Journal of Materials Processing Tech.

305 (2022) 117600

Contents lists available at ScienceDirect

Journal of Materials Processing Tech.

journal homepage: www.elsevier.com/locate/jmatprotec

Durability of micro diamond tools with different crystallographic planes

Hanzhong Liu *, Wenjun Zong *, Zhipeng Cui
Center for Precision Engineering, Harbin Institute of Technology, P.O. Box 413, Harbin 150001, PR China

A R T I C L E I N F O A B S T R A C T

Associate Editor: Erhan Budak Micro diamond tools are indispensable for machining microstructured arrays. The cutting edge durability and
consistency of micro diamond tools are the determinants of the microstructure quality and accuracy, in addition
Keywords: to the motion accuracy of the machine tool. A strength distribution model of the working area including the
Micro diamond tool cutting edge and rake and flank faces was established considering diamond anisotropy and chip flow direction.
Cutting edge strength
Comprehensive wear resistances of micro diamond tools with different crystal orientation combinations were
Wear resistance
analyzed based on the model, and the wear prone areas of different tools were successfully predicted. The
Crystal orientation
evolution processes of the sharpness and wear topography were monitored for every micro diamond tool in the
micromachining experiments. The morphologies, profile errors and topological characteristic of the micro­
structures machined with different micro diamond tools with increasing cutting distance were analyzed. Finally,
a conclusion was drawn that the wear resistances of the micro diamond tools in ascending order are Aγ{100}
Aα{100}, Aγ{100}Aα{110}, Aγ{110}Aα{100}, and Aγ{110}Aα{110}. The three working areas of the Aγ{100}
Aα{100} tool are prone to wear; in contrast, those of the Aγ{110}Aα{110}tool are resistant to wear. The tool wear
of Aγ{100}Aα{110}is caused by flank face wear, and that of Aγ{110}Aα{100} is caused by rake face wear.

micro-topography of large-size molds, and they concluded that tool wear

decreased the form accuracy of microstructures and surface uniformity.
1. Introduction Their results implied that diamond tool wear has become a technical
difficulty restricting improvement of the accuracy of molds, especially in
Microstructure arrays have been widely used to enhance technical the processing of large-size molds.
surfaces with all kinds of additional functionalities, such as optical Dong et al. (2019) investigated the influence of diamond tool wear
component usage, environmental protection, information storage (Lu on the surface integrity and they found that the surface integrity was
et al., 2014), and other fields (Saga, 2010; Amin et al., 2018). Therefore, gradually deteriorating with the increasing tool wear. Their findings
ultraprecision manufacture of microstructure arrays has been in focus of demonstrated that severe wear of diamond tool has to be retarded
many recent research projects. To date, the most effective method to during the ultraprecision machining process to ensure the integrity of
fabricate microstructure arrays for mass production is mold stamping machined surface. Jia and Zhou (2012) revealed the relationship be­
technology, e.g., roll-to-roll embossing. The quality of microstructure tween the diamond tool wear and the surface roughness, and they
arrays thus directly depends on the surface accuracy of the mold because declared that the surface roughness degeneration is heavily dependent
the profile error of the mold is directly copied to the functional micro­ on the diamond tool wear. Their investigation suggested that the
structure surface. Microstructured molds are usually machined with a roughness of the microstructure surface machined with a worn diamond
micro diamond tool on an ultraprecision machine tool by utilizing slow tool is badly damaged, resulting in degradation of the predesigned
tool servo (STS) (Kong et al., 2016) or fast tool servo (FTS) (Lu et al., function of the microstructure arrays. Apart from the influences on the
2014) technology. The quality of the microstructured mold is deter­ finished surface quality, serious tool wear leads to numerous negative
mined by two aspects, i.e., the accuracy of the machine tool and the effects during the machining operation. Yan et al. (2003) reported some
diamond tool edge. Currently, the normal accuracy of a commercial observations on the diamond tool wear in the ultraprecision machining
ultraprecision machine tool can easily reach the nanometer level; of single-crystal silicon. They claimed that the diamond tool wear raised
therefore, the quality of microstructured molds is mainly dominated by the cutting forces and force ratio, and induced transition of material
the profile accuracy and wear resistance of the micro diamond tool edge. removal mechanism from ductile to brittle. Nether the raising forces nor
Wu et al. (2019) examined the effect of diamond tool wear on the surface

* Corresponding authors.
E-mail addresses: liuhzhit@gmail.com (H. Liu), zongwenjun@hit.edu.cn (W. Zong).

https://doi.org/10.1016/j.jmatprotec.2022.117600
Received 14 March 2022; Accepted 10 April 2022
Available online 14 April 2022
0924-0136/© 2022 Elsevier B.V. All rights reserved.
H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Nomenclature x7N, y7N, z7N coordinate components in x-, y-, z-axis of the point P7N
converted from the region VII to region N (N = III, IV, V, VI)
c coefficient reflecting to the relation of minimum cutting α tool flank angle
thickness to rounded cutting edge radius β tool nose opening angle
dmct minimum cutting thickness γ tool rake angle
duct uncut chip thickness η1, 2, 3 weight coefficients of the {100}, {110}, {111} crystal facet
rn rounded cutting edge radius strength
rn_0, _10, _20, _30 cutting edge radii of the fresh tool, and used tool with θ angle used to describe the point position in the direction of
cutting distance of 10 km, 20 km, and 30 km round tool nose profile
rε tool corner radius θcts comprehensive tool strength
xP, yP, zP coordinate components in x-, y-, z-axis of a random point P λ1, 2, 3 weight coefficients of the cutting edge, rake face and flank
xi1, yi1, zi1 coordinate components in x-, y-, z-axis of the converted face strength
point Pi1 in region I (i = 1, 2, 3, 4, 5, 6, 7) μ friction coefficient between the micro diamond tool and
Fc nominal cutting force composed of the cutting force and the workpiece
frictional force on the rake face σP cutting edge strength at a random point P
Ff resultant force of the thrust force and frictional force on the σ d(θ, φ) function of cutting edge strength
flank face σ {100}, {110}, {111} diamond strengths of the {100}, {110}, {111}
Fr resultant force of the cutting force and frictional force on crystal facet
the rake face σ e, r, f average strengths of the cutting edge, rake face and flank
Ft thrust force on the flank face face
Fcr cutting force on the rake face φ generating angle used to describe the point position in the
ff frictional force between the flank face the machined direction of cutting edge rounding
surface φc critical angle of φ in the case of duct = dmct
fr frictional force between the chip and the rake face ω an angle used to denote the cutting direction
xPM, yPM, zPM coordinate components in x-, y-, z-axis of the cutting ω0 correction angle between the < 111 > crystal orientation
direction vector PM at the point P on the cutting edge and the cutting direction
xP′ M′ , yP′ M′ , zP′ M′ coordinate components in x-, y-, z-axis of the Δrn_10, _20, _30 cutting edge radius increments of the micro diamond
modified cutting direction vector P′M′ reflecting the chip tool after used with the first, second and third 10 km
flow direction along the cutting edge cutting distance

