstract

High-speed grinding (HSG) is an advanced technology for precision machining of difficult-to-cut materials in aerospace and other fields, which could solve surface burns, defects and improve surface integrity by increasing the linear speed of the grinding wheel. The advantages of HSG have been preliminarily confirmed and the equipment has been built for experimental research, which can achieve a high grinding speed of more than 300 m/s. However, it is not yet widely used in manufacturing due to the insufficient understanding on material removal mechanism and characteristics of HSG machine tool. To fill this gap, this paper provides a comprehensive overview of HSG technologies. A new direction for adding auxiliary process in HSG is proposed. Firstly, the combined influence law of strain hardening, strain rate intensification, and thermal softening effects on material removal mechanism was revealed, and models of material removal strain rate, grinding force and grinding temperature were summarized. Secondly, the constitutive models under high strain rate boundaries were summarized by considering various properties of material and grinding parameters. Thirdly, the change law of material removal mechanism of HSG was revealed when the thermodynamic boundary conditions changed, by introducing lubrication conditions such as minimum quantity lubrication (MQL), nano-lubricant minimum quantity lubrication (NMQL) and cryogenic air (CA). Finally, the mechanical and dynamic characteristics of the key components of HSG machine tool were summarized, including main body, grinding wheel, spindle and dynamic balance system. Based on the content summarized in this paper, the prospect of HSG is put forward. This study establishes a solid foundation for future developments in the field and points to promising directions for further exploration.

1 Introduction

Material removal from grinding processes accounts for more than 60% of all processes in aerospace and various other fields. In 1931, high-speed machining was first proposed by Salomon, and it has since evolved into an indispensable processing technology in the realm of mechanical manufacturing, owing to its distinctive advantage in speed [1]. High-speed grinding (HSG) stands as the current frontier in advanced processing, enabling the precision manufacturing of components such as camshafts and crankshafts for automobile engines, as well as plates, shafts, blades, and other parts for aviation engines [2,3,4,5,6,7,8], all of which require high machining accuracy [9,10,11,12,13]. The handling of difficult-to-machine materials has perpetually posed a technical challenge in the field of grinding, necessitating the elevation of grinding speeds to achieve superior surface quality [14,15,16].

Currently, grinding speeds equal to or greater than 45 m/s are referred to as HSG, which represents an advanced processing technology aimed at achieving efficient material removal with a focus on high quality and high efficiency [17, 18]. When the ratio of v_s (grinding speed) to v_w (feed speed) remains constant, an increase in v_s alone leads to an increase in grinding force and temperature, while an increase in only the feed speed (v_w) results in a decrease in both grinding force and temperature. When the v_s/ v_w ratio is not constant, a decrease in grinding temperature and force occurs as v_s is increased to the critical speed associated with the workpiece material.

The research on HSG is mainly in the grinding mechanism, grinding equipment and other aspects of the research. The mechanism of HSG with single abrasive was investigated in Refs. [3, 19,20,21]. Zhao et al. [22,23,24,25] for the first time built a quasi-liquid phase impact chip formation model based on the theoretical model of the indentation experiment of brittle materials and the concept of impact chip formation, put forward the chip formation hypothesis, and found that the material removal mechanism (MRM) under HSG conditions was completely different from that of ordinary grinding. Zhang et al. [26] found that WC/Co and RB-SiC/Si had different MRMs. Yin et al. [27] found that the v_s affected the material removal effect of SiC_f/SiC. Cheng et al. [28] found that the HSG of GH4169 alloy resulted in the formation of jagged abrasive chips due to concentrated shear slip caused by adiabatic shear. Wang [29] found that the grinding process of a single abrasive was divided into three stages: sliding friction, ploughing and material removal, and chips were produced when the grinding depth (a_p) reached the critical. Li [30] indicated that material removal was achieved by dislocation movement in the crystal through HSG of silicon carbide. Zhou et al. [31] found that brittle removal of TiC_p and plastic removal of the Ti-6Al-4V matrix occurred simultaneously during the material removal process for HSG of particulate reinforced titanium matrix composites (PTMCs). Chen [32] studied the dynamic characteristics of the components of HSG machines. Yeo et al. [33] investigated spindle characteristics on HSG using oil/air mist lubrication. Sun and Yao [34] found that lowering the spindle temperature could be achieved by optimizing the operating parameters of the spindle. Liu et al. [35] found an improved thermal resistance network model for high-speed motorized spindle. Liang [36] built a vibration characteristic analysis model of balancing head rotor system.

Despite extensive research on the grinding mechanism, force, and temperature models within the context of HSG, there remains an insufficiency in comprehensive reviews summarizing prior investigations. As a response to this gap, a consolidation of previous studies has been undertaken to offer insights for future research directions, providing guidance for scholars to pursue deeper understanding and research in this area. The schematic representation of this review is depicted in Fig. 1.

Fig. 1

Structure of this study

2 Mechanism of HSG

HSG represents a sophisticated manufacturing technology that enhances machining precision through elevated v_s, enabling mill-turn or even superior removal rates. Within the HSG process, the deformation zone of grinding experiences significant strain (γ), elevated strain rates ($\dot{\gamma }$), and high temperatures. Consequently, modeling the dynamic properties of materials and providing an accurate depiction of their inherent models are fundamental in characterizing material deformation behaviors. These aspects serve as crucial prerequisites for the numerical simulation of the machining process. This chapter aims to deliver an exhaustive analysis of the MRM and a comprehensive overview of the force, temperature, and material constitutive models, as depicted in Fig. 2.

Fig. 2

Structure of material removal mechanism

The advancement in surface quality has experienced a significant qualitative enhancement with the development of technology. This improvement in surface quality can be attributed to the underlying mechanisms of material removal, which are elucidated through the study of v_s, as depicted in Fig. 3 [5, 37,38,39,40,41,42,43]. Furthermore, the material removal process during HSG is intricate and multifaceted. The alterations occurring during this process have been meticulously analyzed through numerical simulations, as illustrated in Fig. 4 [37, 44,45,46,47,48,49,50].

Fig. 3

Grinding speed milestone diagram [5, 37,38,39,40,41,42,43]

Fig. 4

Numerical modelling research milestones [37, 44,45,46,47,48,49,50]

2.1 Modelling of material removal strain rate

The strain rate effect embodies an intrinsic mechanical response property of materials [51]. This response varies markedly between quasi-static and high $\dot{\gamma }$, leading to distinct deformation and fracture mechanisms [52, 53]. Variations in $\dot{\gamma }$ during the cutting process are a primary factor influencing MRM. Under HSG conditions, an increase in $\dot{\gamma }$ alters the material response, which can be classified into static, quasi-static, and dynamic categories. These responses further bifurcate into medium $\dot{\gamma }$ and high $\dot{\gamma }$ regimes, each characterized by unique mechanical behaviors.

The single abrasive grinding formation zone has zone I deformation and zone II deformation. Chen et al. [54] also observed the above phenomenon by simulating the HSG of single abrasives of high-temperature nickel-based alloys. A single abrasive’s grinding force and deformation mechanism can be described as follows.

In zone I deformation A point force diagram, as shown in Fig. 5 [55], the material fracture into chip direction (shear band direction F_s) and the angle of the combined force F_r is π/4, shear angle φ₁ in the horizontal direction; during this period, the friction force F_f ascends along the interface between the abrasive and chip, thereby facilitating the fragmentation of the material into chips, denoted as φ₁

$$\varphi_{1} = \frac{{\uppi }}{4} + \beta_{{\text{f}}} - \gamma_{0} .$$

(1)

Fig. 5

Mechanism of material deformation in the chip-forming region a force analysis of the first deformation zone of workpiece material, b force analysis of the second deformation zone of workpiece material [55]

For abrasive cutting processing chip thickness to length ratio of about 1% [56], so the negative front angle of abrasive cutting for γ₀ ≈ θ/2, the friction angle for β_f = arctan μ, substitute it into Eq. (1) as

$$\varphi_{1} = \frac{{\uppi }}{4} + \arctan \mu - \frac{\theta }{2}.$$

(2)

In zone II deformation C point force diagram, as shown in Fig. 5b, F_f and F_n is F_r; the angle between F_s and F_r is π/4; φ₂ is under the horizontal direction. During this period, F_f is downward along the interface between abrasive and chip, thereby obstructing the fragmentation of the material into chips, denoted as φ₂

$$\varphi_{2} = \beta_{{\text{f}}} + \gamma_{0} - \frac{{\uppi }}{4} = \arctan \mu + \frac{\theta }{2} - \frac{{\uppi }}{4}.$$

(3)

The deformation of materials causes γ hardening and $\dot{\gamma }$ strengthening, which significantly affects the removal mechanism of materials under HSG. Jin et al. [57, 58] established the formula for strain and $\dot{\gamma }$ in the abrasive shear zone

$$\gamma = \frac{{\cos \left( {\frac{\theta }{2}} \right)}}{{\sin \varphi \cos \left( {\varphi + \frac{\theta }{2}} \right)}},$$

(4)

$$\dot{\gamma } = \frac{{2\lambda_{1} v\cos \left( {\frac{\theta }{2}} \right)\sin \phi }}{{a_{\text{g max} } \cos \left( {\phi + \frac{\theta }{2}} \right)}}.$$

(5)

