A Study on the Rock-Breaking Characteristics of an Arcing-Blade Cutter under Different Cutting Parameters

Abstract

To analyze the rock-breaking characteristics of an arcing-blade cutter in cutting red sandstone, a two-cutter cutting model was established based on the finite element method. Then, the cutting processes of the arcing-blade cutter at penetrations of 2 mm, 4 mm, and 6 mm with different cutter spacings were investigated, and the changing rules of the rock-breaking load, rock crushing state, and rock-breaking efficiency were obtained. Subsequently, the obtained simulation results were validated through linear cutting experiments. The research results showed that, as the penetration of the arcing-blade cutter increased, the rock-breaking load also increased; specifically, under 2 mm penetration, the rock-breaking load remained stable, irrespective of the cutter spacing. However, under 4 mm and 6 mm penetration, the vertical and rolling force increased and then stabilized with an increase in the cutter spacing, while the lateral force decreased and then stabilized, attributed to the synergistic effect between the cutters. At 2 mm penetration, the absence of interaction between the cutting of two cutters in sequence resulted in two separate crushed areas on the rock surface. However, at 4 mm and 6 mm penetration, the rock ridge could be crushed under a smaller cutter spacing. Meanwhile, with an increase in the cutter spacing, the synergistic effect between the cutters diminished, causing the rock ridge between two cuttings to remain uncrushed. The specific energy at the 4 mm and 6 mm penetrations decreased initially with an increase in the cutter spacing, then increased, and eventually stabilized. The optimal cutter spacings at these penetrations were determined as 50 mm and 60 mm, respectively. Conversely, at 2 mm penetration, the specific energy remained almost unchanged with an increase in the cutter spacing, maintaining at a high level and resulting in a low efficiency in cutting rock.

Full text

Citation: Ma, Z.; Ye, J.; Zhang, X.; Ye,
W. A Study on the Rock-Breaking
Characteristics of an Arcing-Blade
Cutter under Different Cutting
Parameters. Appl. Sci. 2024,14, 1241.
https://doi.org/10.3390/app14031241
Academic Editor: Stefano Invernizzi
Received: 25 December 2023
Revised: 26 January 2024
Accepted: 29 January 2024
Published: 2 February 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
applied
sciences
Article
A Study on the Rock-Breaking Characteristics of an Arcing-Blade
Cutter under Different Cutting Parameters
Zhao Ma 1,2, Junjie Ye 1,*, Xin Zhang 2and Wenhua Ye 1
1School of Mechanical and Electronical Engineering, Xidian University, Xi’an 710071, China;
mazhaooa@163.com (Z.M.); 23041212693@stu.xidian.edu.cn (W.Y.)
2Shanxi Tiandi Coal Mining Machinery Co., Ltd., Taiyuan 030032, China; zhangxin@tyccri.com
*Correspondence: xd_yejj@163.com
Abstract: To analyze the rock-breaking characteristics of an arcing-blade cutter in cutting red sand-
stone, a two-cutter cutting model was established based on the finite element method. Then, the
cutting processes of the arcing-blade cutter at penetrations of 2 mm, 4 mm, and 6 mm with different
cutter spacings were investigated, and the changing rules of the rock-breaking load, rock crushing
state, and rock-breaking efficiency were obtained. Subsequently, the obtained simulation results were
validated through linear cutting experiments. The research results showed that, as the penetration
of the arcing-blade cutter increased, the rock-breaking load also increased; specifically, under 2 mm
penetration, the rock-breaking load remained stable, irrespective of the cutter spacing. However,
under 4 mm and 6 mm penetration, the vertical and rolling force increased and then stabilized with
an increase in the cutter spacing, while the lateral force decreased and then stabilized, attributed to
the synergistic effect between the cutters. At 2 mm penetration, the absence of interaction between
the cutting of two cutters in sequence resulted in two separate crushed areas on the rock surface.
However, at 4 mm and 6 mm penetration, the rock ridge could be crushed under a smaller cutter
spacing. Meanwhile, with an increase in the cutter spacing, the synergistic effect between the cut-
ters diminished, causing the rock ridge between two cuttings to remain uncrushed. The specific
energy at the 4 mm and 6 mm penetrations decreased initially with an increase in the cutter spacing,
then increased, and eventually stabilized. The optimal cutter spacings at these penetrations were
determined as 50 mm and 60 mm, respectively. Conversely, at 2 mm penetration, the specific energy
remained almost unchanged with an increase in the cutter spacing, maintaining at a high level and
resulting in a low efficiency in cutting rock.
Keywords: arcing-blade cutter; red sandstone; penetration; cutter spacing; specific energy
1. Introduction
Tunnel Boring Machines (TBM) are widely utilized in underground construction due
to their superior safety and efficiency compared to traditional tunneling methods [
1
–
3
].
At present, there are many projects using TBM construction internationally, but due to
complex global geological conditions, the excavation efficiency of TBMs varies within
different geological conditions. For example, low-strength rock can cause instability in
tunnel excavation, while high-strength rock can lead to a low penetration rate. TBMs
primarily operate by using the disc cutter on the cutter head to interface with the rock,
and its substantial thrust and torque enable the cutter to effectively excavate the rock [
4
,
5
].
Generally, a good rock-breaking performance of the disc cutter directly determines the
tunnelling efficiency of the TBM. Therefore, the rock-breaking characteristics of disc cutters
have attracted great attention from researchers around the world. The cutting parameters
and structural parameters of the disc cutter are the most important factors affecting the
rock–cutter interaction behavior [
6
,
7
]. Among them, the structural parameters of the
disc cutter are mainly affected by the cross-sectional shape of the cutter. Thus, selecting
Appl. Sci. 2024,14, 1241. https://doi.org/10.3390/app14031241 https://www.mdpi.com/journal/applsci

Appl. Sci. 2024,14, 1241 2 of 16
an appropriate blade shape for the cutter according to the specific rock formations can
significantly enhance the TBM’s construction efficiency [
8
,
9
]. Consequently, research on the
blade shape of the cutter has received considerable attention among scholars, as it has the
potential to improve TBM performance.
Currently, the flat-blade cutter is widely used and has been the focus of extensive
research, as shown in Figure 1a. Liu et al. [
10
] studied the rock-breaking characteristics
of the flat-blade cutter with the assistance of pre-cutting grooves, and studied the rock-
breaking load and the distribution of the internal stress of the rock under experimental
and simulation conditions. Hu et al. [
11
] conducted a numerical simulation of press in rock
breaking with different edge widths of the flat-blade cutter to investigate its impact on
rock-breaking efficiency. Wen et al. [
12
] used discrete elements to analyze the cutting charac-
teristics of the flat-blade cutter under coupled strata, identifying the laws of rock-breaking
load and efficiency. Additionally, Li et al. [
13
] examined different cutting sequences of
the flat-blade cutter using discrete elements and established a rotary cutting model with
various arrangements of multiple cutters to study the mechanical response characteristics.
Agrawal et al. [
14
] investigated the cutter force and cutter wear with the discrete element
method. Comakli et al. [
15
] conducted linear cutting tests with small flat-blade cutters
and tried to use the testing results to predict the TBM performance. Ayawah et al. [
16
]
proposed a new method to decide the cutting geometry of the flat-blade cutter based on
cutting experiments and simulations. Zare et al. [
17
] optimized the cutter spacing of the
flat-blade cutters considering the joint with the distinct element method.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 2 of 16
appropriate blade shape for the cuer according to the specific rock formations can sig-
nificantly enhance the TBM’s construction efficiency [8,9]. Consequently, research on the
blade shape of the cuer has received considerable aention among scholars, as it has the
potential to improve TBM performance.
Currently, the flat-blade cuer is widely used and has been the focus of extensive
research, as shown in Figure 1a. Liu et al. [10] studied the rock-breaking characteristics of
the flat-blade cuer with the assistance of pre-cuing grooves, and studied the rock-break-
ing load and the distribution of the internal stress of the rock under experimental and
simulation conditions. Hu et al. [11] conducted a numerical simulation of press in rock
breaking with different edge widths of the flat-blade cuer to investigate its impact on
rock-breaking efficiency. Wen et al. [12] used discrete elements to analyze the cuing char-
acteristics of the flat-blade cuer under coupled strata, identifying the laws of rock-break-
ing load and efficiency. Additionally, Li et al. [13] examined different cuing sequences of
the flat-blade cuer using discrete elements and established a rotary cuing model with
various arrangements of multiple cuers to study the mechanical response characteristics.
Agrawal et al. [14] investigated the cuer force and cuer wear with the discrete element
method. Comakli et al. [15] conducted linear cuing tests with small flat-blade cuers and
tried to use the testing results to predict the TBM performance. Ayawah et al. [16] pro-
posed a new method to decide the cuing geometry of the flat-blade cuer based on cut-
ting experiments and simulations. Zare et al. [17] optimized the cuer spacing of the flat-
blade cuers considering the joint with the distinct element method.
Figure 1. Two types of cuer: (a) flat-blade cuer and (b) arcing-blade cuer.
In TBM engineering, the flat-blade cuer is prone to overload due to its large contact
area with rocks under hard rock conditions, resulting in significant deformation or even
the failure of the flat-blade cuer. In response to these limitations, the arcing-blade cuer
was developed as a modification of the flat-blade cuer, as shown in Figure 1b. Due to its
structural characteristics, the contact area of the arcing-blade cuer with rocks is small,
providing a significant advantage in load reduction. There is also a small amount of re-
search on the arcing-blade cuer. Jiang et al. [18] used PFC3D to establish a rotational
cuing model of the arcing-blade cuer and simulate its rock-breaking process. Zhang et
al. [19] simulated the dynamic indentation process of the arcing-blade cuer and analyzed
the change in rock-breaking load under different peripheral pressures. Furthermore,
Duan et al. [20] compared the rock-breaking mechanisms of flat- and arcing-blade cuers
under hard rock, summarizing the characteristics of rock-breaking load, rock chips, rock-
breaking efficiency, and stress distribution. Zhang et al. [21] simulated the crack propaga-
tion induced by the arcing-blade cuer.
The above studies have a preliminary understanding of the action mechanism of the
arcing-blade cuer, but lack research on its performance under different cuing parame-
ters, such as cuer spacing and penetration, which cannot effectively guide the arrange-
ment and construction of the arcing-blade cuer. As a comprehensive approach, numeri-
cal simulation has proven to be an effective method for studying the rock-cuing process
of TBM cuers [22,23]. Consequently, this paper establishes a linear cuing model of the
arcing-blade cuer based on the finite element method, analyzes the influence of different
Figure 1. Two types of cutter: (a) flat-blade cutter and (b) arcing-blade cutter.
In TBM engineering, the flat-blade cutter is prone to overload due to its large contact
area with rocks under hard rock conditions, resulting in significant deformation or even
the failure of the flat-blade cutter. In response to these limitations, the arcing-blade cutter
was developed as a modification of the flat-blade cutter, as shown in Figure 1b. Due to
its structural characteristics, the contact area of the arcing-blade cutter with rocks is small,
providing a significant advantage in load reduction. There is also a small amount of research
on the arcing-blade cutter. Jiang et al. [
18
] used PFC3D to establish a rotational cutting
model of the arcing-blade cutter and simulate its rock-breaking process. Zhang et al. [
19
]
simulated the dynamic indentation process of the arcing-blade cutter and analyzed the
change in rock-breaking load under different peripheral pressures. Furthermore, Duan
et al. [
20
] compared the rock-breaking mechanisms of flat- and arcing-blade cutters under
hard rock, summarizing the characteristics of rock-breaking load, rock chips, rock-breaking
efficiency, and stress distribution. Zhang et al. [
21
] simulated the crack propagation induced
by the arcing-blade cutter.
The above studies have a preliminary understanding of the action mechanism of the
arcing-blade cutter, but lack research on its performance under different cutting parameters,
such as cutter spacing and penetration, which cannot effectively guide the arrangement
and construction of the arcing-blade cutter. As a comprehensive approach, numerical
simulation has proven to be an effective method for studying the rock-cutting process of
TBM cutters [
22
,
23
]. Consequently, this paper establishes a linear cutting model of the
arcing-blade cutter based on the finite element method, analyzes the influence of different