transition of cutting mode are conducive to the improvement of surface restraining diamond tool wear by modifying the surface of AISI 4140 die
quality. Subsequently, Mir et al. (2016) further studied the influence steel with plasma nitriding treatment and realized the ultraprecision
mechanism of diamond tool wear on the transition of cutting mode by machining of die steel. This method can only be limited to a small
utilizing a numerical simulation method, and their results showed that amount of materials, because most materials are hardly to obtain a
the location of maximum failure stress gradually displaced from the satisfactory machinability via surface modification. Zhang et al. (2019)
main cutting edge towards the machined surface, resulting in the tran­ disclosed the influence mechanism of oxygen on diamond tool wear and
sition of cutting mode. The findings suggest that the machined surface proposed an oxygen-shielded cutting method, and the experiments
quality and cutting mode are mainly dominant by the diamond tool showed that diamond tool wear is effectively alleviated in an oxygen
flank wear. Ge et al. (2010) found that the material plastic side flow was free condition. Their method enriched the means to inhibit diamond tool
so severe due to the diamond tool wear that an obvious material flow wear in ultraprecision machining. Recently, Wang et al. (2021a) re­
vestige remained on the machined surface in ultraprecision turning. The ported a novel method of multi-axis ultrasonic vibration to control the
residual material on the finished surface seriously reduces the surface effective cutting edge radius, and they claimed that the effective radius
quality. Zhang et al. (2016) studied the relationships of diamond tool could be reduced. Their method weakens the negative influence of
wear to cutting mechanics, chip formation, and surface quality in ul­ diamond tool wear on the machined surface quality, to a certain extent.
traprecision machining, and they observed that many burrs formed on All the above approaches and others (Wang et al., 2011a; Yip et al.,
the machined surface. The formation mechanism of the burrs may be 2017), which should be classified as indirect methods, restrain tool wear
cause by plowing effect and plastic side flow due to the diamond tool by changing the cutting conditions or cutting mode.
wear and blunt cutting edge. At present, several direct methods have been attempted to extend the
Compared with a diamond tool with a large nose radius, the cutting tool life purely based on diamond tools, i.e., changing the tool material
performance of a micro diamond tool decreases more obviously in properties to restrain tool wear. For instance, Lee et al. (2019) applied a
machining microstructure arrays because the engaged length of the focused ion beam (FIB) to implant Ga ions into a diamond tool to opti­
cutting edge is very limited and rapidly wears. Tool wear has to be mize its cutting performance, and their calorimetric tests showed that
strictly restrained for micro diamond tools to achieve a satisfactory the activation energy of graphitization increased by more than 40%.
quality of the microstructure surface. Restraining tool wear to extend Micromachining experiments indicated that the reduction of friction and
tool life is an eternal topic in ultraprecision machining, and conse­ heat generation at the tool-chip interface prolonged the tool life. Addi­
quently, multifarious suppression approaches and techniques have been tionally, to improve the cutting performance of a diamond tool, Kawa­
developed. For instance, Bagherzadeh and Budak (2018) proposed a segi et al. (2017) carved microgrooves with a depth of 43 nm and a
new cryogenic cooling approach to inhibit tool wear by obtaining an width of 1.8 µm on the diamond tool rake face by utilizing FIB followed
ultralow temperature in turning of Ti6Al4V and Inconel 718, and they by heat treatment. They declared, based on the experiments, that the
achieved a good effect in restraining tool wear. However, their approach microgrooves are capable of reducing the frictional force between the
cannot extend to the ultraprecision machining which must be operated diamond tool and chips, cutting force, and temperature, all of which are
in a thermostatic chamber, because the cryogenic coolant breaks the beneficial for improvement of wear resistance. Recently, Wang et al.
stability of temperature. Wang et al. (2011b) achieved the goal of (2021b) reported that the friction coefficients decreased to different

2
H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Fig. 1. Enlarged schematics for the cutting edge of the diamond tool in the ultraprecision machining process: (a) ultraprecision machining process; (b) sectional view
of micro diamond tool in xoz plane; (c) sectional view of micro diamond tool in yoz plane.

diamond tool wear resistance is dependent on the crystal facets and

orientations while they conducted turning experiments of silicon. They
speculated that the dependence might be caused by the different
microstrengths and graphitization of diamond along different crystal
orientations, but they failed to give strong evidence or detailed analysis.
On this basis, Zong et al. (2010) established a semiquantitative model to
evaluate the wear resistance of diamond tools with different crystal
facets by means of the mechanical microstrength of diamond crystal.
Although their model could be used to explain why diamond tool wear
resistance depends on the arrangement of crystal facets, their semi­
quantitative model still has the following deficiencies: (1) the model
idealized the actual cutting edge as an infinitely sharp edge, but
recently, more experiments have authenticated that the interaction be­
tween the cutting edge and workpiece is so intricate that the cutting
edge radius cannot be ignored in discussing the tool wear or material
removal mechanism; (2) the ultraprecision machining process is usually
at the micrometer or even nanometer scale, resulting in diamond tool
wear being limited to the cutting edge, which means that diamond tool
Fig. 2. Modeling coordinate system for the cutting edge strength of the
failure is mainly caused by edge passivation rather than by serious wear
Aγ{110}Aα{100} micro diamond tool.
of rake and flank faces; and (3) due to the above idealization, variable
direction of the chip flow around the cutting edge is indistinguishable,
which is equivalent to ignoring the anisotropy of diamond at the cutting
degrees when they performed ultraprecision machining experiments edge, leading to a reduction of the model accuracy. Hence, to compen­
using diamond tools with microtextures fabricated by a femtosecond sate for the shortcomings, a quantitative model of the 3D spatial dis­
laser on rake faces. Their experimental results showed that the micro­ tribution of the cutting edge strength of micro diamond tools during the
textures shift the crater wear further from the cutting edge, preventing ultraprecision and micro machining processes is deduced in the present
the diamond tool from early edge chipping wear. work. As a significantly supplementary model, it extends the previous
Grillo et al. (2000) investigated the wear resistance of diamond model (Liu and Zong, 2022) used in the micro diamond tool fabrication
crystals in different orientations and reported that the wear resistance to the machining process, providing a guidance for diamond tool design
heavily depends on the crystal facets and orientations. Their findings in terms of cutting edge sharpness and waviness. The mechanism of tool
mean that tool wear resistance may be effectively improved by making wear resistance depending on crystal facets and orientations is quanti­
full use of the connatural anisotropy of diamond crystals. Furthermore, tatively disclosed based on the established model. According to the
Ge et al. (2010) examined the different wear resistances of diamond theoretical and experimental results, an optimized combination of
tools in ultraprecision turning of SiCp/2009Al matrix composite. Based crystal facets and orientations is recommended for the design of micro
on the wear morphologies and Raman spectra measurement, they diamond tools to improve the wear resistance and cutting performance
believed that graphitization wear was more likely to occur on a diamond through a direct method.
tool with the both rake and flank faces oriented on the {110} crystal
plane than that with a flank face along the {110} plane and rake face 2. Modeling of the cutting edge strength of micro diamond tools
along the {100} plane. Nevertheless, their experiments seemed to applied in micromachining
indicate that the former has a more resistant of the chipping wear than
the latter. Subsequently, Goel et al. (2012) investigated the influence of As mentioned above, the diamond tool edge is naturally formed with
diamond tools with different orientations on the cutting forces in the a round transition zone instead of perfect sharpness at the nanoscale, as
ultraprecision turning of single crystal silicon by utilizing molecular exaggeratedly shown in Fig. 1. Considering the anisotropy of diamond,
dynamics simulation. The simulation results showed that the thrust the strength of each point on the cutting edge varies, and the cutting
forces with the cubic orientation of the diamond tool was lower than edge of the micro diamond tool is regarded as an envelope surface
that with the dodecahedral orientation of the diamond tool, based on formed by a range of diamond microspheres arranged with different
which they concluded that the cubic orientation tool was highly wear orientations, corresponding to various edge strengths.
resistant than the dodecahedral orientation tool. However, more atten­
tion was paid to the changes of silicon in their work instead of an
in-depth analyses of the relationships between the diamond tool wear
resistance and crystal orientations. Uddin et al. (2004) also found that

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Fig. 3. Algorithm flowchart of calculating the cutting edge strength for micro diamond tools.