Substituting Eq. (16), Eq. (3) and Eq. (4) into Eq. (5), respectively, $\dot{\gamma }$ of the abrasive chips in two deformation zones is obtained as

$$\dot{\gamma }_{1} = \frac{{\lambda v_{{\text{s}}}^{2} \cos \left( {\frac{\theta }{2}} \right)\sin \left( {\frac{{\uppi }}{4} + \arctan \mu - \frac{\theta }{2}} \right)}}{{{\uppi v}_{{\text{w}}} \sqrt {a_{{\text{p}}} D} \cos \left( {\frac{{\uppi }}{4} + \arctan \mu } \right)}},$$

(6)

$$\dot{\gamma }_{2} = - \frac{{\lambda v_{{\text{s}}}^{2} \cos \left( {\frac{\theta }{2}} \right)\sin \left( {\arctan \mu + \frac{\theta }{2} - \frac{{\uppi }}{4}} \right)}}{{{\uppi }v_{{\text{w}}} \sqrt {a_{{\text{p}}} D} \cos \left( {\arctan \mu + \theta - \frac{{\uppi }}{4}} \right)}}.$$

(7)

$\dot{\gamma }$ in both shear zones shows a linear increasing trend, as shown in Fig. 6a. When μ increases, $\dot{\gamma }$ in zone I deformation increases due to the gain effect of F_f on the material removal; $\dot{\gamma }$ in zone II deformation decreases due to the obstruction effect of F_f on the flow of debris, as shown in Fig. 6b. $\dot{\gamma }$ decreases with the increase of a_p, as shown in Fig. 6c. The velocity effect and lubrication effect produced during HSG processing affect $\dot{\gamma }$ variation trend in the two deformation zones, as shown in Fig. 6d.

Fig. 6

Strain rate under different grinding parameters and frictional coefficients a effect of grinding speed on strain rate, b influence of different friction coefficients on strain rate, c effect of different grinding depths on strain rate, d strain rate under different grinding parameters and friction coefficients [54]

The removal of metallic material during the process is a result of plastic deformation occurring when the material undergoes an increase in γ. Previous research has extensively utilized dynamic material tensile tests to illustrate the occurrences of γ hardening and $\dot{\gamma }$ strengthening [59]. Material removal can be divided into three parts due to the softening of the material after grinding heat and the reduction of deformation resistance during $\dot{\gamma }$ strengthening, as shown in Fig. 7 [54].

Fig. 7

Effect of strain hardening, strain rate strengthening and thermal softening in material removal after grinding a stress-strain curves under “speed effect”, b debris forming mechanism under quasi-static condition, c debris forming mechanism under high strain-isothermal condition, d debris forming mechanism under high strain condition [54]

Yang [39] found that the relationship between $\dot{\gamma }$ strengthening and thermal softening changed with the increase of v_s in the HSG of GH4169 using single abrasive. The materials under high $\dot{\gamma }$ loading would produce embrittlement effect [53, 60], which was conducive to reducing subsurface depth damage of the workpiece materials and formation of the “damage peeling” effect. Dislocation diffusion and slip are the main causes of plastic deformation and fracture during grinding of plastic metal materials and hard and brittle materials [61]. Liu [62] found that there were dual removal mechanisms of ductile flow and brittle fracture in the grinding process of nanoceramic materials. Wang et al. [63] found that the chip morphology gradually became discontinuous with the increase of $\dot{\gamma }$. Ma et al. [64] found that with the increase of v_s, brittle fracture and ductile fracture were obvious when brittle fracture occurred on the free surface of chips. Zhang et al. [65] found that the average fragment size of brittle materials decreased with the increase of $\dot{\gamma }$ at high $\dot{\gamma }$.

2.2 Modelling of material removal constitutive

During the grinding of metallic materials, the workpiece material is subjected to significant structural transformations when the heat generated from deformation and friction exceeds a critical threshold [66, 67]. These transformations are effectively captured by the intrinsic model of the material, which delineates the variations in flow stresses experienced during material deformation. Table 1 presents the principal parameters of the Johnson-Cook (J-C) model, outlining their values for several types of workpiece materials [37, 66, 68,69,70,71,72].

Table 1 Workpiece material J-C model main parameters

The J-C model considers the changes of γ, $\dot{\gamma }$, temperature and other factors, and can be expressed as [73]

$$\sigma = \left( {A + B\varepsilon^{{\text{n}}} } \right)\left( {1 + C\ln \frac{{\dot{\varepsilon }}}{{\dot{\varepsilon }_{0} }}} \right)\left( {1 - \left( {\frac{{T - T_{0} }}{{T_{{{\text{melt}}}} - T_{0} }}} \right)^{m} } \right).$$

(8)

Johnson and Holmquist [74, 75] proposed a J-H constitutive model for brittle materials

$$\sigma^{*} = \sigma_{\text{i}}^{*} - D\left( {\sigma_{\text{i}}^{*} - \sigma_{\text{f}}^{*} } \right).$$

(9)

The dimensionless expression is

$$\sigma^{*} = \sigma /\sigma_{{{\text{HEL}}}} .$$

(10)

The strength of the intact material $\sigma_{\text{i}}^{*}$ is

$$\sigma_{\text{i}}^{*} = A\left( {P^{*} + T^{*} } \right)^{N} \left( {1 + C\ln \dot{\varepsilon }^{*} } \right).$$

(11)

The dimensionless pressure P^* and the maximum tensile strength T^* are

$$P^{*} = \frac{P}{{P_{{{\text{HEL}}}} }},$$

(12)

$$T^{*} = \frac{T}{{P_{{{\text{HEL}}}} }}.$$

(13)

The dimensionless strength $\sigma_{{\text{f}}}^{*}$ of the partially damaged material is

$$\left\{ \begin{gathered} \sigma_{{\text{f}}}^{*} = B\left( {P^{*} } \right)^{M} \left( {1 + C\ln \dot{\varepsilon }^{*} } \right), \hfill \\ \sigma_{{\text{f}}}^{*} \le \sigma_{{{\text{fmax}}}}^{*} . \hfill \\ \end{gathered} \right.$$

(14)

J-C constitutive model considers the effects of γ, $\dot{\gamma }$ and temperature on material load response in machining simulation. In order to adapt to the response of different parameters to dynamic load under different materials and loading conditions, a modified model is proposed based on the J-C constitutive model, as shown in Table 2 [77,78,79,80,81,82,83,84].

Table 2 Several typical modified J-C constitutive models [76]

2.3 Modelling of debris geometry

The foundational concept of the HSG mechanism can be traced to the seminal high-speed cutting theory postulated by the renowned German physicist Solomon in 1931 [1]. This theory posits a critical velocity threshold, beyond which the cutting temperature notably decreases. This phenomenon is effectively illustrated in Fig. 8 [76].

Fig. 8

Solomon “speed-temperature” curve diagram [76]

The deformation behavior of materials under HSG and their corresponding removal mechanisms markedly differ from those observed in traditional grinding. This distinction arises primarily from the interactions between the abrasives and the workpiece material. The complexity of the MRM in HSG is heightened due to variables such as the quantity and shape of abrasives, the randomness of their positioning, and the variability in cutting strength. In the context of grinding, each abrasive represents a microcosmic view of the cutting process, which manifests in three distinct stages: the elastic deformation phase, the elastic-plastic deformation stage, and the chip formation stage, as depicted in Fig. 9a.

Fig. 9

Single abrasive slip model in grinding process a grinding process diagram [47], b thickness of abrasive chips, c cross-sectional shape and area of abrasive [54]

For a single abrasive HSG with the same chip shape each time, the maximum chip thickness is called the maximum undeformed chip thickness a_{g max} [54]. The a_g function is discussed into A-B and B-C, because the cutting thickness changes differently before and after point B, as shown in Fig. 9b [54].

In phase A-B the α interval is [0, α₁] can be obtained

$$\alpha_{1} = {\text{arc}}\cos \frac{{D - 2a_{{\text{p}}} }}{{D - 2a_{{{\text{g}}\max }} }}.$$

(15)

When the abrasive cuts to point B, the abrasive spacing λ is equal to the circumference of the grinding wheel disc πD, so a_{g max} can be expressed as

$$a_{{{\text{g}}\max }} = 2{\uppi }\frac{{v_{{\text{w}}} }}{{v_{{\text{s}}} }}\sqrt {a_{{\text{p}}} D} .$$

(16)

When the abrasive cuts to α (0≤α≤α₁) and α₁ (α₁≤α≤α₂), the chip thickness formula of abrasives can be calculated as

$$a_{{\text{g}}} \left( \alpha \right) = \left\{ \begin{gathered} {\uppi }D\frac{{v_{{\text{w}}} }}{{v_{{\text{s}}} }}\sqrt {2\left( {1 - \cos \alpha } \right)} ,0 \le \alpha < \alpha_{1} , \hfill \\ \frac{{a_{{\text{p}}} - \frac{D}{2}\left( {1 - \cos \alpha } \right)}}{\cos \alpha },\alpha_{1} \le \alpha \le \alpha_{2} . \hfill \\ \end{gathered} \right.$$

(17)

According to the geometric relationship between the abrasive cutting path and the abrasive chip section height, the calculation formula of the abrasive chip cross-sectional area S can be obtained, as shown in Fig. 9c

$$S\left( \alpha \right) = \left\{ \begin{gathered} a_{{\text{g}}} \left( \alpha \right)\tan \frac{\theta }{2}\left( {2h\left( \alpha \right) - a_{{\text{g}}} \left( \alpha \right)} \right),0 \le \alpha < \alpha_{1} , \hfill \\ h\left( \alpha \right)^{2} \tan \frac{\theta }{2},\alpha_{1} \le \alpha \le \alpha_{2} . \hfill \\ \end{gathered} \right.$$

(18)

The study of chip morphology is the most direct way to explore the mechanism of cutting and grinding of metal materials, but it is rarely studied. During the formation of chips and scratches in HSG, the workpiece undergoes plastic deformation and fracture removal. Yang [39] found that with the increase of v_s, chips became longer and thinner; the equivalent stress, plastic strain, strain and grinding temperature increased; and the grinding force, residual stress and strain decreased, as shown in Fig. 10a. Liu et al. [85] found that the removal process of PTMCs material was divided into four stages: plastic removal of matrix material, crack initiation of reinforced abrasives, crack propagation of reinforced abrasives and brittle destruction of reinforced abrasives, as shown in Fig. 10b. Wu et al. [86] performed HSG of enamel surfaces, in which the fracture modes of the occlusal surface were steady-state shear material removal, flexural shear complex fracture material removal and ironing, as shown in Fig. 10c, tongue in cheek/surface for the unsteady shear complex material removal, bending shear fracture material removal and ironing, as shown in Fig. 10d.