Appl. Sci. 2024,14, 1241 3 of 16
cutter spacings and penetrations on its performance, and provides valuable insights for
optimizing the parameters and cutter arrangement of the arcing-blade cutter. It should be
noted that the rock surface simulated in this paper is smooth and intact, which is slightly
different from the rock surfaces cut by TBM cutters in actual TBM engineering. Meanwhile,
this paper only studied the cutting process of two TBM cutters, which differs from the
actual sequential cutting of multiple TBM cutters.
2. Calibration of Rock Materials
The mechanical parameters of red sandstone were obtained through uniaxial com-
pression and Brazilian splitting experiments, which are summarized in Table 1. In this
paper, the rock-breaking process of an arcing-blade cutter is simulated using the finite
element method, and the Riedel–Hiermaier–Thoma (RHT) material intrinsic model is uti-
lized to describe the red sandstone material. The RHT material model divides the stress
development of rock materials under dynamic loading into three stages: the elastic stage,
linear strengthening stage, and damage softening stage, and correspondingly introduces
two limit surfaces: the elastic yield surface and failure surface. The residual strength
surface is used to describe the change patterns of material failure strength, initial yield
strength, and residual strength, which can better simulate the rock failure process and crack
propagation [
24
]. In order to accurately simulate red sandstone, it is necessary to calibrate
this rock sample.
Table 1. Rock mechanics parameters of experiment.
Rock Type Compressive
Strength/MPa
Tensile
Strength/MPa Density/kg m−3Elastic
Modulus/GPa
Red sandstone 71.8 4.7 2370.6 6.2
Taking uniaxial compression calibration as an example, a cylindrical rock sample
with a size of
∅
50 mm
×
100 mm corresponding to the uniaxial compression experiment
was generated and compressed in the simulation. Then, the calculated curves of the axial
compressive stress and axial strain in the simulation results were extracted. Following this
step, the simulation parameters were adjusted to fit the simulation curve to the experimental
curve. Figure 2shows the results of the uniaxial compression experiments and simulations.
Among them, the rock in Figure 2b has the same size as the rock in Figure 2a. In the
simulation, a certain displacement was applied to the upper surface of the rock, causing
the rock to break. The rock-breaking process in Figure 2a was simulated, and the output
stress–strain curve was compared with the experimental data. Figure 2indicates that the
crack extension and material failure in the simulation of the rock sample was in good
agreement with the experimental phenomenon.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 3 of 16
cuer spacings and penetrations on its performance, and provides valuable insights for
optimizing the parameters and cuer arrangement of the arcing-blade cuer. It should be
noted that the rock surface simulated in this paper is smooth and intact, which is slightly
different from the rock surfaces cut by TBM cuers in actual TBM engineering. Mean-
while, this paper only studied the cuing process of two TBM cuers, which differs from
the actual sequential cuing of multiple TBM cuers.
2. Calibration of Rock Materials
The mechanical parameters of red sandstone were obtained through uniaxial com-
pression and Brazilian spliing experiments, which are summarized in Table 1. In this
paper, the rock-breaking process of an arcing-blade cuer is simulated using the finite
element method, and the Riedel–Hiermaier–Thoma (RHT) material intrinsic model is uti-
lized to describe the red sandstone material. The RHT material model divides the stress
development of rock materials under dynamic loading into three stages: the elastic stage,
linear strengthening stage, and damage softening stage, and correspondingly introduces
two limit surfaces: the elastic yield surface and failure surface. The residual strength sur-
face is used to describe the change paerns of material failure strength, initial yield
strength, and residual strength, which can beer simulate the rock failure process and
crack propagation [24]. In order to accurately simulate red sandstone, it is necessary to
calibrate this rock sample.
Table 1. Rock mechanics parameters of experiment.
Rock Type Compressive
Strength/MPa
Ten sile
Strength/MPa Density/kg m−3 Elastic Modulus/GPa
Red sandstone 71.8 4.7 2370.6 6.2
Taking uniaxial compression calibration as an example, a cylindrical rock sample
with a size of ∅50 mm × 100 mm corresponding to the uniaxial compression experiment
was generated and compressed in the simulation. Then, the calculated curves of the axial
compressive stress and axial strain in the simulation results were extracted. Following this
step, the simulation parameters were adjusted to fit the simulation curve to the experi-
mental curve. Figure 2 shows the results of the uniaxial compression experiments and
simulations. Among them, the rock in Figure 2b has the same size as the rock in Figure 2a.
In the simulation, a certain displacement was applied to the upper surface of the rock,
causing the rock to break. The rock-breaking process in Figure 2a was simulated, and the
output stress–strain curve was compared with the experimental data. Figure 2 indicates
that the crack extension and material failure in the simulation of the rock sample was in
good agreement with the experimental phenomenon.
Figure 2. Experimental and simulated phenomena in uniaxial compression test: (a) uniaxial com-
pression experiment and (b) uniaxial compression simulation.
Figure 2. Experimental and simulated phenomena in uniaxial compression test: (a) uniaxial compres-
sion experiment and (b) uniaxial compression simulation.

Appl. Sci. 2024,14, 1241 4 of 16
Figure 3illustrates a comparison of the extracted axial compressive stress and axial
strain curves. It can be seen that the simulation result exhibits a high consistency with
the experimental one. This outcome serves as a foundation for the subsequent numerical
modeling of cutting rock with arcing-blade cutters.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 4 of 16
Figure 3 illustrates a comparison of the extracted axial compressive stress and axial
strain curves. It can be seen that the simulation result exhibits a high consistency with the
experimental one. This outcome serves as a foundation for the subsequent numerical
modeling of cuing rock with arcing-blade cuers.
0.000 0.003 0.006 0.009 0.01
2
0
20
40
60
80
Stress(MPa)
Strain(%)
Experiment
Simulation
Figure 3. Comparison of uniaxial compression data between experiment and simulation.
3. Rock-Cuing Model of Two Arcing-Blade Cuers
This paper mainly focuses on the influence of cuer spacing and penetration on the
rock-breaking characteristics of the arcing-blade cuer. Additionally, the cuer ring, ra-
ther than the complete arcing-blade cuer, was used to cut the rock sample in these sim-
ulations, considering the calculation cost. Therefore, a sequential cuing model of two
arcing-blade cuer rings with different cuing parameters was established, as depicted in
Figure 4. In fact, the TBM cuer cut the rock with a rotary cuing mode. However, it can
be regarded as a linear cuing model due to the large radius of rotary cuing. Therefore,
a linear cuing simulation model is established in this article that is consistent with sub-
sequent linear cuing experiments.
The two cuers were arranged coaxially, with the distance between the centers of the
blades of the two cuers representing the cuer spacing and the depth of cuing the rock
denoting the penetration. The section of the red sandstone was rectangular, with a width
and height of 230 mm and 100 mm, respectively, and the length of the rock in the cuing
direction set at 400 mm. In these simulations, the penetration of the arcing-blade cuer
was varied at 2, 4, and 6 mm, with each penetration corresponding to different cuer spac-
ings of 40 mm, 50 mm, 60 mm, 70 mm, and 80 mm. During the cuing process, the left
arcing-blade cuer (cuer 1) first cut a length of 75 mm, then the right arcing-blade cuer
(cuer 2) started to cut the rock sample subsequently.
Figure 4. Rock-cuing model of two arcing-blade cuers.
Figure 3. Comparison of uniaxial compression data between experiment and simulation.
3. Rock-Cutting Model of Two Arcing-Blade Cutters
This paper mainly focuses on the influence of cutter spacing and penetration on the
rock-breaking characteristics of the arcing-blade cutter. Additionally, the cutter ring, rather
than the complete arcing-blade cutter, was used to cut the rock sample in these simulations,
considering the calculation cost. Therefore, a sequential cutting model of two arcing-blade
cutter rings with different cutting parameters was established, as depicted in Figure 4. In
fact, the TBM cutter cut the rock with a rotary cutting mode. However, it can be regarded as
a linear cutting model due to the large radius of rotary cutting. Therefore, a linear cutting
simulation model is established in this article that is consistent with subsequent linear
cutting experiments.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 4 of 16
Figure 3 illustrates a comparison of the extracted axial compressive stress and axial
strain curves. It can be seen that the simulation result exhibits a high consistency with the
experimental one. This outcome serves as a foundation for the subsequent numerical
modeling of cuing rock with arcing-blade cuers.
0.000 0.003 0.006 0.009 0.01
2
0
20
40
60
80
Stress(MPa)
Strain(%)
Experiment
Simulation
Figure 3. Comparison of uniaxial compression data between experiment and simulation.
3. Rock-Cuing Model of Two Arcing-Blade Cuers
This paper mainly focuses on the influence of cuer spacing and penetration on the
rock-breaking characteristics of the arcing-blade cuer. Additionally, the cuer ring, ra-
ther than the complete arcing-blade cuer, was used to cut the rock sample in these sim-
ulations, considering the calculation cost. Therefore, a sequential cuing model of two
arcing-blade cuer rings with different cuing parameters was established, as depicted in
Figure 4. In fact, the TBM cuer cut the rock with a rotary cuing mode. However, it can
be regarded as a linear cuing model due to the large radius of rotary cuing. Therefore,
a linear cuing simulation model is established in this article that is consistent with sub-
sequent linear cuing experiments.
The two cuers were arranged coaxially, with the distance between the centers of the
blades of the two cuers representing the cuer spacing and the depth of cuing the rock
denoting the penetration. The section of the red sandstone was rectangular, with a width
and height of 230 mm and 100 mm, respectively, and the length of the rock in the cuing
direction set at 400 mm. In these simulations, the penetration of the arcing-blade cuer
was varied at 2, 4, and 6 mm, with each penetration corresponding to different cuer spac-
ings of 40 mm, 50 mm, 60 mm, 70 mm, and 80 mm. During the cuing process, the left
arcing-blade cuer (cuer 1) first cut a length of 75 mm, then the right arcing-blade cuer
(cuer 2) started to cut the rock sample subsequently.
Figure 4. Rock-cuing model of two arcing-blade cuers.
Figure 4. Rock-cutting model of two arcing-blade cutters.
The two cutters were arranged coaxially, with the distance between the centers of
the blades of the two cutters representing the cutter spacing and the depth of cutting the
rock denoting the penetration. The section of the red sandstone was rectangular, with a
width and height of 230 mm and 100 mm, respectively, and the length of the rock in the
cutting direction set at 400 mm. In these simulations, the penetration of the arcing-blade
cutter was varied at 2, 4, and 6 mm, with each penetration corresponding to different cutter
spacings of 40 mm, 50 mm, 60 mm, 70 mm, and 80 mm. During the cutting process, the left
arcing-blade cutter (cutter 1) first cut a length of 75 mm, then the right arcing-blade cutter
(cutter 2) started to cut the rock sample subsequently.