2.1. Cutting edge strength model of the Aγ{110}Aα{100}1micro diamond where σ {100}, σ {110}, and σ {111} are the strength of the {100}, {110}, and
tool {111} crystal facets; η1, η2, and η3 are the coefficients for characterizing
the contributions of the three crystal facets to the cutting edge strength
The cutting edge strength of each point is related to not only its at point P; ω is the angle of the cutting direction at point P; and ω0 is a
position but the orientation combination of micro diamond tool, and correction angle between the cutting direction and < 111 > crystal
during the machining process, the cutting direction of each point is also orientation. The five parameters are all functions of the coordinates of
determined by its position. Therefore, a tool coordinate system is point P, which exactly reflects the strength anisotropy of the cutting
established to describe the position of each point at the cutting edge, as edge.
configured in Fig. 2. For convenience of the modeling procedure, the In the coordinate system in Fig. 2, the coordinates of random point P
tool coordinate system is fixed in a spherical diamond crystal with a can be written as
radius of unit one. The rake face and flank face of the micro diamond ⎧ /√̅̅̅
tool in Fig. 2 are oriented on the (110) facet and (001) facet, respec­ ⎪
⎨ xP = (cos φ + sin φ sin θ)/ 2
⎪
tively. Seven regions are defined to facilitate the following description of √̅̅̅ (2)
⌢ ⎪ yP = (cos φ − sin φ sin θ) 2
the modeling process: (1) the area surrounded by the blue arcs of AB , ⎪
⎩
zP = sin φ cos θ
⌢ ⌢ ⌢ ⌢
BC and CA is designated region I; (2) the area surrounded by AE , EC
⌢
and CA is designated region II; (3) the area surrounded by EC , CG and
⌢ ⌢ where θ is an angle defined to determine the position of point P along the
⌢ ⌢ ⌢ ⌢ cutting edge direction, representing the angle GOI in Fig. 2, with θ being
GE is designated region III; (4) the area surrounded by GE , EJ and JG is in the range of –β/2 ≤ θ ≤ β/2, where β is the opening angle; φ is an
⌢ ⌢ ⌢
designated region IV; (5) the area surrounded by AE , EJ and JA is angle defined to determine the position of point P along the sharpness
designated region V; (6) the area surrounded by AL , LJ and JA is
⌢ ⌢ ⌢
direction, representing the angle BOP in Fig. 2, with φ being in the range
⌢ ⌢ ⌢ of –γ ≤ φ ≤ π/2 + α, where γ and α are the rake angle and clearance
designated region VI; and (7) the area surrounded by LG , GT , TN and
⌢ ⌢
angle, as dimensioned in Fig. 1(b).
NL is designated region VII. The green arc BPI represents a random The cutting direction at point P is along the vector PM, whose co­
profile of the cutting edge, and a random point P lies on the profile. If ordinates are denoted by
point P falls in region I, then the corresponding cutting edge strength is ⎧
expressed by (Liu and Zong, 2022) ⎨ xPM = (cos φ sin θ − sin φ)/(cos φ sin θ + sin φ)
⎪
σ {100} ⋅η1 σ {110} ⋅η2 σ{111} ⋅η3
yPM = − 1
√̅̅̅ / (3)
⎪
σP = ( )2 + ( )2 + ( ( ))2 (1) ⎩ zPM = 2 cos φ cos θ (cos φ sin θ + sin φ)
7
+ 183 cos 4ω 18
+ 10 cos 2ω 5
+ 34 cos 3 ω − ω0
Fig. 2 shows that regions I ~ VII are the same in area and shape, but
18 35 35 4

they are along different directions in the coordinate system. The corre­
sponding crystal facets of these regions are equivalent to each other
1 owing to the high symmetry of the diamond crystal, and their me­
Aγ{110}Aα{100} means that the rake face and flank face of the diamond
chanical properties are similar (Huang et al., 2018). Hence, the cutting
tool are oriented on octahedral and cubic facets, respectively.

4
H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Table 1 vector Pi1Mi1 are listed in Table 1.

Coordinates of point Pi1 and vector Pi1Mi1. Due to region VII being composed of four incomplete curved tri­
Region Component Coordinates of Coordinates of vector Pi1Mi1 angles, the procedure of conversion from region VII to region I is rela­
point Pi1 tively complicated compared with other regions, as the algorithm
I x (cos φ sin θ − sin φ)/(cos φ sin θ + flowchart illustrates in Fig. 3. If point P and vector PM are located in
(cos φ +
√̅̅̅
sin φ sin θ)/ 2 sin φ) region VII, then they are converted as point P7N and vector P7NM7N in
y (cos φ − -1 region N (N = 3, 4, 5, 6), followed by the conversion from region N to
region I, repeating the conversion procedures of regions III ~ VI until the
√̅̅̅
sin φ sin θ)/ 2
√̅̅̅
z sin φ cos θ 2 cos φ cos θ/(cos φ sin θ + coordinates are converted to region I to calculate the strength of the
sin φ) cutting edge in region VII. The coordinates of point P7N and vector
II x
P7NM7N are given by
(cos φ + (cos φ sin θ − sin φ)/(cos φ sin θ +
√̅̅̅
sin φ sin θ)/ 2 sin φ)
⎧
√̅̅̅ /√̅̅̅
y sin φ cos θ 2 cos φ cos θ/(cos φ sin θ + ⎪
sin φ)
⎨ x7N = (sin φ sin θ − cos φ) / 2
⎪
z (cos φ − -1 y7N = − (cos φ + sin φ sin θ)
√̅̅̅
2 (4)
√̅̅̅ ⎪
⎪
sin φ sin θ)/ 2 ⎩
√̅̅̅ z7N = sin φ cos θ
III x sin φ cos θ 2 cos φ cos θ/(cos φ sin θ +
sin φ) ⎧
⎪
y (cos φ + (cos φ sin θ − sin φ)/(cos φ sin θ + ⎨ xP7N M7N = 1
⎪
(5)
√̅̅̅ yP7N M7N = (sin φ − cos φ/
sin θ)/(cos φ sin θ + sin φ)
sin φ sin θ)/ 2 sin φ)
√̅̅̅
⎪
z (cos φ − -1 ⎪
⎩ zP7N M7N = 2 cos φ cos θ (cos φ sin θ + sin φ)
√̅̅̅
sin φ sin θ)/ 2
√̅̅̅
IV x sin φ cos θ 2 cos φ cos θ/(cos φ sin θ + The parameter values of ω, ω0, η1, η2, and η3 can be obtained by
sin φ)
substituting the coordinates expressed by Eqs. (4) and (5) and those
y (cos φ sin θ − sin φ)/(cos φ sin θ +
listed in Table 1 into the relevant formulae in the previous work (Liu and
(cos φ +
√̅̅̅
sin φ sin θ)/ 2 sin φ)
z (sin φ sin θ − 1 Zong, 2022).
√̅̅̅
cos φ)/ 2 It should be emphasized that the above cutting edge strength model
V x (cos φ + (cos φ sin θ − sin φ)/(cos φ sin θ + is developed under the assumption that the uncut chip thickness (duct) is
less than the minimum cutting thickness (dmct), and all the material of
√̅̅̅
sin φ sin θ)/ 2 sin φ)
√̅̅̅
y sin φ cos θ 2 cos φ cos θ/(cos φ sin θ + the uncut chip layer flows along the flank face, forming a machined
sin φ) surface. However, duct must be greater than dmct (Yuan et al., 1996)
z 1
(sin φ sin θ −
√̅̅̅ during the actual machining process owing to the existence of cutting
cos φ)/ 2
VI x (cos φ sin θ − sin φ)/(cos φ sin θ +
edge radius; otherwise, no chips form. Meanwhile, the machining pro­
(cos φ +
√̅̅̅ cess degenerates into plowing and friction (Waldorf et al., 1998). In the
sin φ sin θ)/ 2 sin φ)
y (sin φ sin θ − 1 case of duct > dmct in ultraprecision machining, the chip flow direction
√̅̅̅
cos φ)/ 2 along the cutting edge is different due to the existence of a cutting edge
radius, which means that the direction of friction on the chips and the
√̅̅̅
z sin φ cos θ 2 cos φ cos θ/(cos φ sin θ +
sin φ) machined surface is distinct at each point of the cutting edge. Therefore,
the established model needs to be modified for the case of duct > dmct.
The interaction mechanism between the micro diamond tool and
workpiece is pictorially demonstrated in Fig. 4.
The material located above point A in Fig. 4, corresponding to the
condition of φ < φc, clearly flows along the cutting edge to the rake face,
forming chips removed from the substrate during the ultraprecision
machining process. In contrast, the material located below point A,
corresponding to the other condition of φ > φc, is squeezed by the cut­
ting edge and flank face, forming a machined surface. The critical angle
φc depends on the minimum cutting thickness dmct and cutting edge
radius rn, and the relation function among them is described by
( )
dmct
φc = arcsin 1 − (6)
rn
In ultraprecision machining, the minimum cutting thickness is uni­
versally acknowledged to be proportional to the cutting edge radius, as
formulized by
dmct = crn (7)