Fig. 10

HSG of different materials to remove the changes produced by grinding chips a plastic strain and $\dot{\gamma }$ of GH4169 at v_s=240 m/s [39], b material removal process in grinding of PTMCs [85], c mechanism of occlusal surface material removal [86], d mechanism for removal of buccal/lingual material [86]

Setti et al. [87] found that chip morphology changed greatly under different grinding conditions. The shapes of abrasive chips were mainly divided into bands, nodules and spheres [88, 89]. Wu et al. [86] found that the steady-state grinding process of the occlusal surface was less at high feed rate, and the chips under the cheek/tongue surface were larger and more irregular, which was more difficult to be broken by magic shear, as shown in Figs. 11a, b. Xia et al. [90] found that the wear chips had adiabatic shear sliding properties when grinding GH4169 alloy with a single abrasive, as shown in Fig. 11c. Cheng et al. [28] found that with the increase of v_s on the free surface of GH4169 alloy scraps, the thermal softening effect was enhanced and the grinding resistance decreased.

Fig. 11

Chip morphology of different workpiece materials after HSG a enamel surface grinding of occlusal surfaces and chip shape of occlusal surface grinding [86], b buccal/lingual enamel surface grinding and chip shape of buccal/lingual surface grinding [86], c morphology of abrasive chips and workpiece surface for grinding GH4169 with a single abrasive [90]

2.4 Modelling and change rule of grinding force

The grinding force mainly consists of the cutting force and friction force in the removal of abrasive grinding materials, surface friction and material adhesion [69, 91]. In different stages of friction cutting, the grinding force mainly comes from the grinding abrasive overcoming the deformation of parts and the friction of parts materials. The grinding force model of a single abrasive is [92]

$$\left\{ \begin{gathered} F_{{{\text{gt}}}} = F_{{{\text{gtc}}}} + F_{{{\text{gts}}}} , \hfill \\ F_{{{\text{gn}}}} = F_{{{\text{gnc}}}} + F_{{{\text{gns}}}} . \hfill \\ \end{gathered} \right.$$

(19)

On the X-X plane, the grinding force model is simplified by considering the cutting force, and the cutting force dF_gc perpendicular to the contact surface between a single abrasive and the sample is decomposed into normal and tangential grinding forces, as shown in Fig. 12a.

$${\text{d}}F_{{{\text{gc}}}} = \frac{1}{2}F_{{\text{p}}} \rho^{2} \sin \theta \cos \theta \cos \alpha {\text{d}}\alpha .$$

(20)

Fig. 12

Grinding force model in HSG a force on abrasive [5], b, c schematic diagram of grinding force [93]

Therefore, the grinding force of the abrasive is

$$\left\{ \begin{gathered} F_{{{\text{gtc}}}} = \int_{{ - \frac{{\uppi }}{2}}}^{{\frac{{\uppi }}{2}}} {{\text{d}}F_\text{gtc} } = \frac{{\uppi }}{4}F_{{\text{p}}} \rho^{2} \sin \theta \cos^{2} \theta = \frac{{\uppi }}{4}F_{{\text{p}}} \overline{{a_{{\text{g}}} }}^{2} \sin \theta , \hfill \\ F_{{{\text{gnc}}}} = \int_{{ - \frac{{\uppi }}{2}}}^{{\frac{{\uppi }}{2}}} {{\text{d}}F_\text{gnc} } = F_{{\text{p}}} \rho^{2} \sin^{2} \theta \cos \theta = F_{{\text{p}}} \overline{{a_{{\text{g}}} }}^{2} \sin \theta \tan \theta . \hfill \\ \end{gathered} \right.$$

(21)

Unit grinding force F_p represents the main cutting force acting on abrasive per unit area

$$F_\text{P} = \sigma_{0} \overline{A_{\text{g}}}^{ - \varepsilon } 0.5 < \varepsilon <\,0.95.$$

(22)

Then the single abrasive cutting force equation is

$$\left\{ \begin{gathered} F_{{{\text{gtc}}}} = \int_{{ - \frac{{\uppi }}{2}}}^{{\frac{{\uppi }}{2}}} {{\text{d}}F_\text{gtc} } = \frac{{\uppi }}{4}F_{{\text{p}}} \rho^{2} \sin \theta \cos^{2} \theta = \frac{{\uppi }}{4}\sigma_{0} \overline{{A_{{\text{g}}} }}^{ - \varepsilon } \overline{{a_{{\text{g}}} }}^{2} \sin \theta , \hfill \\ F_{{{\text{gnc}}}} = \int_{{ - \frac{{\uppi }}{2}}}^{{\frac{{\uppi }}{2}}} {{\text{d}}F_\text{gnc} } = F_{{\text{p}}} \rho^{2} \sin^{2} \theta \cos \theta = \sigma_{0} \overline{{A_{{\text{g}}} }}^{ - \varepsilon } \overline{{a_{{\text{g}}} }}^{2} \sin \theta \tan \theta . \hfill \\ \end{gathered} \right.$$

(23)

When a single abrasive acts on the workpiece, the part is plastic-deformed and slides along the abrasive surface; and friction is generated. For the spherical cone wear abrasive model, the workpiece material has dynamic friction in the conical surface of the wear abrasive, and the sphere top surface region, then the conflict of a single wear abrasive is [73]

$$\left\{ \begin{gathered} F_{{{\text{gts}}}} = \mu \overline{p} \overline{A}_{{\text{g}}} , \hfill \\ F_{{{\text{gns}}}} = \overline{p} \overline{A}_{{\text{g}}} . \hfill \\ \end{gathered} \right.$$

(24)

In the grinding process, the abrasive cutting workpiece will produce elastic deformation force, plastic deformation force, chip deformation force, friction between the sand and the workpiece, and the fluid resistance of the coolant to the grinding wheel. For single-abrasive grinding, there is no friction between the workpiece and the use of the binder because of the control of the a_p; the total grinding force is

$$\left\{ \begin{gathered} F_{{\text{t}}} = F_{{{\text{tc}}}} + F_{{{\text{ts}}}} = \frac{\uppi }{4}\sigma_{0} \overline{A}_{{\text{g}}}^{ - \varepsilon } \overline{{a_{{\text{g}}} }}^{2} \sin \theta + \mu \overline{p} \overline{A}_{{\text{g}}} , \hfill \\ F_{{\text{n}}} = F_{{{\text{nc}}}} + F_{{{\text{ns}}}} = F_{{{\text{nc}}}} = \sigma_{0} \overline{A}_{{\text{g}}}^{ - \varepsilon } \overline{{a_{{\text{g}}} }}^{2} \sin \theta \tan \theta + \overline{p} \overline{A}_{{\text{g}}} . \hfill \\ \end{gathered} \right.$$

(25)

There are four contacts between the abrasive and the workpiece, as shown in Fig. 12b: shear deformation, friction between the chip and the abrasive, cutting edge related to abrasive sharpness, and friction between the abrasive and the workpiece [93]. The normal force F_t (F_tc+F_tf) and tangential force F_n (F_nc+F_nf) are the combined normal and tangential components of the chip-forming and friction forces, as shown in Fig. 12c.

Dai et al. [66] found that in the HSG of Inconel 718 alloy, the chip formation stage began, accompanied by the shear slip of the adiabatic shear band, and finally the chip formation was completed, among which the chip was the cause of the grinding force jitter [94]. Liu et al. [95] found that in HSG 18CrNiMo7-6 with a certain material removal rate, the grinding force decreased with the increase of v_s, and the cutting thickness of a single abrasive became thinner, as shown in Fig. 13a. Patidar et al. [96] found that the grinding force of yttrium-stabilized zirconia (YZS) in HSG decreased with the increase of v_s, and the grinding force ratio was close to that of metal alloy, as shown in Fig. 13b. Liu et al. [85] found that the rise and fall of the grinding force during the removal of reinforced abrasivs in HSG PTMCs was related to the interaction between abrasive and reinforced abrasives, as shown in Fig. 13c. Cheng et al. [28] found that as the grinding force of GH4169 decreased during HSG with a single grit, as shown in Fig. 13d. Zhang [47] found that after AISI 1045 steel of HSG, the plastic deformation and adiabatic shear effect of the material increased and the grinding force decreased with the increase of v_s; the number of abrasives involved in grinding and grinding force increased with the increase of a_p; the force of the abrasive along the cutting direction became smaller; and the cutting efficiency increased with the increase of the angle of the front end of the abrasive, as shown in Fig. 13e.