Appl. Sci. 2024,14, 1241 5 of 16
In Figure 5, the detailed parameters of the arcing-blade cutter are presented, with a
cutter diameter of 432 mm and a cutting blade radius of 9 mm. During the simulation, the
cutter ring was treated as a rigid body with a cutting speed set at 15 m/s. The mesh of
the rock was entirely a hexahedral mesh. To save computing resources, the rock grid was
divided into three layers. Specifically, the mesh size was set at 2 mm for the top 25 mm
depth, 3 mm for the 25–50 mm depth range, and 4 mm for the remaining 50–100 mm
depth range of the rock sample. Given the rigidity of the cutter, a six-plane mesh mixed
with a four-plane mesh dominated its mesh type, with a mesh size set at 4 mm. Rigid
walls were installed on the left and right sides, as well as at the bottom of the rock, to
maintain its position. Additionally, non-reflective boundary conditions were applied to all
faces except the upper surface of the rock sample to eliminate the boundary effect on the
rock-breaking process.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 5 of 16
In Figure 5, the detailed parameters of the arcing-blade cuer are presented, with a
cuer diameter of 432 mm and a cuing blade radius of 9 mm. During the simulation, the
cuer ring was treated as a rigid body with a cuing speed set at 15 m/s. The mesh of the
rock was entirely a hexahedral mesh. To save computing resources, the rock grid was di-
vided into three layers. Specifically, the mesh size was set at 2 mm for the top 25 mm
depth, 3 mm for the 25–50 mm depth range, and 4 mm for the remaining 50–100 mm depth
range of the rock sample. Given the rigidity of the cuer, a six-plane mesh mixed with a
four-plane mesh dominated its mesh type, with a mesh size set at 4 mm. Rigid walls were
installed on the left and right sides, as well as at the boom of the rock, to maintain its
position. Additionally, non-reflective boundary conditions were applied to all faces except
the upper surface of the rock sample to eliminate the boundary effect on the rock-breaking
process.
Figure 5. Dimensions of the arcing-blade cuer.
4. Analysis of Calculation Results
4.1. Rock-Breaking Load of Arcing-Blade Cuers
In the cuing process, the cuer is primarily subject to three loads, as indicated in
Figure 6. These loads consist of the vertical force (FV), rolling force (FR), and lateral force
(FL). The vertical force (FV) is applied in the normal direction of the cuer, while the rolling
force (FR) is directed tangentially to the cuer ring. The lateral force (FL) is applied in the
direction of the cuer shaft.
Figure 6. Three-way loads on the cuers.
The dynamic rock-breaking load under the working conditions of 2 mm penetration
and 80 mm cuer spacing was taken as an example to study the dynamic process of the
rock-breaking load of two cuers cuing in sequence. As observed from Figure 7, at the
beginning of the cuing stage, the rock-breaking loads of cuer 1 and cuer 2 first
Figure 5. Dimensions of the arcing-blade cutter.
4. Analysis of Calculation Results
4.1. Rock-Breaking Load of Arcing-Blade Cutters
In the cutting process, the cutter is primarily subject to three loads, as indicated in
Figure 6. These loads consist of the vertical force (F
V
), rolling force (F
R
), and lateral force
(F
L
). The vertical force (F
V
) is applied in the normal direction of the cutter, while the rolling
force (F
R
) is directed tangentially to the cutter ring. The lateral force (F
L
) is applied in the
direction of the cutter shaft.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 5 of 16
In Figure 5, the detailed parameters of the arcing-blade cuer are presented, with a
cuer diameter of 432 mm and a cuing blade radius of 9 mm. During the simulation, the
cuer ring was treated as a rigid body with a cuing speed set at 15 m/s. The mesh of the
rock was entirely a hexahedral mesh. To save computing resources, the rock grid was di-
vided into three layers. Specifically, the mesh size was set at 2 mm for the top 25 mm
depth, 3 mm for the 25–50 mm depth range, and 4 mm for the remaining 50–100 mm depth
range of the rock sample. Given the rigidity of the cuer, a six-plane mesh mixed with a
four-plane mesh dominated its mesh type, with a mesh size set at 4 mm. Rigid walls were
installed on the left and right sides, as well as at the boom of the rock, to maintain its
position. Additionally, non-reflective boundary conditions were applied to all faces except
the upper surface of the rock sample to eliminate the boundary effect on the rock-breaking
process.
Figure 5. Dimensions of the arcing-blade cuer.
4. Analysis of Calculation Results
4.1. Rock-Breaking Load of Arcing-Blade Cuers
In the cuing process, the cuer is primarily subject to three loads, as indicated in
Figure 6. These loads consist of the vertical force (FV), rolling force (FR), and lateral force
(FL). The vertical force (FV) is applied in the normal direction of the cuer, while the rolling
force (FR) is directed tangentially to the cuer ring. The lateral force (FL) is applied in the
direction of the cuer shaft.
Figure 6. Three-way loads on the cuers.
The dynamic rock-breaking load under the working conditions of 2 mm penetration
and 80 mm cuer spacing was taken as an example to study the dynamic process of the
rock-breaking load of two cuers cuing in sequence. As observed from Figure 7, at the
beginning of the cuing stage, the rock-breaking loads of cuer 1 and cuer 2 first
Figure 6. Three-way loads on the cutters.
The dynamic rock-breaking load under the working conditions of 2 mm penetration
and 80 mm cutter spacing was taken as an example to study the dynamic process of the
rock-breaking load of two cutters cutting in sequence. As observed from Figure 7, at the
beginning of the cutting stage, the rock-breaking loads of cutter 1 and cutter 2 first increased
from 0 to a certain value. Subsequently, the rock-breaking loads exhibited a certain degree
of volatility. Comparisons of the three rock-breaking loads reveal that the F
V
was the
largest and the F
L
was the smallest, which fluctuated around 0. The magnitudes of the