Fig. 4. Schematic diagram of the interaction between the diamond tool and where c is a proportional coefficient generally ranging from 0.2 to 0.4
workpiece in ultraprecision cutting. (Yuan et al., 1996), related to the workpiece material.
Substituting Eq. (6) into Eq. (7), the calculated critical angle φc is
edge strength in each region can be converted to that in a certain region ranging from 36.9◦ to 53.1◦ . That is, in the region of φ > φc, the flow
for convenience of calculation, and in this work, the calculation of the direction of the material forming the machined surface is along the
cutting edge strength is performed in region I. The algorithm flowchart prescribed direction in Fig. 2, and the model is suitable for this case;
for converting other regions to region I is illustrated in Fig. 3. however, in the region of φ < φc, the chip flow direction is opposite to
According to the conversion procedures in Fig. 3, the original point P the prescribed direction in Fig. 2, and the model needs to be modified.
and vector PM in regions I ~ VI are converted to their corresponding The difference between this case and the original model is the chip flow
point Pi1 and vector Pi1Mi1 in region I. The coordinates of point Pi1 and direction. Consequently, the model can be utilized in the case of φ < φc

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

case of c = 0.35).
As a result of the intrinsic anisotropy of diamond, the cutting edge
strength of the micro diamond tool strongly varies with the coordinates,
as shown in Fig. 5, and the maximum strength of 27.9 GPa is 21.5 times
larger than the minimum strength of 1.3 GPa. On the whole, the cutting
edge strength on the flank face, i.e., corresponding to the region of
φ > 90◦ , is larger than that on the rake face, i.e., corresponding to the
region of φ < 90◦ , and the difference in the cutting edge strength on the
flank face is relatively inconspicuous compared with that on the rake
face. The cutting edge strength in the region around θ = 0◦ , φ = 35.5◦ ,
which represents the {111} crystal facet, reaches the maximum. Inter­
estingly, the strength distributes in a symmetrical triangular star shape
in this region, coinciding well with the characteristics of the {111}
crystal facet. Fig. 5 shows that the cutting edge strength presents a
fourfold symmetric distribution in the region around θ = 0◦ , φ = 90◦
Fig. 5. Cutting edge strength distribution of the Aγ{110}Aα{100} micro dia­ because the facet at this point belongs to the {100} crystal facet group,
mond tool (γ = 0◦ , α = 10◦ ). which is a fourfold symmetrical facet group. In addition, the cutting
direction at θ = 0◦ , φ = 90◦ along the (001)[110]crystal orientation,
classified into the {100}< 110 > group, is a ‘hard’ direction to wear,
and consequently, the predicted cutting edge strength is much larger
than that of other regions.

2.2. Cutting edge strength model of the Aγ{110}Aα{110}2micro diamond

tool

The cutting edge of the Aγ{110}Aα{110} micro diamond tool is

closely related to that of Aγ{110}Aα{100} in terms of the crystal
orientation combination, as illustrated in Fig. 6. The Aγ{110}Aα{110}
micro diamond tool can be effortlessly obtained only by rotating the
cutting edge of the Aγ{110}Aα{100} micro diamond tool 90◦
counterclockwise.
Fig. 6. Spatial relation of the Aγ{110}Aα{100} to Aγ{110}Aα{110} cutting
tools in a diamond crystal. If the round cutting edge is extended to a whole circumference, then
the cutting edge of the Aγ{110}Aα{110} diamond tool can also be
regarded as a part of the cutting edge of the Aγ{110}Aα{100} diamond
tool. Therefore, the calculation method described in Section 2.1 is
suitable for determining the cutting edge strength of the Aγ{110}
Aα{110} micro diamond tool as long as the value range of θ is limited to
the interval of [− 120◦ , − 60◦ ]. The cutting edge strength of the Aγ{110}
Aα{110} micro diamond tool with the same geometric parameters as the
Aγ{110}Aα{100} micro diamond tool is calculated with the above
model, and the strength distribution nephogram is shown in Fig. 7 (in
the case of c = 0.35).
Similar to the Aγ{110}Aα{100} micro diamond tool, the strength of
each point on the Aγ{110}Aα{110} cutting edge also varies, and the
maximum value of 17.65 GPa is approximately 6.7 times greater than
the minimum value of 2.65 GPa. As shown in Fig. 7, the strength dis­
tribution nephogram also presents a fourfold symmetrical characteristic
in the region surrounding the point of θ = 0◦ , φ = 90◦ , corresponding to
point L in Fig. 2, which corresponds well to the four symmetrical regions
Fig. 7. Cutting edge strength distribution of the Aγ{110}Aα{110} micro dia­ intersecting at point L. The cutting directions at the two points of θ = 0◦ ,
mond tool (γ = 0◦ , α = 10◦ ). φ = 0◦ and θ = 0◦ , φ = 90◦ are along the(110)[110]and(110)[110]crystal
orientations, respectively, both of which belong to the {110}<
as long as the vector PM is modified as P′M′, whose coordinates are 110 > orientation group of diamond crystal, another ‘hard’ direction to
modified as wear. The cutting edge strength, approximately 17.0 GPa, in both re­
⎧ gions near the two points is obviously greater than that in other regions
⎪ sin φ − cos φ sin θ except for the regions surrounding the two points of θ = ± 30◦ , φ = 0◦ .
⎪ xP′ M′ = cos φ sin θ + sin φ
⎪
⎪
⎪
⎨ Note that the maximum strength of the Aγ{110}Aα{100} micro diamond
yP′ M′ = 1 (8) tool cutting edge is achieved at the two points θ = ± 30◦ , φ = 0◦ because
⎪
⎪
⎪
⎪
√̅̅̅
2 cos φ cos θ the two points are approaching the {111} crystal facet and only shifted
⎪
⎩ z P′ M ′ = −
cos φ sin θ + sin φ 5.26◦ along the θ direction. The strength at the two points is dominated
by the {111} facet strength, which is much larger than those of the other
The cutting edge strength of the Aγ{110}Aα{100} micro diamond
tool with an opening angle of 60◦ (from − 30◦ to 30◦ ), a rake angle of
0◦ and a clearance angle of 10◦ , can be obtained by the modified model, 2
Aγ{110}Aα{110} means that both the rake face and flank face of the micro
and the strength distribution nephogram is presented in Fig. 5 (in the diamond tool are oriented on the dodecahedral facet.

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Fig. 8. Cutting edge strength distribution of the micro diamond tools (γ = 0◦ , α = 10◦ ): (a) Aγ{100}Aα{100}; (b) Aγ{100}Aα{110}.

facet groups (Zong et al., 2010), resulting in a larger cutting edge

strength at both points.