Fig. 13

Change of grinding force of different workpiece materials in HSG a HSG of 18CrNiMo7-6 material to obtain the relationship between grinding force and the v_s [95], b variation of force ratio with the v_s [96], c grinding force profile of PTMC material obtained by finite element modeling [85], d HSG of GH4169 alloy to obtain the variation of single abrasive grinding force versus grinding speed [28], e effect of the v_s, a_p, and abrasive front angle on grinding force [47]

2.5 Modelling and change rule of grinding temperature

The material removal rate of HSG is higher than that of other processing. About 60%–95% of the heat is transferred to the workpiece, and less than 10% of the heat is taken away by the chips, which easily leads to the temperature of the grinding wheel and the workpiece [97, 98]. Because the v_s is very high, the heat can not be transferred to the depth of the workpiece and the thin layer temperature continues to rise to a certain point. The machined surface will produce various thermal damage and thermal deformation affecting the quality of the machined surface. Controlling and reducing grinding temperature is an important step to improve grinding quality.

The heat generated by the contact between the workpiece and the grinding wheel is mainly transferred to the workpiece, the grinding wheel, the chip and the coolant, as shown in Fig. 14a

Fig. 14

Distribution of grinding heat and grinding heat source model in HSG a heat transfer path [93], b–f several grinding heat source distribution models, g coordinate system for circular heat source modeling [69, 100]

$$q_{{\text{t}}} = q_{{\text{w}}} + q_{{{\text{ch}}}} + q_{{\text{s}}} + q_{{\text{f}}}.$$

(26)

The total heat flux q_t is

$$q_{{\text{t}}} = \frac{{F_{{\text{t}}} \times v_{{\text{s}}} }}{{b \times l_{{\text{c}}} }}.$$

(27)

Rowe [99] proposed the heat distribution theory and obtained the grinding temperature as follows

$$ T_{\max } = \frac{{q_{\text{w}} }}{{h_{\text{w}} }} = \frac{{\left( {q_{\text{t}} - q_{\text{ch}} - q_{\text{f}} } \right)R_{\text{ws}} }}{{h_{\text{w}} }} $$

(28)

The analysis of grinding temperature takes into account the shape and distribution of heat source. Makino et al. [101] discovered that the length of the grinding heat source was 2–3 times of the geometric length. Tönshoff et al. [102] discovered that contact length could be predicted by considering both geometric contact length and deformable contact length caused by stress-induced deformation. Guo and Malkin [103] discovered that more than 60% of the grinding heat was transferred to the workpiece through the geometric contact length.

So far, three heat source distribution shapes have been proposed based on the different contact states between the grinding wheel and the workpiece: the heat source region is approximately flat and regarded as moving on a semi-infinite surface, as shown in Fig. 14b; the heat source in the grinding zone is applied to the angle between the grinding surface and the unground surface to cause the temperature rise of the workpiece, as shown in Fig. 14c; the circular heat source model, as shown in Fig. 14d [100]. The temperature predicted by the uniformly distributed heat source is not in good agreement with the measured temperature, as shown in Fig. 14e. So a triangular heat source distribution with good agreement with the measured temperature distribution is proposed, as shown in Fig. 14f.

Based on the circular heat source model, a coordinate system, is established, as shown in Fig. 14g. According to the distribution of the grinding force, the conical surface of the grinding contact surface can be regarded as a heat source with a moving speed of v_f. The motion contact arc length is l_k; the heat source contact surface is differentiated into the heat source curve l_i. Then the temperature rise in time t is

$$\theta = \frac{1}{{{\uppi }k}}\int_{0}^{{l_{\text{k}} }} {q{\text{e}}^{{ - \frac{{\left( {x - x_{\text{i}} } \right)v_{x} + \left( {y - y_{\text{i}} } \right)v_{y} }}{2\alpha }}} K_{{\text{t}}} (\frac{{vr_{\text{i}} }}{2\alpha })} {\text{d}}l_{\text{i}} .$$

(29)

The corresponding dimensionless temperature can be obtained as

$$\overline{\theta } = \frac{{{\uppi }Kv_{{\text{s}}} }}{{2\alpha \overline{q} }}T{.}$$

(30)

The maximum grinding temperature θ_m is when the heat source of the 2D heat transfer model is uniformly distributed

$$\theta_{{\text{m}}} = \frac{{2.256\alpha qL^{\frac{1}{2}} }}{kV}.$$

(31)

The heat source half-length l is half the contact arc length l_c

$$l = \frac{{l_{{\text{c}}} }}{2} = \frac{{\left( {a_{{\text{p}}} d_{{\text{e}}} } \right)^{\frac{1}{2}} }}{2}.$$

(32)

Combining Eq. (31) and Eq. (32) gives the max temperature rise in the grinding zone as

$$\theta_{{\text{m}}} = \frac{{1.128q\alpha^{\frac{1}{2}} a_{{\text{p}}}^{\frac{1}{4}} d_{{\text{s}}}^{\frac{1}{4}} }}{{kv_{{\text{w}}}^{\frac{1}{2}} }}.$$

(33)

3 Grindability and surface integrity of typical material

Different workpiece materials necessitate distinct grinding parameters, each exerting a unique impact on grinding efficiency. Among these parameters, surface roughness stands as a critical metric for assessing the machining outcome. This chapter provides a comprehensive analysis of how various workpiece materials influence surface roughness, as illustrated in Fig. 15. Additionally, it delves into the effects of these materials on the HSG testing process, detailed in Table 3 [5, 45, 47, 72, 107, 109, 118,119,120,121,122,123,124,125,126,127,128,129,130,131,132].

Fig. 15

Surface topography and structure of different workpiece materials

Table 3 Influence of different workpiece materials on grinding experiment

3.1 Alloy and steel

The incorporation of elements such as iron, carbon, chromium, and nickel into alloy steel imbues it with superior properties, including high strength, cost-effectiveness, and enhanced corrosion resistance. In their research on JIS SUJ2 bearing steel, Ichida et al. [104] observed that an increase in v_s led to a reduction in grinding-induced grooves and surface roughness, alongside an elevation in the grinding force ratio, as depicted in Fig. 16a. Concurrently, Zhang [47] reported that augmenting v_s attenuated the grinding scratch intensity on AISI 1045 steel surfaces when subjected to single abrasive grinding, as illustrated in Fig. 16b. Furthermore, Fan [69] discovered that reducing the a_p during the single abrasive grinding of AISI 1045 steel significantly enhanced the surface quality of the workpiece, a finding demonstrated in Fig. 16c.

Fig. 16

Relationship between surface morphology of different alloy steel materials and v_s in HSG a surface morphology of JIS SUJ2 bearing steel obtained at different grinding speeds [104], b surface morphology of single abrasive grinding of AISI 1045 steel at different wheel speeds [47], c surface topographic characterization and 3D dimensional morphology of grinding gouges [69]

Chen et al. [105] found that the residual stress and pressure first increased and then decreased with the increase of v_s during HSG of 18GrNiMo7-6 gear steel. Xiao [106] conducted HSG experiments on GCr15 bearing steel and found that tangential grinding force and surface roughness gradually decreased with the increase of v_s, and increased with the increase of v_w.

3.2 Difficult-to-machine material

Inefficiencies in machining performance and pronounced tool wear during the processing of challenging materials pose significant hurdles in various industries, including aerospace, automotive, and medical sectors. Materials notoriously difficult to machine, such as titanium alloy, GH4169 alloy, and K4169 alloy, are frequently employed in aerospace applications. HSG has been identified as an effective method for high-efficiency machining of these materials. In their study, Jiang and Liao [107] observed that during single-abrasive HSG of K4169 alloy, the rapid movement of abrasives induced shear slip in localized regions of the material, resulting in the formation of shear steps, as illustrated in Fig. 17.

Fig. 17

Surface morphology of different difficult materials under HSG a macroscopic morphology of diamond abrasive and abrasive after brazing, b grinding morphology and energy spectrum analysis of K4169 alloy, c scanning electron microscope morphology of K4169 alloy under HSG, d grinding morphology of K4169 alloys under the action of diamond abrasive, e abrasive chip morphology of K4169 alloy under HSG [107]

Lin et al. [40] carried out single abrasive grinding of GH4169 alloy and showed that the chip formation line at v_s=165 m/s was more upwardly shifted than at v_s=100 m/s; the critical thickness shifted upward more; the skid marks in the grinding area were more pronounced; the plough zone build-up was higher and wider; the grooves were deeper; and the temperature and plasticity were increased, as shown in Figs. 18a, b. Cheng et al. [28] studied the surface wear characteristics of GH4169 during HSG, observed that the inlet and outlet patterns of abrasions formed by diamond abrasive cutting into and out of the workpiece surface were relatively regular at v_s=150 m/s. The surfaces of abrasions formed by the two types of abrasive were smooth and flat, with localized adherence phenomenon, which was more serious in the case of CBN abrasive, as shown in Fig. 18c.