Appl. Sci. 2024,14, 1241 6 of 16
rock-breaking loads for cutter 1 and cutter 2 were almost identical, and varied only at the
start and end time.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 6 of 16
increased from 0 to a certain value. Subsequently, the rock-breaking loads exhibited a cer-
tain degree of volatility. Comparisons of the three rock-breaking loads reveal that the FV
was the largest and the FL was the smallest, which fluctuated around 0. The magnitudes
of the rock-breaking loads for cuer 1 and cuer 2 were almost identical, and varied only
at the start and end time.
0.000 0.005 0.010 0.015 0.020 0.025 0.030
20
30
40
50
60
Vertical force (k N)
Time
(
s
)
Cutter1
Cutter2
(a)
0.000 0.005 0.010 0.015 0.020 0.025 0.030
0
4
8
12
16
Rolling force (kN)
Time (s)
Cutter1
Cutter2 (b)
0.000 0.005 0.010 0.015 0.020 0.0 25 0.030
−4
−2
0
2
4
Lateral force (kN)
Time
(
s
)
Cutter1
Cutter2
(c)
Figure 7. Three-directional loads: (a) vertical force; (b) rolling force; and (c) lateral force.
The data represented in Figure 8 depict the average values of the three-directional
loads applied to cuer 2 at various penetrations and cuer spacings. At a penetration of 2
mm, the three-directional loads exhibited minimal variation with an increase in the cuer
spacing. Specifically, the FV remained nearly constant at around 40 kN, the FR remained
steady at approximately 4 kN, and the FL essentially stayed at about 0. It can be observed
that the three-directional loads did not change significantly with an increase in the cuer
spacing at such a low penetration. Upon increasing the penetration to 4 mm, the FV and
FR initially displayed an upward trend as the cuer spacing increased, followed by a sub-
sequent decline and eventual stabilization. To elaborate, the FV increased from 80.5 kN to
105.5 kN as the cuer spacing grew from 40 mm to 60 mm, after which, it remained stable
around 105 kN as the cuer spacing extended to 80 mm. Conversely, the FL demonstrated
an inverse paern to the FV and FR, as it decreased from 1.7 kN to 0.7 kN with a rise in the
cuer spacing from 40 mm to 60 mm, ultimately plateauing near 0 kN with further in-
creases in the cuer spacing. Similarly, at a penetration of 6 mm, the trend of the three-
directional loads with an increase in cuer spacing was similar to that observed for 4 mm
penetration. It should be pointed out that the three-directional loads at a penetration of 6
mm began to be stable as the cuer spacing reached 70 mm, which is different from the
situation for 4 mm penetration. Moreover, for a given cuer spacing, the change trend of
the three-directional loads showed an increase with a rise in penetration. For instance, at
a cuer spacing of 60 mm, the FV increased from 38.4 kN to 141.7 kN and the FR increased
from 4.3 kN to 15.9 kN as the penetration expanded from 2 mm to 6 mm.
In summary, the rock-breaking loads of the arcing-blade cuer did not change sig-
nificantly as the cuer spacing increased at a penetration of 2 mm. However, when the
penetration was 4 mm or 6 mm, the three-directional loads were significantly affected by
an increase in the cuer spacing. This change trend is aributed to the synergistic effect
between cuer 1 and cuer 2. Cuer 1 initiated the rock-cuing process before cuer 2,
then cuer 2 cut the rock under a given cuer space. At a penetration of 2 mm, there was
no synergistic effect between the cuers for different cuer spacings, causing cuer 2 to
independently function like a single unit in rock cuing. Consequently, the rock-breaking
load did not change with an increase in the cuer spacing. Conversely, when the penetra-
tion was 4 mm, the smaller cuer spacing enabled the two cuers to synergistically cut
the rock. As the cuer spacing exceeded a certain value, this synergistic effect weakened
or disappeared. Observably, at a cuer spacing of 60 mm, the synergistic effect vanished,
causing cuer 2 to be similar to a single unit in rock cuing, thereby maintaining a stable
rock-breaking load, as shown in Figure 8.
When the penetration reached 6 mm, it can be found that the synergistic effect be-
tween cuer 1 and cuer 2 was eliminated when the cuer spacing increased to 70 mm,
Figure 7. Three-directional loads: (a) vertical force; (b) rolling force; and (c) lateral force.
The data represented in Figure 8depict the average values of the three-directional
loads applied to cutter 2 at various penetrations and cutter spacings. At a penetration
of 2 mm, the three-directional loads exhibited minimal variation with an increase in the
cutter spacing. Specifically, the F
V
remained nearly constant at around 40 kN, the F
R
remained steady at approximately 4 kN, and the F
L
essentially stayed at about 0. It can be
observed that the three-directional loads did not change significantly with an increase in
the cutter spacing at such a low penetration. Upon increasing the penetration to 4 mm, the
F
V
and F
R
initially displayed an upward trend as the cutter spacing increased, followed
by a subsequent decline and eventual stabilization. To elaborate, the F
V
increased from
80.5 kN to 105.5 kN as the cutter spacing grew from 40 mm to 60 mm, after which, it
remained stable around 105 kN as the cutter spacing extended to 80 mm. Conversely, the
F
L
demonstrated an inverse pattern to the F
V
and F
R
, as it decreased from 1.7 kN to 0.7 kN
with a rise in the cutter spacing from 40 mm to 60 mm, ultimately plateauing near 0 kN with
further increases in the cutter spacing. Similarly, at a penetration of 6 mm, the trend of the
three-directional loads with an increase in cutter spacing was similar to that observed for
4 mm penetration. It should be pointed out that the three-directional loads at a penetration
of 6 mm began to be stable as the cutter spacing reached 70 mm, which is different from the
situation for 4 mm penetration. Moreover, for a given cutter spacing, the change trend of
the three-directional loads showed an increase with a rise in penetration. For instance, at a
cutter spacing of 60 mm, the F
V
increased from 38.4 kN to 141.7 kN and the F
R
increased
from 4.3 kN to 15.9 kN as the penetration expanded from 2 mm to 6 mm.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 7 of 16
and the rock-breaking loads stayed stable with a further increase in the cuer spacing, as
shown in Figure 8. This indicates that the cuer spacing had a signicant impact on the
rock-breaking load for a large penetration. Moreover, the dierence in the rock-breaking
load between cuer 2 and cuer 1 was very small when the synergistic eect disappeared,
as depicted in Figure 7. Consequently, the cuer spacing associated with the synergistic
eect could reduce the rock-breaking load of cuer 2 for a large penetration. Specically,
when the penetration level is xed, a smaller cuer spacing strengthens the synergistic
eect, while a larger cuer spacing weakens or even eliminates the synergistic eect for
two cuers, leading to the stabilization of the rock-breaking loads with an increase in cut-
ter spacing.
38.7 39.5 38.4 41.2 40.6
80.5
95.6
105.5 103.2 104.8
109.2
121.4
141.7
167.5 170.3
40 50 60 70 80
0
40
80
120
160
Vertical force (kN)
Cutter spacing(mm)
2mm
4mm
6mm
(a)
4.7 3.9 4.3 4.1 4.4
8.9
11.5
13.4 12.9 12.8
10.3
14.5
15.9
18.8 19.1
40 50 60 70 80
0
5
10
15
20
25
Rolling force (kN)
Cutter spacing(mm)
2mm
4mm
6mm(b)
0.4 0.3 0.3 0.2 0.3
1.7
1.3
0.7
0.4 0.2
3.9
3.1
1.9
0.6 0.7
40 50 60 70 80
0
2
4
6
Lateral force (kN)
Cutter spacing(mm)
2mm
4mm
6mm
(c)
Figure 8. The average values of three-directional loads: (a) vertical force; (b) rolling force; and (c)
lateral force.
4.2. Rock Crushing State Induced by Arcing-Blade Cuers
At 2 mm penetration, the crushing states on the rock surface are depicted in Figure 9.
The rock surface displayed two distinct “strip” crushed areas, which resulted from the
successive cuing actions of cuer 1 and cuer 2. Notably, the cuers left undamaged
rock ridges between the crushed areas. This observation aligns with the rock-breaking
load law discussed in Section 4.1. Specically, at a 2 mm penetration, there was a lack of
synergistic eect between the cuers at any spacing. Therefore, the two cuers operated
independently, leading to the formation of separate and non-interacting crushed areas.
Furthermore, it was evident that these independent crushed areas did not aect each
other. Additionally, with an increase in the cuer spacing, there was a corresponding in-
crement in the width of the rock ridge.
Figure 8. The average values of three-directional loads: (a) vertical force; (b) rolling force; and
(c) lateral force.
In summary, the rock-breaking loads of the arcing-blade cutter did not change sig-
nificantly as the cutter spacing increased at a penetration of 2 mm. However, when the
penetration was 4 mm or 6 mm, the three-directional loads were significantly affected by
an increase in the cutter spacing. This change trend is attributed to the synergistic effect
between cutter 1 and cutter 2. Cutter 1 initiated the rock-cutting process before cutter 2,
then cutter 2 cut the rock under a given cutter space. At a penetration of 2 mm, there was
no synergistic effect between the cutters for different cutter spacings, causing cutter 2 to
independently function like a single unit in rock cutting. Consequently, the rock-breaking

Appl. Sci. 2024,14, 1241 7 of 16
load did not change with an increase in the cutter spacing. Conversely, when the penetra-
tion was 4 mm, the smaller cutter spacing enabled the two cutters to synergistically cut
the rock. As the cutter spacing exceeded a certain value, this synergistic effect weakened
or disappeared. Observably, at a cutter spacing of 60 mm, the synergistic effect vanished,
causing cutter 2 to be similar to a single unit in rock cutting, thereby maintaining a stable
rock-breaking load, as shown in Figure 8.
When the penetration reached 6 mm, it can be found that the synergistic effect between
cutter 1 and cutter 2 was eliminated when the cutter spacing increased to 70 mm, and the
rock-breaking loads stayed stable with a further increase in the cutter spacing, as shown in
Figure 8. This indicates that the cutter spacing had a significant impact on the rock-breaking
load for a large penetration. Moreover, the difference in the rock-breaking load between
cutter 2 and cutter 1 was very small when the synergistic effect disappeared, as depicted
in Figure 7. Consequently, the cutter spacing associated with the synergistic effect could
reduce the rock-breaking load of cutter 2 for a large penetration. Specifically, when the
penetration level is fixed, a smaller cutter spacing strengthens the synergistic effect, while
a larger cutter spacing weakens or even eliminates the synergistic effect for two cutters,
leading to the stabilization of the rock-breaking loads with an increase in cutter spacing.
4.2. Rock Crushing State Induced by Arcing-Blade Cutters
At 2 mm penetration, the crushing states on the rock surface are depicted in Figure 9.
The rock surface displayed two distinct “strip” crushed areas, which resulted from the
successive cutting actions of cutter 1 and cutter 2. Notably, the cutters left undamaged
rock ridges between the crushed areas. This observation aligns with the rock-breaking
load law discussed in Section 4.1. Specifically, at a 2 mm penetration, there was a lack of
synergistic effect between the cutters at any spacing. Therefore, the two cutters operated
independently, leading to the formation of separate and non-interacting crushed areas.
Furthermore, it was evident that these independent crushed areas did not affect each other.
Additionally, with an increase in the cutter spacing, there was a corresponding increment
in the width of the rock ridge.
At a penetration of 4 mm, the crushing state of the rock surface is depicted in Figure 10.
Figure 10a,b reveal an interconnected crushed area on the rock surface at cutter spacings
of 40 mm and 50 mm, suggesting the crushing of the rock ridge by the two cutters. When
the cutter spacing increased over 60 mm, the rock surface displayed two distinct crushed
areas along with uncrushed rock ridges. Considering the analysis in Section 4.1, it can be
concluded that, at the penetration of 4 mm, there existed a synergistic effect between the
cutters under cutter spacings of 40 mm and 50 mm. This synergistic effect facilitated rock
ridge crushing. However, with a further increase in cutter spacing, the synergistic effect
weakened and may even have disappeared, leading to a failure in rock ridge crushing.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 7 of 16
and the rock-breaking loads stayed stable with a further increase in the cuer spacing, as
shown in Figure 8. This indicates that the cuer spacing had a significant impact on the
rock-breaking load for a large penetration. Moreover, the difference in the rock-breaking
load between cuer 2 and cuer 1 was very small when the synergistic effect disappeared,
as depicted in Figure 7. Consequently, the cuer spacing associated with the synergistic
effect could reduce the rock-breaking load of cuer 2 for a large penetration. Specifically,
when the penetration level is fixed, a smaller cuer spacing strengthens the synergistic
effect, while a larger cuer spacing weakens or even eliminates the synergistic effect for
two cuers, leading to the stabilization of the rock-breaking loads with an increase in cut-
ter spacing.
Figure 8. The average values of three-directional loads: (a) vertical force; (b) rolling force; and (c)
lateral force.
4.2. Rock Crushing State Induced by Arcing-Blade Cuers
At 2 mm penetration, the crushing states on the rock surface are depicted in Figure 9.
The rock surface displayed two distinct “strip” crushed areas, which resulted from the
successive cuing actions of cuer 1 and cuer 2. Notably, the cuers left undamaged
rock ridges between the crushed areas. This observation aligns with the rock-breaking
load law discussed in Section 4.1. Specifically, at a 2 mm penetration, there was a lack of
synergistic effect between the cuers at any spacing. Therefore, the two cuers operated
independently, leading to the formation of separate and non-interacting crushed areas.
Furthermore, it was evident that these independent crushed areas did not affect each
other. Additionally, with an increase in the cuer spacing, there was a corresponding in-
crement in the width of the rock ridge.
Figure 9. Cont.