2.3. Cutting edge strength model of the Aγ{100}Aα{100} and Aγ{100}

Aα{110}3 micro diamond tools

Without regard to the chip flow direction, the cutting direction of the
Aγ{100}Aα{100} and Aγ{100}Aα{110} micro diamond tools is the same
as the polishing direction during the tool fabrication process. The cut­
ting edge strength of both orientation micro diamond tools along the Fig. 9. Division diagram of the micro diamond tool working area.
cutting direction is equivalent to the strength during the polishing
process. However, considering the chip flow direction, as discussed in
Section 2.1, the unwanted material located above point A in Fig. 4 flows group of diamond, another ‘hard’ direction to wear, and along the (110)
along the rake face, forming the chip to be removed. At this moment, the [001] crystal orientation belonging to the {110}< 100 > crystal orien­
direction of friction on the cutting edge is opposite to that during the tation group of diamond, another ‘soft’ direction to wear. Notably, the
polishing process. Consequently, the cutting edge strength of the cutting edge strength of Aγ{100}Aα{110} is extremely weak in the re­
Aγ{100}Aα{100} and Aγ{100}Aα{110} micro diamond tools in the cut­ gion of φ > 75◦ , which is unfavorable for improving the tool wear
ting process can be deduced directly from the cutting edge strength resistance.
model established for the polishing process by modifying the friction
direction on the cutting edge above point A (i.e., in the case of φ < φc). 2.4. Comparative analysis of the wear resistance of the four types of micro
That is, the polishing angle ω in the previous strength model (Liu and diamond tools
Zong, 2022) is replaced by ω + π. The cutting edge strength of the
Aγ{100}Aα{100} and Aγ{100}Aα{110} micro diamond tools in the cut­ The cutting edge strength distributions of the micro diamond tools
ting process is depicted in Fig. 8 (in the case of c = 0.35). with the four types of crystal orientation combinations are calculated
Fig. 8 clearly depicts the change in the strength at each point on the according to the as-established theoretical model in Section 2.1–2.3 (For
cutting edge and the cutting edge strength anisotropy of the Aγ{100} the convenience of description, the four types of Aγ{110}Aα{100},
Aα{100} and Aγ{100}Aα{110} micro diamond tools. The maximum Aγ{110}Aα{110}, Aγ{100}Aα{100}, and Aγ{100}Aα{110} micro dia­
strength of the two cutting edges is 17.05 GPa and 27.09 GPa. The mond tools are denoted T1, T2, T3, and T4, respectively, in the following
minimum strength of the two cutting edges is 1.85 GPa and 1.30 GPa. discussion.). A comparative analysis of the wear resistances of the micro
The Aγ{100}Aα{100} micro diamond tool achieves the maximum diamond tools is performed based on the above theoretical cutting edge
strength at θ = 0◦ , φ = 45◦ as a result of the cutting direction being strengths in this section. For the sake of comprehensive evaluation of the
along the (101)[101] crystal orientation, which belongs to the {110}< tool wear resistance, the working area of the micro diamond tools is
110 > crystal orientation group of diamond, a ‘hard’ direction to wear. divided into three parts: cutting edge, rake face and flank face, as
The minimum cutting edge strength is achieved near the regions of illustrated in Fig. 9.
θ = ± 30◦ , φ = 90◦ , which can be explained by the cutting direction Figs. 1 and 9 clearly show that the cutting edge profile in the case of
being almost along the (110)[001] and (110)[001]crystal orientations. φ = 0◦ is the dividing line between the cutting edge and rake face, which
Both crystal orientations belong to the {110}< 100 > crystal orienta­ means that this profile belongs to both the cutting edge and rake face in
tion group of diamond, a ‘soft’ direction to wear. For the Aγ{100} geometry. Hence, the cutting edge strength on the profile in the case of
Aα{110} micro diamond tool, the maximum and minimum cutting edge φ = 0◦ is the rake face strength in theory. Likewise, the cutting edge
strengths are achieved at θ = 0◦ , φ = 0◦ and θ = 0◦ , φ = 90◦ , respec­ profile in the case of φ = 100◦ is the dividing line between the cutting
tively. The corresponding cutting directions are along the (001)[110] edge and flank face, and the cutting edge strength on the profile at
crystal orientation belonging to the {100}< 110 > crystal orientation φ = 100◦ is also the flank face strength.
The comprehensive tool strength of the working area in the
machining process is pictorially presented in Fig. 10. Fig. 10 (b) and (c)
3
Aγ{100}Aα{100} means that both the rake face and flank face of the dia­ suggest that the value range of the cutting edge strength of the T2 micro
mond tool are oriented on the cubic facet; Aγ{100}Aα{110} means that the rake diamond tool has an inconspicuous difference from that of the T3 micro
face and flank face of the diamond tool are oriented on cubic and dodecahedral diamond tool, both of which range from approximately 1.85 GPa to
facets, respectively. 17.65 GPa. In contrast, the cutting edge strength distributions vary

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Fig. 10. Strength distribution in the micro diamond tool working area with different orientations: (a) T1 tool; (b) T2 tool; (c) T3 tool; (d) T4 tool (γ = 0◦ , α = 10◦ , c
= 0.35).

enormously, the reason for which has been analyzed in Sections 2.2 and resistance of the T4 micro diamond tool rake face than that of the T1
2.3. It should be emphasized that the strength of the T2 micro diamond micro diamond tool rake face. In contrast, the strength of the T4 micro
tool flank face is much greater than that of the T3 micro diamond tool diamond tool flank face is much lower than that of the T1 micro dia­
flank face. From this point, the T2 micro diamond tool should have a mond tool flank face, resulting in poorer wear resistance of the T4 micro
better wear resistance than the T3 micro diamond tool. diamond tool flank face compared with the T1 micro diamond tool flank
Comparing Fig. 10 (a) and (d), both the maximum and minimum face.
strengths of the T1 micro diamond tool are the same as those of the T4 Similarly, according to Fig. 10 (c) and (d), the T3 micro diamond tool
micro diamond tool, but the strength of the former in most of the cutting has better wear resistance than the T4 micro diamond tool in terms of
edge region is relatively large, which may be beneficial for keeping the the flank face strength, but the rake face of the T4 micro diamond tool is
cutting edge sharp for a long time. The higher strength of the T4 micro more wear resistant than that of the T3 micro diamond tool in terms of
diamond tool is mainly concentrated in the middle of the rake face. The the rake face strength.
strength of the T4 micro diamond tool rake face is much higher than that Unlike the T1 micro diamond tool, the weak strength of the T2 micro
of the T1 micro diamond tool rake face, resulting in a better wear diamond tool cutting edge presents a convergent distribution, i.e., the
symmetrical triangular blue region shown in Fig. 10 (b). The cutting
edge strength of the former is slightly higher than that of the latter,
meaning that the former has better wear resistance only in terms of the
cutting edge strength, but the rake face strength of the former is far
weaker than that of the latter, resulting in much poorer wear resistance
of the rake face. For the flank face strength, both are equivalent. Overall,
the strength of the T2 micro diamond tool is relatively more uniform
than that of the T1 micro diamond tool, which means that the T2 micro
diamond tool has more uniform wear resistance.
In light of the above analyses, a significant difference obviously ex

Table 2
Cutting edge, rake face and flank face strengths and comprehensive tool strength
of micro diamond tools.
Tool serial σe [GPa] σr [GPa] σf [GPa] σcts [GPa]
T1 9.99 ~ 10.27 3.53 14.20 9.66 ~ 9.83
T2 9.45 ~ 9.78 12.30 14.52 11.09 ~ 11.26
T3 8.70 ~ 9.20 6.82 5.09 7.81 ~ 8.14
Fig. 11. Force diagram of the micro diamond tool for machining a micro­
T4 8.30 ~ 8.85 13.60 2.49 8.41 ~ 9.70
structure array.

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Table 3 face and flank face, respectively, and it should be noted that σ e maybe
The geometric and machining parameters of the sinusoidal grid array. varies with the change of coefficient c for the different workpiece ma­
Wavelength Amplitude Feed Max cutting Arc length of two terials; λ1, λ2 and λ3 are the weight coefficients of the cutting edge, rake
rate depth adjacent points face and flank face strengths, respectively; and σ d(θ, φ) is a function to
100 µm 1 µm 3 µm/r 5 µm 1 µm describe the relationship between the cutting edge strength and point
coordinates. Specifically, σd(θ, -γ) and σ d(θ, α + 90◦ ) are the unary
functions degenerated from σ d(θ, φ) in the cases of φ = -γ and
ists not only in the strength value but also in the strength distribution φ = α + 90◦ , describing the strength on the cutting edge boundary
among the micro diamond tools with different crystal orientation com­ profiles.
binations as a result of diamond crystal anisotropy. Such differences The three coefficients to reflect the contributions of the cutting edge,
hinder quantitative comparison of the wear resistance of micro diamond rake face and flank face strengths to the comprehensive tool strength of
tools. To overcome this obstacle, the comprehensive tool strength (σ cts ) the micro diamond tool are defined in Eq. (9-a). Their values are
of the micro diamond tool is defined as assigned based on the contributions of forces applied to the cutting edge,
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ rake face and flank face during the ultraprecision machining processes.
σ cts = λ1 ⋅σ2e + λ2 ⋅σ 2r + λ3 ⋅σ2f (9-a) The comprehensive tool strength is dominated by the cutting edge
strength of the micro diamond tool because the material removal is
∫ ∫
mainly performed by the cutting edge, where the stress state is always
◦
β/2 α+90
1
σe = σ d (θ, φ)dθdφ (9-b) protean. In response to the predominant contribution, λ1 is set to 0.6.
β(α + γ + 90◦ ) − β/2 − γ
Furthermore, an analysis diagram of the forces applied to the rake and
1
∫ β/2 flank faces of the micro diamond tool in machining microstructure ar­
σr = σd (θ, − γ)dθ (9-c) rays is exhibited in Fig. 11. The relationships among them can be
β − β/2
expressed as
∫ β/2 ⎡ ⎤ ⎡ ⎤
1
(9-d) 1 μ [ ]
◦
σf = σ d (θ, α + 90 )dθ Fc
β ⎢ ⎥ ⎢ ⎥ Fcr
− β/2
⎣ Fr ⎦ = ⎢ ⎣ 1 + μ 0 ⎥
⎦ Ft (10)
Ff
where σ e , σ r and σf are the average strengths of the cutting edge, rake 0 1+μ