Fig. 18

Surface morphology of GH4169 alloy at different v_s a morphology of the surface and its detailed views at v_s=100 m/s [40], b morphology of surface and its detailed views at v_s=165 m/s [40], c macroscopic and microscopic morphology of the surface of GH4169 alloy, elemental energy spectroscopy, exit and entrance morphology of the abrasive marks formed by diamond abrasive and CBN abrasive, as well as microscopic morphology of the abrasive surface formed by the abrasive marks and adhesion phenomena (v_s=150 m/s) [28]

Huang [108] found that grinding temperature was negatively correlated with workpiece speed and positively correlated with v_s and a_p when grinding titanium alloy TC4 at high speed; grinding force and surface roughness were negatively correlated with v_s and positively correlated with v_w and a_p. Xu et al. [109] conducted HSG of TC4-DT and found that the better grinding surface morphology could be obtained when v_s=60–80 m/s, due to high grinding temperature, the grinding surface was prone to surface burns, micro-cracks and other thermal damage defects when v_s=100 m/s, as shown in Fig. 19a. Xiao [42] conducted HSG experiments on TC4 and found that with the increase of v_s, the grinding force decreased; the adhesion and adhesion plugging of the grinding wheel were reduced; the workpiece surface roughness decreased; and the cracks decreased, as shown in Figs. 19 b, d.

Fig. 19

Surface morphology of titanium alloy at different v_s a TC4-DT titanium alloy grinding surface topography [109], b effect of the v_s on surface morphology of titanium alloy TC4 [42], c influence of the v_s, a_p and v_w on surface roughness [42], d grinding wheel morphology before and after grinding [42]

3.3 Hard and brittle materials

Traditional manufacturing techniques struggle to efficiently process engineering ceramics and other materials characterized by high hardness and brittleness. HSG has emerged as a viable solution for machining such materials, finding applications in the biomedical, aerospace, and automotive industries. In the aerospace sector, advanced ceramics have demonstrated superiority over metallic superalloys in withstanding the extreme temperatures experienced by structural components and aero-engine parts. Beyond their capability to endure high temperatures, these advanced ceramics are renowned for their exceptional wear resistance, corrosion resistance, and chemical inertness. Shih et al. [110] observed that silicon nitride and zirconium oxide showed less wear of grinding wheels in HSG. Wu [111] found that the surface roughness of HT300 was better during HSG of HT300 and QT600-3 materials, as shown in Fig. 20a. Yin et al and Huang [112] found that the surface quality became smoother and smoother when grinding hard and ductile ceramics at HSG, as shown in Fig. 20b.

Fig. 20

Changes of surface morphology and grinding force ratio of hard and brittle materials under HSG a grinding force ratios of HT300, QT600-3, quenched HT300, and quenched QT600-3 materials at different v_s and surface morphology at v_s=60 m/s [111], b SEM micrographs of different materials grinding at different v_s

Dai [113] found that the plastic removal rate of the grinding surface increased with the increase of v_s, and the pit size, crack damage depth, grinding force and specific grinding energy of the grinding subsurface decreased when a single abrasive grinding was performed on SiC, as shown in Fig. 21a. Li et al. [45] found that the multi-step HSG processing technology of zero-dur glass-ceramics had obvious advantages in terms of material removal rate and surface roughness, as shown in Fig. 21b. Assuming that HSG is performed at different machining allowances, the material removal rate Q_w varies greatly, which the average value is as high as 1 528.3 mm³/min, so that multistep HSG can easily obtain products with lower surface roughness, as shown in Fig. 21c.

Fig. 21

Change of surface morphology of SiC ceramic materials and the change and advantages of multi-step HSG parameters a effect of v_s on surface damage, subsurface damage and grinding force of SiC [113], b advantages of multi-step HSG based on material removal rate and surface roughness [45], c multi-step HSG grinding parameter optimization [45]

3.4 Composite materials

Metal matrix composites (MMCs) constitute a new class of materials that are garnering significant interest across scientific, technical, and commercial domains. These composites exhibit superior specific strength and stiffness, augmented temperature resistance, and outstanding corrosion resistance compared to their non-reinforced metal alloy counterparts. Owing to these enhanced properties and the escalating performance requirements in various sectors, MMCs are increasingly being adopted as substitutes for traditional materials in a wide array of engineering applications within the aerospace, aircraft, electronics, and automotive industries [67]. Guo et al. [114] conducted HSG experiments on Al/SiCp MMCs and obtained better surface quality at high v_s, as evidenced by grinding scratches, surface craters and lower surface roughness, as shown in Fig. 22b. Guo et al. [115] conducted HSG experiments on Al/SiCp MMCs and found that grinding scratches, chips, surface craters, and side streams were the main features of the grinding process due to the fragmentation and strong plastic deformation of SiC abrasives.

Fig. 22

Change of surface morphology and material removal behavior of composite materials under HSG a removal behavior of PTMCs material with different thickness of undeformed chips [85], b polishing surface and grinding surface of Al/SiCp MMC workpiece at different v_s [114]

Abrasive-reinforced titanium matrix composite (PTMCs) is a kind of MMCs. Compared with traditional titanium alloys, PTMCs has high specific stiffness and high specific strength due to the addition of abrasive reinforced phase, and has broad application prospects in aerospace industry [116, 117]. Liu et al. [85] found that the material removal behavior of PTMCs in HSG process could be divided into plastic removal of matrix material, crack initiation of reinforced abrasives, crack propagation of reinforced abrasives and brittle damage of reinforced abrasives, as shown in Fig. 22a.

4 Improvement with using cooling/lubrication methods

In HSG operations, challenges such as inefficient heat dissipation, accelerated wear of the workpiece, and reduced lifespan of the grinding wheel complicate the machining process. An effective strategy to enhance surface quality under these conditions is the application of grinding fluid. This chapter delves into the utilization of techniques such as minimum quantity lubrication (MQL), nano-lubricant minimum quantity lubrication (NMQL), and cryogenic gas-liquid lubrication. These methods are instrumental in achieving lower grinding temperatures and mitigating environmental contamination at high grinding speeds, as elucidated in Fig. 23.

Fig. 23

Structure diagram of experimental results under different lubrication conditions of HSG

4.1 MQL

Coolant reduces the grinding zone temperature by removing heat from the grinding zone during the HSG, and access to the grinding zone is an urgent problem to be solved, so MQL comes into being. It can effectively enter the grinding zone to provide lubrication, thereby reducing the grinding zone temperature [133]. Boswell et al. [134] summarized the application of MQL in metal processing to improve machining performance. Tawakoli et al. [135] found that MQL could achieve a good reduction in grinding zone temperature when grinding hardened steel at low speed. Emami et al. [136] found that MQL could effectively reduce grinding force and surface roughness during the HSG. Choudhary et al. [133] found that HSG of alumina in different environments, low friction under MQL pure oil conditions increased the amount of plastic deformation in the grinding area, and its efficient grinding performance achieved high-quality grinding surfaces, as shown in Fig. 24.

Fig. 24

SEM photos, three-position surface profiles and Abbots-Firestone curves of the ground alumina surface under different lubrication conditions (from left to right) a MQL-neal b MQL-soluble, c conventional flood [133]

Many researchers have found that several advanced ceramics can effectively reduce grinding forces and surface roughness at HSG [112, 137, 138]. Choudhary et al. [139] proposed a new model to demonstrate the interaction of nano-abrasives with brittle materials in the grinding area. Compared with other grinding environments, the straight cutting oil MQL has the highest tangential grinding force and the lowest normal grinding force, as well as the highest specific grinding energy and the highest apparent friction coefficient, as shown in Fig. 25.

Fig. 25

Grinding mechanism and morphological changes in high-speed grinding using MQL lubrication a mechanism of MQL in grinding of hard and brittle materials, b effect of different nozzle orientations on the sum of non‐dimensional grinding forces, and optimum MQL nozzle position, c effect of HSG alumina on surface quality in different grinding environments [139]

4.2 NMQL

NMQL represents an innovative approach in precision grinding, characterized by its high efficiency, low resource consumption, environmental friendliness, and a low carbon footprint [140]. This method addresses the existing limitations in micro-lubrication applications. The inclusion of nano-abrasives significantly enhances the lubrication efficacy within the grinding zone, owing to their exceptional anti-wear and anti-friction properties. This advancement not only improves the machining accuracy and surface quality of the workpiece, particularly in terms of surface integrity, but also ameliorates the working environment and boosts the heat transfer efficiency of MQL [141, 142].

Zhang et al. [55] conducted HSG experiments on a single abrasive in different grinding processes, and found that under three lubrication conditions, the scratch cutting efficiency increased with the increase of a_p, as shown in Figs. 26 a, b. Under different conditions, NMQL, due to its excellent cooling lubrication performance, reduces the temperature of the grinding zone and the thermal softening effect of the material to be removed, so that its deformation is more reflected in the fracture of the material, thus entering the cutting stage earlier, achieving higher grinding efficiency and lower unit grinding force, as shown in Fig. 26c. After measuring the scratched surface under different lubrication conditions, the cooling lubrication performance is improved under MQL condition, but the best workpiece surface and cooling lubrication performance are obtained under NMQL condition, as shown in Fig. 26d. Dry grinding formed banded chips due to the thermal softening effect; abrasive chip fracture due to excessive shear layer spacing occurred in the MQL condition; and the fracture was greater in the NMQL condition, as shown in Fig. 26e.