Appl. Sci. 2024,14, 1241 8 of 16
Appl. Sci. 2024, 14, x FOR PEER REVIEW 8 of 16
Figure 9. Rock surface crushing state under 2 mm penetration with different cuer spacings: (a) 40
mm; (b) 50 mm; (c) 60 mm; (d) 70 mm; and (e) 80 mm.
At a penetration of 4 mm, the crushing state of the rock surface is depicted in Figure
10. Figure 10a,b reveal an interconnected crushed area on the rock surface at cuer spac-
ings of 40 mm and 50 mm, suggesting the crushing of the rock ridge by the two cuers.
When the cuer spacing increased over 60 mm, the rock surface displayed two distinct
crushed areas along with uncrushed rock ridges. Considering the analysis in Section 4.1,
it can be concluded that, at the penetration of 4 mm, there existed a synergistic effect be-
tween the cuers under cuer spacings of 40 mm and 50 mm. This synergistic effect facil-
itated rock ridge crushing. However, with a further increase in cutter spacing, the synergistic
effect weakened and may even have disappeared, leading to a failure in rock ridge crushing.
Figure 10. Rock surface crushing state under 4 mm penetration with different cuer spacings: (a) 40
mm; (b) 50 mm; (c) 60 mm; (d) 70 mm; and (e) 80 mm.
Figure 9. Rock surface crushing state under 2 mm penetration with different cutter spacings:
(a) 40 mm; (b) 50 mm; (c) 60 mm; (d) 70 mm; and (e) 80 mm.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 8 of 16
Figure 9. Rock surface crushing state under 2 mm penetration with different cuer spacings: (a) 40
mm; (b) 50 mm; (c) 60 mm; (d) 70 mm; and (e) 80 mm.
At a penetration of 4 mm, the crushing state of the rock surface is depicted in Figure
10. Figure 10a,b reveal an interconnected crushed area on the rock surface at cuer spac-
ings of 40 mm and 50 mm, suggesting the crushing of the rock ridge by the two cuers.
When the cuer spacing increased over 60 mm, the rock surface displayed two distinct
crushed areas along with uncrushed rock ridges. Considering the analysis in Section 4.1,
it can be concluded that, at the penetration of 4 mm, there existed a synergistic effect be-
tween the cuers under cuer spacings of 40 mm and 50 mm. This synergistic effect facil-
itated rock ridge crushing. However, with a further increase in cutter spacing, the synergistic
effect weakened and may even have disappeared, leading to a failure in rock ridge crushing.
Figure 10. Rock surface crushing state under 4 mm penetration with different cuer spacings: (a) 40
mm; (b) 50 mm; (c) 60 mm; (d) 70 mm; and (e) 80 mm.
Figure 10. Rock surface crushing state under 4 mm penetration with different cutter spacings:
(a) 40 mm; (b) 50 mm; (c) 60 mm; (d) 70 mm; and (e) 80 mm.
The crushing state on the rock surface when the penetration was 6 mm is illustrated
in Figure 11. It is evident that a synergistic effect occurred between the two cutters when
they were spaced at 40 mm, 50 mm, and 60 mm. Notably, in Figure 11a, the rock surface
at the 40 mm position displays a strong synergistic effect, with the two adjacent crushed
areas intersecting with each other and causing the intermediate rock ridge between two
cutters to disappear. As the cutter spacing increased to 50 mm and 60 mm, as depicted in
Figure 11b,c, the weakening of the synergistic effect between the cutters correlated with
a gradual reduction in the level of rock ridge crushing. Moreover, as the cutter spacing

Appl. Sci. 2024,14, 1241 9 of 16
reached over 70 mm, as demonstrated in Figure 11d,e, the absence of the synergistic effect
prompted the appearance of two distinct crushed areas and undamaged rock ridges on the
rock surface.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 9 of 16
The crushing state on the rock surface when the penetration was 6 mm is illustrated
in Figure 11. It is evident that a synergistic effect occurred between the two cuers when
they were spaced at 40 mm, 50 mm, and 60 mm. Notably, in Figure 11a, the rock surface
at the 40 mm position displays a strong synergistic effect, with the two adjacent crushed
areas intersecting with each other and causing the intermediate rock ridge between two
cuers to disappear. As the cuer spacing increased to 50 mm and 60 mm, as depicted in
Figure 11b,c, the weakening of the synergistic effect between the cuers correlated with a
gradual reduction in the level of rock ridge crushing. Moreover, as the cuer spacing
reached over 70 mm, as demonstrated in Figure 11d,e, the absence of the synergistic effect
prompted the appearance of two distinct crushed areas and undamaged rock ridges on
the rock surface.
Figure 11. Rock surface crushing state under 6 mm penetration with different cuer spacings: (a) 40
mm; (b) 50 mm; (c) 60 mm; (d) 70 mm; and (e) 80 mm.
In summary, the degree of rock surface crushing was influenced by the penetration
and cuer spacing. For instance, with a small penetration, such as 2 mm, there was an
absence of synergy between two cuers at different cuer spacings in this paper. Under
these cuing conditions, the two cuers acted independently to cut the rock, leading to a
lack of interaction and inability to crush the rock surface. However, as the penetration
increased to 4 mm and 6 mm, the synergistic effect between the cuers could effectively
crush the rock surface given an appropriate cuer spacing. Notably, a smaller cuer spac-
ing enhanced the synergistic effect and increased the degree of crushing.
The crushing state inside the rock could be observed through a section cuing in the
middle of the rock, where the cuer cut 200 mm, as shown in Figure 12. The variations in
the crushing state with the cuer spacings under different penetrations are presented in
Figure 13. When the penetration was 2 mm, the two crushed areas inside the rock were
Figure 11. Rock surface crushing state under 6 mm penetration with different cutter spacings:
(a) 40 mm; (b) 50 mm; (c) 60 mm; (d) 70 mm; and (e) 80 mm.
In summary, the degree of rock surface crushing was influenced by the penetration and
cutter spacing. For instance, with a small penetration, such as 2 mm, there was an absence
of synergy between two cutters at different cutter spacings in this paper. Under these
cutting conditions, the two cutters acted independently to cut the rock, leading to a lack of
interaction and inability to crush the rock surface. However, as the penetration increased to
4 mm and 6 mm, the synergistic effect between the cutters could effectively crush the rock
surface given an appropriate cutter spacing. Notably, a smaller cutter spacing enhanced
the synergistic effect and increased the degree of crushing.
The crushing state inside the rock could be observed through a section cutting in the
middle of the rock, where the cutter cut 200 mm, as shown in Figure 12. The variations
in the crushing state with the cutter spacings under different penetrations are presented
in Figure 13. When the penetration was 2 mm, the two crushed areas inside the rock
were not connected and were independent of each other, which aligns with the observed
phenomenon on the rock surface in Figure 9. On the other hand, under the 4 mm penetration
condition, the two crushed areas inside the rock were connected with each other at cutter
spacings of 40 mm and 50 mm, accompanied by the outward expansion of cracks, as
exemplified in Figure 13(b1,b2). Similarly, the 6 mm penetration condition demonstrated
analogous characteristics to the 4 mm penetration condition, with the two crushed areas
being connected at the cutter spacings of 40 mm, 50 mm, and 60 mm, as depicted in
Figure 13(c1–c3).