Fig. 12. Cutting edge topography for the fresh micro diamond tools obtained by AFM: (a) T1 micro diamond tool; (b) T2 micro diamond tool; (c) T3 micro diamond
tool; (d) T4 micro diamond tool (The upper subfigure is the 3D topography result, and the lower subfigure is a 2D cross-sectional profile for each micro dia­
mond tool).

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Fig. 13. Cutting edge topography for the micro diamond tools with different cutting distances: (a)–(c) T1 micro diamond tool with cutting distances of 10 km, 20 km
and 30 km; (d)–(f) T2 micro diamond tool with cutting distances of 10 km, 20 km and 30 km; (g)–(i) T3 micro diamond tool with cutting distances of 10 km, 20 km
and 30 km; (j)–(l) T4 micro diamond tool with cutting distances of 10 km, 20 km and 30 km (The upper subfigure is the 3D topography result, and the lower
subfigure is a 2D cross-sectional profile for each micro diamond tool).

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Table 4 can be attributed to the weak strength of the flank face, and that of the
Radii and radius increments of the micro diamond tool edges. latter can be attributed to the weak strength of the rake face.
Tool rn_0 rn_10 rn_20 rn_30 Δrn_10 Δrn_20 Δrn_30 The above analyses suggest that the comprehensive tool strength
could be applied to characterize the wear resistance of micro diamond
T1 38.2 564.4 ~ 837.3 ~ 1081.2 539.9 269.2 304.1
~ 598.8 855.1 ~ tools with different crystal orientation combinations. A higher value of
41.7 1194.3 the comprehensive tool strength means that the micro diamond tool has
T2 46.8 372.3 ~ 627.7 ~ 873.5 ~ 334.5 251.7 281.8 a higher wear resistance, and vice versa. Moreover, the working area
~ 387.4 640.2 946.4 prone to wear may be predicted based on the three components of the
51.2
T3 52.4 1462.2 1922.8 2886.1 1449.7 557.7 1010.3
comprehensive tool strength.
~ ~ ~ ~
57.5 1533.5 2131.3 3203.7 3. Experiments
T4 59.1 734.8 ~ 988.5 ~ 1479.3 689.3 281.8 498.1
~ 771.1 1101.2 ~
3.1. Experimental equipment and conditions
64.6 1610.2

Notes: The unit of data in the table is nm. rn_0 denotes the radius of the fresh tool; The micro diamond tools used in the experiments were fabricated on
rn_10, rn_20 and rn_30 denote the radii of the tool with cutting distances of 10 km, a PG3B special machine for polishing diamond tools provided by Coborn
20 km and 30 km, respectively; Δrn_10, Δrn_20 and Δrn_30 denote the average
Co., Ltd. The sharpness of the micro diamond tools was measured with
radius increments of the tool after the first, second and third 10 km cutting
an atomic force microscope (AFM) of the NaniteAFM type produced by
distances, respectively. The range of rn_0, rn_10, rn_20 and rn_30 are obtained by five
repeated measurements, and Δrn_10, Δrn_20 and Δrn_30 are calculated with the
Nanosurf Co., Ltd. Topographies of the fresh and worn micro diamond
average of rn_0 rn_10, rn_20 and rn_30. tool noses were obtained by a Scios2 scanning electron microscope
(SEM) made by Thermo Fisher Scientific Brno S.r.o. Cutting experiments
of a sinusoidal grid array were conducted on a homemade 5-axis ultra­
where Fc is the nominal cutting force composed of the cutting force Fcr precision turning-milling compound machine tool. The geometric and
on the rake face and the frictional force f f (in Fig. 11) between the flank machining parameters of the sinusoidal grid array are listed in Table 3.
face and the machined surface; Ft is the thrust force on the flank face; Fr Al6061 alloy, a typical duralumin material of high strength, is selected
is the resultant force of Fcr and the frictional force f r (in Fig. 11) between as the workpiece material because of its good machinability, in order to
the chip and the rake face; and Ff is the resultant force of Ft and the obtain an obvious tool wear compared with the similar materials. The
frictional force f f on the flank face. All of the above forces are vectors. μ topographies of the machined sinusoidal grid arrays were measured
is the friction coefficient between the diamond tool and the workpiece, with a 3D optical profiler of the NewView 9000 type developed by Zygo
which changes with workpiece material, as for the common nonferrous Co., Ltd. All the above experiments were carried out in a constant
material μ ranging from 0.06 to 0.3 (Uegami et al., 1988; Yuan et al., temperature and humidity laboratory.
1992). Zhu et al. (2019) performed an investigation of the cutting forces
in the STS diamond turning of a 2D sinusoidal microstructure. Their 3.2. Results and discussions
experiments showed that the average nominal cutting force and thrust
force were approximately 40 mN and 6 mN. Based on their experimental Four types of micro diamond tools were fabricated, corresponding to
measurements, a theoretical result can be deduced from Eq. (10) that the the micro diamond tools discussed above. All the rake and clearance
resultant force value on the rake face and flank face are in the range of angles were designed to be 0◦ and 10◦ ; the tool nose radius was designed
32.12 mN ~ 37.77 mN and 6.01 mN ~ 6.12 mN, respectively, meaning to be 50 µm. The topographies and cutting edge radii of the fresh tools
⃒ ⃒
that |Fr | > ⃒Ff ⃒ even if μ varies from 0.06 to 0.3. The theoretical results are presented in Fig. 12, which shows that the fresh tool cutting edges
support that the coefficient λ2 should be larger than the coefficient λ3, have a fine uniformity without obvious defects, and the cutting edge
and hence, λ2 and λ3 are set to 0.25 and 0.15, respectively. radii are in the range of 38–65 nm.
Substituting the above parameters into Eqs. (9-a) ~ (9-d), the values
of σ e , σ r , σ f and σcts are calculated for the four types of micro diamond 3.2.1. Cutting edge sharpness of the micro diamond tools with different
tools, and the results are listed in Table 2, in which σ e is evaluated by cutting distances
taking account into the difference of the minimum cutting thickness for To avoid the error introduced by repeat tool installation, a nano­
different workpiece materials, i.e. different values of the coefficient c. duplication method (Li et al., 2003) was applied to duplicate the cutting
The variation of c only changes the position of chip separation point A in edge profile of the fresh tool as well as those after cutting 10 km, 20 km
Fig. 4, but it has no influence on the chip flow direction along the rake and 30 km to monitor the variation in the microdiamond cutting edge
and flank faces. Therefore, σe varies in a certain range and σ r and σf are radius during the machining process. Then, the cutting edge profile was
constant in response to the change of c. However, variation intervals of indirectly obtained by the AFM, as illustrated in Fig. 13, in order to
σ e are very small compared with their values, less than 6.3%, because semi-quantitatively evaluate the cutting edge wear process at different
the change of critical angle φc caused by c is limited. Although the cutting stages. Fig. 13 clearly shows that serious micro-edge collapse
comprehensive tool strength of the four micro diamond tools varies in a was generated with the cutting process of the T3 micro diamond tool;
range because of the variation of σe , as listed in Table 2, the results can however, only slight or inconspicuous micro-edge collapse was gener­
still indicate that the comprehensive tool strength of the T2 micro dia­ ated with the cutting process of the other three micro diamond tools. The
mond tool is the highest among the four types of micro diamond tools, full cutting edge topographies during the cutting process can be found in
supporting that the T2 micro diamond tool has the best comprehensive Supplementary material. Such serious micro-edge collapse results in a
wear resistance among all of them. In contrast, the T3 micro diamond much larger cutting edge radius of the T3 micro diamond tool than that
tool has the weakest comprehensive tool strength and the poorest of the other three micro diamond tools.
comprehensive wear resistance among all of them. The strength of the Fig. 13 intuitively shows that all the cutting edge radii of the micro
T3 micro diamond tool working area has no advantage, and even has a diamond tools increase with increasing cutting distance; that is, the
distinct disadvantage compared with the other three types of micro cutting edge sharpness decreases. The increments of the cutting edge
diamond tools, resulting in poor wear resistance over the whole tool. In radii were calculated at every 10 km cutting distance, as listed in
contrast to the T3 micro diamond tool, the poor wear resistances of the Table 4, to disclose the cutting edge evolution rule of different micro
T4 and T1 micro diamond tools are caused by the weak strength of a diamond tools with cutting distance.
local working area. For instance, the poor wear resistance of the former The results in Table 4 suggest that in the initial cutting stage, the