Fig. 26

Changes of grinding mechanism, grinding force, surface morphology and grinding chips in NMQL lubrication HSG a experiment platform of single abrasive cutting test and surface morphology of single diamond abrasive, b the effect of the a_p on grinding efficiency, c cutting efficiency and unit grinding force under different working conditions, d furrow morphology at different lubricating conditions, e debris morphology at different lubricating conditions [54]

4.3 Cryogenic air

Cryogenic gas-liquid two-phase injection cooling is the use of cryogenic compressed gas to carry a small amount of coolant, spray impact jet injected into the processing area to achieve enhanced heat transfer cooling method. Its core is through the cryogenic spray jet to achieve cryogenic gas-liquid two-way strong convection, full vaporization and jet impact three enhanced heat transfer advantages, make full use of the cryogenic gas-liquid heat transfer potential to obtain a better enhanced heat transfer effect.

Wang [143] conducted HSG experiments on cryogenic gas-liquid two-phase injection technology and found that under the condition of cryogenic gas-liquid cooling, the heat in the grinding process was easily carried away by the vaporized droplets; the surface roughness value was lower; and the surface quality of the machined workpiece was better, as shown in Fig. 27a. With the increase of v_s, the grinding force under both cooling methods decreases; with the increase of v_w, the metal removal rate, cutting thickness, a_{g max} and grinding force increase accordingly; with the increase of a_p, the a_{g max} of a single abrasive and the length of the workpiece-grinding wheel contact arc increase; the grinding force, and the number of abrasives involved in cutting increase; and the cryogenic gas-liquid grinding force is smaller, as shown in Fig. 27b.

Fig. 27

Changes of surface morphology and grinding force during HSG in low temperature gas-liquid environment a variation of surface roughness with the v_s, v_w, a_p and surface microstructure under specific conditions, b variation of grinding force with the v_s, v_w, a_p [143]

5 Key components of HSG grinder

The grinding machine tool is the primary instrument by which high-end precision components achieve their surface and dimensional accuracy, and its manufacturing standards have emerged as a critical benchmark for assessing a nation’s high-end manufacturing capabilities. In recent years, significant advancements in grinding technology, both domestically and internationally, have transformed conventional grinding grinders into the current high-speed machining systems, resulting in substantial enhancements in both grinding precision and efficiency, as depicted in Fig. 28.

Fig. 28

Development of HSG grinder

For ordinary grinding machines, appropriate modifications are needed to enable the realization of HSG [144]. Some of the modifications and requirements include the incorporation of HSG wheel spindle bearings characterized by high rigidity [145], strong vibration absorption capabilities, and minimal temperature elevation. Additionally, there is a need for the augmentation of motor power, enhancements to the dynamic rigidity and vibration resistance of the entire machine tool. Other requirements include the addition of a dynamic balancing device for the grinding wheel adjustment, the implementation of reliable measures to bolster safety and security. Finally, the cooling system should be improved by elevating both pressure and flow rates to ensure that a sufficient quantity of coolant can be introduced into the grinding zone [146]. In this chapter, key components of high-speed machining are examined, as depicted in Fig. 29.

Fig. 29

Analysis structure diagram of HSG machine

5.1 Structure and stiffness of main body

The traditional structure can result in significant vibrations due to the abrupt increase in spindle speed, leading to inadequate machining quality, buffeting, and increased wear of the grinding wheel. Hence, there is a necessity for the redesign of the support structure of the high-speed surface grinder.

The fundamental components of a grinding machine, such as the bed, column, grinding head, and table, among others, constitute the “major components”. They are classified, based on their motion, into stationary supporting components for the bed and column, and mobile supporting components for the grinding head and table. In the case of the stationary supporting components, vibrations in these parts and the entire machine can be induced by dynamic forces, including the dynamic grinding force of the grinding machine, the table’s inertia, and the imbalance of the grinding wheel. For HSG grinders, the potential for vibration generation increases significantly due to the substantial rise in v_s. It becomes imperative to ensure that the machine’s inherent frequency remains beyond the v_s range, thereby necessitating a more rigorous design of the supporting components. In HSG machining, although the grinding force is generally lower compared to conventional grinding, the unbalanced force stemming from the high acceleration and deceleration inertial forces of the grinding wheel is substantial. As a result, sizable components, such as the grinding machine’s bed, must possess adequate rigidity and strength. In the design of moving support components, a significant reduction in weight is imperative to ensure the high-speed operation and acceleration of these moving parts. The weight of the grinding machine supports should be reduced by 30%–40% compared to conventional grinding machine structures. This reduction should be achieved through the incorporation of highly rigid fixed supports and lightweight kinematic supports, allowing HSG grinders to exhibit dynamic characteristics that are tenfold higher than those of ordinary grinding machines, as illustrated in Fig. 30.

Fig. 30

Several types of HSG grinder a double-column HSG grinder [147], b zero multi-step HSG grinder, the max speed of the spindle of the machine tool reaches 10 000 r/min [45], c a grinding machine with an active magnetic bearing spindle, the max rotational speed and output power are 55 000 r/min and 7.5 kW [104], d the MGKS 1332/H CNC cylindrical-grinding grinder [148]

High-speed machine structures can be optimized by using lightweight or welded steel structures for movable parts, and whole-cast bed post structures to enhance stiffness and vibration resistance. Incorporating new materials like epoxy resin, polymer concrete, and high-nickel cast iron with lower thermal expansion can further improve vibration resistance and thermal stability [149]. The adoption of novel principles in motion mechanisms, exemplified by Giddings & Lewis’s introduction of the parallel machine known as the Variax machining center, also referred to as the Hexapod, a six-legged machine, and the virtual axis machine. These innovations have emerged as significant advancements in the construction of the new generation of grinders.

The grinding process in high-precision grinding machines demands excellent performance characteristics, including high precision and stability. To fulfill these requirements, the bed, as a supporting component, needs to possess robust stiffness, thermal stability, and damping properties. Grey cast iron is widely employed in grinder manufacturing due to its favorable attributes such as excellent castability, resistance to abrasion, vibration damping, compressive strength, machinability, minimal volume shrinkage, line shrinkage, and low notch sensitivity. Moreover, as the manufacturing industry advances, materials such as marble, concrete, and steel-fiber-reinforced polymer concrete have been explored for application in grinder beds. Table 4 provides a summary of the physical parameters of these four materials, which are used for analysis and comparison of the dynamic properties of the beds [150,151,152,153,154,155].

Table 4 Physical parameters of HT200, concrete, steel fiber polymer concrete and marble [32]

The mechanical structure of the bed remains unaltered, and the dynamic characteristics of the bed crafted from marble are the most superior, followed by those of the beds constructed from HT200 and steel-fiber-reinforced polymer concrete, with the plain concrete bed exhibiting the least desirable properties. Upon comparison, it becomes evident that among the four materials, marble is the most suitable for the fabrication of grinding machine beds due to its exceptional dynamic performance. However, due to its substantial size and higher cost, its practical application is limited. Among the four materials, HT200 offers dynamic performance that falls short of marble but surpasses that of steel-fiber-reinforced polymer concrete and conventional concrete. Additionally, it facilitates the casting of large mechanical structural components in a single operation, making it a commonly utilized material in practice. In actual design, one should thoroughly consider the inherent advantages of each material and incorporate them into the design of critical structural components.

5.2 Structure and rotate speed of spindle

The spindle system comprises the spindle, bearings, spindle motor, drive controller, encoder, and the corresponding communication cable, with its dynamic behavior being influenced by the stiffness of the bearing support and the spindle’s own structure [32]. Chen [32] established the finite element model of the HSG grinding machine’s spindle and generated vibration pattern cloud diagrams for both unconstrained and constrained conditions. In the constrained state, the frequency of the low-order modes is slightly lower compared to that in the free state. However, the maximum modal displacement is notably reduced, indicating a relationship between the spindle’s vibration characteristics and its constrained state. The low-order vibration modes predominantly manifest as bending deformations in various directions, with the maximum displacements primarily occurring at the end of the smaller shaft. Therefore, the improvement of shaft structure can enhance resistance to bending deformation, as depicted in Fig. 31d. Mei [156] found that the grinding electric spindle converted electrical energy into mechanical energy through the built-in motor, and directly acted on the workpiece through the grinding wheel installed on the rotor spindle, making the structure more compact and the transmission accuracy higher [157].

Fig. 31

Structure diagram and dynamic simulation model analysis of HSG spindle a general design unit diagram of electric spindle unit, b the first four orders of intrinsic frequency and vibration pattern of spindle column test mode and the results of finite element modal analysis of spindle column, c analysis results of the whole machine modal test and finite element mode shapes [39], d HSG grinding machines spindle finite element mode, the first and sixth orders of the spindle vibration pattern HSG grinding machines in the unconstrained state and in a restrained state [32]

Yang [39] designed a motor-built HSG spindle and carried out finite element static structural analysis in Ansys software, as shown in Fig. 31a, where a vertically upward force was applied to the wheel mounted on the front section of the spindle, and by analyzing the radial deformation cloud diagram of the spindle, the static stiffness value of the spindle could be calculated, as shown in Fig. 31b. According to the results of finite element analysis, it is found that the simulated values of the modal parameters of the whole machine are close to the test values, and the corresponding error between the two is less than 10%, as shown in Fig. 31c. The results show that the optimization and identification results based on the main components such as spindle column and linear motor driving platform can reflect the dynamic characteristics of the grinder of the HSG test equipment.