Appl. Sci. 2024,14, 1241 10 of 16
Appl. Sci. 2024, 14, x FOR PEER REVIEW 10 of 16
not connected and were independent of each other, which aligns with the observed phe-
nomenon on the rock surface in Figure 9. On the other hand, under the 4 mm penetration
condition, the two crushed areas inside the rock were connected with each other at cuer
spacings of 40 mm and 50 mm, accompanied by the outward expansion of cracks, as ex-
emplified in Figure 13(b1,b2). Similarly, the 6 mm penetration condition demonstrated
analogous characteristics to the 4 mm penetration condition, with the two crushed areas
being connected at the cuer spacings of 40 mm, 50 mm, and 60 mm, as depicted in Figure
13(c1–c3).
Figure 12. Section position in the middle of rock sample.
Figure 13. Crushing state of the cross-section at the middle position of the rock, P denotes penetration and
S denotes cuer spacing. (a1) P = 2 mm, S = 40 mm; (a2) P = 2 mm, S = 50 mm; (a3) P = 2 mm, S = 60
mm; (a4) P = 2 mm, S = 70 mm; (a5) P = 2 mm, S = 80 mm. (b1) P = 4 mm, S = 40 mm; (b2) P = 4 mm,
S = 50 mm; (b3) P = 4 mm, S = 60 mm; (b4) P = 4 mm, S = 70 mm; (b5) P = 4 mm, S = 80 mm. (c1) P =
6 mm, S = 40 mm; (c2) P = 6 mm, S = 50 mm; (c3) P = 6 mm, S = 60 mm; (c4) P = 6 mm, S = 70 mm; and
(c5) P = 6 mm, S = 80 mm.
In order to visually understand the size characteristics of the crushed area, the
crushed areas under different cuing parameters from Figure 13 are summarized in Fig-
ure 14. This reveals that the crushed area size was largest for penetration under 6 mm and
smallest for penetration under 2 mm. Moreover, the crushing area size demonstrated an
increasing trend with an increase in penetration. For instance, at a cuer spacing of 50
mm, as the penetration increased from 2 mm to 6 mm, the crushed area size escalated
from 62.1 mm2 to 1216.8 mm2, leading to a nearly 19-fold increase. Notably, the crushing
area size was also notably influenced by the cuer spacing when the penetration was con-
sistent. At 2 mm penetration, the two cuers acted independently, resulting in similar
crushing area sizes. At 4 mm penetration, the cuers exhibited a synergistic effect at cuer
spacings of 40 mm and 50 mm, thereby crushing the rock ridge, leading to a substantial
increase in the crushed area size from 340.8 mm2 to 560.4 mm2, an improvement of ap-
proximately 1.6 times. However, at a cuer spacing of 60 mm, the synergistic effect be-
tween the cuers diminished and the crushed area size decreased to 276.9 mm2 and stayed
stable at around 270 mm2 with a further increase in the cuer spacing. When the penetra-
tion was 6 mm, the change trend in the crushed area was consistent with that of the 4 mm
Figure 12. Section position in the middle of rock sample.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 10 of 16
not connected and were independent of each other, which aligns with the observed phe-
nomenon on the rock surface in Figure 9. On the other hand, under the 4 mm penetration
condition, the two crushed areas inside the rock were connected with each other at cuer
spacings of 40 mm and 50 mm, accompanied by the outward expansion of cracks, as ex-
emplified in Figure 13(b1,b2). Similarly, the 6 mm penetration condition demonstrated
analogous characteristics to the 4 mm penetration condition, with the two crushed areas
being connected at the cuer spacings of 40 mm, 50 mm, and 60 mm, as depicted in Figure
13(c1–c3).
Figure 12. Section position in the middle of rock sample.
Figure 13. Crushing state of the cross-section at the middle position of the rock, P denotes penetration and
S denotes cuer spacing. (a1) P = 2 mm, S = 40 mm; (a2) P = 2 mm, S = 50 mm; (a3) P = 2 mm, S = 60
mm; (a4) P = 2 mm, S = 70 mm; (a5) P = 2 mm, S = 80 mm. (b1) P = 4 mm, S = 40 mm; (b2) P = 4 mm,
S = 50 mm; (b3) P = 4 mm, S = 60 mm; (b4) P = 4 mm, S = 70 mm; (b5) P = 4 mm, S = 80 mm. (c1) P =
6 mm, S = 40 mm; (c2) P = 6 mm, S = 50 mm; (c3) P = 6 mm, S = 60 mm; (c4) P = 6 mm, S = 70 mm; and
(c5) P = 6 mm, S = 80 mm.
In order to visually understand the size characteristics of the crushed area, the
crushed areas under different cuing parameters from Figure 13 are summarized in Fig-
ure 14. This reveals that the crushed area size was largest for penetration under 6 mm and
smallest for penetration under 2 mm. Moreover, the crushing area size demonstrated an
increasing trend with an increase in penetration. For instance, at a cuer spacing of 50
mm, as the penetration increased from 2 mm to 6 mm, the crushed area size escalated
from 62.1 mm2 to 1216.8 mm2, leading to a nearly 19-fold increase. Notably, the crushing
area size was also notably influenced by the cuer spacing when the penetration was con-
sistent. At 2 mm penetration, the two cuers acted independently, resulting in similar
crushing area sizes. At 4 mm penetration, the cuers exhibited a synergistic effect at cuer
spacings of 40 mm and 50 mm, thereby crushing the rock ridge, leading to a substantial
increase in the crushed area size from 340.8 mm2 to 560.4 mm2, an improvement of ap-
proximately 1.6 times. However, at a cuer spacing of 60 mm, the synergistic effect be-
tween the cuers diminished and the crushed area size decreased to 276.9 mm2 and stayed
stable at around 270 mm2 with a further increase in the cuer spacing. When the penetra-
tion was 6 mm, the change trend in the crushed area was consistent with that of the 4 mm
Figure 13. Crushing state of the cross-section at the middle position of the rock, P denotes penetration
and S denotes cutter spacing. (a1) P = 2 mm, S = 40 mm; (a2) P = 2 mm, S = 50 mm; (a3) P = 2 mm,
S = 60 mm; (a4) P = 2 mm, S = 70 mm; (a5) P = 2 mm, S = 80 mm. (b1) P = 4 mm, S = 40 mm; (b2)
P = 4 mm, S = 50 mm; (b3) P = 4 mm, S = 60 mm; (b4) P = 4 mm, S = 70 mm; (b5) P = 4 mm, S = 80 mm.
(c1) P = 6 mm, S = 40 mm; (c2) P = 6 mm, S = 50 mm; (c3) P = 6 mm, S = 60 mm; (c4) P = 6 mm,
S = 70 mm; and (c5)P=6mm,S=80mm.
In order to visually understand the size characteristics of the crushed area, the crushed
areas under different cutting parameters from Figure 13 are summarized in Figure 14. This
reveals that the crushed area size was largest for penetration under 6 mm and smallest for
penetration under 2 mm. Moreover, the crushing area size demonstrated an increasing
trend with an increase in penetration. For instance, at a cutter spacing of 50 mm, as the
penetration increased from 2 mm to 6 mm, the crushed area size escalated from 62.1 mm
2
to 1216.8 mm
2
, leading to a nearly 19-fold increase. Notably, the crushing area size was
also notably influenced by the cutter spacing when the penetration was consistent. At
2 mm penetration, the two cutters acted independently, resulting in similar crushing area
sizes. At 4 mm penetration, the cutters exhibited a synergistic effect at cutter spacings of
40 mm and 50 mm, thereby crushing the rock ridge, leading to a substantial increase in
the crushed area size from 340.8 mm
2
to 560.4 mm
2
, an improvement of approximately
1.6 times. However, at a cutter spacing of 60 mm, the synergistic effect between the cutters
diminished and the crushed area size decreased to 276.9 mm
2
and stayed stable at around
270 mm
2
with a further increase in the cutter spacing. When the penetration was 6 mm, the
change trend in the crushed area was consistent with that of the 4 mm penetration, where
the crushed area size substantially escalated from 480.1 mm
2
to 1550.7 mm
2
as the cutter
spacing increased from 40 mm to 60 mm. When the cutter spacing was over 60 mm, the
synergistic effect between two cutters disappeared, subsequent to which, the crushed area
size rapidly decreased to 343.2 mm2and stabilized.