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Fig. 14. Topographic images of the fresh and worn micro diamond tool noses obtained by SEM: (a)–(d) fresh tool topography for the T1, T2, T3 and T4 micro
diamond tools; (e)–(h) worn tool topography for the T1, T2, T3 and T4 micro diamond tools.

cutting edge radii of the micro diamond tools rapidly increased in polishing process of fresh tools, the phase transformation induced by
response to rapid wear. Then, the cutting edge radii steadily increased, mechanical stress near the tool noses further weakens the cutting edge
and the tool wear turned into a stable wear stage after the cutting dis­ strength (Gogotsi et al., 1999; Grillo and Field, 2003). With the increase
tance reached a certain value, which agrees well with the wear rule of in the cutting edge radius and removal of the phase transformation layer
traditional tools (Vaughn, 1966). These characteristics of cutting edge due to tool wear, the cutting edge strength gradually rose to the diamond
radius variation could be attributed to the insufficient strength of the crystal strength; therefore, the cutting edge radii steadily increased after
fresh cutting edge with an extremely fine radius. In addition, during the the cutting distance reached a certain value.

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Fig. 15. Shapes of microsinusoidal grids machined with different oriented micro diamond tools after cutting different distances: (a)–(d) machined with an T1 micro
diamond tool, (a) cutting with a fresh tool and (b)–(d) for cutting distances of 10 km, 20 km and 30 km; (e)–(h) machined with an T2 micro diamond tool, (e) cutting
with a fresh tool and (f)–(h) for cutting distances of 10 km, 20 km and 30 km; (i)–(l) machined with an T3 micro diamond tool, (i) cutting with a fresh tool and (j)–(l)
for cutting distances of 10 km, 20 km and 30 km; (m)–(p) machined with an T4 micro diamond tool, (m) cutting with a fresh tool and (n)–(p) for cutting distances of
10 km, 20 km and 30 km.

For every additional 10 km of cutting distance, the average radius demonstrated in Fig. 14. Even when magnified 10,000 times with an
increments of the micro diamond tool cutting edges in descending order SEM, the fresh tool cutting edges still retained such excellent sharpness
are T3 > T4 > T1 > T2. However, in terms of only the cutting edge and intact edge profile that no obvious edge defects were observed, as
strengths listed in Table 2, the increments of the micro diamond tool clearly shown in Fig. 14 (a)–(d). Distinguishing the differences among
cutting edges in descending order should be T4 > T3 > T2 > T1, which the four fresh tools from the appearance is difficult. After the cutting
seems to be inconsistent with the conclusions drawn from the experi­ distances reached 30 km, as shown in Fig. 14 (e)–(h), the T3 micro
mental results listed in Table 4. In fact, the increment of the micro diamond tool was worn the most seriously, whereas the T2 micro dia­
diamond tool cutting edge radius is the result of tool wear, and the tool mond tool was worn the least among the four micro diamond tools. The
wear resistance is also related to the rake and flank face strengths in wear degree of the T4 micro diamond tool was slightly greater than that
addition to the cutting edge strength. As listed in Table 2, the cutting of the T1 micro diamond tool, and both of them were within the wear
edge strength of the T2 micro diamond tool in the range of 9.45 ~ range of the T3 and T2 micro diamond tools. The experimental results
9.78 GPa is closed to that of the T1 diamond tool in the range of 9.99 ~ are also consistent with the comprehensive tool strengths of the micro
10.27 GPa, but the rake face strength of the former of 12.30 GPa is diamond tools discussed in Section 2.4.
approximately 3.5 times that of the latter of 3.53 GPa. Likewise, the By further comparing and analyzing the nose wear topographies of
cutting edge strength of the T4 micro diamond tool in the range of 8.30 the four micro diamond tools, the wear regions and characteristics can
~ 8.85 GPa is also close to that of the T3 diamond tool in the range of be found to be distinct from each other. For the T3 micro diamond tool,
8.70 ~ 9.20 GPa, whereas the rake face strength of the former of serious wear occurs not only at the cutting edge but also on the rake and
13.60 GPa is twice that of the latter of 6.82 GPa. Moreover, as analyzed flank faces, in addition to obvious micro-chipping and scratching wear
in Section 2.4, the force acting on the rake face is much larger than that on the rake face, as marked in Fig. 14 (g). The reason for the above
acting on the flank face during the machining process of the sinusoidal phenomenon is the weak strength of the rake face and the largest cutting
grids. Therefore, the rake face strength has a greater influence on the force being loaded on the rake face, as also mentioned in Section 3.2.1.
tool wear resistance than the flank face. Taking the effect of the rake and Compared with the T3 micro diamond tool, no obvious wear marks were
flank face strengths into account, the increment order of the cutting edge observed on the rake face of the T4 micro diamond tool; instead, tool
radius inferred from the theoretical results listed in the last column of wear mainly occurred on the flank face, as shown in Fig. 14 (h), which
Table 2 is well consistent with that observed in the experiments, i.e., the can be easily explained by the strength theory proposed in Section 2.4.
increment of the cutting edge radius is negatively correlated with the In terms of strength, the flank face with a strength of 2.49 GPa is the
comprehensive tool strength. weakest region among the three parts of the working area (cutting edge
strength in the range of 8.30–8.85 GPa and rake face strength of
3.2.2. Wear characteristics of the micro diamond tools 13.60 GPa). In contrast to the T4 micro diamond tool, tool wear marks
The topographies of the fresh and worn micro diamond tool noses are were concentrated on the rake face of the T1 micro diamond tool, and

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Fig. 16. Theoretical and experimental profile shapes of the sinusoidal grid microstructured array machined with micro diamond tools over different cutting dis­
tances: (a)–(d) machined with an T2 micro diamond tool, (a) cutting with a fresh tool, (b) cutting distance of 10 km, (c) cutting distance of 20 km and (d) cutting
distance of 30 km; (e)–(h) machined with an T3 micro diamond tool, (e) cutting with a fresh tool, (f) cutting distance of 10 km, (g) cutting distance of 20 km and (h)
cutting distance of 30 km.

micro-chipping wear was also observed on the rake face, as shown in sharp point corresponds to the narrow area located on both sides of the
Fig. 14 (e). The wear characteristics of the T1 micro diamond tool are symmetry axis in Fig. 10 (b), i.e., the area near θ = 0◦ . In theory, the
caused by the weakest rake face strength compared with the cutting strength of this area is highest at the tool nose, which makes the wear
edge and flank face strengths, as listed in Table 2. For the T2 micro resistance of this region much higher than that of the other regions, and
diamond tool, distinguishing how the tool wear is dominated by which this region wears slowly compared with the near regions. However, the
parts of the working area is difficult due to the sufficiently high strengths symmetrical triangular blue region rapidly wears owing to its weak
of the cutting edge, rake face and flank face, as shown in Fig. 14 (f). strength. Therefore, the wear morphology in Fig. 14 (f) is naturally
There is an exciting result that tool wear at the T2 micro diamond formed because of the different wear rates. That such a detail can be
tool nose is significantly less than that in the other areas such that a predicted so accurately suggests that the spatial distribution model of
sharp point is left, as enclosed by a red circle in Fig. 14 (f). A clear the micro diamond tool edge strength established in the present work
evolution process of the sharp point can be found in the Supplementary has high accuracy and reliability.
material. The wear topography in Fig. 14 (f) is surprisingly similar to the
distribution nephogram shown in Fig. 10 (b). The area surrounding the

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Fig. 17. Profile error of the sinusoidal grids machined with micro diamond tools for different cutting distances: (a) machined with the T2 micro diamond tool; (b)
machined with the T3 micro diamond tool.