During the operation of the grinding electric spindle, thermal deformation is induced by the heat generated from the electromagnetic losses of the integrated motor and bearing friction losses, which in turn diminishes the machining accuracy of the grinding electric spindle. Within the grinding electric spindle system, the stator and rotor constitute the primary sources of heat generation for the integrated motor. The effective input power of the integrated motor is as follows

$$P_{\text{i}} = \sqrt 3 UI\cos \varphi .$$

(34)

During the operational process of the built-in motor, a significant portion of the effective input power is converted into effective output power to drive external loads, while the remaining portion is transformed into thermal energy and consumed, resulting in motor heating. This consumed energy is referred to as motor losses. The integrated motor used in the introduced grinding spindle is a permanent magnet synchronous motor, with primary motor losses encompassing mechanical losses, winding copper losses, stator core losses, permanent magnet eddy current losses, and additional losses, as shown in Fig. 32 [158], where the additional losses account for only 1%–5% of the motor losses, and therefore can be ignored [159]. The stator core loss is categorized into hysteresis loss and eddy current loss, with eddy current loss further divided into classical eddy current loss and additional loss [158, 160]. Hysteresis loss occurs when the stator core is magnetized by the alternating magnetic field, resulting in friction between magnetic domains and consequent loss. Classical eddy current loss arises when the stator core, subjected to alternating current, generates eddy currents due to closed inductive electromotive forces, leading to the loss known as eddy current loss [161].

Fig. 32

Internal motor of the grinding spindle is the main motor loss in the permanent magnet synchronous motor a mechanical wear and tear [162], b winding loss [163], c stator core loss [156, 164], d permanent magnet eddy current loss [165]

Bearings are important mechanical basic parts that reflect the level of industrial development of a country [145, 166]. Magnetic levitation bearings separate the inner and outer rings from each other during rotation and do not produce friction losses due to contact, reducing the system temperature rise, but they are not suitable for large-scale use due to their high cost, as shown in Fig. 33a [170]. Zhang et al. [168] studied a new type of hybrid gas-powered bearing with high structural stiffness and viscous damping, as shown in Fig. 33b. Angular contact ball bearings can bear both axial and radial loads at the same time, with low cost and high limit speed ratio. Two-half inner ring four-point contact ball bearings have the advantages of bearing bidirectional axial forces, high stiffness and small occupied space, as shown in Fig. 33d [172]. Grinding spindle in high-speed operation, steel ball bearings will produce the gyroscopic torque and centrifugal force, increasing the contact stress, bearing temperature, fatigue pitting and thermal occlusion of the possibility of increasing, so that the bearing life is reduced, in the project more mixed ceramic ball to replace the traditional steel ball. Compared with steel ball bearings, ceramic ball bearings have the advantages of small density, non-conductive, non-conducting, low coefficient of friction, good wear resistance, long service life, self-lubricating and so on, as shown in Fig. 33c [171].

Fig. 33

Schematic diagram of different bearings used in HSG a mechanical structure of motorized spindle and schematic diagram of magnetic bearing [170], b schematic diagram of the novel hybrid gas dynamic bearing (HGDB) [168], c schematic diagram of ceramic ball bearing [171], d structural diagram of double half inner ring four-point contact ball bearings (FPCBB), which consists of outer ring, inner ring, cage and ball [172]

5.3 Structure and principle of dynamic balancing system

In order to meet the higher requirements of HSG, more and more attention is paid to the research of dynamic characteristics and dynamic balancing technology of grinding wheel spindle system [173, 174].

At present, there are three main types of more mature dynamic balancing techniques [36]. Process dynamic balancing: the use of balancing machine to detect and balance the spindle monomer by adding or reducing weight [175]. On-site dynamic balancing: balance the installed rotor system to avoid equipment installation and assembly errors [176]. Online automatic balancing technology: Install a balancing device on the rotor to detect the vibration of the rotor in real time [177]. There are two main types of auto-balancing technology [178]: (i) passive auto-balancing technology relies on the energy generated by the system response to drive the corrected mass, which has the advantages of simple structure and low energy consumption, but the device has the inherent defects of subcritical state exacerbating rotor imbalance and is difficult to design [179]. (ii) active auto-balancing technology achieves the unbalanced mass compensation by means of external energy [180].

Liang [36] found that there was a causal relationship between whether the mass distribution of the rotor was balanced and whether the centrifugal force of the rotor was balanced. They simplified the system of centrifugal force on the mass point of the rotor, reflecting whether the mass distribution of the rotor was balanced and symmetrical, as shown in Fig. 34a. The centrifugal force system of the rotor mass point is simplified to any point as a result of a total of five states, in addition to the rotor center of the main axis of inertia and the axis of rotation coincide with the rotor presents a balanced distribution state, the remaining four imbalance states, as shown in Fig. 34b. Assuming that there is a certain degree of unevenness on each disk axis of the rotor, the unevenness of the whole rigid rotor will be distributed along the Z-axis of the random space curve. No matter how asymmetric and uneven the mass distribution of the rigid rotor is, as long as there are two correction measures of concentrated distribution, the balance mass can be reduced or eliminated, which is the basic condition of the mechanical balance of the rigid rotor, as shown in Fig. 34c.

Fig. 34

Unbalanced state of spindle rotor and the corrective measures for balance a simplification of the centrifugal force system at the rotor mass point, b the rotor with four states of imbalance, c unbalance curves for rigid rotors [36]

The span between the two bearings of the grinding spindle rotor system is large, and because the rotor body rotates with a small axial runout, its imbalance is mainly manifested as its comprehensive imbalance. There are three ways to achieve on-line dynamic balancing including mass compensation method, coordinate rotation automatic balancing strategy and implementation of error analysis, as shown in Fig. 35.

Fig. 35

Methods for realizing on-line dynamic balancing a mass compensation method, b polar coordinate balancing process with fixed radius for double counterweights, c coordinate rotation auto-balancing strategy, d execution error analysis [36]

The unbalance vector consists of phase and magnitude, so the error is mainly composed of phase error and magnitude error, assuming that the initial unbalance amount is U₀; the synthetic compensation of the counterweight mass block is U; and the step angle is φ. The phase error arises from the fact that no matter how to regulate the mass block, and it can not be compensated for its synthetic vector and the initial imbalance vector covariant, taking into account that the step angle is generally smaller; the residual imbalance vector and the initial imbalance vector are approximate orthogonal to each other; and the magnitude of the residual imbalance amount is approximated to be , as shown in Fig. 35d,

$$U_{\text {r}} = U_{0} \sin \left( {\frac{1}{2}\varphi } \right).$$

(35)

The amplitude error exists only when two counterweight masses are required to rotate simultaneously. After phase balancing, the two mass blocks are located at P₁₁ and P₂₂ or at P₁₂ and P₂₁, respectively, which can be converted into a phase error by means of an optimized regulation algorithm, for example located at P₁₂ and P₂₁.

5.4 Structure and strength of grinding wheel

HSG wheel is usually composed of substrate and abrasives with high mechanical properties, which should have good wear resistance, dynamic balance accuracy, crack resistance, damping performance, stiffness and thermal conductivity [19]. Materials with high elastic modulus/density ratio and low thermal expansion coefficient are sought in order to meet the performance requirements of HSG wheels. HSG wheels can be made of corundum, silicon carbide, CBN, and diamond abrasives, and the bond can be made of ceramic, resin, or metal bond [181]. The maximum speed of the grinding wheel using resin combined with corundum, silicon carbide and cubic boron nitride abrasive has reached 125 m/s; the maximum speed of the single-layer electroplated CBN grinding wheel has reached 250 m/s, which has reached 340 m/s in tests; and the maximum speed of the ceramic bonded grinding wheel has reached 200 m/s [182]. Compared to other types of wheels, ceramic-bonded grinding wheels are easy to trim and can be obtained with a wide range of porosity by changing the production process.

Performance requirements for grinding wheel substrates for HSG [39] including (i) static characteristics: the extremely high speed of the HSG spindle system and the small rotor diameter limit the power of the internal motor of the grinding spindle structurally; (ii) dynamic characteristics: higher natural frequency can improve the working speed of the spindle system in the resonance range; (iii) grinding performance: the grinding wheel substrate itself has good static and dynamic performance and dynamic balance.

Emerging applications of HSG technologies mainly include high efficiency deep grinding (HEDG), ultra high-speed grinding (UHSG), quick point grinding (QPG), and high-speed stroke grinding (HSSG). UHSG wheels consist of an abrasive layer and a grinding wheel substrate, and their working layer consists of a binder, a void, and an abrasive, and several typical grinding wheels, as shown in Fig. [36, 39, 181, 183,184,185,186,187].

Fig. 36

Several typical HSG wheels [39, 181, 183,184,185,186,187]

CBN wheels including electroplated and brazed wheels, typically consist of a single layer of super abrasives nickel-coated or brazed filler bonded to a metal wheel substrate, as shown in Fig. 37a. Ghosh and Chattopadhyay [188] proposed a possible failure mode for CBN abrasive in electroplated wheels, as shown in Fig. 37b. At low levels of plating, abrasives are easily pulled out from the Ni-bond encapsulation, on the contrary at high levels of plating, abrasive failure is determined by the defect structure of the CBN abrasive. For single-layer brazed CBN wheels, abrasive pull out and bond shear may be due to poor surface wettability of CBN abrasives or low alloy strength, as shown in Fig. 37c [191].