Appl. Sci. 2024,14, 1241 11 of 16
Appl. Sci. 2024, 14, x FOR PEER REVIEW 11 of 16
penetration, where the crushed area size substantially escalated from 480.1 mm2 to 1550.7
mm2 as the cuer spacing increased from 40 mm to 60 mm. When the cuer spacing was
over 60 mm, the synergistic effect between two cuers disappeared, subsequent to which,
the crushed area size rapidly decreased to 343.2 mm2 and stabilized.
40 50 60 70 80
0
200
400
600
800
1000
1200
1400
1600
Crushed area size (mm
2
)
Cutter spacing(mm)
2mm
4mm
6mm
Figure 14. Statistics on crushed areas.
4.3. Crushing Efficiency of Arcing-Blade Cuers
The specific energy (SE) refers to the energy required by the cuer to cut a unit vol-
ume of rock. A lower specific energy indicates a higher crushing efficiency of the cuer
[25–27]. The calculation formula is as follows:
R·FL
SE
V
= (1)
where SE is the specific energy; FR is the rolling force; and V is the volume of the crushed
rock.
The variation in the specific energy with different cuing parameters when cuing
the red sandstone is illustrated in Figure 15. Regardless of the type of penetration, the
specific energy exhibited a decreasing trend followed by an increasing trend with an in-
crease in the cuer spacing, and eventually stabilized. Notably, for the 4 mm and 6 mm
penetrations, there was an optimal cuer spacing that yielded the lowest specific energy,
referred to as the optimal cuer spacing, which corresponds to the highest crushing effi-
ciency. For instance, with a 4 mm penetration, the specific energy decreased from 36.5
MJ/m3 to 28.7 MJ/m3 as the cuer spacing increased from 40 mm to 50 mm, reaching its
minimum at a cuer spacing of 50 mm. Subsequently, the specific energy began to rise
with further increases in the cuer spacing, stabilizing at the cuer spacing of 60 mm.
Similarly, for a 6 mm penetration, the specific energy decreased from 32.1 MJ/m3 to 20.5
MJ/m3 as the cuer spacing increased from 40 mm to 60 mm, then increased to 93.1 MJ/m3
at 70 mm, after which, it stabilized. In contrast, for a penetration of 2 mm, the specific
energy remained stable at approximately 86 MJ/m3 across various cuer spacings, without
displaying the aforementioned trend.
This change trend can be explained by the crushing states under different cuing
conditions. When the penetration was small, such as 2 mm, each arcing-blade cuer oper-
ated independently of the other, leading to a limited crushed area in the middle of the
rock cross-section (Figure 14). Consequently, there was minimal change in the specific en-
ergy under different cuer spacings, resulting in a low rock-crushing efficiency. As the
penetration increased to 4 mm, a synergy effect between the cuers was observed at cuer
spacings of 40 mm and 50 mm (Figure 10a,b), with the synergy effect being stronger at 40
mm than at 50 mm. This resulted in excessive crushing of the rock ridges, subsequently
leading to higher specific energy values at a 40 mm cuer spacing than those at a 50 mm
cuer spacing. However, as the cuer spacing further increased, the synergy effect
Figure 14. Statistics on crushed areas.
4.3. Crushing Efficiency of Arcing-Blade Cutters
The specific energy (SE) refers to the energy required by the cutter to cut a unit volume
of rock. A lower specific energy indicates a higher crushing efficiency of the cutter [
25
–
27
].
The calculation formula is as follows:
SE =
FR·L
V(1)
where SE is the specific energy; F
R
is the rolling force; and Vis the volume of the
crushed rock.
The variation in the specific energy with different cutting parameters when cutting the
red sandstone is illustrated in Figure 15. Regardless of the type of penetration, the specific
energy exhibited a decreasing trend followed by an increasing trend with an increase in the
cutter spacing, and eventually stabilized. Notably, for the 4 mm and 6 mm penetrations,
there was an optimal cutter spacing that yielded the lowest specific energy, referred to as the
optimal cutter spacing, which corresponds to the highest crushing efficiency. For instance,
with a 4 mm penetration, the specific energy decreased from 36.5 MJ/m
3
to 28.7 MJ/m
3
as the cutter spacing increased from 40 mm to 50 mm, reaching its minimum at a cutter
spacing of 50 mm. Subsequently, the specific energy began to rise with further increases
in the cutter spacing, stabilizing at the cutter spacing of 60 mm. Similarly, for a 6 mm
penetration, the specific energy decreased from 32.1 MJ/m
3
to 20.5 MJ/m
3
as the cutter
spacing increased from 40 mm to 60 mm, then increased to 93.1 MJ/m
3
at 70 mm, after
which, it stabilized. In contrast, for a penetration of 2 mm, the specific energy remained
stable at approximately 86 MJ/m
3
across various cutter spacings, without displaying the
aforementioned trend.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 12 of 16
diminished and the rock ridges remained uncrushed (Figure 10c–e). This caused the spe-
cific energy to quickly reach a stable value, making the sequential cuing similar to a sin-
gle cuing operation. Subsequently, with a further increase in penetration to 6 mm, a sim-
ilar trend in specific energy as that with 4 mm penetration was observed. Notably, the
specific energy reached its minimum value when the cuer spacing was 60 mm, signifying
the highest crushing efficiency. This also indicates that, at cuer spacings 40 mm and 50
mm, the specific energy for 6 mm penetration was marginally higher than that for 4 mm
penetration, owing to the excessive crushing of the rock ridges at these spacings. In sum-
mary, the most optimal cuer spacings under the conditions of 4 mm and 6 mm penetra-
tion were 50 mm and 60 mm, respectively. At these cuer spacings, the specific energy
was the lowest, corresponding to the highest crushing efficiency.
40 50 60 70 80
20
40
60
80
100
Specific energy (MJ/m
3
)
Cutter s
p
acin
g(
mm
)
penetration=2mm
penetration=4mm
penetration=6mm
Figure 15. Specific energy of rock crushing by arcing-blade cuer.
5. Rock-Cuing Experiments with Arcing-Blade Cuer
In order to verify the reliability of the simulation in this paper, linear cuing experi-
ments were conducted with an arcing-blade cuer, and the rock crushing states under
different cuer spacing were observed. The size of the arcing-blade cuer ring for the ex-
periment was consistent with that for the simulation, as depicted in Figure 16. In these
cuing experiments, the penetration was set at 2 mm and 4 mm, resulting in correspond-
ing cuer spacings of 40 mm, 50 mm, 60 mm, and 70 mm. Subsequently, the crushing state
of the rock surface was observed upon the completion of the cuing process.
Figure 16. Arcing-blade cuer for experiment.
Figure 17 illustrates the crushing state of the red sandstone caused by the sequential
cuing of the arcing-blade cuer. Figure 17a,b present the crushing state of the rock sur-
face with 2 mm and 4 mm penetration. When the penetration was 2 mm, the cuer left a
“strip” crushed area on the rock surface, while the rock ridge between the cuers
Figure 15. Specific energy of rock crushing by arcing-blade cutter.

Appl. Sci. 2024,14, 1241 12 of 16
This change trend can be explained by the crushing states under different cutting
conditions. When the penetration was small, such as 2 mm, each arcing-blade cutter
operated independently of the other, leading to a limited crushed area in the middle of
the rock cross-section (Figure 14). Consequently, there was minimal change in the specific
energy under different cutter spacings, resulting in a low rock-crushing efficiency. As
the penetration increased to 4 mm, a synergy effect between the cutters was observed
at cutter spacings of 40 mm and 50 mm (Figure 10a,b), with the synergy effect being
stronger at 40 mm than at 50 mm. This resulted in excessive crushing of the rock ridges,
subsequently leading to higher specific energy values at a 40 mm cutter spacing than those
at a 50 mm cutter spacing. However, as the cutter spacing further increased, the synergy
effect diminished and the rock ridges remained uncrushed (Figure 10c–e). This caused the
specific energy to quickly reach a stable value, making the sequential cutting similar to a
single cutting operation. Subsequently, with a further increase in penetration to 6 mm, a
similar trend in specific energy as that with 4 mm penetration was observed. Notably, the
specific energy reached its minimum value when the cutter spacing was 60 mm, signifying
the highest crushing efficiency. This also indicates that, at cutter spacings 40 mm and
50 mm, the specific energy for 6 mm penetration was marginally higher than that for
4 mm penetration, owing to the excessive crushing of the rock ridges at these spacings.
In summary, the most optimal cutter spacings under the conditions of 4 mm and 6 mm
penetration were 50 mm and 60 mm, respectively. At these cutter spacings, the specific
energy was the lowest, corresponding to the highest crushing efficiency.
5. Rock-Cutting Experiments with Arcing-Blade Cutter
In order to verify the reliability of the simulation in this paper, linear cutting exper-
iments were conducted with an arcing-blade cutter, and the rock crushing states under
different cutter spacing were observed. The size of the arcing-blade cutter ring for the
experiment was consistent with that for the simulation, as depicted in Figure 16. In these
cutting experiments, the penetration was set at 2 mm and 4 mm, resulting in corresponding
cutter spacings of 40 mm, 50 mm, 60 mm, and 70 mm. Subsequently, the crushing state of
the rock surface was observed upon the completion of the cutting process.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 12 of 16
diminished and the rock ridges remained uncrushed (Figure 10c–e). This caused the spe-
cific energy to quickly reach a stable value, making the sequential cuing similar to a sin-
gle cuing operation. Subsequently, with a further increase in penetration to 6 mm, a sim-
ilar trend in specific energy as that with 4 mm penetration was observed. Notably, the
specific energy reached its minimum value when the cuer spacing was 60 mm, signifying
the highest crushing efficiency. This also indicates that, at cuer spacings 40 mm and 50
mm, the specific energy for 6 mm penetration was marginally higher than that for 4 mm
penetration, owing to the excessive crushing of the rock ridges at these spacings. In sum-
mary, the most optimal cuer spacings under the conditions of 4 mm and 6 mm penetra-
tion were 50 mm and 60 mm, respectively. At these cuer spacings, the specific energy
was the lowest, corresponding to the highest crushing efficiency.
40 50 60 70 80
20
40
60
80
100
Specific energy (MJ/m
3
)
Cutter s
p
acin
g(
mm
)
penetration=2mm
penetration=4mm
penetration=6mm
Figure 15. Specific energy of rock crushing by arcing-blade cuer.
5. Rock-Cuing Experiments with Arcing-Blade Cuer
In order to verify the reliability of the simulation in this paper, linear cuing experi-
ments were conducted with an arcing-blade cuer, and the rock crushing states under
different cuer spacing were observed. The size of the arcing-blade cuer ring for the ex-
periment was consistent with that for the simulation, as depicted in Figure 16. In these
cuing experiments, the penetration was set at 2 mm and 4 mm, resulting in correspond-
ing cuer spacings of 40 mm, 50 mm, 60 mm, and 70 mm. Subsequently, the crushing state
of the rock surface was observed upon the completion of the cuing process.
Figure 16. Arcing-blade cuer for experiment.
Figure 17 illustrates the crushing state of the red sandstone caused by the sequential
cuing of the arcing-blade cuer. Figure 17a,b present the crushing state of the rock sur-
face with 2 mm and 4 mm penetration. When the penetration was 2 mm, the cuer left a
“strip” crushed area on the rock surface, while the rock ridge between the cuers
Figure 16. Arcing-blade cutter for experiment.
Figure 17 illustrates the crushing state of the red sandstone caused by the sequential
cutting of the arcing-blade cutter. Figure 17a,b present the crushing state of the rock surface
with 2 mm and 4 mm penetration. When the penetration was 2 mm, the cutter left a
“strip” crushed area on the rock surface, while the rock ridge between the cutters remained
uncrushed. On the other hand, with a 4 mm penetration (as depicted in Figure 17b), the
rock ridge was effectively crushed at cutter spacings 40 mm and 50 mm, as shown in
Figure 17(b1,b2). Further analysis reveals that, at cutter spacings of 60 mm and 70 mm,
as illustrated in Figure 17(b3,b4), the rock ridge between two cuts could not be effectively
crushed, resulting in only two distinct “strip” crushed areas produced by the arcing-blade