Fig. 18. Frequency analysis of the sinusoidal grid surface machined with micro diamond tools over different cutting distances: (a) machined with a T2 micro
diamond tool; (b) machined with a T3 micro diamond tool. (The curves denote the surface machined with a fresh tool, cutting distance of 10 km, cutting distance of
20 km and cutting distance of 30 km from the top downwards. Dashed light blue lines represent the region of main peaks; dashed lines in other colors represent the
cut-off frequencies of the curves in corresponding colors.).

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

3.2.3. Influence of micro diamond tool wear on microstructured arrays reach up to 0.76 µm− 1, 1.02 µm− 1 and 1.23 µm− 1 are obviously smaller
Tool wear inevitably leads to deterioration of machining quality and than the corresponding frequencies of the surface machined with T3
precision. The morphologies of the sinusoidal grid arrays machined at diamond tool, 0.95 µm− 1, 1.5 µm− 1 and 2.03 µm− 1, respectively. The
various cutting distances were analyzed to investigate the influence of slow velocity of frequency increasing suggests that the T2 micro dia­
wear of micro diamond tools with different crystal orientation combi­ mond tools is more durable than the T3 micro diamond tools, which can
nations on the machining quality of the sinusoidal grid arrays. The be supported by the tool topographies in Fig. 14 (f) and (g).
morphologies obtained by the 3D optical profiler are illustrated in
Fig. 15, which intuitively shows that all the surface qualities of the 4. Conclusions
microstructure arrays machined by utilizing the fresh tools are uniform,
and there is no significant difference in the microstructure arrays A 3D spatial strength distribution for micro diamond tool nose
machined by the different tools. As the cutting distance increases, the engaged in machining process was proposed in the present work, and a
surface qualities of the sinusoidal grid arrays machined with different corresponding model of the spatial strength distribution was developed
micro diamond tools decrease to varying degrees. The surface quality of by considering the chip flow direction and the minimum cutting thick­
the sinusoidal grid array machined with the T3 micro diamond tool ness. Relevant verification cutting experiments were designed for the
deteriorates most seriously, as shown in Fig. 15 (i)–(l), while the surface model. The spatial strength and wear resistance of the micro diamond
quality of the sinusoidal grid array machined with the T2 micro diamond tools were analyzed based on the theoretical calculation and experi­
tool deteriorates the least, as shown in Fig. 15 (e)–(h). mental results, according to which several important conclusions can be
Cross-sectional profiles of the machined (blue curves) and designed drawn:
(red curves) sinusoidal grids in Fig. 15 (e)–(l) were extracted, as pre­
sented in Fig. 16, to analyze the machining errors induced by tool wear. (1) The durability of the micro diamond tools with different crystal
The profile curves in Fig. 16 clearly show that the convergence be­ orientation combinations is directly related to the 3D spatial
tween the machined and designed profiles gradually decreases with strength of the micro diamond tool noses.
increasing cutting distance; that is, the profile errors become increas­ (2) The wear position and wear resistance of micro diamond tools
ingly larger as a result of the progressive wear of the micro diamond with different crystal orientation combinations could be pre­
tools. However, note that the error of the profile machined with the T2 dicted by the spatial strength distribution model. The micro
micro diamond tool is significantly smaller than that of the profile diamond tool with an Aγ{100}Aα{100} crystal orientation com­
machined with the T3 micro diamond tool, as shown in Fig. 17. Owing to bination has the weakest wear resistance, and the cutting edge,
the lighter wear of the former than the latter, as comparatively shown in rake face and flank face are prone to wear. The micro diamond
Fig. 14 (f) and (g), the profile convergence of the sinusoidal grids tool with an Aγ{110}Aα{110} crystal orientation combination has
machined with the former tool is still acceptable, except for some high- the strongest wear resistance, and the cutting edge, rake face and
frequency errors, even when the cutting distance reaches 30 km, as flank face are resistant to wear. Aγ{100}Aα{110} micro diamond
shown in Fig. 16 (d). The profile error of the sinusoidal grids machined tool wear is mainly caused by the flank face. In contrast, Aγ{110}
with the T3 micro diamond tool increases constantly and obviously, Aα{100} micro diamond tool wear is mainly caused by the rake
while the profile error of the sinusoidal grids machined with the T2 face. However, their comprehensive wear resistances are similar
micro diamond tool inconspicuously increases until the cutting distance to each other and between those of the Aγ{100}Aα{100} and
is extended to 20 km, which also indicates that the micro diamond tools Aγ{110}Aα{110} micro diamond tools.
with the T2 crystal orientation combination have a better wear resis­ (3) The profile accuracy and surface quality of the microstructures
tance than those with the T3 crystal orientation combination. are positively related to the cutting edge strength with increasing
The above profile error analysis is performed to macroscopically cutting distance.
evaluate the influences of micro diamond tool wear on the micro­ (4) Considering the tool life and the profile accuracy of machined
structured arrays. Besides, the wear marks of the cutting edge are microstructures, the {110} crystal facet is a priority recommen­
inevitably duplicated on the machined surface, which has essential in­ dation for rake and flank faces when designing a micro diamond
fluences on the topological characteristic of microstructure surface in tool applied to machining microstructure arrays.
microscopic scale. And conversely, topology of the machined surface can
also reflect the degree of the micro diamond tool wear. Fourier analysis CRediT authorship contribution statement
method is applied to extract the machined surface topological charac­
teristic in this work. The analysis results performed for micro diamond Hanzhong Liu: Conceptualization, Investigation, Experiment,
tools with different cutting distances are demonstrated in Fig. 18. Writing – original draft. Wenjun Zong: Investigation, Writing – review
It can be seen from the frequency-amplitude curves in Fig. 18 that all & editing, Project administration, Funding acquisition. Zhipeng Cui:
the main peaks, reflecting the tool feed path, are in the interval of Validation, Experiment.
0.3–0.4 µm− 1, which is consistent with the theoretical value 0.33 µm− 1
induced by the feed movement with a feed rate of 3 µm/r. However, the
Declaration of Competing Interest
frequency ranges of the machined surface topologies, achieved in
different cutting distances, are various. For the fresh tools, the frequency
The authors declare that they have no known competing financial
range is relatively narrow compared with the used tools, as the blue
interests or personal relationships that could have appeared to influence
curves showing in Fig. 18. The frequency ranges of the surface machined
the work reported in this paper.
with both T2 and T3 micro diamond tools are gradually broadening with
the increment of cutting distance. High frequency components (relative
Acknowledgments
to the theoretical value of 0.33 µm− 1), which is closely related to the tool
wear, are appearing. When the cutting distance is 10 km, 20 km and
The authors would like to thank the Science Challenge Project (No.
30 km, the frequencies of the surface machined with T2 diamond tool
TZ2018006-0202) for the support of this work.

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H. Liu et al. Journal of Materials Processing Tech. 305 (2022) 117600

Appendix A. Supporting information Mir, A., Luo, X., Sun, J., 2016. The investigation of influence of tool wear on ductile to
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Saga, T., 2010. Advances in crystalline silicon solar cell technology for industrial mass
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online version at doi:10.1016/j.jmatprotec.2022.117600. Uddin, M.S., Seah, K.H.W., Li, X.P., Rahman, M., Liu, K., 2004. Effect of crystallographic
orientation on wear of diamond tools for nano-scale ductile cutting of silicon. Wear
257, 751–759.
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