Fig. 37

Possible abrasive failure modes of single-layer brazed CBN grinding wheel and electroplated CBN grinding wheel a schematic diagram of single-layer plated and brazed CBN wheel, b possible abrasive failure modes in electroplated CBN wheels, c possible abrasive failure modes in brazed CBN wheels [191]

There were three types of grinding wheel wear during the grinding, namely, abrasion, abrasive fracture and bond fracture [192, 193]. CBN wheels often have special requirements for resistance to breakage and wear resistance, and also require good damping characteristics, rigidity and thermal conductivity [194]. In this case, the HSG wheel usually needs to consist of a wheel body with high strength and a thin layer of CBN super abrasive coating, which is attached to the wheel body using a high strength adhesive, and only a single layer of CBN wheel can achieve the highest v_s. Electro-plated wheels consist of a single layer of abrasive, which enables maximal material removal rates, as shown in Fig. 38 [195].

Fig. 38

Affordable the v_s and materials removal rates of different CBN wheels [195]

Liu et al. [196] proposed a fabrication process for brazed diamond grinding wheels, in which the blade portion of a diamond saw was brazed in a high-vacuum furnace, and then the brazed blade was welded to a steel substrate by laser, as shown in Fig. 39.

Fig. 39

Production process and microstructure of brazed diamond grinding wheel a production process of brazed diamond wheel, b initial, heated, and brazed microstructures of diamond abrasives [196]

Based on CFRP material light weight, high specific strength, high specific modulus of elasticity, good damping and vibration resistance and other excellent properties. Yang et al. [197] found that the natural frequencies of each order of CFRP wheel were higher than the natural frequencies of the spindle system of steel-based wheel, and with the increase of v_s and v_w, the surface roughness of CFRP wheel was lower than that of steel-based wheel. Yang [39] conducted high-speed grinding tests with self-developed CFRP wheel and found that with the increase of v_s, the radial deformation and equal effectiveness of the substrate of CFRP wheel under three layering methods increased significantly, as shown in Fig. 40 [198]. Subsequently, an experimental study on HSG with CFRP wheel and rigid matrix wheel was carried out, and it was found that as the v_s increased, its no-load power consumption, radial deformation, amplitude and temperature of the grinding wheel substrate also increased. However, the ratio of no-load power consumption, radial deformation and amplitude of the CFRP wheel were lower compared to those of the steel matrix grinding wheel, and the gradient of the temperature rise of the CFRP wheel was significantly higher than that of the steel matrix wheel. The grinding force was reduced with the increase in the v_s, and the CFRP wheel produced a much lower grinding force [39].

Fig. 40

Results of radial deformation and equivalence of CFRP grinding wheel under different layering methods and different grinding experimental parameters a variation of radial deformation and equivalent stress of CFRP wheel substrate with speed and deformation distribution of CFRP wheel substrate with different layups at v_s=150 m/s, b influence of CFRP and steel grinding wheels on no-load power consumption, radial deformation, temperature rise of the wheel, amplitude and grinding force as the v_s increases [198]

6 Conclusions and prospect

6.1 Conclusions

By reviewing the progress of HSG, the MRM, machined surface integrity, grinding force and temperature, as well as the key equipment for HSG in the HSG process are summarized and discussed. The main conclusions are drawn as follows.

• (i) Based on the MRM study of HSG, the deformation mechanism and mechanical behavior of workpiece materials in the abrasive forming area are sorted out. The calculation formulas of strain rates in the first and second deformation zones were established, and the mechanism of chip formation under the combined effect of strain hardening, strain rate strengthening and heat softening were revealed. The theoretical model of grinding force and grinding temperature is established. The effects of geometric parameters of simplified model on grinding force and grinding temperature were studied. The differences of material removal constitutive models and grinding properties of different workpiece materials under high strain rate were analyzed.

• (ii) Through the study of surface topography of difficult-to-machine materials, hard and brittle materials, alloy steels and composite materials after HSG, it is found that the surface roughness of the surface roughness is better than that of conventional grinding, and the grinding force is smaller. The research of different workpiece materials is extended, which provides the basis for establishing the database.

• (iii) In the HSG process, adding some cooling processes such as MQL, NMQL, cryogenic air, etc., will obtain lower grinding force, grinding temperature and surface roughness than ordinary grinding. By comparing the surface roughness of three cooling processes: NMQL < MQL < cryogenic air, it is found that NMQL can obtain better HSG surface topography. In summary, NMQL has better cooling lubrication effect and surface quality after grinding.

• (iv) The HSM from the supporting parts to the spindle, the grinding wheel is the main structure of the grinder, and HT200 material can be selected as the bed structure of the grinder. The dynamic characteristics of the main shaft, the conditions of the dynamic balance of the main shaft and the strength of HSG grinding wheel are described.

6.2 Prospect

In recent years, the research progress of HSG on MRM, material constitutive model, grinding force model, grinding temperature model, microstructural changes of typical materials under HSG, the laws generated by different grinding processes and the research progress in HSG key components such as the body mechanism, grinding wheels, spindles, dynamic balancing, etc., which has an important practical significance at the present stage, and scholars still have a lot of work to do in this regard, as shown in Fig. 41.

Fig. 41

Outlook of HSG

Combined with the research review in this paper, several future research directions are proposed.

• (i) The development trend of HSG is reviewed in this paper. By summarizing the strain hardening effect, strain rate strengthening effect and heat softening effect of materials produced by HSG, it is found that the increase of grinding speed brings some urgent problems to the research of grinding mechanism. At present, the constitutive model is found through the Hopkinson pressure bar test. As the increase of grinding speed, shear, plastic deformation and heat-affected zone formation, as well as the change of temperature and pressure in the grinding zone, lead to the change of physical properties of the material, which makes it difficult to establish the constitutive model and residual stress model of material removal. The material constitutive model needs to be theoretically simulated by molecular dynamics experiment and experimentally explored by a single abrasive slip test. For the efficient deep grinding combined with HSG and deep grinding, it is difficult to achieve high power and high speed of the spindle, which requires scholars to continue their research in the future. At present, due to the lack of some research data, the development law cannot be well summarized, and it is necessary to conduct a large number of research experiments on some difficult materials in the future, and establish a complete material constitutive model, residual stress model and other databases. In view of the complexity of the grinding force modeling formula caused by the change of grinding force under the action of HSG, it has become an urgent problem to be solved. At present, the measurement of grinding temperature is mostly through thermodynamic coupling, which is not accurate enough, and the heat source model of grinding temperature modeling has some limitations. Due to the increase of grinding speed, grinding temperature changes too fast, and the collection of grinding temperature in grinding zone is still a bottleneck to be explored by young scholars. The study of grinding chips is also a reliable way to determine the grinding mechanism. At present, it is difficult to collect abrasive dust at the current level of research, and future scholars will need to spend a lot of time to study the collection of abrasive dust.

• (ii) An in-depth study of the material removal behavior of different types of workpiece materials under high-speed grinding, especially some difficult materials such as high-entropy alloys and composites used in aerospace. In order to better help future scholars to understand the research faster, the future needs to establish a complete database through the analysis of its system, including grinding force, grinding temperature, surface roughness, sub-surface roughness and grinding abrasive collection and research.

• (iii) In this study, the research results of MQL, NMQL and HSG workpiece under low temperature cold air. In view of the limitations of the grinding process introduced at present, more new grinding processes can be introduced in the future, for example, For the nanofluids in NMQL, different additives, electrostatic atomization minimum quantity lubrication and electrostatic atomization minimum quantity lubrication (some low temperature cooling conditions can be added) can be selected, and efficient cooling lubrication methods can be found by studying different lubrication conditions under HSG and analyzing different grinding parameters. It is best to establish a complete database through a large number of studies on HSG of different workpiece materials under different lubrication methods, so as to provide research ideas for young scholars and facilitate future scientific research.

• (iv) According to the content summarized in this review, it is found that the stiffness and strength of the main structure of the grinder is still not high enough, and better materials can be explored through research to make the main weight of the grinder 50% lighter than the traditional grinder, and improve the dynamic balance of the spindle. For the spindle part of the grinding machine, the test platform can be optimized by reducing the weight and step angle, and the dynamic balance test speed can be increased to solve the dynamic balance problem of high-speed grinding. From the current point of view, after long-term development, the manufacturing and application technology of ordinary grinding wheel has been very mature, but the preparation method of HSG wheel is relatively simple and the price is relatively expensive, and the current HSG wheel has the risk of grinding wheel explosion, and the adhesive at the interface between the grinding wheel matrix and the abrasive layer is unstable, uneven and aging. Once the adhesive fails, the stress of the abrasive layer will increase dramatically, and the risk of wheel explosion will also increase, which is an urgent problem that needs to be solved. At present, with the development of intelligent grinding, improving the correction accuracy and automation of the grinding wheel is the current development direction, and the future needs scholars to study and explore the intelligent control and remote control of the grinding machine to achieve the safe operation of the grinder and ensure the safety of the operator.