Appl. Sci. 2024,14, 1241 13 of 16
cutter. Compared with the rock crushing state from Section 4.2, it can be found that the
crushing state observed from this experiment was similar to that observed in the simulation,
confirming the reliability of the simulation results.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 13 of 16
remained uncrushed. On the other hand, with a 4 mm penetration (as depicted in Figure
17b), the rock ridge was effectively crushed at cuer spacings 40 mm and 50 mm, as shown
in Figure 17(b1,b2). Further analysis reveals that, at cuer spacings of 60 mm and 70 mm,
as illustrated in Figure 17(b3,b4), the rock ridge between two cuts could not be effectively
crushed, resulting in only two distinct “strip” crushed areas produced by the arcing-blade
cuer. Compared with the rock crushing state from Section 4.2, it can be found that the
crushing state observed from this experiment was similar to that observed in the simula-
tion, confirming the reliability of the simulation results.
(a) (b)
Figure 17. Crushing state of rock surface in experiments: (a) 2 mm penetration and (b) 4 mm pene-
tration. (a1) P = 2 mm, S = 40 mm; (a2) P = 2 mm, S = 50 mm; (a3) P = 2 mm, S = 60 mm; (a4) P = 2
mm, S = 70 mm. (b1) P = 4 mm, S = 40 mm; (b2) P = 4 mm, S = 50 mm; (b3) P = 4 mm, S = 60 mm; (b4)
P = 4 mm, S = 70 mm.
The specific energy in the cuing experiments under different cuing parameters is
illustrated in Figure 18. At 2 mm penetration, the specific energy of the arcing-blade cuer
remained consistently high, regardless of an increase in cuer spacing. This observation
suggests a low crushing efficiency of the arcing-blade cuer at such a low penetration.
However, at a penetration of 4 mm, the specific energy initially decreased, then rose before
stabilizing. Based on the above observations, the variation trend of the specific energy of
the arcing-blade cuer in the experiment is consistent with the simulation, further demon-
strating the reliability of the simulation results.
40 50 60 70
0
50
100
150
200
Cutter spacing(mm)
penetration=2mm
penetration=4mm
Specific energy (MJ/m
3
)
Figure 18. Specific energy in experiments.
6. Discussion
By calibrating the material parameters of the rock, the simulation results were
matched with the uniaxial compression test. On this basis, a simulation model for cuing
red sandstone with an arcing-blade cuer was established. Based on the above analysis,
the rock-breaking load of the arcing-blade cuer exhibited fluctuation characteristics
Figure 17. Crushing state of rock surface in experiments: (a) 2 mm penetration and (b) 4 mm penetration.
(a1)P=2mm,S=40mm;(a2)P=2mm,S=50mm;(a3)P=2mm,S=60mm;(a4) P = 2 mm, S = 70 mm.
(b1) P = 4 mm, S = 40 mm; (b2) P = 4 mm, S = 50 mm; (b3) P = 4 mm, S = 60 mm; (b4) P = 4 mm, S = 70 mm.
The specific energy in the cutting experiments under different cutting parameters is
illustrated in Figure 18. At 2 mm penetration, the specific energy of the arcing-blade cutter
remained consistently high, regardless of an increase in cutter spacing. This observation
suggests a low crushing efficiency of the arcing-blade cutter at such a low penetration.
However, at a penetration of 4 mm, the specific energy initially decreased, then rose before
stabilizing. Based on the above observations, the variation trend of the specific energy
of the arcing-blade cutter in the experiment is consistent with the simulation, further
demonstrating the reliability of the simulation results.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 13 of 16
remained uncrushed. On the other hand, with a 4 mm penetration (as depicted in Figure
17b), the rock ridge was effectively crushed at cuer spacings 40 mm and 50 mm, as shown
in Figure 17(b1,b2). Further analysis reveals that, at cuer spacings of 60 mm and 70 mm,
as illustrated in Figure 17(b3,b4), the rock ridge between two cuts could not be effectively
crushed, resulting in only two distinct “strip” crushed areas produced by the arcing-blade
cuer. Compared with the rock crushing state from Section 4.2, it can be found that the
crushing state observed from this experiment was similar to that observed in the simula-
tion, confirming the reliability of the simulation results.
(a) (b)
Figure 17. Crushing state of rock surface in experiments: (a) 2 mm penetration and (b) 4 mm pene-
tration. (a1) P = 2 mm, S = 40 mm; (a2) P = 2 mm, S = 50 mm; (a3) P = 2 mm, S = 60 mm; (a4) P = 2
mm, S = 70 mm. (b1) P = 4 mm, S = 40 mm; (b2) P = 4 mm, S = 50 mm; (b3) P = 4 mm, S = 60 mm; (b4)
P = 4 mm, S = 70 mm.
The specific energy in the cuing experiments under different cuing parameters is
illustrated in Figure 18. At 2 mm penetration, the specific energy of the arcing-blade cuer
remained consistently high, regardless of an increase in cuer spacing. This observation
suggests a low crushing efficiency of the arcing-blade cuer at such a low penetration.
However, at a penetration of 4 mm, the specific energy initially decreased, then rose before
stabilizing. Based on the above observations, the variation trend of the specific energy of
the arcing-blade cuer in the experiment is consistent with the simulation, further demon-
strating the reliability of the simulation results.
40 50 60 70
0
50
100
150
200
Cutter spacing(mm)
penetration=2mm
penetration=4mm
Specific energy (MJ/m
3
)
Figure 18. Specific energy in experiments.
6. Discussion
By calibrating the material parameters of the rock, the simulation results were
matched with the uniaxial compression test. On this basis, a simulation model for cuing
red sandstone with an arcing-blade cuer was established. Based on the above analysis,
the rock-breaking load of the arcing-blade cuer exhibited fluctuation characteristics
Figure 18. Specific energy in experiments.
6. Discussion
By calibrating the material parameters of the rock, the simulation results were matched
with the uniaxial compression test. On this basis, a simulation model for cutting red
sandstone with an arcing-blade cutter was established. Based on the above analysis, the
rock-breaking load of the arcing-blade cutter exhibited fluctuation characteristics when
cutting rock. The three-directional loads obtained from the simulations were compared
with the maximum vertical force, followed by the rolling force and the minimum lateral
force. At a penetration of 2 mm, the rock-breaking load of the arcing-blade cutter did
not change with an increase in the cutter spacing. At penetrations of 4 mm and 6 mm, as
the cutter spacing increased, the vertical force and rolling force showed a trend of first

Appl. Sci. 2024,14, 1241 14 of 16
increasing and then maintaining stability, while the trend of the lateral force change was
the opposite, showing a first decreasing trend and then maintaining stability around 0. The
above explanation shows that there was a synergistic effect between the two arcing-blade
cutters under the conditions of penetrations of 4 mm and 6 mm. The synergistic effect
can promote rock crushing. However, this synergistic effect between the arcing-blade
cutters will weaken or even disappear with an increase in cutter spacing. In addition, under
the condition of a penetration of 2 mm, there was no synergistic effect between the two
arcing-blade cutters, so the rock-breaking load did not change significantly.
The rock crushing state was closely related to the rock-breaking load. At a penetration
of 2 mm, due to the inability of the arcing-blade cutters to synergistically break the rock,
unbreakable rock ridges appeared at different cutter spacings in this paper. The crushed
area generated by the two arcing blade cutters could not be effectively connected. Under
the 4 mm and 6 mm penetrations, there existed a limit on the cutter spacing value, which
connected the crushing area generated by the two arcing-blade cutters. The rock ridge was
completely crushed. As the cutter spacing further increased beyond the limit value, the
rock ridge could not be broken. The cutter spacing limit values at the 4 mm and 6 mm
penetrations were about 50 mm and 60 mm, respectively.
In addition, the crushing efficiency of the arcing-blade cutter was related to the crush-
ing state of the rock. At a penetration rate of 2 mm, the two arcing-blade cutters were
unable to synergistically break the rock, resulting in a stable specific energy at any cutter
spacing. However, at penetration rates of 4 mm and 6 mm, the specific energy showed
a trend of first decreasing, then increasing, and finally maintaining stability as the cutter
spacing increased. This indicates that the arcing-blade cutter had the highest crushing
efficiency at the cutter spacings of 50 mm and 60 mm under the penetration rates of 4 mm
and 6 mm. Interestingly, the experimental results from the liner cutting of the arcing-blade
cutter also confirmed this conclusion. It shows that the simulations are reliable.
7. Conclusions
The rock-breaking characteristics of arcing-blade cutters under various cutting param-
eters using both finite element analysis and experimental methods were investigated in
this paper. The study leads to the following conclusions:
(1) At a penetration of 2 mm, the rock-breaking load of the cutter remained constant across
three directions, regardless of the cutter spacing. However, when the penetration
increased to 4 mm and 6 mm, the vertical and rolling force of the cutter initially rose
with an increase in the cutter spacing before stabilizing. In contrast, the tangential
force decreased at first and then stabilized with an increase in the cutter spacing.
(2)
When the penetration was 2 mm, two cutters performed sequential cutting without
any synergy effect at different cutter spacings, resulting in a rock ridge formation
between two sequential cuts. With a penetration of 4 mm, the rock ridge could be
crushed under cutter spacings of 40 mm and 50 mm. Increasing the penetration to
6 mm allowed for the successful crushing of the rock ridge under cutter spacings of
40 mm, 50 mm, and 60 mm.
(3)
There was no significant difference in the specific energy among different cutter
spacings at a 2 mm penetration, and it remained consistently high. However, for
the penetrations of 4 mm and 6 mm, the specific energy initially decreased, then
increased, and ultimately stabilized. The optimal cutter spacings were 50 mm and
60 mm, respectively, at the penetrations of 4 mm and 6 mm.
(4)
The change trend of the crushing state and specific energy under different cutting
parameters observed from the experiments was consistent with that observed from
the simulations, confirming the reliability of the simulation results.
(5)
The rock-breaking characteristics of the arcing-blade cutter are also related to other
factors, such as rock types and the blade radii of the arcing-blade cutter. In the future,
the impacts of different blade radii of the arcing-blade cutter and the rock types on
rock-breaking characteristics will be studied.

Appl. Sci. 2024,14, 1241 15 of 16
Author Contributions: Conceptualization, Z.M.; methodology, Z.M. and J.Y.; software, Z.M.; vali-
dation, Z.M. and J.Y.; formal analysis, X.Z.; investigation, X.Z.; resources, J.Y.; data curation, X.Z.;
writing—original draft preparation, Z.M.; writing—review and editing, X.Z.; visualization, W.Y.;
supervision, J.Y.; project administration, W.Y.; funding acquisition, J.Y. All authors have read and
agreed to the published version of the manuscript.
Funding: This work was supported by the National Natural Science Foundation of China under
grant nos. 52175112.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: All data, models and codes that support the findings of this study are
available from the corresponding author upon reasonable request. The data are not publicly available
due to privacy restrictions.
Acknowledgments: The experimental operation process was supported by Dingbang Hu, Thanks for
his help.
Conflicts of Interest: Authors Zhao Ma and Xin Zhang were employed by the company Shanxi Tiandi
Coal Mining Machinery Co., Ltd. The remaining authors declare that the research was conducted
in the absence of any commercial or financial relationships that could be construed as a potential
conflict of interest.
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